A II I] V 1 E W 
 
 or THE iliOailESS 
 
 OF 
 
 iV: 
 
 THEMATICAL AND PHYSICAL SCIENCE 
 
 IN MOIJE RECENT TIMES. 
 
 BY 
 
 JAMES D. FORBES, D.C.L., E.R.S. 
 
 PRril-E.^.sOK I-..' NAHTvAL I'lHf.OSi iPilV IX THE UN'[VE1!SITY OF KlJlNUUKGll. 
 
 EDINBURGH: ADAM AND CHARLES BLACX. 
 
 MD^ OLVilI. 
 
 

 afarneU Utttucrattg ffithrarg 
 
 atttaca, Mem ^ark 
 
 BOUGHT WITH THE INCOME OF THE 
 
 SAGE ENDOWMENT FUND 
 
 THE GIFT OF 
 
 HENRY W. SAGE 
 
 1891 
 
Cornell University Library 
 QA 21.F69 
 
 A review of the progress of mathematical 
 
 3 1924 005 726 330 
 
The original of this book is in 
 the Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924005726330 
 
PROCEEDINGS 
 
 ROYAL SOCIETY OF EDINBURGH. 
 
 Monday, 20th March 1848. 
 
 On an Instrument for measuring the extensibility of 
 Elastic Solids. By Professor Forbes. 
 
 This instrument is almost a faithful reproduction of S'Graves- 
 ande's apparatus described in his " Physices Elementa Mathema- 
 tica," 1742 (but not in the previous editions). It is described or 
 alluded to by few modern writers, except Biot in his " Traite de 
 Physique." It consists of a strong wooden table or frame, with a vice 
 at each end, between which a wire or lamina may be stretched with a 
 determinate tension by means of a weight attached by a cord, pass- 
 ing over a pulley in the manner of the musical apparatus, called a 
 Monochord. After'the tension is adjusted both vices are screwed 
 fast, the space included between them being exactly 50 inches. If 
 now, any deviation of the middle point of the wire included by the 
 vices be made (similar to the action of sounding a harp-string), the 
 force required to pull it a certain distance aside will depend, 1st, on 
 the length of the wire ; 2d, on its tension ; 3d, on its extensibility, 
 or the modulus of elasticity. 
 
 S'Gravesande employed his apparatus to verify Hooke's law, 
 that the extension is as the extending force within the limits of per- 
 fect elasticity. But it does not seem to have occurred to him, nor 
 (singularly enough) to later experimenters, to deduce from the ^rces 
 required to produce given deviations, the specific extensibility, or 
 what Dr Young calls the Modulus of Elasticity of the body. 
 
 It is essential that the deviation from the rectilinear position of the 
 wire should be ascertained with great nicety, and S'Gravesande's 
 contrivance effects this in a very neat and satisfactory way. A 
 fine steel chain attaches by a hook to the middle point of the 
 
174 
 
 extended wire, the other end being secured to the circumference of a 
 nicely-centred wheel. Another chain attached similarly to the wire 
 of the same wheel, has a scale attached to it, a weight placed in 
 which causes the wheel to revolve, and by means of the first chain 
 and hook, pulls the wire out of the straight line. A long index 
 fixed to the same axis with the wheel, points out the deviation on a 
 much magnified scale, referred to a divided semicircle of brass. 
 Thus a weight being placed in the scale, the corresponding deviation 
 is instantly shewn. 
 
 Let P be the weight in the scale, D the deviation of the wire, 
 s = half the length of the wire between the vices ; it was proved in 
 this communication that, 
 
 P = 2 TT + M 
 
 (?)■ 
 
 where M is the modulus of elasticity, measured in grains, which is 
 easily reduced to the equivalent length of a similar wire or lamina, 
 according to Dr Young's definition. This is on the supposition that 
 Hooke's Law of Elasticity (the extension is as the extending force) 
 
 — I be found for 
 
 the same wire practically to vary as the cube of the deviation. The 
 value of M, the modulus, is also at once given by a single observed 
 deviation, the tension being known. 
 
 A small correction in the value of P is to be made, for the weight 
 of the wire deflecting it from a straight line. This small correction 
 had not escaped the notice of S'Gravesande when he verified Hooke's 
 law. 
 
 Example. — A steel pianoforte wire, tension 50,000 grains = T ; 
 s =25 inches. 
 
 Values of Values of o m '^ ii 
 
 D. P. ^ i - M 
 
 (!)■ 
 
 •26 inch 1100 grains 1000 100 
 
 •50 ... 2720 ... 2000 720 
 
 •75 ... 5400 ... 3000 2400 
 
 The numbers in the last column should vary as the cubes of those 
 in the first, or be as 1, 8, 27. If we deduct 10 grains from each of 
 them for the action of the weight of the wire depressing it, we shall 
 have these numbers — 
 
175 
 
 90 710 2390 
 
 dividing respectively by 1,8, and 27, 
 
 90 89 88-6 
 
 Hence the mean result for M f ~ | for D = -25, or ? 
 
 (?)■ 
 
 — — T5?F> 
 
 is nearly 89 grains, consequently, 
 
 (100)' 
 and M = 89,000,000 grains. 
 
 But a foot in length of the wire in question weighs ll grains. The 
 equivalent modulus of elasticity is therefore very nearly 8,000,000 
 feet of the wire in question, which agrees closely with the received 
 numbers for steel-wire. 
 
 Note respecting the Refractive and Dispersive Power of 
 Chloroform. By Professor Forbes. 
 
 From an experiment made in very cloudy weather, and therefore 
 rather unfavourable light, I determined the following indices of re- 
 fraction for pure chloroform, prepared by Dr George Wilson, of sp. 
 gr. 1-4966. 
 
 The measure of the refracting angle of the prism was 39° 41'. 
 References were made to the principal lines of the spectrum, as 
 below : the temperature of the fluid Was probably 54°. 
 
 Extreme red, . . . fi = l'i4:75 
 
 B (in the red), .... 1-4488 
 
 D (in the orange-yellow), . . . 1'451 
 
 6 (in the green), .... 1*456 
 
 F (in the blue), .... 1-457 
 
 H (in the violet, being the least refrangible of 
 
 the two groups so designated), . . 1'463 
 
 Extreme violet, .... 1-4675 
 
 Hence the refractive index is by no means remarkably great, 
 
 being nearly that of wax, spermaceti, and several of the essential 
 
 oils. 
 
 The dispersive power, or — ^ is equal to -045, which again agrees 
 fi — 1 
 
 nearly with that of the essential oils. The high specific gravity of 
 
 the body appears to have no marked influence in increasing its action 
 
 on light. 
 
A 
 
 EETIEW OF THE PROGRESS 
 
 OF 
 
 MATHEMATICAL AND PHYSICAL SCIENCE 
 
 IN MORE RECENT TIMES, 
 
 AND PARTICULARLY BETWEEN THE YEARS 1775 AND 1850; 
 
 BEING ONE OF THE DISSEETATIONS PEEFIXED TO THE EIGHTH EDITION OF THE 
 
 ENCYCLOPiEDIA BEITANNIGA. 
 
 BY 
 
 JAMES D. rOHBES, D.C.L., F.R.S., 
 
 SEC. R.S. ED., F.G.S., &c. 
 
 COKBESPONDINQ MEMBER OF THE IMPEEIAL INSTITUTE OF FRANCE, ASSOCIATE OR HONORARY MEMBER 
 
 OF THE BAVARIAN ACADEMY OF SCIENCES, OF THE ACADEMY OF PALERMO, OF THE DUTCH SOCIETY OF SCIENCES (HAAELEM), OF 
 
 THE HELVETIC SOCIETY, OF THE PONTIFICAL ACADEMY OF " NUOVI LINCEl" AT ROME, AND OF THE 
 
 NATURAL HISTORY SOCIETIES OF HEIDLEBEEG, GENEVA, AND VAUD ; 
 
 HONORARY MEMBER OF THE ROYAL MEDICAL SOCIETY OF EDINBURGH, OF THE CAMBRIDGE, YORKSHIRE, ST ANDREWS, 
 
 AND ISLE OF WIGHT PHILOSOPHICAL SOCIETIES, AND OF THE PLYMOUTH AND BRISTOL INSTITUTIONS, AND 
 
 PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY 
 OF EDINBURGH. 
 
 EDINBURGH: 
 
 ADAM AND CHARLES BLACK. 
 
 MDCCCLVIII. 
 
h 
 
 'b%CiC% 
 
ADVERTISEMENT. 
 
 This Essay was written as a continuation of the Dissertations on the Progress 
 of Mathematical and Physical Science by Professor Playfaie and Sir John 
 Leslie, which appeared in the later Editions of the Encyclopedia Britannica. 
 It is now reprinted for general circulation, in consequence of repeated applica- 
 tions to that effect. Only a few inconsiderable alterations have been made upon 
 it. For information as to the plan of the Work, the reader is referred to the 
 Introductory Chapter. 
 
 Edinbubgh, January 1858. ^ 
 
CONTENTS. 
 
 CHAPTER I.— INTRODUCTORY. 
 
 1. On the Plan of this Dissertation p&gc 1 
 
 2. On the Relations between Mathematics and Natural 
 
 Philosophy, and between the latter and the Mechanical 
 Arts page 7 
 
 CHAPTER H.— PHYSICAL ASTRONOMY AND ANALYTICAL MECHANICS. 
 
 § 1. Lagrange. — Variation of Parameters — Application 
 to Physical Astronomy. The Stability of the Planetary 
 System, ; Laplace ; Poisson, Moon^s Libration...^ag& 11 
 
 § 2. Laplace. — Lunar Theory Improved, — Oreat Ine- 
 quality of Jupiter and Saturn. Theory of the Tides 
 — Young; DrWhewellj Mr Airy. — Theory of Pro- 
 babilities — Character of Laplace as a Physicist and 
 Author page 16 
 
 § 3. Leqendee — IVOET. — Theory of Integration ; Hl- 
 liptic Transcendants (Ahei, J acohi). The Attraction 
 
 of Spheroids, and Theory of the Earth's Figure. At- 
 mospherical Refractions page 24 
 
 4. Progress of Physical Astronomy since the publication 
 of the Mecanique Celeste — PoissoN. — Theory of Ro- 
 tation (Poinsot). — Mr Airy — The Solar Theory. — 
 MM. Plana and Hansen — The Lunar Theory. — 
 Physical Astronomy in America page 26 
 
 5. M. Leveerier — Mr Adams. — The inverse method 
 of Perturbations. Prediction of the place and orbit of 
 Neptune from the motions of Uranus page 29 
 
 CHAPTER III— ASTRONOMY. 
 
 § 1. Maskeyline — Delambee. — Progress of Practical 
 Astronomy from 1770 till 1810 — of the Lunar Theory 
 deduced from Obaeniation—^The Density and Figure of 
 the Olobe. Cavendish ; Baily. — Trigonometrical Sur- 
 veys page 34 
 
 § 2. Sir William Heeschel. — History of Sidereal and 
 Telescopic Astronomy to 1820. Herschel as an Opti- 
 cian — Plcmet Uranus — Solar Spots — Orbits of Double 
 Stars — NebulcB — The Milky Way — Swnh Motion in 
 Space page 40 
 
 § 3. Bessel — Mr AlET. — Modem Observatories. Fixed 
 Star Catalogues — Planetary and Lunar Observa- 
 tions page 49 
 
 § 4. BORDA— Kater — Baily. — The Figure of the Earth 
 from Pendulum, Observations — " Reduction to a va- 
 
 cuum;" Mr Stokes — Colonel Everest — M. 
 Steuve. — Latest Measures of the Earth. M. Fou- 
 CAVLt's Pendulum Experiment page 52 
 
 § 5. M. Encke. — Cometary Astronomy — Periodic Comets 
 of Halley and Encke. GaMBARt's and Biela's Co- 
 met — Comets of 1811 and 1843 — Mr Hind — New 
 Planets or Asteroids. Mr Lassell — Newly-disco- 
 vered Satellites. Mr Bond page 57 
 
 § 6. Sidereal Astronomy since 1820. — M. Struve — 
 Double Stars. Observatories of Dorpat and Pullcowa- 
 SiE John Herschel — Orbits of Double Stars. Mag- 
 nitudes of Stars. Variable Stars. Eael OF ROSSE 
 — His Telescopes. Nebulae. Hendeeson and Bes- 
 sel — Parallax of Stars page 63 
 
 CHAPTER IV.— MECHANICS OF SOLID AND FLUID BODIES, CIVIL ENGINEERING, 
 
 AND ACOUSTICS. 
 
 § 1. Watt. — Condition of Practical Mechanics previous 
 to the time of Watt. His genius for the application 
 of Science to Practice. His successive Improvements 
 on the Steam-Engine. Steam Navigation page 67 
 
 § 2. ROBISON. — Application of Statical Principles to 
 EngiTieering, especially to practical Masonry. COU- 
 LOMB. — Friction — Force of Torsion page 72 
 
 § 3. Thomas Young. — Strength of Materials, and Art 
 of construction (continued). — TELrORD — Introduc- 
 tion of Iron into permanent Structures. Suspension 
 Bridges— Treigali ; Mr Hodgkinson ; M. Navier. — 
 Mr Robert Stephenson — Tubular Bridges... ^page 76 
 
 § 4. Sir M. I. Beunel. — Self-acting Machinery. — Thames 
 Tunnel. — MrBABBAGB's Calculating Engines.. .'^a.ge 80 
 
 § 5 Teetithick. — George Stephenson. — The Loco- 
 motive Steam-Engine. — Rise and Progress of Rail- 
 ways. — M. de Pambour o» iooo!KOt»!/es page 83 
 
 § 6. Hydrodynamics. — DuBUAT, Ventuei, Professor 
 Stokes. — Friction and Resistance of Fluids. — MM. 
 Weber, Mr Scott Russell — Propagation of 
 Waves. Their injtuence on Canal Navigation. — MM. 
 Fotjrneybon and Poncelet — Improved Hydraulic 
 Machines; Turbine. Reference to the subject of Capil- 
 lary Attraction page 88 
 
 § 7. Progress of Acoustics. Chladni — Savart. — La- 
 place's Correction of the Theory of Sound, Vibrating 
 Plates and Acoustic Figures. Cagniard de la Tour's 
 "Sirine." page 93 
 
CONTENTS. 
 
 CHAPTER v.— OPTICS. 
 
 1. Thomas Young. — The Undulatory Theory of Light 
 — Its History from the time of Hoohe and Huygens. — 
 The Law of Interference — Its application to DiffraC' 
 tion — (0 the Rainbow — and to other subjects. — The 
 Theory of Polarization referred to another s«c(ion..page 95 
 
 2. Malus. — Discovery of the Polarization of Light by 
 Reflection — Early History of Double Refraction and 
 Polarization page 103 
 
 3. Fresnel. — The Undulatory Theory of Light con- 
 tinued — Diffraction — Transverse Vibrations; Young. 
 — Polarization and Double Refraction explained. — 
 Lighthouse Illumination , P^-g© 1 '^S 
 
 4. Arago. — Short Account of his Scientific Career — He 
 discovers the Colours of Polarized Light — Lavis and 
 Theory of Depolarization ; M. Biot ; Young; Pres- 
 nel. — Non-interference of oppositely Polarized Rays — 
 Rotatory Action of Quartz. — M. FoucauU'a Experi- 
 ment on the Velocity of Light page 109 
 
 § 6. Sir David Brewster. — Progress of Experimental 
 Optics — Laws of Polarization — Double Refraction pro' 
 duced by Heat and Compression — Discovery ofBiaxal 
 Crystals — Laivs of Metallic Reflection — Absorption of 
 Light ; and Lines of the Solar Spectrum ; Fraun- 
 HOFER. — Seebeck ; M. Biot page 113 
 
 § 6. Mr Airy, Sir William R. Hamilton, and Profes- 
 sors Lloyd and Maccullagh. — Confirmation of 
 FresneVs Theory — Investigation of the Wave Surface 
 completed ; Conical Refraction. — M. Cauchv — Me- 
 chanical Theory of Elastic Media, and of Ordinary and 
 Metallic Reflection; M. Jarain. — Theory of Dispersion ; 
 Professor Powell page 119 
 
 § 7. RiTTER. — Chemical Raysof the Spectrum. — Niepce; 
 Dauguerre ; Mr Talbot. Art of Heliography or 
 Photography — Daguerreotype — Calotype, — Professor 
 Stokes. Chemical Rays rendered visible — Fluores- 
 cence. P^ge 123 
 
 CHAPTER, VI.— HEAT, INCLUDING SOME TOPICS OF CHEMICAL PHILOSOPHY. 
 
 1. Black. — Latent and Specific Heat. — Irvine. — Hut- 
 ton. — Doctrines of Heat applied to some Natural Phe- 
 nomena page 127 
 
 2. Cavendish. — His Singular Character and Attain- 
 ments — Em,inent Chemical Discoveries — Observations 
 on Heat and on other Branches of Physics. — Lavoi- 
 sier — The Calorimeter — Theory of Combustion and of 
 Oxidation page 1 30 
 
 3. Dalton. — Theory of Oases and Vapours — Law of 
 Expansion by Heat — Atomic Theory of Chemistry, — 
 GrAY-LussAC , page 135 
 
 4. Romford. — Economical applications of Heat. — Point 
 of Maximum Density of Water ; Hope. — Friction as a 
 source of Heat. Theory that Heat is convertible into 
 Mechanical Energy ; Mr Joule page 142 
 
 5. Sir John Leslie. — Establishment of certain Laws 
 
 of Radiant Heat. — Pictet. — Prevost page 144 
 
 § 6. Fourier. — Mathematical Theory of the Conduction 
 of Heat — Lambert ; Poisson. — Temperature of the 
 Earth and of Space page 148 
 
 § 7. DuLONG. — The Law of Cooling. — Progress of the Sci' 
 ence of Radiant Heat between Leslie's and MellonVs 
 Discoveries ,■ transmission of Radiant- Heat through 
 Glass. Herschel ; De la Roche ; Professor Powell. 
 — Theory of Dew; Wells page 164 
 
 § 8, Melloni. — Recent History of Radiant Heat — 
 Transmission and Refraction of Heat j Properties of 
 Heat analogous to Colour — Experiments in Great 
 Britain on the Polarization and Double Refraction of 
 Heat page 157 
 
 § 9. M. Regnault. — Numerical Laws of Expansion by 
 Heat; Rudberg. — Vaporization; Dulong. — Latent 
 Heat; Hygrometry page 159 
 
 CHAPTER VIL— ELECTRICITY— MAGNETISM— ELECTRO-MAGNETISM. 
 
 t 1. CtALVani. — Discovery of Qalvanism ; Proper Animal 
 Electricity. — The suijectrevived Jj/Nobili. — MM. Mat- 
 teucoi aMii Du Bois-Eeymond page 160 
 
 2. VOLTA. — Progress of Discovery in Common and At- 
 mospheric Electricity — The Electro-motive Theory — 
 Voltaic Pile — Chemical Analogies and Decomposition ; 
 Fabroni; Nicholson and Carlisle page 163 
 
 3. Sir Humphky Davy. — Progress of Voltaic Electri- 
 city — Electro-chemistry ; Berzelius.' — Davy^s Inven- 
 tion of the Safety-Lamp. — WoiLASTON ; his Electri- 
 cal and other Observations. Contrast of his Charac- 
 ter ivith that of Davy page 168 
 
 i. Oersted. — Ampere. — Discovery of Electro-Magnet, 
 ism — Electro-Dynamic Theory — Discovery of Thermo- 
 Electricity; SEEBECK.-TAe Galvanometer of SahMveig- 
 ger and Nobill page 175 
 
 5. Dt'Pkra.-dxy.— Progress of the Theory of Electro- Che- 
 
 mical Decomposition — Volta-Electric Induction — 
 Magneto-Electricity — Diamagnetism— Optical Changes 
 induced by Magnetism. — Professor Pliicker — Magne- 
 optic Action page 179 
 
 § 6. Ohm — Daniel — Mr Wheatstone — M. Jacobi. 
 — Laws of Electrical Conduction ; — Constant Battery; 
 — Applications of Electricity to Telegraphs — Cloohi — 
 Motive Engines — the Electrotype page 184 
 
 § 7. Cavendish— Coulomb.— On tAcTJirtriiun'ono/ Sta- 
 tical Electricity, and on the Mathematical Theory of 
 the same. — POISSON — Mathematical Theory of Stati- 
 cal Electricity and of Magnetism generalized. Green ; 
 Professor William Thomson page 189 
 
 § 8. Professor Hansteen— Baron A. von Humboldt — 
 Gauss— Major-General Sabine — Captain Sir J. C. 
 Ross. — Progress of our Knowledge of Terrestrial Mag- 
 netism in the Present Century page 192 
 
CONSULTING INDEX 
 
 TO THE 
 
 PRINCIPAL NAMES AND SUBJECTS* MENTIONED IN THE FOLLOWING DISSERTATION. 
 
 TI16 Rcforenoes are to tho Articles or Faragrajjh, not to the Pages. 
 
 Alel, 98. 
 
 Absorption of Light, 536. 
 
 Acceleration of tbe Moon, Secular, 62. 
 
 Acoustics, 433, &o. 
 
 Adams, Mr, 127, &c. 
 
 Airy, Mr, 82,115, 228, &c. ; 421, 549,879. 
 
 Ampere, 792, 794, &e. 
 
 Arago, 166, 500, 792. 
 
 Asteroids, 282. List of, 283, and Addi- 
 tions, p. 996. 
 
 Astronomy, Piiysical, 41, &c. ; Practical, 
 149, &c. ; 218, &c. ; Sidereal, 172, &c. ; 
 289, &o. 
 
 Atomic Theory, Dalton's, 618. 
 
 Attraction of Spheroids, 99, &c. ; of Moun- 
 tains, 154, &c. 
 
 Attractions, Theorems about, 99, &c. ; 
 877, 905. 
 
 Bablage, Mr, 377. 
 
 Baily, 158, 242, &c. 
 
 Balloon ascents, 630, and note. 
 
 Barlow, Mr, 879. 
 
 Berselius, 763, 767, and note. 
 
 Bessel, 221, 310. 
 
 Biaxal Crystals, 529 ; Theory of, 493. 
 
 Biot, M., 545, 662. 
 
 Black, 318, 583. 
 
 Block Machinery, 370. 
 
 Borda, 237, &c. 
 
 Bowditch, 126. 
 
 Brewster, Sir David, 519, &c. 
 
 Bridges, Suspension, 351; Wooden, 356 ; 
 
 Girder, 358 ; Tubular, 359, &c. 
 Brinkley, 307, and note. 
 Brunei, Sir M. I., 366. 
 
 Cagniard de la Tour, M., 441. 
 
 Calculating Engine, 377. 
 
 Calorimeter, 88, 607. 
 
 Calotype, The, 571. 
 
 Canal Navigation, 422. 
 
 Capillary Attraction, 88, 432. 
 
 Catenary, 353. 
 
 Gauchy, M., 556. 
 
 Cavendish, 156, 593, &c. ; 871. 
 
 Cavendish Experiment, 156, &c. 
 
 Chances, 83. 
 
 Chemical Subjects connected with Na- 
 tural Philosophy, 582, 596, 618, &c. ; 
 763, &c. ; 811. 
 
 Chemical action of Light, 562. 
 
 Chemical Equivalents, 628. 
 
 Chemical Theory of Galvanism, 751, 763, 
 811. 
 
 Ohladni, 434. 
 
 Civil Kngineering, 312-431. 
 
 Clairaut, 235. 
 
 Clock, Electric, 231, 862. 
 
 Coloration of Heat, 713. 
 
 Combustion, 608, 775. 
 
 Comets, 262; Halley's, 26.'3 ; Encke's, 
 267 ; Gambart's or Biela's, 276 ; Co- 
 mets of 1811 and 1843, 281. 
 
 Conduction of Heat, 661, &c. 
 
 Conduction of Electricity, 813, 842. 
 
 Cornish Steam Engines, 323. 
 
 Conical Refraction, 551. 
 
 Cooling, Law of, 654, 694. 
 
 Coulomb, 339, 413, 873. 
 
 Daguerre, 569. 
 
 Balton, ^10, 721, note. 
 
 Daniell, 852. 
 
 Davy, Sir H., 758, &c. ; 792, 808. 
 
 Declination of the Needle, 881. 
 
 Delamhre, 164, &c. 
 
 De la Roche, 704. 
 
 Density of the Earth, 154, &c. 
 
 Depolarization, 505. 
 
 Detrusion, 346. 
 
 Diamagnetism, 823. 
 
 Diffraction of Light, 458, 486, &c. 
 
 Dip, Magnetic, 882, note ; 883. 
 
 Discontinuous functions, 31, 685. 
 
 Dispersion of Light, 559. 
 
 Double Refraction, 475, &c. 
 
 Du Bois-Reymond, M., 739. 
 
 Duhuat, 410. 
 
 Duhng, 693, 721. 
 
 Earth's Figure, 163, 234, 249, &c.; Den- 
 sity, 154, &c. ; Rotation, 258. 
 
 Earth, Proper Heat of the, 675. 
 
 Economical application of Heat, 634. 
 
 Elastic Solids, 342, &c. 
 
 Electricity, 728, &c. ; Animal, 734, 738, 
 872 ; Atmospheric, 743 ; Mathemati- 
 cal Theory of, 869, &c. ; Distribution 
 of, 871, 874. 
 
 Electric Telegraph and Clock, 856, &c. 
 
 Electro-chemistry, 751, 754, 763, 811. 
 
 Electrodynamic Machines, 866. 
 
 Electro-Slagnetism, 786, &c. 
 
 Electrotype, 868. 
 
 EUipticity of the Earth, 256. 
 
 Ellis, Mr Leslie, 20, note ; 86. 
 
 Emanation of Radiant Heat, 651, 667. 
 
 Encke, M. 262, &c.; Encke's Comet,267. 
 
 English Arc of Meridian, 167. 
 
 Erman, M. Ad., 885. 
 
 Evaporation, 613, 744. 
 
 Everest, Colonel, 250. 
 
 Expansion of the Gases, 617, 721, and 
 
 note. 
 Fabbroni, 751. 
 Eairbairn, Mr W., 363. 
 Faraday, Dr, 798, 807, &c. 
 Feehnor, 851, 
 Figure of the Earth, 163, &c. ; 234, &c. 
 
 249, &c. ; Results, 256. 
 Flame, 770. 
 
 Flexure of Beams, 347, &c. 
 Fluids, Friction and Resistance of, 410. 
 Fluorescence, 579. 
 Foucauh, M., 258, 514. 
 Fourier, 663, &c. 
 Fourneyron's Turbine, 427, 
 Fraunkofer, 538. 
 French Arc of Meridian, 165. 
 French experimenters. Skill of, 720. 
 Fresnel, 468, 485, &c. 
 Frog, Electricity of the, 734. 
 
 Galle, M., 137. 
 
 Oalloway, 212. 
 
 Galvani, 728, &c. 
 
 Galvanism, Discovery of, 732. 
 
 Gases and Vapours, Dalton's Theory of, 
 
 613, 615, 617. 
 Gauss, 48, 856, 896. 
 Gay-Lussac, 617, 625, 630. 
 Green, 558 and note, 878. 
 Greenwich Observatory, 150, 159, 227. 
 Gregory, Duncan, 31, note, 
 
 Ealley, 882. 
 
 Hamilton, Sir W. K., 550, 552, note. 
 
 Hansen, M., 57, note; 122, &c., 261. 
 
 Hansteen, Professor, 881, &c. 
 
 Heat, 582, &c. ; Economical Applica- 
 tions of, 634 ; Hypoihesis on the Na- 
 ture of, 639 ; Radiant, 641, &c. ; 692, 
 &c. ; Mathematical Theory of, 661, &c.; 
 Motion in a Sphere, 673; Solar, 679. 
 
 Heliometer, 310. 
 
 Henderson, 304. 
 
 Herschel, Caroline, 269, note. 
 
 Herschel, Sir J. F. W., 294, 549. 
 
 Herschel, Sir William, 172, &c. ; 702. 
 
 Hind, Mr, 282. 
 
 Historic periods in Science, 2, &c. 
 
 HodgUnson, Mr, 352, 353, 363. 
 
 Hooke, 452. 
 
 Hope, 636. 
 
 ' For the Grounds of Selection of these, and on the Use of the Index, see Articles (13) and (23). 
 
INDEX. 
 
 Humboldt, Baron A. von, 734, 892, &c. 
 
 Button, 591. 
 
 Huygens, 453, 47S. The Principle of, 
 
 454. 
 Hydrodynamics, 408, &o. 
 Hygrometry, 614, 727. 
 
 Indian Arc of Meridian, 250. 
 Induction of Electric Currents, 816. 
 Inequalities, Secular and Periodic, 47. 
 Intensity, Magnetic, 885, 911. 
 Integration, 31, 97. 
 Interference of Light, 460 ; of Chemical 
 
 Rays, 565. 
 Isothermal Lines, 894. 
 Irvine, 586, 589. 
 Ivory, 103. 
 
 Jacobi, C. G. I., 98. 
 
 Jacobi, Mr M. H., 848, 868. 
 
 Jamin, M., 557. 
 
 Joule, Mr, 640. 
 
 Jupiter and Saturn, Theory of, 65. 
 
 Kelland, Professor, 421, 690. 
 EaUr, 240. 
 
 Lagrwnge, 20, note ; 41, Sc, 90. 
 
 Lalande, 162, 
 
 Lambert, 661. 
 
 Lambton, 250. 
 
 Laplace, 51, 60, &c., 199, 235, note, 433. 
 
 Lasaell, Mr, 284. 
 
 Latent Heat, 584, &c., 599, 724. 
 
 Lavoisier, 605. 
 
 Legendre, 85, 95, &c. 
 
 Leslie, Sir John, 641, &,e. 
 
 Leverrier, M., 127, &c. 
 
 Libration of the Moon, 57. 
 
 Lines of the Spectrum, 538. 
 
 Lighthouses, 496. 
 
 Lloyd, Dr., 550, &c., 900, 910. 
 
 Locomotive Engine, 383, &c. 
 
 Lubbock, Sir J. W., 79, 117. 
 
 Luminous Waves, Length of, 463. 
 
 Lunar Observations, 152, 229. 
 
 Lunar Theory, 61, &c., 118, &c., 229. 
 
 Maccullagh, 553. 
 
 Magne-crystallic Force, 832. 
 
 Magne-optic Force, 831. 
 
 Magnetism, Terrestrial, 880, &c. ; Theory 
 
 of, 903. 
 Magneto-electricity, 819. 
 Magnifying Power, 179, 180. 
 Mains, 474. 
 Mashelyne, 150. 
 
 Mathematics, Pure, 20, 24, 28, &c. 
 Mathematical Theory of Heat, 661, &c. ; 
 
 of Electricity, 869, &c. ; of Magnetism, 
 
 903. 
 Matteucei, 739. 
 " M6canique Celeste," 89. 
 Mechain, 166. 
 
 Mechanical Arts, 11, 82, &c. 
 Mechanical lactation, 378. 
 Mechanics, 312, &c. 
 Melloni, 707. 
 
 Metallic Polarization, 634. 
 Michell, 86, note, 156, 340. 
 Milky Way, 201, So. 
 miler, Patrick, 325. 
 Modulus of Elasticity, 345. 
 
 Natural Philosophy, its Connection with 
 
 Mathematics, 24 ; with the Mechanical 
 Arts, 32, &c. 
 
 Ifautical Almanac, 153. 
 
 Navier, M., 354. 
 
 Nebulae, 190, 302. 
 
 Kebular Theory, 198, &c. 
 
 Ifeptune, Discovery of, 127, &c. ; Ele- 
 ments of, 143. 
 
 Nicholson and Carlisle, 754. 
 
 Niepce, Nicephore, 569. 
 
 Nobili, 708, 738, 802. 
 
 Oersted, 786, &c., 803, &c. 
 Olbers, 161. 
 Ohm, 840. 
 Optics, 444, &c. 
 
 Parallax of Stars, 188, 306, &c. 
 Parameters, Variation of, 44. 
 Pendulum Observations, 236; M. Fou- 
 
 cault's Pendulum, 258. 
 Perturbations, Planetary, 46. 
 Peters, M., 311. 
 Photography, 567. 
 PicUt, 648. 
 
 Pile of Volta, 750, 752. 
 Plana, M., 118, &e. 
 Planets, New small, 282, &c. 
 Playfair, 16, note. 
 Plenitude of Stars, 203. 
 Pliicker, Professor, 831. 
 Poinsot, M., 113. 
 Poisson, 55, 112, &c., 689. 
 Polarization of Light, 474, &c., 625, &c. ; 
 
 affected by Magnetic Actions, 834 ; of 
 
 Heat, 717; of Chemical Rays, 665; 
 
 Circular, 491 ; by Metals, 634. 
 Poles, Terrestrial Magnetic, 882, 884. 
 Poncelet, M., 431. 
 Pond, 227, 307. 
 Potential, 877, 905. 
 Powell, Professor, 560, 705. 
 Prevost, 649. 
 Probabilities, 83. 
 Proper Motions of Stars, 209, &c. 
 Pulkowa, Observatory of, 293. 
 
 Quartz, Optical Properties of, 511. 
 Quaternions, 562, note. 
 
 Radiant Heat, 641, &c., 692, &c. 
 
 Railways, History of, 398. 
 
 Rainbow, Theory of the, 465. 
 
 Reflection and Refraction of Light, 490. 
 
 Refrangibility of Heat, 714. 
 
 Refractions, Astronomical, 107. 
 
 Regnault, M., 719, &c. 
 
 Rheostat, 848. 
 
 Ritter, 563. 
 
 Rivers, Theory of, 410. 
 
 Bobison, 329, &c., 749. 
 
 Ross, Sir J. C, 884, 910. 
 
 Rosse, Earl of, 299. 
 
 Rotation of the Earth, 258. 
 
 Royal Institution, 637. 
 
 Rumford, 632, &c.; Rumford Prize, 637. 
 
 RuaseU, Mr J. S., 421. 
 
 Russo-ScandinavianAroofMeridian,254. 
 
 Sabine, Major-General, 238, 246, 909. 
 
 Safety Lamp, 393, 770. 
 
 Satellites, New, 284. 
 
 Savart, 441. 
 
 Schehallicn Experiment, 165. 
 
 Scheutz, M., 380. 
 
 Schuieigger, 802. 
 
 Seebech, 612, 644, 801. 
 
 Ships, Magnetism of, 879. 
 
 " Sirfene," 441. 
 
 Slide-Rest, and Planing Machine, 372. 
 
 Solar Heat, 679. 
 
 Somerville, Mrs, 566 and note. 
 
 Sound, Theory of, 433. 
 
 Specific Heat, 588, 599, 607, 727. 
 
 Spectrum, Lines of the, 638 ; Heat of the, 
 
 702, 715. 
 Stability of the Solar System, 50. 
 Stars, Double, 187, 291, 296; Proper 
 
 Motions of, 209, 292 ; Parallax of, 188, 
 
 306; Brightness of, 297; Variable, 
 
 298. 
 Steam, Elastic Force of, 699. 
 Steam Carriage, 384. 
 Steam Engine, 317, &c. 
 Steam Navigation, 325. 
 Stephenson, George, 392, &c. 
 Stephenson, Mr R., 365, &c. 
 Stereoscope, 581. 
 Stohes, Professor, 235, note; 247, 416, 
 
 679, 691. 
 Struve, M. W., 209, note ; 252, 290, &c. 
 Sun, The, 185. 
 Suspension Bridges, 361. 
 
 Falbot, Mr Fox, 571. 
 
 Telegraph, Electric, 856. 
 
 Telescopes, 178, &c., 299, &c. 
 
 Telford, 351. 
 
 Thermo-electricity, 801. 
 
 Thermo-multiplier, 709. 
 
 Thomson, Professor W., 878. 
 
 Tides, 69, &c. 
 
 Torpedo, 872. 
 
 Torsion Balance, 167, 340, 874. 
 
 Transverse Vibrations, 488. 
 
 Tredgold, 352. 
 
 Trevithich, 385, &c. 
 
 Turbine, 425. 
 
 Tunnel, The Thames, 373. 
 
 Undulatory Theory of Light, 452, &c. 
 Uranus, Discovery of, 183; Perturbations 
 of, 132, &c. 
 
 Variable Stars, 298. 
 
 Variation or Declination of the Needle, 
 
 881. 
 Variation of Parameters, 44. 
 Venturi, 413. 
 Venus and the Earth, long Inequality of, 
 
 115. 
 Vision, 471, 581. 
 Yoka, 740, &c. 
 
 Volta-electric Induction, 817. 
 Voltaic Pile, 749. 
 
 Waves, Theory of, 419, &c. 
 
 Water, Composition of, 697; Maximum 
 
 Density of, 636. 
 Water Wheels, 426. 
 Watt, James, 312, Sc, 597. 
 Weber, The MM., 420, 866, 899. 
 Wells, 706. 
 
 Wheatstone, Mr, 581, 853, &c. 
 Whewell, Dr, 19, 79. 
 Wilson, P., 185. 
 WoUaston, 476, 638, 664, 780, &c. 
 
 Young, Thomas, 80, 342, &c., 445, &c., 
 488, 606, 780. 
 
DISSEETATIO:^^ SIXTH. 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 CHAPTER I. 
 
 INTROOrCTOEY. 
 
 § 1. On the Plan of this Dissertation. 
 
 (1.) 
 Modern 
 Advances 
 in Science. 
 
 (2.) 
 Period 
 1450-1550. 
 
 (3.) 
 Period 
 1550-1650. 
 
 The year 1850 may be said to complete the Third cen- 
 tury of modern scientific progress, or the Fourth if 
 we include its earliest dawn. To each of these ages 
 of discovery may be assigned a peculiarity in the cha- 
 racter of its improvements, and even in the methods 
 which conduced to that improvement. 
 
 Between 1450 and 1550 (a period so distinguished 
 in letters and the arts), some great truths in physics 
 and mathematics had presented themselves to a few 
 precocious minds, yet they had not received any 
 public acknowledgment, nor perhaps an adequate de- 
 monstration. Algebra then first became a science. 
 Leonardo da Vinci made the earliest steps since the 
 time of Archimedes, in rational mechanics, and Co- 
 pernicus almost at the close of this period promul- 
 gated the true system of the world. 
 
 But the next centenary (1550-1650) was the first 
 of true scientific activity. Its characteristic feature 
 was the vindication of observation and experiment as 
 the prime essentials to the increase of natural know- 
 ledge, with the consequent repudiation of the dogmas 
 of the schoolmen, and the baseless methods of d priori 
 reasoning. The men of science formed a goodly array 
 at this stirring time ; and signal were their triumphs. 
 Galileo was beyond all comparison the glory of his 
 age. His sagacity, his knowledge, his versatility of 
 talent, his ingenuity as an inventor, his success in 
 prosecuting his discoveries, and his zeal and elo- 
 quence in making known their importance, gave him 
 an enviable pre-eminence even amidst a mighty gene- 
 ration. Bacon laid down the canons of a new method 
 
 in philosophy which Gilbert and Kepler, as well as 
 Galileo, had already acted on. Napier and Descartes 
 prepared for the general application of mathematics 
 in the coming struggle. 
 
 The hundred years which next succeeded (1650- W) 
 1750) saw the triumphant application of mathema- igso-iyso 
 tics to Mechanics and Physics, and the establishment 
 of the greatest mechanical theory of any age, that of 
 Gravitation. The preparatory labours of a hundred 
 and fifty years were brought, chiefly by the unparal- 
 leled sagacity and genius of Newton, to a speedy and 
 dazzling climax. His success brought numerous and 
 worthy labourers into the field, but they found enough 
 to do in gathering in the harvest which he had pre- 
 pared for them. 
 
 If we look for the distinguishing characteristic of (5.) 
 the centenary period just elapsed (1750-1850), ^®f»cn°'*io(:n 
 find it in this, — that it has drawn far more largely 
 upon Experiment as a means of arriving at truth than 
 had previously been done. By a natural conversion 
 of the process, the knowledge thus acquired has 
 been applied with more freedom and boldness to 
 the exigencies of mankind, and to the farther in- 
 vestigation of the secrets of nature. If we com- 
 pare the now extensive subjects of Heat, Electri- 
 city, and Magnetism, with the mere rudiments of 
 these sciences as understood in 1750, or if we think 
 of the astonishing revival of physical and experi- 
 mental Optics (which had well nigh slumbered for 
 more than a century) during the too short lives of 
 Young and Fresnel, we shall be disposed to admit 
 
MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 piss. VI. 
 
 the former part of the statement ; and when we recol- 
 lect that the same period has given birth to the steam- 
 engine of Watt, with its application to shipping and 
 railways, — to the gigantic telescopes of Herschel and 
 Lord Kosse, wonderful as works of art as well as in- 
 struments of sublime discovery, — to the electric tele- 
 graph, and to the tubular bridge, — we shall be ready 
 to grant the last part of the proposition, that science 
 and art have been more indissolubly united than at 
 any previous period. 
 (6.) The Dissertation of Professor Playfair closes with 
 
 Limits of the period of Newton ; that of Sir John Leslie, pro- 
 tation'^'^"^" fessedly devoted to the history of the eighteenth cen- 
 tury, embraces some matters which belong more 
 properly to those which preceded and followed it. 
 After considering how I might best carry out the plan 
 of these essays, I have adopted the period from about 
 the year 1775 to 1850 as the general limit of my 
 review. We may imagine this period, of three quar- 
 ters of a century preceding the present time, to be 
 divided into three lesser intervals of 25 years each, 
 which have also some peculiar features of their own. 
 (7.) From 1775 to 1800 many branches of science still 
 
 Character continued in the comparatively inert state which cha- 
 °^ *j^g ^gj^ racterized a great part of the eighteenth century, 
 century. There were, however, two or three notable excep- 
 tions. One was the continued successful solution of 
 the outstanding difficulties of the Theory of Gravity 
 applied to the moon and planets, a task in which the 
 continental mathematicians, and of these, in chief, 
 Lagrange and Laplace, had no rivals, or even coad- 
 jutors, on this side of the channel : Another was the 
 foundation of Sidereal Astronomy by Sir William 
 Herschel ; and the last was the commencement of a 
 system of Chemical Philosophy based on new and im- 
 portant experiments, and including the laws of heat 
 in combination with matter, which at that period very 
 naturally ranged themselves within the province of 
 the chemist. In this department two British and 
 one foreign name stand conspicuous, Black, Caven- 
 dish, and Lavoisier. I do not of course mean to affirm 
 that other branches of science were not cultivated 
 with success within the exact period of which we 
 speak. Electricity, for instance, first statical, after- 
 wards that of the pile, had a share in the discoveries 
 and speculations of the time. But these were rather 
 the mere extension of what had previously been thought 
 of; or the first dawn of future important results, whose 
 development fills a large space in the succeeding story. 
 Volta and his inventions belong rather to the nine- 
 teenth than to the eighteenth century. 
 (8.) The first quarter of the present century attained 
 
 Character a higher and more universal celebrity. Scarcely a 
 " .^ branch of physical science but received important 
 1800-1825. ^nd even capital additions. Physical Astronomy in- 
 deed, no longer filled so large a space in the page of 
 discovery, simply because the exhaustive labours of 
 the geometers of the former period had brought it to 
 a stage of perfection nearly co-ordinate with the means 
 
 of observation, and because, by the publication of the 
 MScanique Celeste, Laplace had rendered available M6canique 
 and precise the masses of scattered research accu- 
 mulated by the labours of a century since the close 
 of Newton's career of discovery. It was in some 
 sense a new book of "Principia," — ^not, indeed, 
 the work of one, but of many ; nor of a few years, 
 but of two generations at least. Still there it was, 
 a great monument of successful toil, which, like its 
 prototype, was for many years to be studied, even by 
 minds'of the highest order, rather than to be enlarged. 
 
 But the other branches of Natural Philosophy (9.) 
 were now to make a stride, such as perhaps no pre- ^^P*^J" 
 ceding time had witnessed. The science of Optics pj^y^^g^ 
 was speedily expanded almost twofold, both in its 
 facts and in its doctrines. Galvanic Electricity dis- 
 closed a series of phenomena not less brilliant and 
 unexpected in themselves than important from the new 
 light they threw on the still dawning science of che- 
 mistry, and from the power of the tool which they 
 placed in the hands of philosophers. Before the 
 first quarter of the present century closed, the import- 
 ant and long suspected connection between Electricity 
 and Magnetism was revealed, and its immediate con- 
 sequences had been traced out with almost unpa- 
 ralleled ingenuity and expedition. The basis of the 
 science of Radiant Heat, slightly anticipated by the 
 philosophers of the eighteenth and even the seven- 
 teenth centuries (Lambert and Mariotte), was finally 
 laid in a distinct form, assigning to the agent, heat, 
 an independent position dissociated from grosser 
 matter, such as light had long enjoyed. Astronomy, 
 though enriched on the very first night of the new 
 century by the discovery of a small planet, the he- 
 rald of so many more of the same class, made per- 
 haps less signal progress ; but Chemistry, besides the 
 aid it received from the invention of the pile, had a 
 triumph peculiarly its own in the addition of the 
 comprehensive doctrine of Definite Proportions, des- 
 tined to throw at some later time a steady light on 
 the vexed question of the constitution of matter. 
 The great number of scientific names of the first or- 
 der of merit concerned in these numerous discoveries 
 marks the extraordinary fertility of the period. They 
 are imperfectly comprehended in the following list : 
 Young, Mains, Sir David Brewster, Fresnel, and 
 Arago ; Volta, Dalton, Davy, and Oersted ; Prevost, 
 Leslie, and Fourier ; Gauss, Ivory, Olbers, Bessel, 
 and Encke. 
 
 Of the twenty-five years just elapsed, it is not so (10.) 
 
 easy to speak with precision. The voice of criticism !'o"'"^<,.. 
 ■, n ■ 1 ,, 1 -,1 ,1 , 1 ■ 1 1825-1850. 
 
 may be fairly uttered vnth that reserve which every 
 
 one must feel in speaking of his immediate contem- 
 poraries. Yet it may perhaps be stated without 
 just cause either of offence or regret, that it has not 
 on the whole been characterized by the full maturity 
 of so many commanding minds. Of the great dis- 
 coverers of the former period, several survived an4 
 continued their eflncient labours during no small por- 
 
Chap. L, § 1.] 
 
 PLAN OF THIS DISSEETATION. 
 
 tion of the latter ; and a few happily still remain to 
 ■ claim the respect and veneration of their disciples 
 and successors. But the vast steps so recently made 
 in Optics, in Electricity, in Magnetism, in Thermotics, 
 and in Chemical principles, tended of necessity to call 
 forth such an amount of laborious detail in the de- 
 fining and connecting of facts and laws, and the de- 
 ductions of the theories started to explain them, as 
 seemed to render fresh and striking originality some- 
 what hopeless, whilst they occasioned a vast amount 
 of useful employment to minds of every order of ta- 
 
 Optics. lent. The undulatory Theory of Light, nobly blocked 
 out by the massive labours of Young and Fresnel, 
 has aflforded still unexhausted material to the ma- 
 thematician on the one hand, and to the experimen- 
 talist on the other ; and ably have they fulfilled the 
 double task, aldding at the same time discoveries 
 whose impoi:tance and difficulty would have made 
 them stiU more prominent, had they not been the 
 legitimate consequences of a still greater discovery 
 already in our possession. Nearly the same might 
 have been said for the sciences of Electricity, Electro- 
 magnetism, and Electro-chemistry, had not the com- 
 
 Electricity. parative newness of the whole doctrine of these sci- 
 
 Heat. ences, and the suddenness of their first rise, and, per- 
 
 haps still more, the appearance of a philosopher of the 
 very highest merit, Mr Faraday, who fortunately at- 
 tached himself to this special department, made the 
 last thirty years an almost unbroken period of dis- 
 covery. Radiant Heat, too, has been successfully 
 advanced by labours comparable perhaps to those 
 which marked its first rise as a science, and some 
 other topics connected with heat have risen into 
 
 Astrono- great and practical consequence. Astronomy has 
 
 '°^' been prosecuted with a systematic assiduity and suc- 
 
 cess, especially at the British and Russian national 
 observatories, which yields to that of no former pe- 
 riod, whilst physical astronomy has been cultivated 
 by methods of still improved analysis, and has 
 achieved one triumph which France need not grudge 
 to England, nor England to France, — so signal as 
 to be placed by common consent in a position su- 
 perior to any since the first publication of the theory 
 of gravitation, more than a century and a half be- 
 fore. This was the prediction of the position in 
 space of a planet whose existence was unknown ex- 
 cept by the disturbance which it produced in the 
 
 Magnetism, movements of another. Terrestrial Magnetism has, 
 for the first time, aspired to the rank of an exact 
 science. In an illustrious- philosopher of Germany, 
 it has found its Kepler ; and the combination of na- 
 tional eflforts in collecting reliable data from the re- 
 motest corners of the globe is characteristic of the 
 
 Chemistry, practical energy of the age. Pure Chemistry has 
 been cultivated with extraordinary assiduity ; but 
 though some general principles have emerged, none 
 are comparable, from their importance, to the dis- 
 covery of Dalton. To cite, then, at present, but a 
 few names, amongst the most conspicuous benefac- 
 
 tors of science of the last, or contemporary period, are 
 MM. Airy, Cauchy, Hamilton, and MacCullagh ; 
 MM. Faraday, Melloni, and Gauss ; Sir John Her- 
 schel, M. Struve, and Lord Rosse; MM. Plana, 
 Poisson, Leverrier, and Adams ; MM. Mitscherlich, 
 Liebig, and Dumas. 
 
 It seems to me impossible to exclude from a re- (H-) 
 view, however slight, of contemporary progress in^j" *'"°' 
 the exact sciences, the advantages which have accrued 
 to them both directly, and, as it were, reflexively, by 
 the astonishing progress of the Mechanical Arts. The 
 causes, indeed, which called them forth are some- 
 what different from those which are active in more 
 abstract, though scarcely more difficult, studies. 
 Increasing national wealth, numbers, and enterprise, 
 are stimulants unlike the laurels, or even the golden 
 medals of academies, and the quiet applause of a few 
 studious men. But the result is not less real, and 
 the advance of knowledge scarcely more indirect. 
 The masterpieces of civil engineering — the Steam 
 Engine, the Locomotive Engine, and the Tubular 
 Bridge — are only experiments on the powers of nature 
 on a gigantic scale, and are not to be compassed 
 without inductive skill as remarkable and as truly 
 philosophic as any effort which the man of science 
 exerts, save only the origination of great theories, of 
 which one or two in a hundred years may be con- 
 sidered as a liberal allowance. Whilst then we 
 claim for Watt a place amongst the eminent contri- 
 butors to the progress of science in the eighteenth 
 century, we must reserve a similar one for the Ste- 
 phensons and the Brunels of the present : and 
 whilst we are proud of the changes wrought by the 
 increase of knowledge during the last twenty-five 
 years on the face of society, we must recollect that 
 these very changes, and the inventions which have 
 occasioned them, have- stamped perhaps the most 
 characteristic feature — ^its intense practicalness — on 
 the science itself of the same period. 
 
 Having thus briefly reviewed the course of disco- (12.) 
 very since the latter portion of the eighteenth century, "^^^ij^x"*^ 
 I proceed in the succeeding chapters to attempt to o/science 
 sketch it more in detail, dividing the sciences into in this 
 groups, and in each of these endeavouring to present Essay, 
 a lively view of its progress by connecting it with 
 the individual career of the eminent men who have 
 most contributed thereto, and introducing collaterally 
 the chief results obtained by their contemporaries. 
 In this manner I hope, 6n the one hand, to escape the 
 formality of a history of science, and the meagre de- 
 tail which our limits would prescribe to so vast a sub- 
 ject ; and on the other to be enabled to impress upon 
 the reader (as seems to be the design of these Essays) 
 the leading facts and features of discovery in every 
 age, together with the intellectual characteristics of 
 the greatest minds which contributed to it. 
 
 It is with no overweening confidence that I lay the (13.) 
 
MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 of the sub. 
 ject. 
 
 Scheme of result of this attempt before the reader. During the 
 treatment lenethened period of composition of thisDissertation — 
 protraetedbymdispositionandun toward Circumstances 
 of different lands, I have had abundant leisure to reflect 
 on the advantages and disadvantages of a plan which I 
 had sketched in the previous paragraphs, at the very 
 opening of my task. I am aware that a rigid criti- 
 cism awaits every attempt like the present. I am 
 aware also, that it is far easier to detect real faults, 
 especially of omission, than to make sufficient allow- 
 ance for the exceeding difficulty and delicacy of the 
 undertaking. I have but one ground of confidence, 
 and that is so strong, that I trust it will enable me 
 calmly to meet every just critical reflection. I am 
 conscious of having written in a spirit of absolute 
 impartiality whether as regards persons or subjects, 
 and that I have exercised to the full amount of my 
 opportunities what powers of judgment I possess. 
 I have striven to speak judicially and historically 
 whether of friend or stranger, the dead or the living, 
 Englishman or Foreigner. What I have felt the 
 most constant efibrt, has been the needful exclusion 
 of meritorious names, far more numerous than those 
 especially included and dwelt upon in these pages. 
 But this has appeared to me the cardinal point of 
 my whole plan. The labourers in science have been 
 in these latter days so numerous, that had I noticed, 
 even briefly, every one who had made a real step in 
 science, my pages must have been crowded by names 
 and titles of books. Even with the extension of bulk 
 to which this essay has gradually and unavoidably 
 grown (nearly double of its projected amount), the 
 reader would rather have been bewildered than led by 
 the perusal of such a catalogue. Besides, since such 
 a brief historical synopsis forms very generally an in- 
 troduction to the several articles of the Encyclopedia, 
 to repeat it all here would have been but a tedious re- 
 dundancy. No one conversant vrith such matters will 
 imagine that I have saved myself any labour by this 
 particularity of selection. On the contrary, it would 
 have cost no effort to enumerate under each subject 
 the living or recently deceased authors upon it who 
 are best known ; such a detail must have left a vague 
 and shadowy impression on the mind of the general 
 reader, and when regard is paid to the necessary limits 
 of the essay, and the multitude of technical details and 
 technical words which there is no space to define and 
 illustrate, it is plain that the perusal must have been 
 rendered as dry and unpalatable to those who seek 
 general and elementary yet clear ideas, as it would 
 have been tantalizing and unsatisfactory to the ac- 
 complished student, or to the man of science in 
 search of particular historical details. 
 (14.) rphe end at which I have aimed is to select the 
 
 more striking land-marks of progress in each subject 
 in each age, and endeavour to connect them with the 
 character and position of all the more eminent dis- 
 
 tatioDB. 
 
 coverers, thus conveying to the general reader suffi- 
 cient information on the limited number of particular 
 subjects discussed, and interesting him not only in 
 the science but in the individuals. Then, by a few 
 slighter touches only, and the mention of some 
 secondary names, to connect with one another these 
 brighter periods of eminent progress, in which every 
 country and every age feels a just pride. 
 
 That by many I shall be considered to have dwelt (15.) 
 too much on some eras of invention, and to have 
 omitted others not less important, is a difference of 
 judgment which it is impossible not to anticipate, 
 but equally impossible to prevent. I will only add 
 that I have endeavoured to extend my impartiality 
 to subjects as well as to persons ; and that I have 
 not intentionally dwelt longer on the topics of my 
 own predilection than on those naturally considered 
 by other persons equally or more important. Many 
 subjects as well as persons familiarly known to me 
 are scarcely, if at all, mentioned in these pages. To 
 leave some definite and vivid impressions, selected 
 solely for their importance, on the mind of my reader, 
 has been the great object constantly before me during 
 the composition of this work. 
 
 It will be seen from the preceding paragraphs, ^^^'\ 
 that I have deviated in some respects from the^j^j^jj^jj^^^f 
 scheme of my two distinguished predecessors in the the preced- 
 composition of the Dissertations on Science, Professor i"g DisBer- 
 Playfair and Sir John Leslie. The essay of the for- 
 mer, which is the more finished and methodical, is 
 admirably adapted to the period of the history of 
 science of which he had principally to treat; the 
 period, namely, of Galileo, Bacon, Newton, and 
 Leibnitz. But the amount of material was smaller, 
 and the principle of selection was also much simpler. 
 The positive science of that age might almost be re- 
 duced to two heads, Astronomy, including its mecha- 
 nical principles, and Optics. It was an age not more 
 distinguished for the Truths it disclosed, than for 
 the invention and right appreciation of the Methods 
 of Discovery. Inductive Logic, and Mathematical 
 Logic applied for the first time to dynamics, very 
 justly claimed a place in a dissertation on the pro- 
 gress of science, in a period when these preliminary 
 doctrines and discoveries were the stepping stones by 
 which even the basement story of the Temple of 
 Nature could alone be reached. The Philosophy of 
 Bacon and the discovery of Fluxions, occupied there- 
 fore, with much reason, a large portion of Professor 
 Playfair's beautiful Dissertation ; and it is impossible 
 to regret that an intellect so admirably qualified for 
 tracing and displaying the intimate and historical 
 connection of branches of knowledge so varied in 
 their principles and character, should have been thus 
 congenially employed, to the delight and edification 
 of readers of every degree of acquirement from the 
 highest to the humblest.^ 
 
 ^ In mentioning the name of my distinguished predecessor in the Chair of Natural Philosophy in the University of Edin- 
 burgh, I willingly take the opportunity of noticing, in a few words, his peculiar merits, to which the Dissertation contained in 
 
Chap. I., § 1.] 
 
 PLAN OF THIS DISSERTATION. 
 
 Exteiit^ But the extended domain of the science of the 
 
 variety of last hundred years enhances vastly the difficulty of the 
 materials, subjects Succinctly handled as one by Mr Playfair. 
 The mechanical and experimental sciences alone con- 
 stitute a body of knowledge so large that it is arespon- 
 sibility sufficient for one person to attempt to grasp 
 them all, and to set forth in order the steps of pro- 
 gress and improvement which have been so rapid, and 
 even so startling. Since some of these have scarcely 
 as yet been historically digested, and the broad 
 features of contemporary discovery have not been 
 gradually separated by the judgment of an impartial 
 posterity from those slighter though praiseworthy 
 details, which lapse of time and advance of know- 
 ledge will throw into the shadows of distance, — this 
 difficult and most laborious task falls principally 
 upon the reviewer. The length and breadth of the 
 subject of Natural Philosophy, and the cumbrous 
 and scattered depositories of knowledge in which 
 its records must be sought, combine to render not 
 only the undertaking an arduous one, but the 
 result of it a good deal more bulky than might be 
 desired, or than was easily possible, in dealing with 
 , the glorious, but compact, history of Newton's age. 
 It might be compared to the difference between writ- 
 ing a history of the Jews or Eomans and that of the 
 whole of modern Europe. 
 
 The mere magnitude of the undertaking, then, 
 might well excuse me from entering upon the cog- 
 nate, but exceedingly distinct, subjects of the Logic 
 of Inductive Discovery and the progress of the Pure 
 
 (18.) 
 
 Logic of 
 induction. 
 
 Mathematics. But an equally sound reason might 
 be found in my consciousness of inadequacy to un- 
 dertake, whatever had been the dimensions of my 
 work, a threefold scheme of such magnitude and 
 difficulty. I do not think that any one person could 
 be found to treat the whole as it ought to be treated, 
 and I am certain that I am not that person. 
 
 One attempt — a bold and successful one — has (19.) 
 been made, in our own day, to unite two of tli^ ^'^'/'^^ ^f 
 three departments, — I mean the History and th^ g^j, ^ jf^. g^^. 
 Philosophy of the Inductive Sciences. An English art MiU. 
 philosopher of wonderful versatility, industry, and 
 power has erected a permanent monument to his 
 reputation in a voluminous work bearing the pre- 
 ceding title.'- A slight inspection of that work will 
 show how impracticable and self-destructive a plan it 
 would have been to attempt anything like a syste- 
 matic abridgment of such a mass of facts and specu- 
 lations within our present limits. Mr J. Stuart Mill 
 has also published a work bearing on the origin of 
 our scientific knowledge, diametrically opposed in 
 principle to the preceding one, yet marked by great 
 ability.^ Such disquisitions belong more properly 
 to the philosophy of the human mind than of phy- 
 sics. After all, be it remembered that whatever has 
 been learnt or discussed concerning the means of 
 arriving at truth in Natural Science, it is not pre- 
 tended that we have recently become possessed of 
 any canons or rules of discovery superseding those 
 fundamental principles of observation and experi- 
 ment so well laid down by Bacon, and practised both 
 
 the present volume will bear an enduring testimony. Playfair's original contributions to science were not so marked and consi- Character 
 derable as to justify me in including his name in the comparatively brief catalogue of discoverers chronicled in the succeeding of Professor 
 pages ; but his efforts are, nevertheless, deserving of notice, and indirectly were perhaps hardly less beneficial. He was a most Playfair. 
 patient and admiring student of the greatest mathematical writers of his time, and, when we consider the singularly backward 
 state of that science in Great Britain about the end of the last and commencement of the present century, it was of no slight im- 
 portance to find a man placed in the position of a public instructor able and willing to direct attention to the splendid achieve- 
 ments of the continental mathematicians. By his lectures both on Mathematics and Natural Philosophy — by his luminous articles 
 in the Edinburgh Review — by some of his original papers in the O^ranscbctiona of the Royal Society of Edinhwrgh — he contributed 
 to this useful end, and would have done so still farther had he been enabled to complete the Dissertation which he so ably com- 
 menced. He had an excellent mathematical capacity, and mathematical taste, rather than power. His explanations, even of 
 matters of inherent difficulty, are perspicuous and popular, qualities possessed by few of his contemporaries. His style has been 
 pronounced by the highest authorities to be a model of clearness and eloquence. He was extensively read in subjects of meta- 
 physics and morals, as well as of pure science ; and by a combination of talent rare, I am inclined to say, in a high degree, his 
 taste, though eminently mathematical, was also directed, with signal success (at first through his intimate friendship for Dr Hutton), 
 to the very opposite studies of Geology and Physical Geography, which may be said to have been the subjects of his predilection 
 during the last twenty years of his life. Nor were these labours of the closet merely ; he was far more intimately versed in the 
 mineral structure of the earth, from observation, than any except a few professed geologists ; and he exceeded them all in the 
 ability with which he expounded and maintained the striking doctrines of the Huttonian theory. Though professedly the " illus- 
 trator" of the principles specifically but obscurely laid down by Hutton, he certainly added much of his own. There is no rea- 
 son to doubt that Playfair first apprehended the moving power of glaciers as geological agents in modifying the surface of Alpine 
 countries, a matter which has of late been so earnestly discussed by the ablest geologists. 
 
 What adds to the singularity of the combination of tastes and talents to which I have referred is, that he appears to have 
 bad the slightest possible taste for that art of experiment which he eloquently advocated, with Bacon, as the grand distinction of 
 modern science. I may he wrong in stating it broadly, but I do not now recollect a single experimental novelty, much less dis- 
 covery, which we owe to Playfair, I mean in the department of Natural Philosophy ; for we cannot include barometrical mea- 
 surements under this head, of which, indeed, it was the mathematical theory, and not the application to practice, which chiefly 
 occupied him. The same was the case in Astronomy, which, of the mechanical sciences, interested him most. In two capacities he 
 ' will be remembered, — first, as the able, eloquent, and generally impartial and accurate Historian of Science ; secondly, as the 
 promoter, to so great a degree as to be considered a second founder, of modern Dynamical Geology. He was much beloved in 
 private life, and was singularly free from the tendency to carping criticism and personal prejudices sometimes, unfortunately, 
 found in men of letters. He was the intimate associate of Jeffrey and the other founders of the Edinburgh Review. 
 His ^character has been drawn in three words by Sir James Mackintosh, and as happily contrasted with that of his illustrious 
 
 friend : — " Playfair and Jeffrey ; the first a person very remarkable for understanding, calmness, and simplicity, the 
 
 second more lively, fertile, and brilliant than any Scotchman of letters " {lAfe of Sir James Mackintosh, ii. 251). 
 
 * Whewell's History and Philosophy of the Inductive Sciences, 5 vols, 8vo. " Mill's Logic, 2 vols. 8vo. 
 
MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 piss. VI. 
 
 (20.) 
 Pure ma- 
 thematics 
 — their 
 progress 
 and tech- 
 nicality. 
 
 before him and since by Galileo, Newton, and their 
 disciples. 
 
 With regard to Pure Mathematics, and their pro- 
 gress during the last seventy years, to the difficulty 
 arising from the extent to which the review must have 
 enlarged this Essay, and the enormous and dispropor- 
 tionate labour it must have cost (a labour far greater 
 to the present writer than to one by taste and habit 
 more addicted to the study of merely abstract Ana- 
 lysis), a conclusive argument against their systematic 
 introduction into this historical sketch is to be found 
 in the very nature of these modern improvements. 
 All sciences — but especially the abstract sciences — 
 tend to become more intensely technical the farther 
 they are pursued. These especially are incapable of 
 popular treatment, although in their applications to 
 physical science they occasionally admit of it in a 
 very remarkable manner. The progress of analysis 
 cannot be even enunciated or expressed but in the 
 language of analysis, and the History becomes almost 
 a Treatise, or, if not a Treatise, something nearly as 
 technical. It is partly for this reason that the his- 
 tory of the Pure Mathematics has so seldom been 
 even attempted to be written.^ Mathematicians hav6, 
 since the time of D'Alembert, been noted for being 
 more ready themselves to publish than to become 
 acquainted with what others have done ; and one con- 
 sequence of this has been the formation of a mathe- 
 matical literature, able, profound, and original, but 
 cumbrous, fragmentary, and full of repetitions.^ 
 Besides, the seventeenth century had attained the 
 vantage-ground of those grand and striking im- 
 provements in methods to which no subsequent im- 
 provements, however real and ingenious, can by 
 possibility compare. We shall never have inventions 
 comparable, in universality and importance, to the 
 application of Algebra to Geometry, and the dis- 
 covery of Fluxions. These also admit of being at 
 least partly explained in language not obtrusively 
 technical, and have been so explained by the facile pen 
 of Playfair ; but all subsequent discoveries have been 
 but enlargements and improvements on these pri- 
 mary and distinguishing ones ; and before the date 
 at which our present discourse properly opens, even 
 the larger generalizations of Newton's fertile calcu- 
 lus — the method, namely, of Variations, and the in- 
 tegration of partial differential equations, had been 
 
 established, by the genius of Euler and Lagrange, on 
 an impregnable basis. 
 
 The intense, and praiseworthy, and successful (21.) 
 labours of their followers have been, then, chiefly de- 
 voted to the occupation of the fields of conquest thus 
 summarily opened; or, rather, to storming, one by one, 
 fortresses still unreduced, after the main resisting army 
 had been first routed in the open field. To quit meta- 
 phor, the efforts of mathematicians have for many 
 years been chiefly applied to rendering possible the 
 solution of problems involving quantities which ac- 
 tually occurred in the course of the rapid simulta- 
 neous advances of physical science. They are in a 
 manner inseparable from the branches of physics in 
 aid of which they were originally called forth, and 
 will therefore be most properly noticed, however 
 briefly, in the chapters of this Dissertation where 
 their application is considered. Some farther obser- 
 vations on this subject will be found in the imme- 
 diately succeeding section of the present Essay. 
 
 In reviewing the progress of science— physical (22.) 
 science in particular — during the last seventy or^"^*y'' 
 eighty years, I have thought it advisable not to gj°o.^ajjjg' 
 subdivide the subjects too minutely, and, following matical 
 nearly the arrangements of Dr Whewell's excellent Sciences, 
 treatise, already quoted,' I shall treat, in successive 
 chapters, of Analytical Mechanics including Physical 
 Astronomy as their loftiest and most successful ap- 
 plication ; of Astronomy as a science of observation ; 
 of Mechanics, with reference to the intimate consti- 
 tution of matter, including Hydrodynamics, Acous- 
 tics, and Civil Engineering ; of Optics, or Light ; of 
 Heat, including the Daltonian theory of the gases 
 and chemical elements ; and, finally, of the large and 
 comprehensive science of Electro-magnetism, includ- 
 ing ordinary and Voltaic Electricity, Terrestrial Mag- 
 netism, and Diamagnetism the discovery of Dr Fa- 
 raday, 
 
 The arrangement of the chapters is thus strictly (23.) 
 Methodical ; but in the subdivision into sections, I "^"t"^^!, 
 have allowed the Biographical principle to predomi- meth^dica{ 
 nate, thus giving as much as possible a historical partly bio- 
 character to the whole, and endeavouring to intro- graphical, 
 duce the reader to the intellectual acquaintance of 
 the eminent men who are selected for notice on the 
 principles which have been already detailed. In some 
 
 1 Specimens of what a history of pure mathematics would be, and must be, are to be found in the able " Reports " of Dr 
 Peacock and Mr Leslie Ellis, in the Transactions of the British Association for 1833 and for 1846. A glance at these profound 
 and very technical essays will show the impossibility of a popular mode of treatment, whilst the difficulty and labour of pro- 
 ducing such summaries may be argued from their exceeding rarity in this or any other language. 
 
 2 The celebrated Lagrange, in his later years, contrasting the mathematical works of his own generation with those which he 
 studied when a youth, is said to have observed : — " I pity the young mathematicians who have so many theories to wade through. 
 If I were to begin, I would not study ; these large quartos frighten me too much." — (Thomson's Armals, vol. iv.) And it is stated 
 that whilst his own most abstruse investigations were conducted in Paris, he kept the perusal of M. Grauss's writings for the tran- 
 quil retirement of the country, — a distinction intelligible enough between the intense effort of invention more than sustained by 
 the vU viva of genius which prompts it, and the strain required to master the dead weight of reasoning imposed upon the mind 
 by the discoveries of another. Dr Young, in his biography of Lagrange, observes upon the voluminous mathematical literature 
 of his time, that " unless something be done to check the useless accumulation of weighty materials, the fabric of science will sink 
 in a few ages under its own insupportable bulk." The fact is that a large proportion of the mathematical writings of even 
 eminent authors are in a few years forgotten, or only casually consulted on some matter of history. 
 
 3 Hiitory and Philosophy of the Inductive Scieneet, 
 
Chap. I., § 2.] 
 
 MATHEMATICS — PHYSICS— MECHANICAL AET8. 
 
 instances, however, it has been necessary to introduce 
 the same individual into two or three different sec- 
 tions, and even into different chapters, when his pur- 
 suits have been in very various branches of science. 
 This has been avoided, however, as much as possible, 
 and a sacrifice has occasionally been made of the 
 methodical order of the subjects, so as to combine in 
 one view all that has made an eminent philosopher 
 illustrious. Such little sacrifices of arrangement are 
 
 incidental to the way of treating the whole subject ; 
 and it may be hoped that its practical advantages, 
 in the eye of the general reader, will be found to 
 compensate for its defects as they may appear to the 
 more rigorous student. For the sake of the latter 
 especially, a short but comprehensive index of Names 
 and Terms is prefixed, by which, I believe, it will be 
 easy to trace all that is said of any one person or 
 subject in any of the chapters.' 
 
 § 2. On the relations between Mathematics and Natural Philosophy, and between the latter and 
 
 the Mechanical Arts, 
 
 (24.) 
 Connection 
 of Mathe- 
 matics, 
 physics,and 
 mechaQical 
 arts. 
 
 (25.) 
 Boundaries 
 of Science 
 and Art un- 
 defined. 
 
 (26.) 
 
 The object of this Dissertation has little in com- 
 mon with an attempt formally to subdivide human 
 knowledge into compartments, and to assign their 
 boundaries with metaphysical exactness. It is chiefly 
 in their practical bearing on one another that they 
 must be considered. If one science, like Mathe- 
 matics, furnish the only sure step towards the un- 
 derstanding or the enlargement of another, as Astro- 
 nomy or Optics, a practical link is constructed be- 
 tween them, which renders the progress of the one 
 not independent of the progress of the other. The 
 intimate and reciprocal connection thus subsisting 
 between Mathematics and Physics is to be found in 
 almost an equal degree between Pure Physics and the 
 Mechanical Arts, of which we take Civil Engineer- 
 ing to represent the department most cognate t6 
 that of Natural Philosophy, of which this Disserta- 
 tion more especially treats. 
 
 The history of the last seventy or eighty years 
 enforces this conclusion. The boundaries of Science 
 and Art are as undefinable as those of " fact" and 
 " theory," or those which separate the kingdoms of 
 nature from one another. There are arts which can 
 hardly be called scientific, and there are others which 
 have contributed more to the original stock of know- 
 ledge than they ever drew from it. These last are 
 like the shoots of those tropical plants which at first 
 are mere buds upon the trunk, and are nourished 
 solely by its juices, but which, when they reach the 
 ground, plant themselves there, and become not only 
 the props and stays of the parent stem, but supply it 
 from an ever-increasing area with the sap which they 
 originally borrowed. 
 
 The more closely we examine the subject, the more 
 are we satisfied that it is impossible to teach science 
 
 rightly without teaching its applications; and that 
 the limit to which we are to do so is a limit depend- 
 ing solely on the judgment of the teacher, and on 
 the special purpose of the lesson. But the progress 
 of science is a lesson learnt from the great book* of 
 experience ; and if we are to feel the force of its 
 teachings, we must consult, not one, but many of its 
 pages. Looking to the history of science since 1750, 
 but especially during the present century, it is quite 
 impossible not to admit how large a share the sciences 
 of application have had in moulding the direction of 
 men's thoughts and speculations, and in enabling, 
 nay, compelling them to realize certain abstract no- 
 tions far from easy of conception. Instances of this 
 are to be found in the force of percussion, the co- 
 existence of vibrations in air and other substances, 
 and such notions of hody as we derive from practical 
 efforts of continually-increasing boldness to extend 
 the scale of our constructions. 
 
 The analogy of the relation between Mathematics (27.) 
 and Physics, and of the latter to civil Engineering, is P/'*<=*i<"'l 
 so close that the three subjects might almost be re- ^f (j,e last 
 presented as three terms of a continued proportion. 100 years. 
 What the second is to the first may be affirmed of 
 the third relatively to the second. Physics may 
 exist, at least to a limited extent, without a mathe- 
 matical basis, as the art of construction long preceded 
 a knowledge of the principles on which it is founded. 
 But as knowledge advances it extends in both 
 directions towards speculation and towards practical 
 applications, but most towards the applications. This 
 Bacon well understood, and he has consistently main- 
 tained, that knowledge, to be profitable to its cultiva- 
 tors, must also be fruitful to mankind. And all the 
 history of science since Bacon's day has read this 
 
 1 I have borrowed but sparingly, in the following pages, from the existing compilations on the history of science. Indeed, 
 a writer who intends to make a subject his own by a well-considered, fundamental plan of treating it, will use such works prin- 
 cipally as a guide to his own further inquiries, and to assist him in selecting the topics worthy of fullest discussion. In this 
 respect Dr Whewell's excellent writings, already cited, have been of great use to me ; and in the particular department of 
 Astronomy, I have often referred to Mr Grant's valuable History of that science, as well as to the writings of Delambre, and 
 the very elaborate Historical Essay by M. Gautier, on the problem of the Three Bodies, which is not, I think, noticed by 
 Mr Grant, but which contains a most elaborate history of the researches of Lagrange and Laplace. In optics, I have consulted 
 the systematic treatises of Dr Voung, Sir D. Brewster, Sir J. Hersehel, Dr Lloyd, M. Moigno, and M. Eadicke ; and so of other 
 subjects. Gehler's Phyaikalisches Worterbuch, Fechner's Repertoriwn, and that of Dove, afford a vast amount of historical infor- 
 mation. The Transactions and Proceedings of the various societies, British and Foreign, have of course furnished a great part 
 of my information. Such strictly biographical details as I have made use of, have in general been very carefully taken from 
 the best accessible authority. 
 
MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 lesson more and more loudly in the ears of mankind. 
 The era of Newton and Leibnitz was grandly distin- 
 guished by the continually increasing applications of 
 mathematics to physics, whereof Newton was the great 
 teacher; the century 1750-1850, whilst profiting 
 by the lessons of the past, has added almost a new 
 one in the eminently practical character of its science, 
 and in the no less scientific character of its practice. 
 The result of these gradual modifications of human 
 knowledge has not been in the slightest degree in- 
 jurious to the real progress of the more abstract in- 
 Notinju- gredient of the mixed sciences. Did mathematics 
 nous to g^gj, flouj.jsii more vigorously than under Newton ] 
 science. ^^ 'pvae physical science had greater triumphs than 
 in the era of Volta, Watt, and Young ? It was 
 precisely because the new application of mathematics 
 stimulated their growth, because abstract relations 
 of quantity were vivified by concrete solutions of 
 physical problems, that a new geometry arose. 
 Dynamics could hardly be said to exist as a science 
 without the invention of Fluxions as a language by 
 which its conditions and results might be expressed ; 
 and from that time onwards, the necessities of the 
 natural philosopher have been the prime sources of 
 inspiration to the geometer, while the subjects have 
 become so blended that a mere discoverer in mathe- 
 matics has become a singularity. It would be hardly 
 possible to point out any mathematician of the 
 highest class since Newton, or but a few of the second 
 class, who have not contributed almost as much to 
 physical science as they have to analysis. Of purely 
 mathematical discoveries, the great majority have 
 been called forth by the immediate necessity arising 
 from some problem requiring solution in astronomy, 
 mechanics, optics, or heat. Lagrange's method of 
 Variations of arbitrary Constants in Integration, the 
 artifices for the computation of attractions by Laplace's 
 coefiBcients ; the introduction of the method of fac- 
 torials by Kramp in his solution of the problem of 
 refraction, and numberless improvements in the 
 Theory of Definite Integrals by Fourier and his suc- 
 cessors, sufficiently warrant the statement, and show 
 how richly the physical sciences have repaid to the 
 purely mathematical ones the debt which they origi- 
 nally owed. One other conclusion may be drawn 
 from these and parallel facts. It is that the com- 
 binations arising out of external phenomena are more 
 suggestive of the possible relations of number and 
 quantity than is the most unlimited stretch of fancy 
 and imagination ; and I believe it will be conceded 
 that, with few exceptions, theorems of the greatest 
 value and beauty have been more frequently dis- 
 covered during the attempt to solve some physical 
 or at least geometrical problem, than in compre- 
 hensive yet indefinite attempts to generalize the re- 
 lations of abstract magnitude. 
 (28.) These views are strikingly confirmed by the his- 
 
 torical fact of the paucity of pure mathematicians, The pure 
 and of distinct mathematical treatises of a strictly ^'**^" 
 original character in an age distinguished by the 
 difiusion of mathematical knowledge, and in countries 
 (like France) most celebrated for its triumphs. There 
 are not, perhaps, much more than half a dozen 
 really great mathematicians of the last seventy years, 
 who have not left treatises more numerous and more 
 distinguished on physical science, treated mathe- 
 matically, than on pure mathematics. Among the 
 exceptions which more immediately occur, are Monge, 
 Legendre, and Abel. And of distinct treatises, whilst 
 we have the Micanique Analytique, the MScanique 
 Cdleste, the ThSorie de la Chaleur, and numberless 
 others, containing precious mathematical develop- 
 ments, in connection with the applications which 
 suggested them, the purely mathematical memoirs of 
 the same period are to be sought chiefly in the form 
 of detached essays, in the ponderous volumes of 
 Academical Transactions. 
 
 One point in the History of Mathematics has espe- (29.) 
 cial interest for the English reader, and as such may Their pro- 
 be touched upon here with reference to the progress Country, 
 of, science for the last three quarters of a century. 
 The national pride of England in the triumphs of 
 Newton impelled her ablest mathematicians to at- 
 tempt to carry forward the synthetic methods which 
 he had chiefly used, at least in his published works, 
 to the more arduous and intricate questions of Me- 
 chanics and Astronomy which presented themselves 
 for solution in the course of the 18th century. Mac- 
 laurin was almost the last Englishman of that period 
 whose mathematical writings came into direct com- 
 petition with the rising schools of Germany and 
 France. The labours of Matthew Stewart, and 
 Simpson were mostly geometrical ; those of Landen 
 and Waring, though profound, created little general 
 impression ; and, gradually, the extent and difficulty 
 of the foreign mathematics, increased by the use of the 
 Leibnitzian notation of differentials which was ab- 
 solutely unfamiliar in England, deterred almost every 
 one even from perusing the writings of Clairaut and 
 D'Alembert, Lagrange and Laplace. Of the conti- 
 nental mathematicians, Euler was proTiably the best 
 known, owing to the lucidity of his writings and 
 their eminently practical tendencies. Some idea may 
 be formed of the negation of mathematical talent in 
 Britain during the later portion of the last century, 
 when we find D'Alembert declaring, in 1769, that if 
 an Englishman is to be elected one of the eight 
 foreign associates of the Academy of Sciences, he 
 will vote for Earl Stanhope as the best mathemati- 
 cian there, as he believes, not having read any of 
 his works ! If the choice was to be free, he should 
 prefer M. de Lagrange ! l"- A more cutting, though 
 unintentional satire on the state of Mathematics in 
 this country could not have been written. 
 
 ^ Letters of eminent persons, addressed to David Hume, edited \>j Mr Burton, p. 21S. 
 
Chap. I., § 2,] 
 
 MATHEMATICS — PHYSICS — MECHANICAL ARTS. 
 
 9 
 
 (30.) 
 At Cam- 
 bridge, 
 Edinburgh, 
 and Dublin 
 
 (31.) 
 Improve- 
 ments in 
 Integra- 
 tion. 
 
 Diecontinu- 
 ous func- 
 tions. 
 
 The commencement of a better era originated, early 
 in the present century, with Woodhouse at Cambridge, 
 and Playfair in Edinburgh, by both of whom the con- 
 i tinental methods were introduced into the studies of 
 their respective universities ; whilst Ivory, a native of 
 Scotland, was the first to challenge, by his writings, a 
 place in the list of great living mathematicians. The 
 systematic form of the MScanique Celeste rendered the 
 subject more accessible than were the countless me- 
 moirs by men of the highest name, which then filled 
 the Transactions of Paris, Turin, Berlin, and StPeters- 
 burg. But the notation of differentials, which could 
 alone break down the barrier between the British and 
 foreign mathematicians, was first introduced at Cam- 
 bridge by the efibrts of Sir John Herschel and Dean 
 Peacock about 1816, soon after which the transla- 
 tion of Lacroix's Differential Calculus, which they 
 superintended, came into use as an university text- 
 book. From this time the works of foreign mathe- 
 maticians began to be more generally read, particu- 
 larly the writings of Laplace and Poisson ; and 
 within ten or a dozen years subsequently, a few 
 active and undaunted men, chiefly of the Cambridge 
 school, such as Mr Airy and Sir John Lubbock, 
 grappled with the outstanding difiBculties of physical 
 astronomy, whilst a larger number applied them- 
 selves to the most difficult parts of pure analysis, 
 and acquired great dexterity in its use in the solu- 
 tion of geometrical and mechanical problems. Such, 
 for example, were Mr Babbage, Mr De Morgan, Mr 
 Murphy, and Mr Green ; and at Dublin Sir William 
 E. Hamilton and Mr MacCuUagh, whose names will 
 occur in other parts of this Dissertation. 
 
 No new calculus or great general method in ana^ 
 lysis has resulted from these persevering labours, 
 whether of British or foreign mathematicians, but 
 an increased facility and power in applying the ex- 
 isting resources of mathematics to the solution of 
 large classes of problems previously intractable, or 
 resolved only indirectly or by approximation. The 
 Integral Calculus, in particular, affords an almost 
 boundless field for research, and each branch of 
 science in succession — not only Physical Astronomy, 
 but Optics, Heat, Electricity, and Civil Engineering 
 — ^has offered problems of great importance, which 
 awaited only the skill of the pure mathematician to re- 
 Solve in a practical and finite form.'- Every year, and 
 every civilized community, contribute to these real 
 improvements. The principle of discontinuity, con- 
 
 spicuously introduced into the doctrine of the con- 
 duction of Heat in consequence of the abrupt varia- 
 tion of physical circumstances at the boundary of 
 the conducting body, enters largely into the specula- 
 tions of mathematicians of the present century ; and 
 the doctrine of definite integrals so intimately con- 
 nected with it has received a proportional extension. 
 Next, analytical geometry has acquired a very great Analytical 
 enlargement and by attention principally to symmetry S«°™® '^• 
 in the arrangement of the results, solutions other- 
 wise the most intricate are obtained with facility and 
 directness. Of this we shall find examples in our 
 history of the Undulatory Theory of Light. Lastly, The Calcu- 
 notwithstanding the pre-eminently practical charac- 1"^ of Ope- 
 ter of the mathematics of the last age, speculative 
 geometers and analysts have found time to discuss 
 the metaphysics of their respective sciences, both as 
 regards the foundations of the Differential Calculus 
 and as to the use of imaginary and other symbols in 
 Algebra. An almost new branch of abstract science 
 (though faintly foreshadowed by Leibnitz) has come 
 into existence — ^the separation of symbols of opera- 
 tion from symbols of quantity, and the treatment of the 
 former like ordinary algebraic magnitudes. In some 
 cases remarkable simplicity is thus introduced into 
 the solution of problems, although perhaps few ma- 
 thematicians would choose to depend implicitly upon 
 the method in untried cases. Sir John Herschel and 
 the late Mr Gregory'' were amongst the most active in- 
 troducers of this new algebra, but few of the more 
 eminent living British or foreign mathematicians 
 have failed to contribute their share to this more 
 metaphysical department of analysis. 
 
 I shall now attempt to consider more particu- (32.) 
 larly the reciprocal relations of pure physical science Connection 
 and the mechanical arts. _ scienceTd 
 
 This is evidently a very intimate one. The dis- the arts, 
 coveries of pure physics (such as Astronomy, Acous- (^^■) 
 tics. Magnetism), are the results of either observation 
 or experiment, and they consist in generalizations, 
 by means of which a multitude of facts are reduced 
 under one simple expression of a more general fact 
 or principle. But instruments often very compli- 
 cated are necessary for observation and for experi- 
 ment ; as telescopes in astronomy, organs in acoustics, 
 properly magnetized and suspended steel bars in 
 magnetism. Art is required to construct these. The 
 highest possible degree of science, and the utmost 
 
 1 For example the Lucasian Professor at Cambridge, Mr Stokes, has effected two previously impracticable integrations, one 
 occurring in the theory of the rainbow, the other in that of railway girder bridges. 
 
 ^ Mr Duncan Gregory, a promising mathematician who died 23d February 1844, at the early age of 30, was the youngest Mr Duncan 
 son of Dr James Gregory, the late distinguished Professor of Medicine at Edinburgh. His name deserves a passing record, not only Gregory, 
 from the influence he exercised on the progress of the English mathematics of his time, but as having revived the dormant charac- 
 ter for this peculiar kind of talent, so long connected with the family of Gregory. He was, in fact, the lineal descendant of the 
 inventor of the reflecting telescope. Mr Gregory was the first editor of the Cambridge Mathematical Journal, and author of an 
 excellent book of Examples in the Differential and Integral Calculus, both of which have exercised a beneiicial influence on the 
 progress of science in England. He also wrote several original memoirs on the subjects referred to in the text. Mr Leslie Ellis, 
 a man of congenial ability, has written a short but pleasing biography of his friend. 
 
10 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 (34.) 
 Great Me- 
 chanical 
 inventions 
 presume a 
 knowledge 
 of physical 
 laws; 
 
 (35.) 
 and gene- 
 rally an in- 
 ductive 
 procesSf 
 
 mechanical skill, are both indispensable to make a 
 telescope. A telescope then, though a mechanical 
 invention, inasmuch as it is a deduction from phy- 
 sical principles, not an addition to them, is yet a 
 deduction so ingenious — so far from obvious — so im- 
 possible to be conceived accidentally or by a loose 
 thinker, and so easilymade the instrument of innumer- 
 able discoveries of the highest novelty and grandeur, 
 that no historian of science ever thought of omitting 
 the invention of the telescope, or of giving it an im- 
 portance inferior to that of a discovery, containing as 
 it did the germ of so many discoveries. In like manner 
 a theory of optics might be ■written in which a tele- 
 scope need never be mentioned ; but would not the 
 pedantry of such a work be obvious, or would any 
 reasonable person wish to learn science after such a 
 fashion ? 
 
 The elea/r co-ordination of the parts of an invention 
 towards the attainment of a given result, with a due 
 regard to natural laws, and the properties of the sub- 
 stances used, constitutes the merit of the invention ; 
 and this merit may be irrespective of the precise im- 
 portance of the end of the invention, which may be 
 intended to promote science, or commerce, or con- 
 venience, or even to satisfy mere curiosity. A tele- 
 scope would have been a telescope still, could we have 
 imagined it invented with no other object than a deer- 
 stalker's sport ; and so contrivances which in their ori- 
 gin and application seem remote from scientific uses, 
 constitute nevertheless real steps in the progress of 
 knowledge. The steam-engine is one striking ex- 
 ample. Originally devised with an exclusively com- 
 mercial object — ^the extrication of the Cornish mines 
 from subterranean water, it became in the hands of 
 Watt, first an instrument for experiments on the re- 
 lation of heat to matter ; next, in its improved form, 
 a beautiful exemplification of these laws, and an en- 
 during monument of the sagacity and skill of its 
 author, as well as the most important inorganic 
 agent which exists in modifying the social condition 
 of the entire globe. Finally, to illustrate the posi- 
 tion from which we started, it becomes the instru- 
 ment of fresh discoveries. This very engine has a 
 theory to be worked out, probably unimagined even 
 by its sagacious author — its operation as an agent for 
 obtaining power from matter by the application o£ 
 heat, is shown to be in all probability a single case of 
 a more general law, including all kinds of machines 
 and all sorts of matter ; and this more general theory 
 of heat as a motive power leads, once more, to new 
 practical deductions, to the conditions under which 
 such machines may be most usefully constructed and 
 employed.^ 
 
 Every instrument, every construction, which is 
 founded on a theory, and in which a certain compli- 
 cation of conditions is required to produce a certain 
 
 result ; a telescope, for example, or a steam-engine, 
 or a bridge, is, in the first instance at least, an ex- 
 periment. Few inventions are so simple and straight- 
 forward in their plan, are so independent of the seem- 
 ingly capricious behaviour of matter under untried 
 circumstances, or depend so entirely on physical laws 
 thoroughly understood, that the inventor can await, 
 without the pang — at least of impatience — if not of 
 anxiety, the moment of the realization, by actual 
 trial, of his hopes and his calculations. We can all 
 readily imagine the throb of anxiety with which 
 Galileo pointed his glasses for the first time to the 
 moon — ^with which Watt saw the cylinder of his As in 
 model exhausted, and the piston descend under the Watt's 
 action of his separate condenser — and Stephenson, „j^g' 
 the stupendous iron tube at Conway resting for the 
 first time straight as a ramrod on its two piers— 
 these are moments of anxiety and of triumph, which 
 place the inventor of a machine and the architect of 
 a stiructure on a par with the discoverer of a planet, 
 or with the author of a theory. " Whenever an ori- 
 ginal mind produces new combinations of thought and 
 feeling,'' says Sir James Mackintosh, with equal im- 
 partiality and truth, " whether its means be words or 
 colours, or marble or sound, or command over the 
 mighty agents of nature ; whether the result be an 
 epic poem, or a statue, or a steam-engine, we must 
 equally reverence those transcendent faculties to which 
 we give the name of genius."^ It is almost needless 
 to add the caution, that such praise is only applicable 
 when the invention is such as to call forth the qua- 
 lities which distinguish the Philosopher. It is not 
 the mere command over the agents of nature which 
 challenges our admiration, it is the foresight, the 
 patience, the conceptive faculty, the clear-sighted 
 and confident anticipations of what will be the re- 
 sults of natural laws acting in given circumstances, 
 these circumstances being in some essential particu- 
 lars new. Merely to adopt known contrivances, 
 where experience has already anticipated the result, 
 may exercise judgment, but hardly genius ; and to 
 make contrivances in which the result depends rather 
 upon laws of geometry than of physics, hardly come 
 within the scope of these remarks. 
 
 Watt's Parallel Motion, perhaps the most inge- (36.) 
 nious of his inventions, would not have made a great 
 reputation ; nor does the endless variety of machines 
 used in the arts, as in spinning, printing, and paper- 
 making, stand higher. It is when the inventor 
 places Matter in new relations to Force, or derives 
 power from new sources, or teaches Light or Electri- 
 city to act under new conditions, that he becomes 
 really a Mechanical Philosopher. 
 
 It is not given to man to endue matter with new (37.) 
 properties, or to prescribe the laws under which his The limits 
 inventions are to take effect. A new motive power, °^"*' 
 
 ^ See Carnot, Pumance Motrice du Feu, and the writings of M. Clapeyron, Professor 'W. Thomson, &c. 
 ^ Speech at a meeting for erecting a monument to Watt, in Arago's Moge of Watt. 
 
Chap. II., § 1.] 
 
 PHYSICAL ASTKONOMY — LAGEANGE. 
 
 11 
 
 a new form of construction, are experiments on the 
 resources of nature under new conditions. 
 
 Solutionsof ■'■^ ^**'*' ^^^^ ^^ comparatively simple cases, we 
 mechanical cannot set forces to act on matter, or dispose mat- 
 as of ma- ter so as to resist force, without doing not only what 
 *'iobrems°'* we intend to do, but also a great deal more. Man 
 sometimes ^^7 P"* powers in motion which he is unable to 
 manifold, control ; and whilst he calculates confidently upon 
 the effects of such and such dispositions of force or 
 resistance, he may overlook consequences equally 
 necessary, because resulting from laws of nature 
 which are either unknown to him, or the magnitude 
 of which he had overlooked, in considering those only 
 which he required. A complicated mechanical con- 
 trivance may be compared to the mathematical solu- 
 tion of a problem. It represents commonly a great 
 deal more than is meant to be derived from it. It 
 may represent several distinct results, some possible, 
 some impossible, and of the former only one, it may 
 be, congruous to the real conditions of the problem 
 proposed. In mechanics, the laws of nature are 
 as impatient of control as the laws of quantity in 
 geometry, and the engineer may find, too late, that 
 nature has solved his problem differently from what 
 he expected. But even when successful, it is to be 
 presumed that his own contrivance contains within 
 it results unforeseen by himself. If he is wise he 
 will become a student in his own workshop. The 
 material contrivances are indeed his own, but the 
 powers which they awaken or distribute are beyond 
 his control. Even if his reading of the equation be 
 strictly correct, there may remain in the background 
 others no less important. 
 (39.) ijijie considerations here imperfectly laid before 
 the reader are intended to justify the introduction of 
 certain practical topics into the present Dissertation, 
 which, though many readers will see their insertion 
 without surprise, or would have been sorry to find 
 them omitted, others possibly may think more or 
 less independent of, and separable from a scheme 
 already sufficiently extensive and intricate, if con- 
 fined to mere subjects of scientific doctrine, to the 
 exclusion of its applications. My chief reason for 
 including such subjects as the Steam-engine, the 
 strength of materials and some great examples of 
 
 construction, and the electric telegraph, is that 
 these important practical improvements are both 
 historically and logically interwoven with the pro- 
 gress of pure or abstract physics. They have be- 
 sides impressed upon the character of scientific dis- 
 covery of the last hundred years a peculiar stamp 
 which it would have been absurd to ignore while 
 endeavouring, within a moderate compass, and in the 
 plainest language, to convey a vivid though compre- 
 hensive sketch of the advancement of Natural Philo- 
 sophy during this and the preceding, or rather two 
 preceding generations. 
 
 It is not to be imagined that the difficulty of the (40.) 
 problems which occupy the speculative philosopher, Lessons of 
 or the comprehensiveness of mind required for their gxpraimce. 
 solution, diminishes in any degree as we descend 
 from the regions of pure science to the walks of every- 
 day life — ^from the vast periods and majestic motions 
 which astronomy enables us to explain and predict, 
 to the common details of the workshop and the rail- 
 way. In fact, the former are to be regarded as the 
 simpler investigations, whUst our terrestrial agents 
 have their effects modified by the diversified states of 
 aggregation and various mechanical properties of mat- 
 ter, and by the numerous modifications of force arising 
 from heat, electricity, or magnetism, to which it may 
 be exposed. We have as yet made but an insignificant 
 advance towards that completer system of Natural 
 Philosophy of which Newton's will form but one 
 section, in which all the properties of matter and 
 their consequences shall be as well understood as the 
 particular property of gravity is at present. Many of 
 these are to be learned by daily observation of the 
 effects which occur in the ordinary progress of civi- 
 lization amongst us. We are continually perform- 
 ing experiments on a great scale and on purely com- 
 mercial principles, which no individual philosopher 
 or merely scientific society could have ventured to 
 attempt. And in the midst of these appeals to 
 experience, unexpected results are frequently occur- 
 ring which send us back once more to the study of 
 first principles, which, indeed, while they confound 
 the empiric, do but establish the reputation of the 
 philosophic engineer, who seldom fails to turn them 
 to good account, both in his theory and practice. 
 
 CHAPTER II. 
 
 PHYSICAL ASTRONOMY AND ANALYTICAL MECHANICS. 
 
 (41.) 
 Lagrange. 
 
 1. LaGtRANGE. — Variation of Parameters — Application to Physical Asfronomy. The Stability 
 of the Planetary System ; Laplace ; Poisson. Moon's Libration. 
 
 The period of Lagrange's most celebrated labours 
 extends so far back into the preceding century, that 
 having been already mentioned in Sir John Leslie's 
 
 Dissertation, it might have been excusable, with so 
 great a mass of matter before us, to have passed 
 them over without farther notice. But they are so 
 
12 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (42.) 
 His birth 
 and educa- 
 tion: 
 
 ifitimately connected with the most salient points of 
 the history of physical astronomy, down even to the 
 present time, and are so interwoven with the disco- 
 veries of Laplace, and represent altogether so much 
 of the substantive character of the progress of the 
 age, that I have thought it necessary to devote a 
 small space to the recital of a few of the most pro- 
 minent of them, having regard to the intellectual 
 portraiture of the man as one of the most pre-emi- 
 nent and successful reasoners of his class who have 
 ever done honour to their race. I shall repeat as 
 little as possible what has been said elsewhere, and 
 confine myself to only two or three topics. 
 
 Joseph Louis Lagrange was born at Turin in 1736 ; 
 he died at Paris 10th April 1813. His first paper 
 was written at the age of 17 or 18, and his end was 
 accelerated by the unremitting ardour of his labours 
 at the age of 77- He was consequently an original 
 author during sixty years ; and for the greater part of 
 his contem- this period he, togetherwith Laplace, monopolized the 
 poranes. greatest discoveries connected with analysis and phy- 
 sical astronomy, and exercised an almost undisputed 
 authority in the more recondite sciences. Euler, 
 Lagrange, and Laplace, by a singular coincidence, 
 lived to the respective ages of 90, 77, and 79', and 
 all retained their activity nearly to the last. They 
 produced, by the continuity and friendly rivalry of 
 their labours, carried to an extent in each case which 
 only astonishing physical vigour united to astonish- 
 ing mental aptitude could have produced, during 
 almost a century, an impression on the progress of 
 science altogether remarkable. This coincidence 
 was ;ithe more happy, because physical astronomy 
 was exactly in that predicament when nothing less 
 than such a combination of intelligence and intensity 
 of application systematically urged, could have car- 
 ri«d Newton's theory through the difficulties which 
 at that time beset it— difiiculties which left the Prin- 
 cipia, for so many years alone, and far in advance of 
 the general intelligence of the age, 
 (43.) The pregnant suggestions of Euler were developed 
 
 Euler and and applied by Lagrange, and the trium/phs of Lar 
 Laplace, grange — may, even bis occasional failures — ^were the 
 immediate precursors of some of Laplace's; happiest 
 efforts> 
 
 Amongst the former we reckon the method of the (44.) 
 variation of parameters, expounded to a certain point Variation 
 by Euler, though, as in many other cases, his results "^^P"*™*' 
 were vitiated by the haste and inaccuracy of his cal- 
 culations. That Lagrange borrowed the idea from 
 Euler cannot admit of a doubt, any more than that 
 he was indebted to him for the principles of the Cal- 
 culus of Yariations. Lagrange, with customary truth- 
 fulness, even to his latest days, always spoke of Euler 
 aa his best instructor and model, and as the chief 
 of modem mathematicians, Newton only excepted. 
 We know that he so regarded him in the case of the 
 calculus of variations which he studied in Euler's 
 "Methodus inveniendi lineas curvas, &c.," during 
 the first two years of his application to the higher 
 mathematics ; 1 whilst Euler, with equal candour, 
 acknowledged the transcendent genius of the rising 
 geometer, forcing its way where he himself had 
 failed. 
 
 The method of the Variation of the arbitrary con- (45.) 
 stants or Parameters, though it may be regarded in its^signifi- 
 one point of view as a merely analytical artifice for 
 effecting integrations, is in reality a conception purely 
 geometrical, first introduced by Newton" under the 
 name of " revolving orbits," and applied by him to 
 the explication of the conception (to use a recently 
 introduced phrase) of the liinar inequalities. Neither 
 the moon nor any planet really describes a mathema- 
 tical! ellipse (in consequence of the mutual perturba- 
 tions of the heavenly bodies). They describe curves of 
 double curvature in space, of which we could form 
 no intelligible idea, except by referring them to the 
 very approximate type of the ellipse, of which the 
 eccentricity, line of apsides, inclination, &e., are con- 
 tinually varying, not only from one revolution to 
 another, but throughout every part of a revolution. 
 This representation is not only convenient, but 
 strictly accurate. At each instant the m,oon or 
 planet is describing a portion of an ellipse, which 
 maybe called the instomtaneous ellipse, and which instantane- 
 may be defined as the particular ellipse which the o"^ ellipse, 
 body would go on to describe if it were at that 
 instant freed from all perturbation, and allowed to 
 complete a revolution under the single influence of 
 its acquired motion and the central force. To take 
 
 Lagrange's 1 The following is a list of the books he then read, taken from a paper probably little known, which appeared soon after the 
 early death of Lagrange in the Moniteur newspaper, and which was translated in Thomson's Annals of Philosophy, vol. iv. He 
 
 studies. first read Euclid's Elements, Clairaut's A^ebra ; then, in less than two years, and in the following order, Agnesi's Analy- 
 tical Institutions, Euler's Analysis of Infinites, John- BernouUli's Lectures, Euler's Mechanics, the two first books of Newton's 
 Principia, D'Alembert's Dynamics, and Bougainville's Integral Calculus, Euler's Differential Calculus and Methodus Inveniendi 
 — a pretty course of mathematical reading for a youth between 17 and 19. 
 
 Prom the same paper we abridge a few practical directions given by Lagrange for the study of mathematics, which, if 
 tolerably obvious, are interesting from the extraordinary genius of the man, and from his singular reticence on subjects of a 
 personal nature. " I never," he said, " studied more than one book at a time ; if good, I read it to the end." " I did not 
 Berplex myself with difficulties, but returned to them twenty times if necessary. This failine ,1 examined another author." " / 
 conside^'ed' reading large treatises of pare analysis quite useless. We ought to devote our time and labour chiefly to the applica- 
 tions." Thus he read Euler's Mechanics when he had acquired a very Slight knowledge of the differential and integral calculus. 
 " I always read with my pen in my hand, developing the calculations, and exercising myself on the questions." 
 
 " From the very beginning of my career, I endeavoured to make myself master of certain subjects, that I might have an 
 opportunity- of in-venting improvements ; and I always, as far as possiblfi, made theories to myself of the essential points, in order 
 to fix them morei completely in my mind, to render them my own, and to accustom myself to; composition." " Finally, I every 
 day assigned myself a task for the next. I learned this custom fromi the. King of Prussia." 
 2' This Lagrange himself points out in his Mecanique Analytique. 
 
Chap. II., § 1.] 
 
 PHYSICAL ASTEONOMY — LAGRANGE. 
 
 13 
 
 theory. 
 
 a single example; the planet Uranus has not yet 
 completed one revolution since the time of its disco- 
 very in 1781, yet its observed path diiFered so much 
 from a true elliptic arc (even when we allow for the 
 perturbation of Jupiter and Saturn), that the orbit 
 which satisfied the observations from 1781 to 1800 
 would not satisfy those from 1800 to 1820; and 
 since 1820 a new orbit had to be computed for every 
 few years, so great were the variations of the instant- 
 aneous from any permanent ellipse. These varia- 
 tions led to the discovery of the planet Neptune. 
 (46.) To adapt the notion of the perpetual variation of 
 
 Hicnr^v™^ the elliptic elements to analytical calculation, and to 
 ascribe to each planet its influence in perturbing the 
 elliptic motion of the others, was the great problem 
 mainly solved by Lagrange. In the planetary theory, 
 where the perturbations are all very small, on account 
 of the excessive preponderance of the mass of the 
 sun, the motion of each planet may be considered as 
 under the separate disturbing influence of every 
 other, and the whole perturbation is the sum of the 
 separate perturbations. 
 (47.) Now, these perturbations of elliptic motion may 
 
 Periodic ^,g divided into two great classes, which Lagrange 
 inequali- first, in 1782, included in a common analysis, which 
 ties. expressed the disturbed elements of planetary motion 
 
 by two sets of terms : those which include the rela- 
 tive positions (or configuration) of the disturbing and 
 disturbed planets being the one set, and those which 
 included only the masses and elements being the 
 other. The former are called periodic, the latter 
 secular inequalities. The distinction is important, 
 since, after a suflaciently long time, two planets (sup- 
 pose the Earth and Mars) will have been presented 
 to one another in space in every conceivable posi- 
 tion of which, by the form and position of their or- 
 bits, they are susceptible, a like recurrence of confi- 
 gurations will recommence, and like perturbations 
 will resnlt. Such influences, though running through 
 long periods, will be evidently recurring. But there 
 is another class of disturbances, which may in thought 
 be entirely separated from the former, being the ulti- 
 mate or average effect of the influence of one planet 
 on another, arising, not from the position of the pla- 
 nets in their orbits at any one time, but from the po- 
 sition of the orbits themselves. Thus in a single 
 revolution (and on account of the independent excen- 
 tricities of the orbits during many successive revo- 
 lutions) of Mars and the Earth, the attraction of the 
 former on the latter sometimes conspires with the 
 sun's attraction, sometimes opposes it, sometimes 
 urges the Earth forward in its path, and sometimes 
 pulls it back, producing numerous periodic inequali- 
 ties ; but it is quite evident that, in the long run, 
 the attraction of Mars on the Earth tends to pull it 
 away from the sun, and to diminish the effect of the 
 solar attraction — in fact, to increase the length of 
 our year ; and that this influence will be precisely 
 the same if we take the average of a great many re- 
 
 volutions now, and compare them with a similar ave- 
 rage hereafter, provided that the orbits undergo no 
 permanent change. This , therefore, though not strictly 
 an inequality, because the length of the year is per- 
 manently changed by it, shows an average effect in- 
 dependent of the configuration of the planets. An 
 example of a true secular inequality is the revolution 
 of the line of apsides or major axis of any orbit, by 
 the influence of the disturbing forces of the planets, 
 whether interior or exterior to the one considered. , .„ 
 
 Few of the secular inequalities have been detected by change of 
 observation throughout the entire records of Astro- apsides and 
 nomy. It is known, however, that the apsides of the excentn- 
 planetary orbits (at least in the case of the old 
 planets) all progress, with the exception of those of 
 Venus, which retrograde, and that the inclination of 
 all is at present diminishing. The excentricity of the 
 Earth's orbit is decreasing at the rate of 40 miles per 
 annum. The exclusive dependence of the secular ine- 
 qualities on the orbits, not on the places of the planets, 
 may be well illustrated by a method actually employed 
 by Gauss for computing them (though it does not 
 appear to be attended by any special advantage). 
 He conceives the orbit of the disturbing planet to be 
 strewed with attractive matter, whose thickness at 
 any point is inversely as the planet's velocity there, 
 or directly as the time of its sojourn in any small 
 length of the orbit. , . . 
 
 The method of variations of the elements is evidently 
 most applicable to the determination of Secular Per- 
 turbations ; for to compute by means of it the ordi- 
 nary inequalities involves an apparently unnecessary 
 labour. The place of a planet is completelydetermined 
 by three co-ordinates — its longitude, latitude, and 
 radius vector; whilst the elements of the orbit are six in 
 number, and when found, a further calculation must 
 be made to find the co-ordinates of position. The 
 more direct method of deducing the co-ordinates at 
 once from the conditions of perturbation, was gene- 
 rally followed until 1808, when Lagrange and 
 Laplace almost simultaneously devised methods of 
 using the variation of the elements with directness 
 and despatch in the calculation of Planetary Pertur- 
 bations. In the estimation of the second and higher 
 orders of disturbance, it has even the advantage in 
 these respects over the other method. 
 
 Stability and Permanence of the Solar System,. — gtavrt f 
 After it had been clearly recognised, principally by the solar 
 the labours of Lagrange, that the elements of the pla- system. 
 netary orbits are in a condition of perpetual change, 
 it came to be a most interesting question how far 
 such variations were likely to be continuous, and ulti- 
 mately so great as to modify altogether the forms of 
 the orbits, and even endanger the separate existence 
 of the planets. This is a question which has excited 
 a very general, as well as scientific interest. It is 
 evident that the variations of the different elements 
 are not all equally important in affecting the perma- 
 nence of an orbit. The five properly orbital ele- 
 
14 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 ments (the sixth being the longitude of the planet on 
 its orbit at a given time) may conveniently be con- 
 sidered thus : 1st, the major axis, which, for one and 
 the same system, involves the periodic time or mean 
 motion; 2d, the excentricity and position of the line of 
 apsides; 3d, the inclination and position of the line of 
 nodes . Of these, the stability primarily depends upon 
 the first. If the major axis and mean period increase 
 or diminish without limit, the planets will diverge 
 into infinite space, or rush after myriads of ages to 
 utter annihilation in the burning embrace of the sun. 
 The latter alternative was the popular belief about 
 the middle of last century, and was maintained by 
 the grave authority of Euler ; whilst Darwin, in his 
 florid but picturesque language, described the order 
 and beauty of the planetary system as but a little 
 more permanent than the glowing ornaments of the 
 gay parterre.^ The principal reason for this conclu- 
 sion, and its refutation, will be mentioned in the next 
 section. 
 (51.) The first person who perceived the probable sta- 
 
 Laplace's bility of the major axes and mean motions was not 
 disco rery. Lagrange but Laplace, who, in a paper published in 
 1773, gave a demonstration, the sufficiency of which 
 has not been doubted, that the major axes are in- 
 variable, so far as the influence of the principal 
 terms of the disturbances are concerned, that is as 
 far as terms containing the cubes of the excentrici- 
 ties inclusive, and the first powers of the perturbing 
 masses. Nor does Laplace appear to have doubted 
 that the mutual distinction of the terms, including 
 secular changes, was not accidental, but would ex- 
 tend also to the farther approximations. Lagrange, 
 however, in a celebrated though short memoir of 
 1776, demonstrated the truth of the conclusion for 
 the higher powers of quantities contained in the per- 
 turbations of the first order, and that by methods 
 peculiarly comprehensive and elegant, which he far- 
 ther extended in 1781 to the other five orbital ele- 
 ments, showing the periodicity within certain narrow 
 limits of the excentricity and inclination, the only 
 elements, except the major axis, whose variations 
 menace the stability of the system. Yet it is quite 
 impossible to separate completely the names of La- 
 grange and Laplace in the efiectual demonstration of 
 this important truth, the former as frequently in- 
 
 dicating the means of overcoming the more purely 
 mathematical difficulties, as the latter was suggestive 
 and far-sighted in anticipating their application to 
 the peculiarities of our system. 
 
 Laplace discovered (1784) two remarkable theo- (52.) 
 rems which limit the whole amount of the excentri- ^^"^'j^^J; 
 cities and inclinations of the orbits of the planetary ues and in- 
 system, showing that if once small, they must ever clinations 
 remain so ; and, in particular, that the most massive °^ P^™^" 
 planets of the system (Jupiter and Saturn) mi»st also "■'^ "'' ^ '' 
 undergo the most trifling variation ia these respects. 
 In the case of the small planets between Mars and 
 Jupiter^a wider range may occur (as indeed we prac- 
 tically find to be the case), without endangering the 
 permanency of the whole. It also follows that these 
 variations, though " secular," are practically " perio- 
 dic ;" that is, that the excentricities and inclinations 
 oscillate about certain mean values and within ex- 
 tremely narrow limits, the periods of these oscillations 
 being also of vast duration. Concerning such changes, 
 theory is our only guide. The whole duration of astro- 
 nomical records can barely reveal the existence of two 
 or three of them, and iells us absolutely nothiag of 
 their remoter consequences. Lagrange calculated 
 the superior limits of the excentricities of the larger 
 planets, and M. Leverrier has recently, by more ac- 
 curate methods, obtained results nearly coincident. 
 According to him, the maximum excentricity of the 
 Earth's orbit is 0-07775, the minimum 0-003314, so 
 that it can never be quite a circle. It is now di- 
 minishing, and will continue (according to the same 
 geometer) to do so for 24,000 years, when it will 
 begin to increase. The inclinations of the Earth's 
 orbit to its equator, and also to a fixed plane, are 
 confined within definite limits which are not perhaps 
 very perfectly known. 
 
 The motions of the apsides and nodes of the orbits (53.) 
 which gradually complete the entire circumference *'°*"'°' "^ 
 have manifestly no tendency to affect the stability of „^j[gg_ 
 the system. The grand cycle of the Earth's perihe- 
 lion will only be completed in 110,000 years. It 
 coincided with the vernal equinox 4089 years before 
 Christ, a period (as Laplace remarks) nearly coinci- 
 dentwith that assigned bychronologerstothe creation. 
 
 These results may be considered as among the (54.) 
 most astonishing with which science brings us ac- 
 
 ^ " Roll on ye stars ! exult in youthful prime, 
 
 Mark with bright curves the printless steps of Time, 
 Near and more near your beamy cars approach, 
 And lessening orbs on lessening orbs encroach; 
 Flowers of the sky ! ye too to age must yield, 
 Frail as your silken sisters of the field ! 
 Star after star from heaven's high arch shall rush, 
 Suns sink on suns, and systems systems crush. 
 Headlong, extinct, to one dark centre fall. 
 And Death and Night and Chaos mingle all ! 
 'Till o'er the wreck, emerging from the storm, 
 Immortal Nature lifts her changeful form, 
 Mounts from her funeral pyre on wings of flame. 
 And soars and shines, another and the same." 
 
 Vanuin'a Botanic Garden, Canto iv., line 367. 
 
Chap. II., § 2.] 
 
 PHYSICAL ASTKONOMY — LAGRANGE. 
 
 15 
 
 quainted. The range of insight which man has ac- 
 quired into the past and future history of the uni- 
 verse throughout periods, compared to which, the 
 whole existence of his species is but a span, enhances 
 our admiration of the reasoning power which can 
 attain to knowledge so high and excellent. And the 
 sublimity of the contemplation is increased when we 
 recollect that these recondite truths are all conse- 
 quences of a law so simple as that of gravity. Ob- 
 servation will reveal only to a late posterity the se- 
 cular modifications of the planetary orbits which geo- 
 metry now predicts to us. Some of the ellipses will 
 elongate, whilst others tend to become circles ; their 
 planes will vary in inclination, but ultimately be 
 stayed within the limit which human sagacity had 
 predicted myriads of years before. "These," says a 
 French analyst, "are the pendulums of eternity, which 
 beat ages whilst ours beat seconds." And amidst 
 all these variations, subject to law and to impass- 
 able limits, the Major Axes of the orbits preserve a 
 stedfast uniformity, or are subject only to transient 
 fluctuations ; and thus permanence arises in the midst 
 of change, and the perfection of the system is demon- 
 strated by the very nature of the disturbances which 
 seemed at one time inevitably to limit its duration. 
 
 It remains to add, in closing this interesting 
 discussion, that Lagrange himself had not quitted the 
 thrtheory" ^^^^ before his able disciple and follower, Poisson, 
 pursued the inquiry of the stability of the system, 
 and the permanency of the major axes particularly, 
 to a degree of approximation not before attempted. 
 He included the perturbations of the second order, 
 or those which arise by correcting the elements for 
 the disturbances first found, and including the effects 
 of the correction in the modification of the perturba- 
 tions themselves. These also are subject to the 
 same laws as found by Laplace and Lagrange for 
 lower degrees of approximation ; and as MM. de 
 Pontecoulant and Leverrier have confirmed the result 
 (at least for all the larger planets of the system), we 
 may conclude it to be a truth as firmly established as 
 any negative fact can be, that our system is arranged 
 for a duration apparently indefinite ; that if the planets 
 cease to roll, and the sun and moon to do their 
 office in enlightening the world, it must be in all 
 
 (55.-) 
 Poisson's 
 addition to 
 
 probability by an interposition of Almighty power, 
 as direct and immediate as the creative energy by 
 which they were launched into space, and (our earth at 
 least) peopled with successive races of animated beings. ' 
 
 We have, in the commencement of this section, (56.) 
 disclaimed the intention of entering at large upon the Lagrange's 
 history of Lagrange's discoveries. They fell more pro- "^-j^ ^ 
 perly under the scope of the preceding Dissertation, 
 and an able summary and enumeration of his writings 
 by no less competent a person than Dr Thomas Young 
 will be found in the alphabetical part of this Encyclo- 
 psedia. I will only add, that while scarcely a topic 
 in physical astronomy, or in pure mathematics, failed 
 to receive important additions from his pen, his 
 memoirs on the Libration of the Moon, his solution 
 of several problems of Sound and vibrating strings, 
 and his methods of computing the perturbations of 
 Comets, are amongst his contributions to science, 
 most vividly remembered and most justly admired as 
 models of analytical ability. He himself is stated 
 to have preferred, amongst all his papers, one in the 
 Turin Memoirs of 1784, on the Integral Calculus.^ 
 
 With reference to the Lunar Libration, Lagrange (57.) 
 confirmed the singular conclusion of Newton, that the Libration 
 moon is a spheroid, having three unequal axes, the ^..^ 
 longest of which is always approximately directed to 
 the earth, and the shortest is her axis of rotation. 
 In consequence of this, the moon, of necessity, re- 
 volves on her axis in the exact time that she circu- 
 lates round the earth (supposing that at any time 
 these periods were nearly, though not absolutely, 
 coincident), and is subject (as Newton had divined) 
 to a species of oscillation upon her axis, owing to the 
 line of the earth's attraction not always coinciding 
 (in consequence of the moon's irregular motion in 
 longitude) with the moon's greatest diameter. This 
 constitutes a physical libration, as inequalities in lon- 
 gitude, by enabling us to see more or less of the 
 lunar hemisphere diametrically opposed to us, con- 
 stitute an optical libration, or apparent to-and-fro 
 motion on her axis. In this investigation Lagrange 
 first used the combination of D'Alembert's Principle 
 with that of Virtual Velocities, afterwards fully ex- 
 panded in the Mecanique Analytique.* 
 
 Lagrange was happy in passing his days with (58.) 
 
 ^ No reasonable doubt exists as to the stability of the planetary system to which our earth belongs, as it is at present consti- 
 tuted. To what extent the laws of order which we observe in it might be transgressed with impunity, it is more difficult to say. 
 The investigations of Laplace and Lagrange assume the motion of the planets in one direction, and their moderate excentri- 
 cities and inclinations, as conditions of the guarantee of stability. But it does not appear by any means certain that all these 
 conditions are essential, and consequently the argument which ha* been sometimes employed, that the concurrence of many in- 
 dependent circumstances were requisite to the stability of the system, is at least incomplete. Compare Laplace, Systtme du 
 Monde, edit. 1824, vol. ii., p. 29, and Herschel's Outlines of Astronomy, art. (669). 
 
 * It is Ifo. 17 in the enumeration of his papers in the article Lagrange in the Encyclopaedia. 
 
 ^ Very recently (1854), M. Hansen of Grotha, a most eminent living authority, has somewhat modified the received opinion jf Hansen 
 respecting the moon's figure. He finds that the presumed ellipticity of the moon in the direction of the radius of her orbit is on the 
 not justified by observations, which ought to show a slight variation in her horizontal diameter when the libration presents to moon'» 
 us oiir satellite in a slightly varied aspect. And he infers from an elaborate investigation of the lunar observations, that her figure, 
 centre of figure does not coincide with her centre of gravity, but lies about 31 English miles nearer to us than the latter. M. 
 Hansen adds that the existence of such a protuberance of the moon's body relatively to the centre of gravity on the side which 
 we can alone view, would account for the apparent absence of water and air, which may abound upon the opposite side.— 
 Astronomical Society^s Notices, vol. xv., p. 13. 
 
16 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Private the tranquillity of a philosopher. He was respected 
 character of a,ii,i rewarded alike by kings and democrats — he was 
 agrange. jjQjjQm.g^ g^jj^ promoted in three great states, Sar- 
 dinia, France, and Prussia. Though patronized by 
 the despotic Frederick, and lodged in her palace by 
 the gentle queen of Louis XVI., he escaped the 
 misfortunes of almost every one of his contempora- 
 ries, including Laplace, Lavoisier, and Delambre ; he 
 retained his scientific appointments throughout all 
 the frenzy of the French Eevolution. His mildness 
 of disposition and disinterested devotion to science, 
 more than the European celebrity of his name, con- 
 tributed to this result. He was equally fortunate 
 in his scientific relations. Euler, D'Alembert, and 
 Laplace, whilst they were emphatically his rivals, 
 were also his sincere friends. If he ever felt jealousy. 
 
 it was perhaps towards those who, he thought, at- 
 tained too easily by circumstances to a high reputa- 
 tion : Monge seems to have been of this number. It 
 is remarkable that for a series of years Lagrange di- 
 verted his mind altogether from mathematics, and 
 studied chemistry, natural history, and even meta- 
 physics. His reply is well known, when asked how 
 he liked the first of these sciences ; " Oh," said he, 
 " I find it on trial as easy as algebra." It may be 
 doubted whether in our own day he would have 
 given as favourable an opinion ! 
 
 He was unassuming in conversation, and dis- (590 
 liked speaking of himself. His commonest answer 
 was " I don't know." He was happy in his domestic 
 relations, and died universally honoured and regret- 
 ted, 10th April 1813. 
 
 § 2. Laplace. — Lunar Theory Improved. — Great Inequality of Jupiter and Saturn. — Theory of 
 the Tides. — Young ; Dr Whewell ; Mr Airy. — Theory of Probabilities. — Character of 
 Laplace as a Physicist and Author. 
 
 (60.) PiERKE Simon Laplace has generally, and not 
 
 jap ace. ^^;];jo^^ reason, been considered as a sort of exemplar 
 or type of the highest class of mathematical natural 
 philosophers of this, or rather the immediately preced- 
 ing age. The causes of this, and the degree in which 
 it is warranted, we shall endeavour to state towards 
 the close of this section. In the meantime, finding it 
 quite impossible within our prescribed limits to notice, 
 ever so briefly, all his more material investigations, 
 we shall select three or four marked by their ori- 
 ginality and general interest. Such are, 1 . His im- 
 provements of the lunar theory. 2. His discovery 
 of the cause of the great inequality of Jupiter and 
 Saturn's motions. 3. His theory of the tides. 4. 
 His work on probabilities. 5. We shall consider 
 his character as a general physicist, and as a writer. 
 
 I. First, then, we are to speak of the improve- 
 
 (61.) 
 
 ments in ments of the lunar theory efiected by him. The ap- 
 the Lunar plication of Newton' s own principles to the perfecting 
 Theory. ^f ^^ theory of the moon's motion has been related 
 in Sir John LesUe's Dissertation, and so far as the 
 labours of Clairaut, D'Alembert, Euler, and Mayer, 
 are concerned, belongs distinctly to the middle por- 
 tion of the last century. The errors of Mayer's 
 tables little exceeded one minute of space, which was 
 twice more accurate than in Halley's time. With 
 one important exception, the main outstanding dif- 
 ferences between theory and observation had disap- 
 peared. The eclipses recorded in the Arabic and 
 Chaldean annals could not (as Halley first observed) 
 be correctly explained by the motion of the moon as 
 given by recent tables. At length it became admit- 
 ted that the mean motion of the moon has been 
 accelerated from century to century by a minute 
 
 quantity, which, in the lapse of thousands of years, 
 has become recognisable. It amounts to this, that 
 the moon comes to the meridian two hours sooner 
 than she would have done had her present period 
 remained invariable from the earliest astronomical 
 records of eclipses. It is at once evident how delicate 
 a test this must be of changes otherwise imperceptible. 
 The effect on the dimension of the moon's orbit maybe 
 thus expressed, that at each lunation she approaches 
 nearer to the earth than during the last by one-four- 
 teenth of an inch ! thus describing a spiral of almost 
 infinitely slow convergence. The minuteness of the 
 effect may be illustrated by the shortening of the 
 pendulum of a clock by an amount absolutely in- 
 sensible, which yet, after days and weeks, will alter 
 by many seconds the time shown by the hands. g v ^ 
 
 After several unsuccessful speculations as to accelera- 
 the cause of this anomaly, Laplace, in 1787, thus sa- tiou of the 
 tisfactorily accounts for it: — It is well known that the ■'*°°°' 
 sun's attraction on the earth and moon lessens, on 
 the whole, the tendency of the latter to the former, 
 and lengthens permanently the lunar period. But, 
 so far as this effect is uniform, it does not directly 
 appear. The effect is greater, however, when the 
 earth is near the sun than when it is farther off. 
 The lunations are therefore longer in winter (when 
 the earth is in perihelion) than in summer. This 
 is called the annual equation, and the amount is 
 very sensible for this reason, that (as may be easily 
 seen) the perturbing force varies inversely as the 
 cube of the sun's distance. Now, though the earth's 
 mean distance from the sun has not varied in the 
 lapse of ages, the excentricity of the earth's orbit 
 has been diminishing from the earliest historic times, 
 and the average inverse cube of the distance has 
 
Chap. II., § 2.] 
 
 PHYSICAL ASTEONOMY — LAPLACE. 
 
 17 
 
 (63.) 
 Earth's 
 eHipticity 
 and solar 
 parallax 
 deduced 
 from the 
 moon's 
 motion. 
 
 been also slowly increasing. The result is that the 
 moon's motion has been continually accelerated. 
 Now, we have in the last section referred by anti- 
 cipation to this acceleration as having led to the 
 belief that the moon must at last fall to the earth. 
 Laplace's discovery, however, shows that the acce- 
 leration has a limit, depending on that of the ex- 
 centricity of the earth's orbit, which having reached 
 its minimum, the lunar mean motion will begin to 
 be retarded, and will continue so through a vast 
 cycle of ages, and so on alternately. Theory enables 
 us to assign, with considerable accuracy, the amount 
 of the acceleration, which is now about 10'' of lon- 
 gitude in a century.* 
 
 Besides this very satisfactory discovery, Laplace 
 investigated three of the lunar inequalities in a man- 
 ner leading to curious and unexpected results. Two 
 of these depend on the spheroidal figure of the earth. 
 The nutation of the earth's axis, which is due to the 
 attraction of the moon on the protuberant equatoreal 
 parts of the earth, is exactly reproduced by the equi- 
 valence of action and reaction in the movements of 
 the lunar orbit, only less perceptible in degree on 
 account of the length of the leverage at which they 
 are eflFected. The inequality of the moon's motion 
 in latitude may be used to determine the degree of 
 compression of our globe at the poles. Laplace de- 
 duced from the Greenwich observations of the moon 
 
 the fraction ^^, and, from a relative inequality in 
 
 longitude, j^^ ; a coincidence really astonishing, not 
 
 only as between themselves, but also when compared 
 with the mean result of laborious investigations by 
 actual measurement of the earth's surface. The other 
 result we referred to was the determination from the 
 lunar theory of the solar parallax, — in other words, 
 the distance of the earth from the sun, which enters 
 into the expression of a certain inequality of the 
 moon's motion in longitude. From the observed 
 amount of this inequality, Laplace obtained a value 
 of the solar parallax exactly coincident with that 
 obtained with so much labour on occasion of the 
 transit of Venus in 1769. Strange and admirable 
 result (as Laplace himself remarks), that the astro- 
 nomer, immured in his observatory, and watching our 
 satellite tbrougb his telescopes, and reading the re- 
 sult by the aid 6f mathematical analysis and the 
 theory of gravitation, should be able to determine the 
 figure of our earth, and its distance from the sun, 
 with- perhaps quite as great accuracy as by any direct 
 measurements. Truly the wonders of fact exceed 
 those of fiction, and the divinations of true science 
 may match the pretensions of her counterfeit, astro- 
 logy. 
 
 In conclusion of this subject, I regret that space (6*0 
 does not allow me to advert particularly to Laplace's j^pj^^.," 
 remarkable success in accounting for some singular satellites, 
 peculiarities in the system of Jupiter's satellites, 
 arising from, and partly occasioning, an exact com- 
 mensurability in the periods of some of them (which 
 Sir John Herschel has lately observed to hold also 
 in the Satumian system in a somewhat different 
 manner), a case which we have seen to be especially 
 excluded in the instance of the planets, and which 
 has been pronounced by a very competent judge (Mr 
 Airy) to be " the most curious and complicated sys- 
 tem that has ever been reduced to calculation." It 
 ought to be stated, however, that Laplace's dis- 
 coveries were based upon a previous and highly 
 original investigation of Lagrange. 
 
 II. In the second place, we shall briefly state the (65.) 
 nature of Laplace's happy explanation of a great in- ^°°S In- 
 equality of the solar system, tc which, like the fact ^f jupiter 
 of the lunar acceleration, especial attention had been and Sa- 
 called by the sagacity of Halley, and which, like it, *'^''°- 
 resisting all the efforts of geometers to interpret, 
 threatened the credibility of the Newtonian theory of 
 gravity. "We are therefore to look upon this step as 
 something more than a solution of a difficult problem; 
 it was a new, peculiar, and unsuspected combination 
 of circumstances on which it depended, and the solu- 
 tion aiforded a key in all time coming to difficulties 
 depending upon a like cause. 
 
 Halley had ascertained, that by comparing mo- (66.) 
 dern with the most ancient observations of Jupiter and^'^'^y °^ 
 Saturn, the mean motion of the former planet had been qualitii 
 accelerated, and that of the latter retarded. Lambert 
 remarked subsequently that, if we confine ourselves 
 to modern observations alone, an opposite change 
 would appear to be in progress. The amount of the 
 error of the tables was so considerable (amounting to 
 20' or more in the middle of the eighteenth century, 
 and capable, in fact, of becoming much larger), as to 
 have been (along with the apsidal motion of the lunar 
 orbit) one of the first subjects of anxiety and specu- 
 lation to geometers, when the Newtonian theory came 
 fairly into discussion. For nearly forty years this 
 stubborn inequality was vainly attempted to be ac- 
 counted for by Euler, Clairaut, D' Alembert, Lagrange, 
 and by Laplace himself, before the latter hit upon 
 the true cause of the anomaly. It was long, and 
 naturally, believed to be a properly secular inequa- 
 lity, arising from the average mutual effects of the 
 planets Jupiter and Saturn, though Lambert's re- 
 mark rendered this less probable. It was in the course 
 of the consequent research that Laplace proved that 
 the mutual action of the two planets could produce 
 
 ine- 
 lies : 
 
 1 We here- add that very recently Mr Adams has discovered that Laplace, and also his followers, in confining their at- 
 tention to the radial effect of the son's interference with the lunar motions, as aiFected by the excentricity of the earth's orbit, 
 have unwarrantably assumed that the area described by the moon a unit of time is invariable. He finds, on the contrary, tan- 
 gential perturbations depending on the same cause, and sensibly modifying the amount of secular mean motion deduced from 
 theory, ^^—(Fhilcsophical TrcmiMtiom, 1853.) 
 
18 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 no permanent alteration of the mean motion of 
 either ; a conclusion which, as we have seen in the 
 last section, he afterwards generalized for the pla- 
 netary system. Several other memoirs by Lagrange 
 and himself followed ; and when the question be- 
 came thus narrowed to periodic perturbations only, 
 Laplace, with characteristic ardour and resolution, 
 determined to search out every term which could affect 
 the result; an irksome task, less congenial to the gene- 
 ralizing spirit of Lagrange. He had already noticed, 
 in his memoir of 1773, thatEuler and Lagrange had, 
 in their researches on this very subject, omitted terms, 
 multiplied by sines and cosines of very small angles, 
 which yet might, in the process of integration, be- 
 come considerable by the largeness of the coefficients, 
 their Eleven years later he detected, in the expansion of 
 
 origin ; ^j^g mutual perturbation of Jupiter and Saturn, terms 
 of this kind. The coefficient (or maximum value of 
 the term) is in this case divided by the square^ of the 
 same quantity which renders the angle under the sine 
 or cosine small. These terms were indeed likewise 
 multiplied by the cubes of the excentricity, or like 
 their small quantities ; but notwithstanding this, by reason 
 
 amount. ^f ^he small divisor just mentioned, they were capable 
 of attaining a formidable magnitude ; in the case of 
 Jupiter, to 21', and of Saturn, to 48' or 49'. That 
 so small a force should produce so large an effect is 
 due to the very long period of the most considerable 
 portion of this inequality, which, in fact, led to its 
 being confounded with perturbations properly secu- 
 lar. The period of complete recurrence of the effects 
 is about 920 years ; and during half this time the 
 motion of one planet is being constantly accelerated, 
 and that of the other retarded ; during the other half 
 the action is reversed. An effect continually in- 
 creasing or diminishing for so long a time, and be- 
 tween the two most massive of the planetary bodies, 
 is evidently liable to become considerable. The 
 maximum displacement of Jupiter and Saturn 
 Laplace found by calculation to have occurred in 
 1560, explaining the peculiarity above mentioned 
 in the comparison of ancient with modem observa- 
 tions. 
 (67.) When we look to the physical cause of the large- 
 
 '^''®."' ness of these particular perturbative terms, it is found 
 
 ^^"° ' to be this ; — that the period of revolution of Jupiter 
 compared to that of Saturn, is almost as the num- 
 bers 2 and 5 : — ^in other words to the near commen- 
 surability of the mean motions. Were they exactly 
 in proportion to these numbers, formidable and per- 
 manent changes would possibly result in the orbits. 
 As it is, the planets come into conjunction when Jupiter 
 has completed 5 revolutions, and about j^jth more ; 
 Saturn 2 revolutions, and j\th more. Consequently 
 the point of conjunction travels round the circumfer- 
 ence after about 44 conjunctions have occurred, which 
 requires nearly 2700 years. But a little considera- 
 
 tion will show that conjunctions occur successively 
 at three nearly equidistant points of the circumference ; 
 consequently the two planets will have been presented 
 to one another in every possible variety of configu- 
 ration, when the point of conjunction has travelled 
 one-third round the circumference, that is in about 
 900 years. 
 
 The effect of this great improvement in the (68.) 
 Theory of Jupiter and Saturn was, that the most an- 
 cient observations were completely reconciled with the 
 modern, and the modem with one another ; the errors 
 of the tables were immediately reduced to one-tenth 
 of their former amount, and soon after to much less. 
 
 III. The third topic which I must shortly discuss in (69.) 
 connection with the career of Laplace, is the Theory Theory of 
 of the Tides. ^he Tides. 
 
 The Newtonian Theory of the Tides has been ex- (70.) 
 plained in Mr Playfair's Dissertation, but its progress Newton's, 
 during the 18th century has not been adverted to iiinouif^g (,, 
 the continuation by Sir John Leslie. It will be suf- the Equ'ili- 
 ficient to state here, that it was pursued into its conse- hrium 
 quences with ability and success by Daniel Bemouilli, Theory, 
 who in 1740 shared a prize of the French Academy 
 of Sciences on this subject, along with Euler, Mac- 
 laurin, and Cavalleri, a Jesuit, the last a supporter of 
 the Cartesian vortices. It was, perhaps, the conclud- 
 ing honour paid to that once popular theory. 
 
 The Tidal Theory of Newton and BernouilU (71.) 
 presumes the earth to be at rest; and also the waters Ks results, 
 of the ocean to be at rest, and at every moment in a 
 state of equilibrium between the force of gravity, 
 tending to the earth's centre, and the lesser forces 
 tending towards the sun and moon. That a theory, 
 founded on suppositions so far from the truth (not to 
 mention the irregular distribution of sea and land on 
 the earth's surface), should in any manner or degree 
 represent correctly what happens, may be matter of 
 just surprise. The leading phenomena are however 
 tolerably consistent with it ; the dependence of the 
 great tides on the moon's position with respect to 
 the meridian of the port ; the spring and neap tides 
 when the sun's action and that of the moon conspire 
 with or oppose one another ; the priming and lagging 
 of the tides depending on the displacement of the vertex 
 of the compound ellipsoid due to the combined effect 
 of the sun's and moon's attraction, depending therefore 
 on the moon's elongation from the sun ; the effects of 
 the moon being in the nearer or remoter part of her 
 orbit ; all these facts are indicated by the Equilibrium 
 Theory (as it has been termed), and are also results 
 of observation. The theory, however, does not give 
 the true depth of tide, nor (except in casual instances) 
 does the time of high and low water coincide with 
 theory ; besides many minor imperfections. 
 
 Laplace had the singular boldness to attempt 
 the solution of a problem, which is more one of hydro- 
 
 ^ In cons equence of a double integration in respect of the time. 
 
Chap. II., § 2.] 
 
 PHYSICAL ASTEONOMY — LAPLACE. 
 
 19 
 
 Laplace's 
 
 Dynamical 
 
 Theory. 
 
 (73.) 
 Its diffi- 
 culty. 
 
 (74.) 
 Its incom- 
 pleteness. 
 
 (75.) 
 Three 
 classes of 
 Tides. 
 
 dynamics than of astronomy, and to estimate all the 
 causes of movement of the particles of a heavy fluid, 
 surrounding a spheroidal rotating nucleus exposed to 
 the attractions of the sun and moon. This he did in 
 a series of memoirs, more systematically condensed in 
 the Traits de Mdcanique CSleste, and it may safely 
 be affirmed that no other mathematician of his day 
 was equal to the labours and disappointments of an 
 investigation attended with every species of difficulty, 
 in which each result must be attained by a combina- 
 tion of general sagacity with mathematical rigour, and 
 for the verification of which observations were yet in 
 a great measure wanting. The Theory of the Tides 
 was, upon the whole, the most arduous and compli- 
 cated problem which could well be conceived, in a 
 branch of science (hydrodynamics) hitherto remark- 
 ably little successful in predicting the results of the 
 most simple and arbitrarily selected experiments. 
 
 That Laplace has been in a measure successful 
 in such an undertaking must be considered the highest 
 test of his genius, especially in reducing his mathe- 
 matics to practical application ; but the result has 
 been a treatise so profound tod obscure (I mean as 
 regards the tide theory), that very few persons have 
 attempted to master its difficulties. Mr Airy, the 
 present astronomer royal, has done a great service 
 to men of science, and to that far wider community 
 whom the laws of the tides nearly interest, by giving 
 a connected and tolerably elementary view of La- 
 place's investigation, which he states confidently to 
 be " the most obscure of the MScanique Cileste." 
 
 In this theory the figure of the ocean at any 
 moment is considered as a dynamical problem ; and 
 that figure as a momentary state arising from the in- 
 ternal movements of the fluid itself, as well as from 
 the variation of the external forces. The resulting 
 differential equations, expressing the attractions of 
 the sui>^ moon, and earth, the rotatory movement of 
 the earth, and the pressure of the water itself in mo- 
 tion, are abundantly complex, and the solutions only 
 partial and imperfect. The inferences from these 
 solutions, too, partake not only of their imperfection, 
 but, since they take no cognisance of the irregular 
 distribution of land and water, present cases almost 
 impossible to verify by observation. Some of the 
 results are indeed so paradoxical, that without bet- 
 ter evidence of their fxuth we do not further allude 
 to them. 
 
 The tidal effects are divided by Laplace into three 
 classes ; the distinction of which, however, cannot be 
 called a discovery of his. The /,rst class are inde- 
 pendent of the earth's rotation, and are practically 
 insignificant. The second class includes the diurnal 
 tide occurring once in about 24 hoursi Concerning 
 
 it, Laplace draws this conclusion, that its rise and fall 
 (not, however, its horizontal motion) are insensible if 
 the depth of the ocean is uniform ;^ and being practi- 
 cally insensible in moat latitudes, we have thence an 
 argument of more or less weight for a general 
 tendency to uniformity in the depth of the sea. The 
 third class of tides are the ordinary semi-diurnal 
 tides. They afford, as Newton acutely perceived, the 
 most direct and attainable measure of the relative at- 
 tractions of the sun and moon. We have the sum of 
 these attractions at the conjunctions and oppositions 
 of the luminaries, and the difference when they are 
 90° apart ; and a higher maximum when both bodies 
 are without latitude. From the observation of the 
 tides on the Severn near Bristol, Newton computed 
 the relative action of the moon and sun to be as 
 4"48 to 1 ; but this value is much too great, and 
 gave far too large a relative mass to the moon. The 
 result in the harbour of Brest, from observations made 
 under Laplace's direction, is about 2-90 to 1 ; and the 
 moon's mass yV^h that of the earth, agreeing almost 
 identically with that deduced from the nutation of 
 the earth's axis caused by her attraction. Observa- 
 tions at London and Liverpool reduced by Sir John 
 Lubbock and Dr Whewell give about 2*66 to 1.^ 
 
 From the general theory of Laplace, the follow- (76.) 
 ing results have been deduced with confidence : — (1.) Laplace's 
 That the stability of the ocean is secure, whilst the '■^^'^''• 
 density of the ocean is inferior to that of the earth 
 generally ; which it is about five or six times. (2.) 
 That the phenomenon of precession is not modified 
 by the fluid covering of the globe. 
 
 In the application of his theory to special cases, (77.) 
 Laplace is compelled to have recourse to an assump- 
 tion entirely arbitrary — namely, that the periodic 
 fluctuations, however otherwise modified by circum- 
 stances, recur in the same periods as the causes to 
 which they are due. In this manner he conciliates the 
 results of observation with his theory, which the latter 
 would have been altogether incompetent to predict. 
 
 The general merits of Laplace's theory we will sum (78.) 
 up in the words of Mr Airy, who, of all his succes- Character 
 sors, has probably most attentively studied it : — " If, , , . 
 puttmg trom our thoughts the details of the investi- vestigation. 
 gation, we consider its general plan and objects, we 
 must allow it to be one of the most splendid works 
 of the greatest mathematician of the past age. To 
 appreciate this, the reader must consider — first, the 
 boldness of the writer who, having a clear under- 
 standing of the gross imperfection of the methods of 
 his predecessors, had also the courage deliberately 
 to take up the problem on grounds fundamentally 
 correct (however it might be limited by suppositions 
 afterwards introduced) ; secondly, the general diffi- 
 
 ^ Dr Young asserts that the conclusion will not hold unless the depth be also evanescent. Laplace has shown in his Fifth 
 Boole that the disappearance of diurnal tides will take place only when the nucleus is completely covered. 
 
 2 These ratios, however, being found to depend upon the configuration of the coast or estuary, cannot he used directli/ to de> 
 termine the relative action of the sun and moon. See Phil, Tratu., 1845, p. 42. 
 
20 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 culty of treating the motions of fluids ; thirdly, the 
 peculiar difficulty of treating the motions when the 
 fluids cover an area which is not plane but convex ; 
 and, fourthly, the sagacity of perceiving that it was 
 necessary to consider the earth as a revolving body, 
 and the skill of correctly introducing this considera- 
 tion. The last point alone, in our opinion, gives a 
 greater claim for reputation than the boasted explana- 
 tion of the long inequality of Jupiter and Saturn." ^ 
 We must, however, qualify this eulogy by adding, in 
 the words of the same writer, that Laplace's theory, 
 though based on sounder principles than the equili- 
 brium theory, " has far too little regard to the actual 
 state of the earth to serve for the explanation of even 
 the principal phenomena of the tides." It is, in fact, 
 like many other productions of the same age and 
 school, a great display of ingenuity and mathemati- 
 cal skill, which hardly yields a single result worthy 
 of confidence, or agreeing with nature, except by the 
 abandonment of its deductive rigour, or a concealed 
 induction backwards from the phenomena to be ac- 
 counted for. The same amount of skill and resource 
 which Mr Airy has shown in adapting it to his own 
 views, and to recent observations, would probably 
 have sufficed to construct a theory from the founda- 
 tion. By others the attempt seems to have been 
 abandoned as hopeless. 
 C^^-) Since our Umits will not permit us to return to 
 
 tjjijgg Pj. the subject of tides, we shall here briefly state the 
 
 Whewell— progress of the subject since the time of Laplace. 
 
 Sir J. Lub- The chief steps have consisted in co-ordinating the 
 results of observation and analyzing them into their 
 partial phenomena, by the help of Newton's and 
 Bernouilli's theory. This labour has been greatly 
 advanced by Dr Whewell, and also by Sir John Lub- 
 
 Cotidal bock. The former has constructed maps of " cotidal 
 lines," which, indicating the relative time of high 
 water in difierent parts of the globe, give us a gra- 
 phic conception of the course and propagation of the 
 tidal wave. The tides of the Eastern Pacific are but 
 little known ; but a vast wave advances northwards 
 between Australia and Africa, diverted or retarded 
 by the obstacles it meets with in the Indian Archi- 
 pela,go. Another (and to us the most important) 
 branch sets from south to north up the vast canal of 
 the Atlantic, where it is gradually complicated by 
 local tides, having their origin in the wide expanse 
 between Afiica and the Gulf of Mexico. The two 
 sets of waves sometimes reinforce, sometimes oppose, 
 one another ; they are prolonged to the western 
 shores of England and Norway, where the tidal im- 
 pulse arrives 24 hours after it passed the Cape of 
 Good Hope. It is propagated most rapidly at a dis- 
 tance from coasts, and is retarded in narrows and 
 shallows. It sends ofishoots into every bay and 
 strait, always greatly retarded in point of time (ap- 
 
 bock. 
 
 lines. 
 
 parently by friction), but often increased in elevation 
 by concentration of the effect in a gradually narrow- 
 ing channel, as we see in the exaggerated tides of the 
 river Amazon, the Severn, and the Bay of Fundy. 
 The same place may be the seat of several tides at 
 once, which may increase or destroy one another ; 
 thus, a small tide is propagated through the Straits 
 of Dover as far as the Dutch coast, where it only 
 arrives simultaneously with the principal wave, 
 which has made the entire tour of Great Britain. 
 
 As regards the progress of theory, Dr Thomas ^^^^°-)^j. 
 Young, whose character as one of the greatest Dr Young, 
 philosophers of the past age we shall have to con- 
 sider in another chapter, next after Laplace grappled 
 with the difficulties of this arduous subject. Em- 
 ploying mathematical methods of inferior power but 
 greater directness, and taking into account causes of 
 local action which Laplace had not ventured to in- 
 clude in his analysis, he gradually matured a theory 
 adequate to represent many of the results of ex- 
 perience, of which Laplace gives no account. 
 
 He distinguishes the results of the forced and free ^^^'K 
 oscillations of the sea ; the former resulting from the forced 
 direct action of the sun and moon combined with the waves, 
 rotation of the earth, and whose periods of rise and 
 fall are determined solely by those external causes 
 (external, I mean, to the mass of the ocean) ; the 
 free waves, on the contrary, derived from the former, 
 are transmitted with velocities depending on the me- 
 chanism of the fluid itself, on its depth, and on the 
 resistances arising from friction to which those mo- 
 tions are exposed. These all -important modifications 
 of the dynamical Theory of the Tides were deduced 
 by Dr Young from the general theory of oscillations 
 and resistances, and from the laws of fluids detected 
 by Dubuat,^ and he applied them with no ordinary 
 skill to the solution of the problems of tides in 
 oceans, estuaries, and rivers. It is an extraordinary 
 fact, and not without significance, in the history of 
 science, that these researches of Young, published 
 anonymously in the Supplement to the Sixth Edition 
 of the Eneyclopsedia Britannica, and in the Seventh 
 Edition of this work, and likewise in several jour- 
 nals and reviews, so generally escaped notice as to 
 have been almost unknown till Dr Peacock, in his 
 recently published " Life and Miscellaneous Works 
 of Dr Thomas Young" has fortunately recalled 
 attention to their existence and their important 
 results. 
 
 In doing so, Dr Peacock has communicated with (^O 
 Mr Airy, whose very valuable article on IXdes and Tideg'nnd™ 
 Waves has been above referred to (78), and has Waves, 
 ascertained from him that Dr Young's researches 
 had escaped his notice when he undertook that 
 elaborate recension of Laplace's theory, and made 
 those important additions to it to which I have 
 
 ^ Encyclopaedia MetropoUlana, " Tides and Waves," art. 117. 
 
 2 See Chapter IV., Section 6, where we shall return to some portion of this subject. 
 
Chap. II., § 2.] 
 
 PHYSICAL ASTRONOMY — LAPLACE. 
 
 21 
 
 called attention.! It is very satisfactory to find that, 
 by their independent and very different modes of 
 analysis, Mr Airy and Dr Young have arrived at 
 results generally coincident. It is in the essay 
 of the former that most readers will now seek for an 
 acquaintance with Laplace's abstruse investigations, 
 whilst they will find in it the bearing of experiments 
 more recent than the time of Young on the propa- 
 gation of waves in canals, the theory of Mr Airy, 
 beginning as it were at the opposite end from that of 
 Laplace, and offering far more p\)ints of contact with 
 actual observation, particularly in the Tides of 
 Rivers and Estuaries. The theory of Young will 
 naturally be best studied in his own article Tides, 
 in this Encyclopajdia. 
 
 (83.) IV. In the fourth place, we connect the name of 
 
 Probablli- ■'-"^P^*"^ 'With, the progress, during the period we are 
 ties. considering, of the curious doctrine of probability, 
 
 or the laws of chance and expectation. These he 
 discussed in two works, the ThSorie Analytique and 
 the Essai Philosophique sur les ProbahilitSs — the first 
 the most mathematically profound, the last the most 
 popular and elegant, account of the subject which 
 has yet been given. Nearly all mathematicians are 
 agreed on two points — first, in considering this the 
 " most subtle" and " difiicult to handle" of all the 
 applications of their science, involving a perpetual 
 recurrence to contingencies, and to elements of the 
 argument easily left out of account, and in which, 
 more than in any other, it is dangerous to let sleep 
 for a moment the severely reasoning faculty, or per- 
 mit it to be lulled to security amidst the maze of 
 symbolic transformation. In truth, from experience, 
 I am disposed to receive with doubt the solution of 
 even a tolerably simple problem of chances, unless 
 two competent persons at least have concurred in 
 verifying it. Secondly, Mathematicians are agreed 
 in considering Laplace's ThSorie nearly, if not quite, 
 the ablest specimen of mathematical writing of his 
 age, notwithstanding a degree of obscurity and repe- 
 tition in addition to the inherent abstruseness of the 
 subject, which render it, in the opinion of one of the 
 most learned and extensively read of our pure ma- 
 thematicians,* " by very much the most difiicult ma- 
 thematical work he ever met with." 
 (84.) A single paragraph has been devoted to the subject 
 
 Improve- ^f probabilities in Sir John Leslie's Dissertation, 
 investiffa^.'^ relating to its earlier history ; and the subject was so 
 tion by popular during the last century, that there was 
 Laplace, scarcely an eminent mathematician who did not add 
 something to its practical development ; so that La- 
 place may be considered rather to have enlarged 
 widely its applications by means of his almost unex- 
 ampled power in handling the calculus, than to have 
 improved or established its first principles, or even 
 
 applied it to classes of problems altogether new. 
 We find that most of the principles of the Calculus 
 were established by James Bemouilli, in the earliest 
 part of the eighteenth century, who gave the first History of 
 application of the Binomial Theorem to determine *«^o^^'^°« 
 the probability of a particular combination of a given 
 number of tlungs occurring, in preference to all the 
 other equally possible combinations. Stirling dis- 
 covered a curious theorem for approximating to the 
 continued product of the arithmetical series of num- 
 bers carried to any extent, which perpetually occurs 
 in such calculations, Demoivre carried out Halley's 
 application of it to the laws of mortality. Condorcet 
 applied it to moral questions ; Mitchell to natural 
 phenomena, considered as the results of accident or 
 design ; Lagrange to errors of observation. The 
 chief applications of the Theory of Probability are Its chief ap- 
 the following : — 1. To chances known ct priori, as plications, 
 that of throwing two given numbers with dice, the 
 whole range of possibilities being known with preci- 
 sion. 2. The calculation of the expectation of future 
 events on a great or average scale, deduced from the 
 past course of events observed also on a great or 
 average scale. Of this description are the calcula- 
 tions of life assurance, first tabulated by Halley. 3, 
 To find the most probable result of a number of in- 
 dependent observations and problems of a like kind. 
 4. To the proof of causation as opposed to accident 
 or " random," derived from existing combinations of 
 facts. 5. To the probability of testimony, and the 
 confidence due to legal decisions. None of these 
 inquiries are peculiar to Laplace, or originated with 
 him. We select, however, for a brief notice (which 
 must be confined to a few sentences) the third and 
 fourth of these applications. 
 
 The chances are enormous against the most expe- (85.) 
 rienced marksman's hitting the bull's eye of a target. '^° ^°^ **'* 
 But if he make many shots in succession, the balls |,^^,jg ^^°' 
 will be lodged round about the spot at which he suit of a 
 aimed, and they will be fewer in each successive ring number of 
 of equal area drawn round the mark. The degree V" t^^v' 
 of their scattering will depend upon the skill of the vations. 
 marksman ; but in all cases the most probable result 
 will be, that the point aimed at is the centre of gravity 
 of the shots. This may be shown to be equivalent to 
 saying that the most probable result of any number of 
 equally reliable observations is that which will make 
 the sum of the squares of the outstanding errors a 
 minimum. This rule was conjecturally proposed by Legendre's 
 Legendre in 1806. A demonstration of its truth was method of 
 first published by Laplace. It is of great practical ^*^* 
 use in deducing the results. of complex observations, 
 such as those of Astronomy, and generally in com- 
 bining " equations of condition" more numerous than 
 the quantities whose value is sought to be extracted 
 from them. In very many cases, however, a graphical 
 
 ^ See note to p. 262 of the Second Volume of " Young's Miscellaneous Works," by Peacock, 
 2 Professor De Morgan in Encyclopedia MetropoUtcma. 
 
22 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Probable 
 
 (86.) 
 
 method of interpolation will serve the same purpose, 
 as well as save a very tedious calculation. Perhaps too 
 much importance has heen assigned to the " probable 
 mean error" of a single observation deduced from 
 many individual errors by the same theory. If a 
 man has but one shot at a target, it is perfectly un- 
 certain (by hypothesis) whether that shot be one of 
 his best, or one of his worst, or one of his middling 
 ones. But as there are more middling hits than 
 very bad or very good ones, there is a certain dis- 
 tance which it will be safe to bet (i. e. for which the 
 probability is J), that he will not exceed ; though it 
 would be a strange occurrence indeed, if he exactly 
 struck the ring in question. This is all that is meant 
 by the phrase " probable error ;" it is an entirely 
 artificial number, which serves to give a sort of nume- 
 rical value of the skill of the performer, but is other- 
 wise of no importance. Its application has sometimes 
 been strangely mistaken. Even the " rule of least 
 squares" is often misapplied, and empirical laws al- 
 together false have been deduced from it ; for it is 
 rare in practice that the chances of error of observa- 
 tion of a varying quantity are the same throughout 
 the limits of observation. 
 
 But those applications of the doctrine of proba 
 
 the matter, it is one which few persons are competent 
 to handle. The state of health of Mr Ellis leaves us 
 little hope of his resuming the inquiry ; but two 
 eminent mathematicians, Mr De Morgan and Mr 
 Boole, have published considerable works chiefly 
 bearing upon it. 
 
 As an implement bearing upon discovery in (87.) 
 science, the Calculus of Probabilities has as yet I'een P'°''»'^!ljty 
 of little service. Whilst Laplace tries to indicate how ^^ \f^^ ® 
 it guided his researches connected with planetary irre- covery. 
 gularities, every one sees at a glance that, with the 
 data before him, common sense must have outstripped 
 analysis. Laplace has called the doctrines of pro- 
 bability "good sense reduced to calculation." What 
 is to be feared is, that the calculation should outstrip 
 the good sense. 
 
 V. Fifthly, We are to consider Laplace's charac- (88.) 
 ter as a general physicist and as a writer. chMacter 
 
 In the former respect he stands in a higher posi- as a phy- 
 tion than that usually attained by eminent analysts, sicist, and 
 In fact, if we compare him with any of his own J° *" *"' 
 generation, we find him not only better acquainted 
 with physical principles, and more scrupulous in 
 taking account of them in his mathematical discus- 
 
 of T'e^ti-''^ bility which pretend to give us a measure of our belief sions, but even possessing skill and interest in ex. 
 
 ony and in the constancy of natural laws, in the confidence due 
 of Design, tg testimony and to the teachings of history, in the 
 proofs of design in cosmical arrangements, — are 
 inquiries which, from their connection with meta- 
 physics, religion, andmorals,havehad a higher interest 
 for mankind at large than ordinary problems about 
 cards and dice. To these Laplace paid peculiar 
 attention ; and the reputation of his name tended to 
 create in others a belief that the analysis he so power- 
 fully wielded could communicate a portion of its 
 certainty to the data subjected to it, and gave a 
 currency to many of his conclusions to which we 
 believe them by no means entitled. Professor Play- 
 fair, one of the most ardent of Laplace's admirers, has 
 recorded (in a criticism in the Edinburgh Review, of 
 the works we are considering) his total dissent from 
 Laplace's doctrine that the transmission from age to 
 age of the historic record of a fact diminishes its credi- 
 Laplace's bility in a geometrical ratio. But a Cambridge 
 doctrines mathematician and speculative philosopher of singu- 
 qucs lone . ^^^ penetration, Mr Leslie Ellis, has most formally 
 assailed^ the principle of nearly all Laplace's esti- 
 mates of our expectation of events arising from causes 
 unknown or assumed to be so, such, for instance, as that 
 a common cause determined the revolution of all the 
 planets in one direction. The subject of the meta- 
 physics of probability evidently requires a complete 
 reconsideration ; and, owing to the singular subtlety of 
 
 periments. The Calorimeter for measuring the capa- 
 cities of bodies for heat was the joint invention of 
 Lavoisier and himself ; at least their memoir does 
 not assign to either a predominant share in it,* and 
 their determmations of the expansions of the metals 
 by heat seem also to have been made in common. 
 His happy discovery of the chief or sole cause of the Memoirs on 
 discrepancy between the theoretical and observed Heat, in 
 velocity of sound (due to the heat developed by com- <"'™"""' 
 pression) would alone have given him a just reputa- Lavoisier, 
 tion, so anxiously had the matter been debated, and 
 so much was it involved in a purely mathematical 
 intricacy. Even in his great work on physical as- 
 tronomy he takes a peculiar pleasure in embracing 
 topics of terrestrial physics. We there find discussed 
 the theory of barometrical measurements, the ques- on Baro- 
 tion of atmospheric tides, the laws of capillary attrac- metrical 
 tion, and the constitution of the gases. As to the first Measure- 
 of these topics he made a practical improvement on capillary 
 the formulae of his predecessors, so that his rules are Attraction, 
 in fact still in use. As regards capillary attraction, * Astrono- 
 he was materially anticipated by Young, who evi- factions' 
 dently considered his principles to have been pirated ; 
 yet his theory, though obscured by a display of re- 
 dundant mathematics, was a real improvement. His 
 theory of tides, and that of atmospheric refraction's, 
 though closely connected with physical astronomy, 
 were in fact not less so with the doctrines of hydro- 
 
 ^ Cambridge Transactions, Vol. VIII. The writer of these pages has also given his reasons for dissenting from the argu- 
 ments of Michell (which have been sanctioned by the authority of Laplace) on an astronomical question as discussed by the 
 Theory of Probabilities. See Philosophical Magazine for December 1850. 
 
 ^ Dr Black, the discoverer of latent heat (who was probably well-informed), states in a letter to Watt that he believes 
 Laplace to have been the inventor. See Correipondenu of Watt on the Decomposition of Water, p. 66. 
 
Chap. II., § 2.] 
 
 PHYSICAL ASTEONOMY— LAPLACE. 
 
 23 
 
 (89.) 
 His Traite 
 deMi- 
 canigue 
 
 Par less 
 original 
 than the 
 Principia ; 
 
 yet gives 
 him justly 
 a high re- 
 putation. 
 
 dynamics and optics; and we shall find very few 
 important branches of general physics in which he 
 has not left some permanent record of his interest, 
 in the course of his career of fifty-jive years of 
 anxious devotion to science. 
 
 His largest and most systematic work, the Trak4 
 de MScanique CMeste, in five quarto volumes, was 
 not only most ably executed, but exceedingly well 
 timed. The applications of analysis to physical astro- 
 nomy had been accumulating for nearly a century. 
 Hundreds of memoirs relating to them, dispersed 
 through many volumes in different languages, written 
 with varying ability, in various stages of scientific pro- 
 gress, and with differing notations, presented a mass 
 of reading almost beyond the reach of the most reso- 
 lute student. Laplace undertook to digest the whole 
 into one body of doctrine, composed throughout on 
 & uniform plan, with the best mathematical aids which 
 were known at the commencement of this century. 
 And though improvements and discoveries have been 
 since made, the methods and most of the results of 
 the MScanique Cileste remain, with little variation, 
 the preferable ones of our own time. As a work of 
 labour, it may compete with the Principia of New- 
 ton ; as an original work, it is of course immeasur- 
 ably inferior. Its principles are, in fact, the same 
 with those laid down in that immortal code, and its 
 deductions are collected (as we have said) from the 
 writings of Clairaut,D'Alembert, Euler,and Lagrange, 
 as well as from the previous memoirs of the author 
 himself. Laplace has been too sparing of his cita- 
 tions and acknowledgments, and a consequence of 
 this literary avarice has been that he is sometimes 
 considered as more of a compiler and less of a dis- 
 coverer than is justly his due. For however ill he 
 could have dispensed with the skilful preparations 
 of his illustrious rivals and contemporaries, his pre- 
 eminent sagacity furnished on several occasions the 
 key-stone of the arch which imparted at once strength 
 and completeness to the fabric. We have seen in 
 the last section that though the credit of the theo- 
 rems respecting the stability of the solar system is very 
 generally attributed to Lagrange, who, indeed, prin- 
 cipally furnished the methods, and gave great gene- 
 rality to the results, yet the capital discovery of the 
 invariability of the major axes of the planetary orbits 
 is due to Laplace. It was he, again, who removed 
 from the theory of gravity the two greatest and 
 most impracticable difficulties with which it had 
 ever been assailed — the anomaly of the lunar ac- 
 celerations, and the great inequalities of Jupiter and 
 Saturn, and by so doing rendered it almost infinitely 
 improbable that any future discrepancy should more 
 than temporarily embarrass a theory which had tri- 
 
 umphed in succession over such formidable causes of 
 doubt. True that Lagrange, in his memoir of 1783, 
 had come within a single step of the first of these 
 discoveries, and, by a process of exclusion, had almost 
 forced attention in the right direction respecting the 
 latter ; still Laplace seized the prize in both cases, 
 after a fair, prolonged, and arduous struggle. Now 
 these three discoveries were the greatest in physical 
 astronomy between those of D' Alembert and Clairaut 
 on the precession of the equinoxes, the motion of the 
 lunar apse, and the periodicity of comets, — and that 
 of Leverrier and Adams on the perturbations of 
 Uranus about a century later. 
 
 The universal testimony of mathematicians is to ^^ ^^^-^ 
 the efiect that Lagrange was unrivalled as a pure compared 
 analyst, in his power of generalization, and in the with La- 
 inherent elegance of his methods ; that Laplace, grange, 
 with nearly equal power in using the calculus, had 
 more sagacity in its mechanical and astronomical 
 applications, or rather, perhaps, we shoidd say, in 
 directing it to the discrimination of causes, and the 
 revelation of consequences. 
 
 In other respects he difiered far more widely from (91.) 
 his illustrious compeer. He rather courted popu- ^^ public 
 larity, and was pleased at being considered worthy 
 of political distinction. For a short time he was one 
 of Napoleon's ministers ; but the Emperor, it is said, 
 was more satisfied with his mathematical than with 
 his diplomatic talents. He had none of the shyness of 
 Lagrange, nor his repugnance to general socieff . He 
 received with afiability and kindness those who were 
 introduced to him, and his attentions were after- 
 wards recollected with gratitude by rising men of 
 science abroad. He had a villa at Arceuil, adjoining 
 that of BerthoUet, and was one of the original mem- 
 bers of the " Society d'ArceuU," to whose memoirs 
 he contributed. He exercised a powerful influence and as a 
 in the Academy of Sciences, of which for a time he M^^Jier of 
 acted as dictator, and he was not very tolerant of demy of 
 views in science opposed to his own. The undula- Sciences, 
 tory theory of light he always opposed, and was 
 mainly determined in doing so by the facility with 
 which the attraction of luminous corpuscles could be 
 subjected to calculation. 
 
 The weak point of his scientific character was one so (92.) 
 natural, and perhaps so inseparable from his prevail ''^"^j^^*^ 
 ing studies, that it is not fair to criticise it too severely, display. 
 This was a love of analytical display in treating ques- 
 tions which it rather embarrassed than illustrated ; 
 and generally, a disposition to overrate the sphere of 
 mathematical discovery. This he had in common 
 with Euler, to whom he was very superior in physical 
 attainments and sagacity. His language, and that of 
 his eulogists,* often amounts to the assumption that 
 
 1 For instance Arago says (speaking of the invariability of the major axes) : " Enfin par la toute-pnissance d'une formule 
 mathgmatique, le monde materiel se trouva raffermi sur ses fondements" (Annuaire, 1844, p. 304). This is indeed the idolatry 
 of mathematics. Many examples may be found in Laplace's V7ritings on Probability ; vrhich occasioned Mr Ellis to say of him, that 
 " to Laplace all the lessons of History vrere merely confirmations of the ' resultate de calcul.' " To the same effect was the mot 
 of Napoleon, " that Laplace carried into the art of government the principles of the infinitesimal calculus." 
 
24 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 the marvellous power of analysis, in unravelling intri- 
 cate consequences of admitted or assumed laws, could 
 supply deficiencies of primary conceptions of the laws 
 of nature, or could teach men fundamental truths in 
 natural science. 
 (93.) To add to the remarkable list of Laplace's endow- 
 His Systime ments One more ; he was a perspicuous and elegant 
 writer. His Systeme du Monde contains a popular 
 
 exposition of astronomy in theory and practice en- 
 tirely original in its plan and execution, and though 
 frequently imitated, it is still perhaps the first of its 
 class. 
 
 Laplace was born in Normandy 23d March 1749, 
 
 (94.) 
 
 and died the 5th May 1827, leaving in the Academy ^^« °^^ 
 he had so long honoured no one within many degrees ^^^^^^ 
 of his ability in the same peculiar walk of science. 
 
 § 3. Legendre. — Ivory Theory of Integration; Elliptic Tranacendants (Abel, Jacobi). 
 
 The Attraction of Spheroids, and Theory of the Earth's Figure. Atmospherical Refractions. 
 
 (95.) 
 Legendre, 
 
 (96.) 
 Distin- 
 guished as 
 an able 
 mathe- 
 matician. 
 
 (97.) 
 His re- 
 searches on 
 Elliptic 
 Functions. 
 
 Adrien Marie Legendre was born in France in 
 1752, and died in 1833 (10th January); he was 
 consequently three years younger than Laplace, and 
 survived him by nearly six years. He fonned, there- 
 fore, an integral part of that constellation of mathe- 
 matical talent of which Paris was fcfr more than 
 two generations the main centre. Like his illustrious 
 compeers Lagrange and Laplace, he laboured with 
 enthusiasm all the days of his life, and like them was 
 engaged in editing and improving his works down 
 almost to the day of his death, at the ripe age of four- 
 score. 
 
 The mathematical career of Legendre was less 
 splendid than that of the other two whom we have 
 just mentioned. He did not possess the wonderful 
 powers of generalization of Lagrange, and he wanted 
 the flexibility of mind, and the general physical 
 knowledge, of Laplace. Legendre was very strictly a 
 mathematician ; and he has been exceeded by none 
 in the unquenchable zeal with which he pursued sub- 
 jects of a dry and even repulsive character, often 
 till he had hunted them down by sheer force of ap- 
 plication, or, to adopt the metaphor applied to him by 
 Lagrange, until he carried, sword in hand, the strong- 
 hold which he besieged. 
 
 No more striking proof can be given of these state- 
 ments than the unflinching pertinacity with which, 
 during nearly fifty years (1786-1833), he studied and 
 improved the theory of Integration, applicable to those 
 cases frequently occurring, which involve the higher 
 powers of the independent variable, and which do not 
 usually admit of finite expression. Two large works, 
 the Exercises du Calcul Integral (1811), and the 
 Traits des Fonctions Elliptiques (1827-32), — the lat- 
 ter in good measure a republication of the materials of 
 the former, — bear testimony to his diligence ; and these 
 works were almost entirely original, and contained 
 tables of most laboured construction, calculated by 
 himself. Hardly any mathematician entered into 
 competition or co-operation with him until his 
 labours were drawing to a close, when, with a libe- 
 rality worthy of all commendation, he welcomed the 
 
 analytical discoveries of Abel and Jacobi, which 
 were to give an unlooked-for extension to his own. 
 These methods of integration, and their reference to 
 certain properties of the Lemniscate and the Ellipse, 
 originated in the early part of the last century 
 with Fagnano and Euler. Legendre took up the 
 subject exactly where Euler left it, and finally re- 
 duced the large class of expressions to which his 
 methods are applicable to three standard forms or in- 
 tegrals in which the independent variable is always 
 expressed by a circular function, and to which a 
 numerical approximation may always be made by 
 means of the tables calculated by himself. 
 
 Abel, who succeeded in generalizing Legendre's (98.) 
 methods to a far greater extent, was a native of ■^■''el'f dis- 
 Norway, bom in 1802 (25th August),^ and died t""^^^'^'^"" 
 at the premature age of twenty-six (1829, 26th subject; his 
 April). His principal memoir was presented to the personal; 
 Institute when he was only twenty-four years old ; ^^^^"y- 
 and, to use the language of Mr Leslie Ellis, " when 
 the resources of the integral calculus were appar- 
 ently exhausted, Abel was enabled to pass into 
 new fields of research by bringing it into intimate 
 connection with a new Isranch of analysis, namely 
 the Theory of Equations. The manner in which 
 this was done shows that he was not unworthy to 
 follow in the path of Euler and of Lagi-ange."^ 
 Legendre's eulogy of Abel was concise : — " Quelle 
 tete celle du jeune Norvegien!" It is less agreeable 
 to add that the life of Abel was perhaps shortened by 
 poverty and care. Though ultimately befriended by 
 Legendre, Poisson, and others,his firstvisit to Paris (in 
 1826) occasioned nothing but disappointment, and his 
 great memoir (no unusual lot, for the same happened 
 to Fresnel) lay hopelessly lost amidst the papers of the 
 Institute for fifteen years. Much, however, to their 
 credit, the geometers above mentioned at length ad- 
 dressed the King of Sweden on behalf of the rare genius 
 his dominions contained ; but in vain, Abel died ne- 
 glected, unable even to print his researches, which were 
 tardily given to the world in a collected form, at the 
 expense of the government which refused to support 
 
 1 There is some discrepancy, as to the year of his birth, but I believe this to be correct. 
 
 2 Report on the recent progress of Analysis. British Association Report for 1846. 
 
Chap. IT., § 3.] 
 
 PHYSICAL ASTRONOMY — LEGENDEE — IVORY. 
 
 25 
 
 (99.) 
 liegendre's 
 researches 
 on the at- 
 traetion of 
 ElHpsoids, 
 
 (100.) 
 sometimes 
 in part at- 
 tributed to 
 Laplace. 
 
 (101.) 
 History of 
 the subject. 
 
 (102.) 
 Other 
 works. 
 
 (103.) 
 Ivory. 
 
 him when alive. The French Academy, which had 
 buried his memoir in their most inaccessible"archives," 
 decreed too late the unprecedented honour of a post- 
 humous medal to his mother. Jacobi, the friendly 
 rival of Abel in his discoveries, died recently, at a 
 mature though not advanced age, at Konigsberg, 
 where he was professor. 
 
 But to return to the labours of Legendre. The 
 theory of the figure and attraction of the earth 
 and of other planets naturally divides itself into two 
 parts — fl.) the law of attraction of an ellipsoid on 
 a material point without or within it ; (2.) the figure 
 of equilibrium of a fluid subjected to no forces but 
 the mutual attractions of its particles, and the cen- 
 trifugal force due to its rotation. The latter of 
 these problems is still imperfectly solved, the former 
 completely so, and that mainly in consequence of the 
 labours of Legendre and Ivory,' 
 
 Though the services of Legendre are well known 
 and admitted, the superior address of Laplace in the 
 applications of mathematics has occasioned his re- 
 ceiving the credit of what in some instances belonged 
 to the former. 
 
 Maclaurin, by an exercise of synthetic skill not 
 exceeded since the death of Newton, had demon- 
 strated the attraction of an ellipsoid of revolution 
 upon a material point anywhere within it or on its 
 surface, as well as for an exterior point in the 
 prolongation of its axis or in the plane of its 
 equator. The same problem wa« afterwards ana- 
 lytically solved by D'Alembert and Lagrange. In 
 1782, Legendre, by a profound and complicated 
 analysis, obtained an expression, by means of series, 
 for the attraction of an exterior particle generally, 
 and he was the first to imagine and employ those 
 artifices of calculation known usually by the name 
 of " Laplace's functions." Laplace made a step 
 towards the simplification of the expression of ex- 
 terior attractions, but the complete solution was 
 reserved for Mr Ivory, as I shall mention below. 
 
 The other labours of Legendre need not be spe- 
 cified here. He co-operated in the trigonometrical 
 survey of France, and gave the formula, known by 
 his name, for approximately reducing a spherical to 
 a plane triangle. He also wrote on the orbits of 
 comets, and on the method of least squares. 
 
 James Ivoey, the most considerable British mathe- 
 matician of his time, or that had appeared since Mac- 
 laurin, was born at Dundee in 1765, and studied at St 
 Andrews along with Sir John Leslie. The most ac- 
 tive period of his life was passed as mathematical pro- 
 fessor at the Military College of Marlow (afterwards 
 removed to Sandhurst). He was essentially a self- 
 taught mathematician, and spent much of his time in 
 retirement. He fathomed in private the profoundest 
 writings of the most learned continental mathemati- 
 
 cians, and, at a period when but few Englishmen 
 were able to understand those difficult works, he 
 showed his capacity of adding to their value by ori- 
 ginal contributions, not unworthy of the first ana- 
 lysts. We pass over his earlier contributions con- 
 nected with mathematics and astronomy, several of 
 which are contained in the Transactions of the 
 Royal Society of Edinburgh, and proceed to his 
 most celebrated paper, published in the Philoso- 
 phical Transactions for 1809, in which he com- 
 pletely and definitely resolves the problem of attrac- 
 tions for every class of ellipsoidal bodies. After 
 what has been stated above as to the position of the 
 problem as treated by Legendre, a few words will 
 explain the precise import of Ivory's Theorem, one of 
 the most celebrated mathematical results of that time. 
 
 We have seen that the attraction of an ellipsoid (104.) 
 on a point within or at its surface had been assigned ^'^^P°'''" 
 by Maclaurin. The theorem in question enables ^"^^ Q„^°J^g 
 us at once to reduce the case of an exterior attracted attraction 
 point to that of a point on the surface of the ellipsoid, of EUip- 
 Suppose an ellipsoid having the same excentricity, °''"^^' 
 and with the principal sections parallel to the first, 
 but whose surface passes through the given exterior 
 point. Let points on the. surface whose co-ordinates 
 parallel to the three axes of the respective solids are 
 proportional to those axes be called corresponding 
 points; then the attraction parallel to each axis 
 which one of these bodies exerts on a point situated 
 on the surface of the other is to the attsaction of the 
 latter on the " corresponding point" of the sur- 
 face of the former, as the product of the two other 
 axes of the first ellipsoid is to the product of the two 
 other axes of the second. By this means the attrac- 
 tion on an exterior point is accurately expressed in 
 terms of the attraction on an interior point, which 
 is known. It is feir to add that both Legendre and 
 Laplace had some glimpses of the principle, though 
 they failed to apply it to the direct solution of the 
 problem, and between the publication of their Me- 
 moirs and that of Mr Ivory there elapsed nearly a 
 quarter of a century. 
 
 Besides this paper, Ivory contributed many others (105.; 
 on the subject of the attraction of spheroids and the ^*^ °^^^^ 
 theory of the figure of the earth, during a period of P*^®"^^' 
 nearly thirty years ; several of these were controversial, 
 and did not add materially to the progress of the sub- 
 ject; others are considered as masterpieces of analyti- 
 cal skill. One of the last subjects which occupied his 
 attention was the possible equilibrium of a spheroid 
 with three unequal axes, which Jacobi had discovered. 
 
 Between the labours of Ivory and those of Legen- 
 dre a great analogy subsists ; for the doctrine of ellip- 
 tic integrals also occupied the attention of the former. 
 
 But next to the theory of attractions, that of At- 
 mospheric Refraction most seriously engaged Ivory's •*''"<'■ 
 attention. Its great importance in astronomy, and fracTion. ^' 
 
 (106.) 
 
 (107.) 
 
 ^ See the articles Attraction and Figube of the Eabth (the former by Ivory) in this Encyclopaedia. 
 
26 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss, VL 
 
 the curious mathematical difficulties which it pre- 
 sents, renders it very interesting to analysts. La- 
 place had applied to it his method of Generating 
 Functions ; Kramp had introduced into his (now 
 scarce) treatise the almost new Calculus of Factorials ; 
 and others, like Bessel and Atkinson, had skilfully 
 combined theory and observation for the construc- 
 tion of useful tables. One of the most curious re- 
 sults of recent enqiiiries into this subject is, that Sir 
 Isaac Newton's table of refractions (Phil. Trans., 
 1721) must have been founded on a profound con- 
 sideration of the problem, such as no one else thought 
 of till a much later period, and is so numerically ex- 
 act as to agree closely with the later tables, Kramp's 
 for example.^ 
 (108.) Mr Ivory attained the age of seventy-seven, dying 
 
 Hie death. 
 
 on the 21st September 1842. Probably his unceasing 
 devotion to a confined and abstruse topic of enquiry, 
 reacting on a sensitive frame, rendered him in some 
 degree irritable and unsocial. He was not altogether 
 responsible for this ; but students of science should 
 recollect that diversity of occupations and interests is 
 subservient not only to bodily health, but also to men- 
 tal equanimity and vigour. 
 
 The historian of science dwells with a special in- (1*^9;) 
 terest on the results of Ivory's labours, when we re-^g^j 'j_ 
 cal the singular destitution of higher mathematical tion as a 
 talent which had reigned in this country for so long a British Ma- 
 period, and which left us not only no position in tlie*j®"**'" 
 great struggle going on abroad for the advancement 
 of physical astronomy, but scarcely even the rank of 
 intelligent spectators. 
 
 § 4. Progress of Physical Astronomy since the publication of the Mecanique Celeste. — PoiSSON. — 
 Theory of Rotation (Poinsot). — Mr AiKY — The Solar Theory. — MM. Plana and Hansen— 
 The Lunar Theory. — Physical Astronomy in America. 
 
 (110.) The more that any theory of a mathematical kind, 
 mfficuitv^f^'^'*'® *^^* °^ Gravitation, advances to perfection, 
 physical as- the less reason have we to expect great and striking 
 tronomy. results in the prosecution of it, and the more intense 
 and continuous is the labour in matters of detail ne- 
 cessary to make any advance at all. 
 (111.) ^g regards the general and popular view of the 
 
 gj^^g™^'^^^^ subject, we might pass at once from the epoch of La- 
 publication grange and Laplace to that of Leverrier and Adams, 
 of the Notwithstanding, however, the necessity of extreme 
 Mecamqm compression, I must devote one short section to men- 
 tioning the chief labours in connection with physical 
 astronomy of four eminent men mentioned in our title, 
 who may fitly be considered as the immediate succes- 
 sors of Laplace. Two of them will be again referred 
 to in this discourse. 
 (112.) Simeon Denis Poisson, born in 1781, may be 
 said truly to have been brought up at the feet of La- 
 grange and Laplace. He was their pupil in the first 
 and brightest years of the Polytechnic School, where 
 he was especially noticed by the former. He had 
 the distinguished privilege of being literally their 
 fellow-worker, his early memoirs having reference to 
 their labours, and stimulating the still vigorous mind 
 of Lagrange to the production, in his latest years, of 
 several memoirs, which have been considered worthy 
 of his best days. I refer more particularly to Pois- 
 T vrt f ^^"^'^ proof that the stability of the planetary system 
 the system ■ hol^s when perturbations of the second order are 
 taken into account, as has been stated in the first 
 section of this chapter, Art. (55.) This was in 1808. 
 Soon after, following out another of Lagrange's ad- 
 mirable generalizations of his theory of Arbitrary 
 
 Poisson 
 
 Constants, he embraced in a common series of for- °?^^**" 
 mulse the result of those mechanical laws which 
 regulate the rotation of bodies, together with those 
 concerned in their translation in space. This im- 
 portant subject (rotation) continued at intervals to 
 engage the attention of Poisson, not only as re- 
 gards the motions of the heavenly bodies on their 
 axes, but also as a branch of common mechanics. 
 The basis of this intricate doctrine was laid by Huy- 
 gens ; Euler, in a celebrated and original work, 
 gave it a general and analytical form ; D'Alembert 
 solved by it the problems of precession and nutation ; 
 Laplace demonstrated the constancy of the time of 
 the earth's rotation round its axis. This last pro- 
 blem was more fully discussed by Poisson, who showed 
 by theory that neither can the earth ever rotate round 
 an axis different from its present one, nor can the 
 time of its rotation vary in consequence of any ex- 
 ternal attractions to which it is subject. These two 
 matters are of the utmost moment ; the first prevents 
 the latitude of places from varying, and also renders 
 impossible the extensive flooding of dry land by the 
 waters of the ocean, which would be the evident con- 
 sequence of such a change ; the second assures us 
 that the grand unit of reckoning in all ages, the™'^"'"*''^" 
 basis of astronomical chronology and of physical ^JJ^ ^^j^j 
 astronomy generally, the length of the mean solar day, day, 
 has not varied, and never will perceptibly vary under 
 the action of known forces. Laplace had long be- 
 fore proved, by a comparison of ancient eclipses with 
 modern observations, that, practically, the length of 
 the day had not varied in 2000 years. It appears, 
 indeed, that since the earliest recorded Chaldean 
 
 ^ See Biot in Oonnaitsance des T6mps,lS39 ; and Baily's Life of Flamiteed, 
 
Chap. II., § 4.] PHYSICAL ASTRONOMY — MM. AIRY, PLANA, AND HANSEN. 
 
 2T 
 
 eclipse (that of B.C. 720), the rotatory velocity has 
 not altered by one ten-millionth part. 
 (113.). An eminent contemporary and rival of Poisson, M. 
 on Rota- Poinsot, has added many elegant propositions to the 
 tion. Theory of Rotation. . M. Poinsot is also the author of 
 
 the Theory of Statical Couples, which now forms part 
 of all elementary treatises on mechanics. 
 (114.) Poisson wrote many other papers on subjects of 
 
 writings of P^y®^*^^ astronomy, such, for example, as the Lunar 
 Poisson. Theory, but they did not lead, on the whole, to strik- 
 ing conclusions. In fact, he allowed himself to 
 be diverted from this his most natural calling, by 
 the ambition of constructing a system of Physics 
 mainly founded on the applications of analysis. 
 Some bulky volumes of this series appeared, espe- 
 cially those on Capillary Attraction, and on the 
 Theory of Heat. The author here shows him- 
 self as a profound analyst, but adds little to our 
 knowledge either of principles or of important re- 
 sults. A similar criticism may be applied to his 
 theory of Elastic Substances, and to his doctrine of 
 Waves. His papers on Magnetism and Electricity will 
 . be mentioned elsewhere, but their character is some- 
 what similar. In Optics he was attached to the 
 Newtonian theory. In Mechanics not requiring as- 
 sumptions as to the properties of matter, he was very- 
 successful . He was eminently a solver of hard pro- 
 blems : his investigation of the whole circumstances 
 of motion of a projectile in air deserves notice. 
 Indeed every branch of mechanics received his atten- 
 tion, and the number of his printed papers is said to 
 exceed three hundred. On the whole, he will, per- 
 haps, be most generally and favourably known by the 
 His Treay. g^cellent Treatise on Mechanics which he wrote for the 
 chanics. ^ise of advanced students. He was an eminent and 
 diligent Professor, and his whole life was one of almost 
 unremitting study. " La vie c'est le travail" was his 
 reply, when urged to consult his health by reposing 
 from his labours : and he actually died in the dis- 
 charge of his duty as examinator of the Polytechnic 
 School. This occurred on the 25th April 1840, in 
 the fifty-ninth year of his age. 
 
 ^A^^"^ Mr AiET on the perturbation by Venus of the 
 ■ (jjg pertur- EartKs motion. — ^We here detach from what we shall 
 bation of elsewhere have to record of the eminent services ren- 
 the Earth ^ered to the cause of astronomy by the present As- 
 y enus. ^j-Qj^Qj^gr Royal of England, a notice of his chief dis- 
 covery in physical astronomy, the more remarkable 
 from being almost the only improvement in the theory 
 of the planetary motions, as applicable to the tables, 
 which had proceeded from an English mathematician 
 for a very long period. . Sir James South called at- 
 tention, in 1826, to a small but well marked devia- 
 tion of the Sun's place from that given by Delambre's 
 solar theory (the Sun's place or the Earth's are of 
 course convertible terms). Mr Airy, then Lucasian 
 professor at Cambridge, instituted, in 1827, a more 
 extensive comparison with the Greenwich Observa- 
 
 tions, and attributed the error chiefly to the assump- 
 tion of erroneous masses for Venus and Mars. But 
 prolonged study satisfied him that it arose from a "long 
 inequality," arising from the mutual action of the 
 Earth and Venus, similar in its nature to that men- 
 tioned in Art. (66), as detected by Laplace in the 
 case of Jupiter and Saturn. It arises from the cir- 
 cumstance that eight times the orbital period of the 
 Earth is almost equivalent to thirteen times that of 
 Venus. Terms of the series expressive of the mu- 
 tual action of the planets, which are divided by thir- 
 teen times the mean motion of the former minus eight 
 times the mean motion of the latter (which is a very 
 small quantity), may consequently become consider- 
 able ; still more, those involving the square of this 
 quantity. Such terms belong to the fifth and higher 
 orders of the excentricity, and would consequently be 
 very minute indeed, but for the casual magnitude of 
 their coefficient. The labour of tracing out and cal- 
 culating the efiects of these important terms from the 
 vast mass of algebraic developments is enormously 
 great, — much greater than in the corresponding case 
 of Jupiter and Saturn. As the calculations are not 
 very likely to be repeated, Mr Airy took extraordi- 
 nary precautions in their verification. The period 
 of the inequality depends, first, as has been explained 
 in Art. (67), upon the period required to carry the 
 point of conjunction of the two planets completely 
 round the circumference. This period is no less than 
 270 years. The perturbation is of course mutual, 
 and afiects the place of Venus as well as of the Earth. 
 
 Mr Airy is also the author of investigations con- (116.) 
 nected with the Figure of the Earth, and the Theory 
 of the Tides [see Art. (82)] ; and he has published va- 
 luable Tracts on Physical Astronomy for the use of 
 students. 
 
 Sir John Lubbock's name deserves mention here (117.) 
 as having devoted his energies, about the same time ^'"^ ^°^^ 
 with Mr Airy, to intricate and laborious researches " °'^ ' 
 connected with the least inviting parts of physical 
 astronomy, and striven to redeem England from the 
 reproach of indifierence or incapacity in respect of 
 such inquiries. The chief object of his numerous 
 memoirs (in the Philosophical Transactions for 1830, 
 and following years) is to express, in a more conve- 
 nient and exact manner than had been in use, the 
 complicated serieses indicative of the perturbations as 
 well in the Lunar as in the Planetary Theory. 
 
 The Lunar Theory : MM. Plana and Hansen. — jjjj_ pj'^^^ 
 M. Plana, an astronomer and analyst of the greatest and Han- 
 merit, who fortunately still does honour to the native sen on the 
 city of Lagrange (Turin), though the author of a great mh"*"" 
 number of Memoirs in the Transactions of the Turin 
 Academy, on difierent points of Applied Mathema- 
 tics, is, and will be, best known by his elaborate and 
 learned treatise on the Theory of the Moon. This 
 extends to three very bulky quarto volumes, which 
 are, so to speak, one mass of symbols. Nothing caa 
 
28 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 give a more impressive idea of the condition at which 
 Physical Astronomy has now arrived, than a glance at 
 this mountain of intellectual labour, — especially 
 as to the intricacy, inexpressible by words, of the 
 motions of our own satellite. Here we have a work, not 
 much smaller in appearance than the whole Mecanique 
 Cileste, devoted to this one object. It is not super- 
 fluous to add, that this is no chimerical undertaking 
 — no curious puzzle — no learned trifling ; the Lunar 
 Theory is the grand basis of the Art of Navigation. 
 The real and main use to mankind of our companion 
 planet is a discovery of these latter ages : her cheer- 
 ful and beneficial light, which all appreciate, and all 
 enjoy, may almost be termed a secondary boon, 
 r ^^ t^^ k ^ merit of M. Plana is not so much that of 
 of the for- ^^ original geometer, outstripping the theories of La- 
 mer, place and Lagrange, as of a most intrepid and skilful 
 calculator, who has contrived to place in complete 
 order the whole mathematical and many of the arith- 
 metical steps of the solution of one vast problem, ex- 
 tending to some 2000 quarto pages. The calcula- 
 tions he has made unaided ! The details are ar- 
 ranged in so lucid a manner, as to court enquiry 
 from those interested in verifying them ; and though 
 the readers of so abstruse and indeed repulsive a 
 work must be few indeed, it has already proved 
 of essential service in the way which was intended 
 — the improvement of the lunar tables. The ap- 
 proximations by series are in all cases carried to 
 the fifth powers of small quantities, and, in some in- 
 stances, to the seventh powers. Sir John Herschel 
 has expressed in forcible and picturesque language 
 the nature of what is wanting to the completeness 
 of Laplace's investigations and which M. Plana has 
 supplied, as regards the theory of the moon's nttotions : 
 — " In the MScanique Cileste, we admire the elegance 
 displayed in the alternate interlinking and develop- 
 ment of formulae, and exult in the power of the ana- 
 lytical methods used ; but when we come to the 
 statement of numerical results, we quail before the 
 vast task of filling in those distant steps ; and while 
 cloud rolls after cloud in majesty and darkness, we 
 feel our dependence on the conclusions attained 
 to partake of superstitious trust, or of amicable 
 confidence, rather than of clear and demonstrative 
 conviction." 1 The courage of M. Plana did not 
 " quail" before the serried ranks of symbolic legions. 
 He attacked them first, and finally became their com- 
 mander. But more than this ; on the same high 
 authority, " his analysis is always graceful, his com- 
 binations well considered, and his conceptions of the 
 ultimate results to be expected from them perfectly 
 just, and justified by the results when obtained." 
 
 I may here mention that M. Plana, in conjunc- 
 tion with M. Carlini of Milan, undertook the calcula- 
 
 tion of the moon's motions from theory alone (that is. Lunar 
 with only the fundamental constants required to be ^^°^^^ 
 given by observation), in compliance with a pro- Theory 
 gramme issued by the French Academy of Sciences alone, 
 on the proposition of Laplace ; and that a French parlim — 
 geometer, M. Damoiseau, on the same occasion, pro- 
 duced an independent investigation with very elabo- 
 rate and valuable tables founded thereon. 
 
 M. Plana is the author of many other more (121.) 
 circumscribed researches on important points in phy- 
 sical astronomy, in geodesy, and in mathematical 
 physics. 
 
 M. Hansen, a German astronomer and analyst (122.) 
 of great merit, has made the most recent considerable ^- Hansen, 
 improvement in the theory of the moon. We will 
 first, however, allude to an invention which is ap- 
 plicable to the whole theory of perturbation. 
 
 We have seen, in the first section of this chap- (123.) 
 ter, that the effects of perturbation may be considered ^^^} . 
 either as applicable directly to the three co-ordinates perturba- 
 of the perturbed body, or to the variation of the ele- tlons. 
 ments of the orbit considered as instantaneously va- 
 rying ; that the former method has the advantage of 
 being in most cases, and especially in first approxi- 
 mations, most direct ; the latter is most applicable 
 to secular inequalities, and has a great recommenda- 
 tion in the exact physical conceptions on which it is 
 founded. M. Hansen has proposed a third method, 
 a refinement, in fact; on that of Lagrange, in which, 
 by an assumption purely mathematical and arbitrary, 
 he throws the effect of perturbation entirely on the 
 element of time, so that with the time so altered, and 
 invariable elliptic elements, the conditions of pertur- 
 bation may be satisfied, and the true place of the 
 body may result from the calculation. Such is the 
 general nature of the conception, which, to be carried 
 out, requires the introduction of subsidiary terms, 
 which serve to correct the latitude and radius vector. 
 The advantages which are understood to follow from 
 this highly artificial mode of proceeding are stated to 
 be (1 .) that the serieses expressing the perturbation of 
 the co-ordinates are more convergent than in the 
 other methods, and likewise the coefficients of the 
 terms to be retained are more easily calculated ; (2.) 
 M. Hansen considers that his method enables- him 
 to ascertain with certainty those terms which, when 
 fully calculated, will affect the result in a sensible 
 manner. The inventor has applied his methods both 
 to the Lunar and to the Planetary theory. 
 
 We have said that physical astronomy is indebted (124.) 
 to M. Hansen for a notable improvement in the theory '^'^° "^.^ 
 of the Moon,— the discovery, in fact, of two inequali- ^q"oaUtieB. 
 ties of long period, the existence of which had been 
 more than suspected from observation, but which were 
 
 ^ Astronomical Society's Monthly Notices, vol. v., p. 37. The lasb expressions may astonish some persons, but experienced ana- 
 lytical calculators agree in the same view. Mr Airy (probably the most competent authority in Britain) states the same thing 
 in many passages of hia writings, to the effect that the evidence for conclusions so obtained is rather that of moral than of ma- 
 thematical certainty. 
 
Chap. II., § 5.] PHYSICAL ASTRONOMY. — M. LEVERRIER — ME ADAMS, 
 
 29 
 
 not accounted for. In the infancy of the lunar theory, 
 Euler had predicted that it would always be im- 
 possible, on account of the perturbing forces of the 
 planets, to predict the Moon's place within 30" ; and 
 it was a quantity of about this measure which re- 
 mained outstanding after all the resources of analysis 
 seemed exhausted. M. Poisson and Sir J. Lubbock 
 showed that the anomaly could not be due to the 
 solar action, nor yet to the irregularity of the Earth's 
 figure. The planetary attractions, then, alone re- 
 mained. M. Hansen discovered two independent in- 
 equalities due to the action of Venus. One of these 
 is an indirect (or, as it is sometimes called, reflected?) 
 effect depending on the change of form of the Earth's 
 orbit by the attraction of Venus, which, of course, 
 modifies slightly the solar perturbation of the Moon's 
 longitude. It is, in fact, a secondary consequence of 
 long inequality of Venus and the Earth investigated 
 by Mr Airy [Art. (115)], and has the same period, 
 namely, about 240 years. Its greatest amount is 
 23"-2. The other inequality discovered by Hansen 
 is of a still more curious and complicated kind, which 
 goes on increasing for 2000 lunations, when it at- 
 tains a maximum value of 27""4 in longitude (al- 
 though the perturbation of the radius vector does not 
 exceed 10 feet), after which it diminishes for an equal 
 space of time. 
 (125.) By these discoveries, the movements of our re- 
 
 His other ffactory satellite may be considered to be, after an 
 
 works ** V ' 
 
 unprecedented amount of labour, accounted for by 
 theory almost or quite within the limits of the pre- 
 sent accuracy of observation.^ M. Hansen has re- 
 cently been engaged in perfecting the practical details 
 of the lunar theory, in accordance with the extensive 
 reductions of the Greenwich observations which will 
 be mentioned in the next chapter. He has also given 
 the first complete theory of " Foucault's pendulum," 
 also to be mentioned hereafter. Altogether, he 
 stands amongst the most eminent analytical astrono- 
 mers of the present day. 
 
 We have in this section selected (though not by (126.) 
 design) representatives of the four great intellectual <^™eral 
 communities of Europe, engaged in the mighty task ph^idi 
 of perfecting the theories of physical astronomy. Astronomy 
 Poisson for France, Airy for England, Plana for 
 Italy, Hansen for Germany. It would be easy, of 
 course, to add the names of many others engaged in 
 similar works, and scarcely less deserving of notice. 
 Some of these will find a place in other chapters, and 
 we have yet one section of this chapter to devote to 
 the history of a discovery of rare interest, in which 
 France and England have a joint share. We may in Europe, 
 be allowed to mention the names of M. Damoiseau 
 and M. Pontecoulant in France ; the former known 
 by his excellent lunar tables deduced from theory, 
 the latter for his calculations of cometary perturba- 
 tion, and his compendious treatise on physical as- 
 tronomy, based on the MScanique CSleste ; in Italy, 
 MM. Carlini and Santini. But in Germany these 
 studies have been perhaps most systematically pur- 
 sued. MM. Gauss and Encke have only not been 
 included in this section because we find it more suit- 
 able to our plan to associate the name of the former 
 with his theory of Terrestrial Magnetism, and the 
 latter with the recent history of Comets. Bessel 
 likewise was a physical as well as first-rate prac- 
 tical astronomer. I will here only add that these and in 
 severe and arduous studies have at length been America, 
 effectually cultivated beyond the limits of Europe. 
 Mr Bowditch (born 1773, died 1838), a private Bowditch. 
 gentleman of the United States, undertook the 
 gigantic labour of translating and illustrating, with 
 a complete commentary in which every difiiculty is 
 considered, and every step of analysis supplied, the 
 MScanique CSleste of Laplace. Since his death, a 
 younger race of American mathematicians has taken 
 up the great problems of physical astronomy, amongst 
 whom may be mentioned Mr Walker and Mr Peirce. 
 The latter gentleman has recently (1853) published 
 lunar tables, embracing the latest researches of theory. 
 
 (127.) 
 The dis- 
 covery of 
 Neptune 
 from 
 
 theory by 
 MM. Le- 
 verrier and 
 Adams. 
 
 (128.) 
 Its cireum- 
 etances. 
 
 I 5. M. Levekriek — Mr Adams. — The inverse method of Perturbations, 
 and orbit of Neptune from the motions of Uranus. 
 
 Prediction of the place 
 
 We have now to chronicle a discovery which, by 
 general consent, stands first in the achievements 
 of science, not only in the period now under review, 
 but even in the long and eventful series of years 
 which have elapsed since Newton established the 
 doctrine of universal gravitation. 
 
 The discovery of which we speak was no less 
 than the proof of the existence of a planet beyond 
 the recognised boundary of our system, merely as an 
 inference from the perturbed motion of the outmost 
 planet Uranus ; a proof, not general or abstract, but 
 
 particular and specific : " Look, on such a night, 
 and in such a direction, and there you will see (by 
 the telescope) a star, small indeed, but with a distin- 
 guishable disk, — that is the planet which has made 
 Uranus move so unsteadily in its orbit ;" — so spoke 
 the mathematician ; and the zealous astronomer, to 
 whom the call was especially addressed, pointing his 
 glass to the sky, discovered at once, that is, the same 
 evening, a body answering almost precisely in position, 
 as well as in brilliancy, to the oracular announce- 
 ment. 
 
 1 M. Hansen has also discovered the course of a small inequality of the Moon's latitude, detected from observation by Mr 
 Airy. His theory of the Moon's figure has been referred to in a note to Art. (57.) 
 
30 
 
 PHYSICAL ASTRONOMY.— M. LEVERRIER— ME, ADAMS. 
 
 [Diss. VI. 
 
 (129.) Since the publication of the Principia, or rather 
 
 difflcultv ^® should say since the great theory contained in 
 that work had fully attracted the sympathies of 
 thoughtful and able men, nearly the whole science of 
 physical astronomy consisted in the solution of one 
 vast and intricate problem, which has been called the 
 " Problem of the Three Bodies." To this were bent 
 the powers of Clairaut, Euler, Lagrange, Laplace, 
 Plana, Hansen, and so many more. " Let three 
 bodies be placed and move in a given manner in 
 space and attract one another by the Newtonian law, 
 to determine the motions as affected by their mutual 
 influence." The problem solved independently by 
 the tw<;> analysts whose names stand at the head of 
 this section is this, " Given two bodies (the Sun and 
 Uranus) and their relative motion, to find at any 
 moment the position of a third body whose attraction 
 shall be required to account for those motions." To 
 have solved this new and far more difficult problem 
 (under certain limitations) is a triumph altogether 
 unlike in kind to any of the other brilliant successes 
 of which we have had to speak in the preceding 
 
 (130.) Tiie great intricacy of the problem is not perhaps 
 
 at the first moment fully apparent. The pertur- 
 bation of the known planet (Uranus) is not the 
 effect, either in direction or in amount, of the attrac- 
 tion of the body sought, either at the instant, or at 
 any previous instant. It is an accumulated effect 
 arising from the totality of the mutual influences of 
 the two planets during a long space of time, and 
 under a variety of circumstances, which circum- 
 stances it is the aim of the solution to discover. 
 But, more than this, we do not even know the quan- 
 tity or direction of the perturbative action at any 
 moment for which the cause is sought, for we do not 
 knovj the purely elliptic elements of Uranus. His 
 motion has, by hypothesis, been always troubled by 
 this exterior planet, and Uranus has been so short 
 a time known and observed (only accurately since 
 1781) that the motion has not yet been cleared of 
 ordinary inequalities (due to the action of the unseen 
 body), which, therefore, are inextricably mixed up 
 with the elliptic elements. It is absolutely necessary, 
 therefore, to suppose not only the elements of the 
 new planet to be unknown, but also the elements of 
 Uranus to be severally affected by unknown errors. 
 This nearly doubles the unknown quantities to be 
 found; 
 
 (131.) -yy-g gjiall now glance at the history of these un- 
 ■'' explained perturbations, and at the rise and growth of 
 the idea of their being explicable by the influence of 
 an unseen body. 
 
 (132.) After Sir William Herschel had discovered, in 
 
 1781, the planet which he called Georgium Sidus, Irregulari- 
 (afterwards named Herschel, and finally, by general ties of the 
 ^ , XT N V 1, e \. ^ motions of 
 
 consent, Uranus,) it was easy, by a tew observations, upanus. 
 
 to ascertain its approximate orbit and distance from 
 the sun. But the extreme slowness of its motion 
 (it will not have completed a single revolution before 
 1861) made it impossible to determine its elements 
 with precision, until it had been discovered that the 
 records of astronomy contained about twenty observa- 
 tions of this body before its planetary nature was 
 discovered ; being, in fact, registered places of fixed 
 stars where no stars exist, concurring in brightness 
 and position with the circumstances of Uranus at 
 those remoter periods ; the earliest of these obser- 
 vations was one of Flamsteed, in 1690. The first 
 person who constructod tables of the planet was De- 
 lambre ; but even at that early period, it was re- 
 marked, that the modem were not satisfactorily recon- 
 cilable with the ancient observations; and, finally, 
 Delambre included of the latter only one, by Mayer, 
 which he did, he tells us, " out of pure respect," al- 
 though it certainly rendered the tables less exact and 
 less durable. The longer the planet was observed, 
 and the greater the care that was expended in analys- 
 ing and combining the observations, the more clearly 
 it appeared that the tables had only an empirical cha- 
 racter, satisfying observations for a few years before 
 and after the time for which they had been con- 
 structed ; and that, in particular, as the nineteenth 
 century advanced, the deviations from elliptic regu- 
 larity became more and more intolerable, till the " an- 
 cient" observations were at length totally given up. 
 This was the state of matters in 1821, after M. 
 Bouvard of the Observatory of Paris, a most able cal- 
 culator, had exhausted every resource in improving 
 the Tables of Uranus. A few years more gave that 
 patient astronomer the mortification of seeing his 
 tables as obsolete as those of his predecessors, and nu- 
 merous surmises were circulated as to possible expla- 
 nations of the anomaly : a failure' in the law of gra- Hypotheses 
 vity, cometary perturbation, a resisting medium, '° accouDt 
 and, finally, the presence of an unseen planet, were '°^ *™' 
 amongst these guesses. The last and most plausible 
 of these hypotheses occurred to many; amongst 
 others, to Mr Hussey in England, M. Bouvard in 
 France, and later to M. Bessel in Germany.^ The 
 first of these astronomers actually consulted Mr Airy, 
 in 1834, on the possibility of predicting the place of 
 the perturbing planet from theory, and then disco- 
 vering it by observation. Mrs Somerville, in 1836, 
 gave a precise expression to the same idea.^ From 
 this time the subject could not be lost sight of. The 
 errors of the tables which in 1821 were insen- 
 sible, increased in 1830 to 15" or 20", and in 1845 
 
 1 Clairaut, nearly a century before, in calculating the return of Halley's comet, hinted at thei possible perturbation due to a 
 planet superior to Saturn. 
 3 In her Connection of the Phydeal Sciencei, ' 
 
Chap. II., § 5.] PHYSICAL ASTRONOMY. — M. LEVEREIER — MR ADAMS. 
 
 31 
 
 amounted to two minutes of longitude. M. Bouvard 
 to his latest years, perhaps his latest hours, i che- 
 rished the hope of extricating this theory from its 
 difficulties. He also engaged his nephew M. Eugene 
 Bouvard in the same career, who appears to have 
 followed it with much zeal and intelligence, and 
 in 1845 constructed new tables of Uranus. But by 
 this time two geometers had separately and inde- 
 pendently undertaken the problem, with the deter- 
 mination of finding, if possible, a physical solution 
 of all this perplexity. The earliest in point of date 
 was Mr Adams, a young graduate of Cambridge ; the 
 other was M. Leverrier of Paris, -^jrhose attention 
 was directed to the subject by M. Arago. As the 
 researches of M. Leverrier, though second in point of 
 time, occasioned the actual recognition of the planet, 
 and thus stamped the correctness of the solution with 
 success, we shall consider them in the first instance. 
 (133.) M. L:everrier is, we believe, a native of St Lo 
 
 M. Lever- in Normandy, a province which has been singularly 
 tiga'iong?' productive of eminent men (Laplace and Fresnel 
 were of the number). With no advantages, but the 
 reverse, he won a high position at entering the 
 polytechnic school, which he constantly maintained. 
 He at first, we believe, attached himself to chemis- 
 try, but his taste for physical astronomy was soon 
 developed, and was advanced entirely by his private 
 efforts. It is a peculiarity of the mode of culti- 
 vating the sciences in Paris, that such abstruse 
 and difiicult studies are not merely engaged in tem- 
 porarily for purposes of academial distinction, but that 
 they actually become a " carriere" or calling, and are 
 pursued in that methodical manner for which the 
 French are distinguished. In 1845, when he com- 
 menced the careful examination of the theory of 
 Uranus, M. Leverrier was already favourably known 
 by his researches on comets, and on the orbit of 
 Mercury, but especially by immense calculations, con- 
 nected with the secular inequalities of the planets, by 
 which his ability and hardihood in computation had 
 been thoroughly exercised. He began his new en- 
 quiry with the method and intrepidity of calculation 
 which distinguish him. He revised with the most 
 minute care the observations of Uranus, and 
 computed afresh every sensible perturbation which 
 theory recognised as arising from known planets. 
 This done, and having compared the most probable 
 orbit with observations which he collected from 
 authentic sources, and especially from the Greenwich 
 observations which were communicated to him for 
 this purpose, the result was, that even confining 
 himself to observations since 1781, arranged in 
 eleven convenient groups (each resulting from many 
 observed places), and attributing to each group the 
 
 largest error which could be in reason allowed, 
 and even admitting that all these errors were in the 
 direction most favourable to the assumption, it was 
 still' impossible to account for more than one-fourth 
 part of the observed discordances. 
 
 M. Leverrier then assumed that a perturbing (134.) 
 planet existed beyond the orbit of Uranus, and at 
 nearly double its distance from the sun, in conformity 
 with the empirical law, (usually attributed to Bode 
 the German astronomer,) which expresses with gene- 
 ral accuracy, thus far, the arrangement of the planetary 
 system. The law is, that the distances of the planetary 
 orbits from Mercury are successively doubled. This 
 assumption — (it was absolutely necessary to assume 
 some distance to begin with) — was ingeniously con- 
 firmed by other considerations. 
 
 Leaving the perturbations in latitude out of ac- (135.) 
 count, he now considered each error of Uranus in ^°'^ <"'°" 
 longitude as the expression of a perturbation due 
 to the action of the unknown planet, and capable 
 therefore of algebraic expression in terms of the ele- 
 ments of that planet, namely its excentricity, longi- 
 tude of perihelion, epoch in its orbit, and mass ; but, 
 as we have already remarked, the first three of these 
 elements must be considered as incorrectly assumed 
 for Uranus itself, as well as the mean distance of that 
 planet, and, therefore, there are four unknown correc- 
 tions for its elliptic elements, making in all eight quan- 
 tities to be eliminated from the discordances of theory 
 and observation. So complex an elimination cannot 
 be directly efiected ; and even if it could, the result 
 could not be depended on, as the possible error of 
 each observation involves a fresh and important 
 source of doubt in the conclusion. M. Leverrier 
 proceeded, by a series of gradually restricted assump- 
 tions, to find within what limits the more important 
 elements might be made to vary without producing 
 efifects incompatible with observation, and his atten- 
 tion was at first confined to the approximate mean 
 longitude of the planet. He obtained a result after Their re- 
 a prodigious amount of tentative calculation. The ^'^^'• 
 excentricity and position of the perihelion were then 
 inferred. On the 1st June 184,6 he announced to 
 the Academy of Sciences that the true longitude of 
 the expected planet for 1st January 1847 was 325°, 
 with a probable error of 10°. This result was im- 
 mediately published in the Comptes Bendus. 
 
 Between the 1st June and 31st August 1846, (136. 
 when his third memoir on the perturbations of M- Lever- 
 Uranus appeared, M. Leverrier busied himself in oh- '''^'^^^^^ 
 taining a farther approximation to the elements and ment • 
 place of the suspected planet. He now assumed the 
 correction of the mean distance amongst the other 
 quantities to be sought. By a fresh calculation he 
 
 ^ SI. Bouvard was born in 1767. He performed almost all of the numerical calculations required by Laplace in his great 
 work, and was associated with that eminent man by the most friendly ties. He " ceased to calculate and to live" 7th Juna 
 1843. 
 
32 
 
 PHYSICAL ASTRONOMY. — M. LEVERRIER — MR ADAMS. 
 
 [Diss. VI. 
 
 deduced a complete list of elements as regards longi- 
 tude ; and diminislied the mean distance considerably. 
 The true longitude by this calculation differed only 
 1^° from his previous estimation. He finds for the 
 mean distance from the Sun 36 times that of our 
 Earth (that of Uranus being 19), the period 217 
 years, and the mass ^^\-^ of the Sun's. Assuming 
 the density of the planet to be the same as that of 
 Uranus, he conjectures that the apparent diameter 
 will be 3"- 3 ; that it will therefore have a visible disk 
 sufficient to distinguish it from a fixed star, and that 
 its brilliancy should equal that of a star of the 8th 
 or 9th magnitude. As the result of these supposi- 
 tions, he found that the whole errors in the places 
 of Uranus from 1781 to 1844 were reconciled within 
 quantities amounting but in one instance to 5" ; that 
 the ancient observations of the 18th century were 
 reconciled withia 7" or 8" ; and the oldest observa- 
 tion of all, that of Plamsteed in 1690, had an out- 
 standing error of 20", a quantity very far from exces- 
 sive, considering the state of astronomy at that period. 
 (137.) No one who read at the time the abstract of this 
 
 resulting in remarkable paper in the Comptes Rendus failed to 
 te* ^of "' ^ struck with it, not only as regarded the weighty 
 Neptune by matter, thus publicly announced, but also on account 
 M. Galle. of the calm and well-grounded conviction which the 
 author manifested in the truth of his bold conclusions, 
 and the definite manner in which he gives the chal- 
 lenge to practical astronomers to verify or disprove 
 them. " Since Copernicus declared',' (according to the 
 prevalent tradition) " that when means should be dis- 
 covered for improvingthe vision, it would be found that 
 Venus had phases like the moon, nothing," writes Mr 
 Airy, " so bold, and so justifiably bold, has been uttered 
 in astronomical prediction." M.Leverrier had hastened 
 his calculations in anticipation of the approaching 
 opposition of the new planet in the autumn of 1846, 
 but it is very doubtful whether astronomers would 
 have made the discovery at that time, but for his per- 
 sonal application to M. Galle, then assistant-astro- 
 nomer at Berlin, where a powerful refractor suitable 
 for the search existed. So ardent a conviction in a 
 manner compelled the proof which the geometer 
 claimed, and M. Galle, whose intelligence and zeal 
 are well known, pointed his telescope to the sky the 
 very evening that M. Leverrier's letter reached him. 
 Fortunately provided with a newly published star 
 map by Brenicker of that region of the heavens, which 
 was not at that time diffused, generally amongst 
 European observatories, he detected that same night 
 (the 23d September 1846) a star-like body of the 8th 
 magnitude, not noted in the star chart, therefore a 
 wandering body, having a manifest disk from 2J" to 
 3" in diameter, and distant only fifty-four minutes of 
 a degree from the predicted place. 
 (138.) It will be remarked that the discovery in question 
 
 was anticipated and completed in France and Ger- 
 many alone; England hadnodirectparticipation. We 
 must now, however, state briefly what occurred there of 
 a similar character at the same time, and even earlier. 
 
 Mr John Couch Adams, when a student at St (1390 
 John's College, Cambridge, in 1841, formed the de- 
 sign of detecting the position of a perturbing planet 
 which should account for the anomalous motions of 
 Uranus. He made a preliminary essay on the pro- 
 blem in 1843, assuming the distance of the suspected 
 body from the Sun to be double that of Uranus. 
 I learn from good authority that he obtained a place 
 for the unseen planet not very different from that 
 which he finally adopted. Early in 1844 he ob- 
 tained from Greenwich the valuable series of places 
 of Uranus which were afterwards in like manner ap- 
 plied for by M. Leverrier. In September 1845, he 
 communicated to Professor Challis the elements of the 
 new planet's orbit (neglecting the inclination) and an 
 ephemeris of its geocentric place ; and in October he 
 transmitted the elements also to the Astronomer Royal. Mr Adams 
 This, it will be observed, was soon after M. Leverrier's preceded 
 attention was first directed to the subject, and nine ^^^^ j^ ^ 
 months previous to his announcement of the locality similar in- 
 where the new body should be sought. Mr Adams vestiga- 
 afterwards repeated his calculation with a mean dis- ^° ' 
 tance ^'gth less than before, and considered himself 
 warranted, by the improvement thus produced on the 
 residual errors, in inferring that a farther consider- 
 able diminution of the mean distance would satisfy 
 the observations still better. This was communicated 
 to Mr Airy on the 2d September 1846 ; subsequently 
 therefore to the publication of M. Leverrier's Ele- 
 ments. Mr Adams, in communicating his results (at 
 a later time) to the Astronomical Society, with charac- 
 teristic modesty says, " I mention these dates merely 
 to show that my results were arrived at independently, 
 and previously to the publication of M. Leverrier, 
 and not with the intention of interfering with his just 
 claims to the honors of the discovery, for there is no 
 doubt that his researches were first published to the 
 world and led to the actual discovery of the planet by 
 Dr Galle." 
 
 And such is no doubt the fact. The priority of Mr G*".) 
 Adams in the mathematical investigation is as certain ^^^^ was^not 
 as that the researches of M. Leverrier alone produced discovered 
 the discovery of Neptune. Even the search for the in conse- 
 planet which took place in August and September ^"™'^^' 
 1846 at Cambridge by Professor Challis, was not oc- 
 casioned by Mr Adams' researches only ; it was the 
 near coincidence of the longitude assigned by Mr 
 Adams in the previous October with that published 
 by M. Leverrier in June 1846 which induced Mr 
 Airy to suggest this investigation of the heavens, 
 and to offer (if need were) himself to bear the ex- 
 pense. Had the planet been discovered^ at Cambridge 
 
 ^ The planet was indeed seen, at Cambridge by Mr Challis, for it was recorded more than once amongst the numerous fixed 
 stars whose places were taken down in the progress of the Bearch ; but as the comparisons of the " sweeps" were not made at 
 the time, the discovery was anticipated by M. Galle. 
 
Chap. II., § 5.] PHYSICAL ASTRONOMY. — M. LEVERRIER — MR ADAMS. 
 
 33 
 
 (141.) 
 Remarks 
 on the his- 
 tory. 
 
 (1*2.) 
 
 before it was at Berlin, M. Leverrier must still have 
 had a share in the credit of success. 
 
 It is perhaps to be regretted that Mr Adams had 
 not given his -whole investigation to the world, or 
 at least published his results, so as to avouch the 
 confidence which he felt in his own prediction, and 
 to throw upon practical astronomers generally the re- 
 sponsibility of its verification. Had he done so in 
 1845, it is possible that the planet might have been 
 discovered at the opposition of that year ; but it is at 
 least certain that M. Leverrier's claims to priority 
 as regards the discovery of Neptune would have 
 been effectually anticipated. But it is only just to our 
 countryman to recollect the difference of his age and 
 position. M. Leverrier was at the time about 35 
 years of age, and was a candidate for the sub- 
 stantial benefits as well as for the honour of a mem- 
 bership of the Academy of Sciences. Mr Adams 
 must have been nine or ten years younger at the 
 period of this discovery, a circumstance which en- 
 hances our admiraion at the achievement, whilst it 
 gives an additional grace to the modest conduct of 
 the author. 
 
 I have endeavoured to state correctly (with due re- 
 gard to the limits of this essay) the main facts of the 
 most curious case of double discovery which, perhaps, 
 the history of science presents ; and happily as to the 
 facts, down to the minutest detail, no discrepancy of 
 opinion ever existed. Difierent minds will, with per- 
 fect truth, attach more or less distinction to the two 
 illustrious rivals, — neither of whom has for an in- 
 
 stant lowered the dignity of his position by one 
 ungenerous expression, — but that the absolute merit 
 of both is of the very highest character is on all 
 hands admitted. " The names of M. Leverrier and 
 Mr Adams," said Sir John Herschel, addressing the 
 Astronomical Society, " which Genius and Destiny 
 have joined, I shall by no means put asunder ; nor 
 will they ever be pronounced apart so long as lan- 
 guage shall celebrate the triumphs of Science in her 
 sublimest walks." 
 
 But before closing, I must briefly state how far qS}^?'^ 
 the orbit of the planet Neptune, when discovered, yation of 
 realized the previsions of theory. A fortunate cir- Neptune as 
 cumstance rendered it easy to obtain at an early a fixed star, 
 period a correct knowledge of the elements. It seems 
 that the planet Neptune was observed by Lalande at 
 Paris on the 8th and 10th May 1795, and entered 
 as a fixed star, notwithstanding a distinct change of 
 place between the observations, actually corresponding 
 to what the planet should have had.^ But such an 
 oversight had been made by Lemonnier in the case 
 of Uranus. By means of this observation of fifty 
 years back, the orbit was easily computed. It is a 
 singular and startling fact, that, except as regards the 
 longitude on the orbit, the other elements computed 
 from observation were somewhat widely different 
 from those assigned by M. Leverrier and Mr Adams. 
 We shall present them in a tabular view. The value 
 of the mass in the last column is calculated from the 
 elongation and period of a satellite of Neptune dis- 
 covered by Mr Lassell. 
 
 
 Theory — Leverrier. 
 
 Theory — Adams. 
 
 Observation — Walker 
 
 Epocli of Elements, 
 
 1st Jan. 1847, 
 
 eth Oct. 1846, 
 
 1st Jan. 1847. 
 
 Mean Longitude, 
 
 318° 47' 
 
 323° 2' 
 
 328° 33' 
 
 Mean Distance, 
 
 36-15 
 
 37-242 
 
 30-04 
 
 Period, 
 
 217-4 years 
 
 
 164-6 
 
 Long. Perihelion, 
 
 284° 45' 
 
 299° 11' 
 
 47° 12' 
 
 Exoentricity, 
 
 0-1076 
 
 0-1206 
 
 0-00872 
 
 Mass, .... 
 
 ^^jT, of Sun's 
 
 tAti 
 
 I^FTTU ^ 
 
 (144.) The difierences of theory and observation are so 
 
 striking as to have occasioned surprise to many per- 
 sons that, with data so' erroneous, the perturbations 
 of Uranus or the longitude of Neptune at the epoch 
 of discovery should have been obtained even approxi- 
 mately. 
 
 (145.) The fact, however, is this : — that the mutual per- 
 
 [ow a,n as- turbations of Uranus and Neptune are sensible for 
 e™neoua° "'^^J * small portion of the joint orbits when the 
 planets are nearly in conjunction. The conjunction 
 (when the mutual distance is least and the attraction 
 strongest) took place in 1822. Now the places of 
 Uranus from 1690 (the first observation) until 1800 
 can be sufiiciently well represented by elliptic ele- 
 ments. The perturbation of Neptune became sen- 
 
 erroneous 
 elements 
 led to the 
 discovery ; 
 
 sible therefore only twenty years before conjunction. 
 In this time Neptune describes (really) only ^ of a cir- 
 cumference, or 45°, and relatively to the motion of 
 Uranus about the same. It is evident then that 
 even a considerable error in the period of Neptune 
 would scarcely sensibly affect the law of perturba^ 
 tion during twenty years, and that the approximate 
 determination of the place of the perturbing planet 
 about the time of conjunction will not be much 
 aficcted by the error of that assumption. Again, 
 as to the error of mean distance, we may observe, 
 that since the mutual action of the planets is 
 confined within such (comparatively) narrow limits 
 of space and time, though we might anticipate a toler- 
 able approximation to the interval between the bodies 
 
 1 One of the observations was suppressed in the puhlication, and only discovered on searching Lalande's MS. 
 " This was the hypothesis upon which Mr Adams made his second or corrected calculation of elements. Nevertheless, he 
 inferred from that calculation that the mean distance might with much probability be reduced to 33-4. 
 3 Pierce. Struve's mass is tiJut- 
 
ASTRONOMY. — MASKELYNE — DEL AMBRE . 
 
 [Diss. VI. 
 
 at that time, it would be unreasonable to expect a 
 correct determination of the form and ellipticity of the ' 
 orbit of Neptune, such as might belooked forif theper- 
 turbations weresensible throughthe entire orbits; and 
 in fact, by varying the position of the perihelion and 
 the amount of excentricity, we may, for an assumed 
 mean distance, obtain any value whatever for the in- 
 terval of the two planets at a particular time. We 
 have seen the origin of the false assumption of mean 
 distance on the part both of M. Leverrier and Mr 
 Adams, and we find that the mathematical solution 
 corrects to a great extent the error of that assump- 
 tion by giving a correspondingly incorrect position of 
 the perihelion, and also an exaggerated measure of 
 the excentricity, by which two circumstances the 
 planets of both mathematicians would have had, near 
 the time of conjunction, a distance from the sun of 
 only 32 or 33 radii of the earth's orbit, the true dis- 
 tance being about ^ part less. This still remaining 
 error was palliated, and evidently might for a time 
 have been completely masked, by assuming a mass of 
 Neptune proportionally too great, as indeed the table 
 we have given shows was the case. 
 (146.) That the discovery of Neptune took place at the 
 
 th <r - *™® when it did was no accident. The conjunction 
 very took of Uranus and Neptune, when alone the perturbation 
 place when of the elliptic elements is perceptible, is a rare phe- 
 it did. nomenon, occurring but once in about 172 years. 
 The last conjunction previous to 1822 was in 1649 : 
 we have seen that the attention of astronomers was 
 importunately called to the subject by the irregu- 
 larities in the motions of Uranus at the first con- 
 junction succeeding its discovery. 
 (147.) We are indebted to Professor Peirce and Mr 
 
 Walker of the United States for many useful inves- 
 tigations connected with the orbits of Uranus and 
 Neptune ; but it is to be wished that tbe theory were 
 completely re-examined, and also the problem of the 
 inverse method of perturbations which has now be- 
 come a systematic portion of physical astronomy. 
 The near commensurability of the two periods pre- 
 sents a peculiar case of perturbation similar to the 
 long inequality of Jupiter and Saturn ; but as its 
 period is no less than 4047 years,^ although the 
 coefficient of the inequality is considerable, it will 
 not perceptibly alter the motions of either planet 
 except in a long course of years. 
 
 It will not be supposed that either M. Leverrier or 
 Mr Adams could, after such a memorable triumph, 
 abandon the pursuits of physical astronomy. The 
 first has continued his researches on the orbits of 
 comets and on the perturbations of the solar system ; 
 arid having been recently appointed to succeed M. 
 Arago in the direction of the Paris Observatory, we 
 cannot doubt that he will infuse new life into its 
 management. Mr Adams has made the discovery of 
 some important oversights in the details of the lunar 
 theory. One of these, with reference to Laplace's 
 Theory of the Secular Acceleration of the Moon's 
 mean Motion, has been referred to in a note to Art. 
 (62). Though Mr Adams occupies no public post, and 
 though he has declined the honours of a title, his con- 
 tinued residence at Cambridge must influence very 
 beneficially the studies of the place, where some of 
 his many friends have founded in memory of his 
 achievements a perpetual prize for the advancement 
 of physical astronomy, which is denominated the 
 Adams Prize.* 
 
 Principal 
 inequality 
 of Uranus 
 and B^ep- 
 tune. 
 
 (148.) 
 Other 
 works of 
 MM. Adams 
 and Lever- 
 
 CHAPTER III. 
 
 ASTRONOMY. 
 
 § I MASKELYNE — Delambre. — Progress of Practical Astronomy from 1770 till 1810 — Of the 
 Lunar Theory deduced from Observation — The Density and Figure of the Globe. Cavendish ; 
 Baily. Trigonometrical, Surveys. 
 
 As examples of those astronomers who most contri- whether of the motions of the heavenly bodies or of 
 buted in the period of which we now principally speak the figure and density of our own planet, Ihave se- 
 l770-l8T(f (^'^'^^~^^^*^) *" *^® progress of exact observation, lected Maskelyne and Delambre. Their characters 
 
 (149.) 
 
 Practical 
 
 1 According to the calculations of M, Peirson {Comb. Trans, vol. ix.). 
 
 " It has been our business to condense the history of the discovery of Neptune within a compass proportioned to the general 
 scheme of this Dissertation. The reader who desires farther details will consult M. Leverrier's Memoir on the Perturbations of 
 the Herschel planet (Uranus) in the ComnaiisaMce dei Tempi for 1849 (also published separately), and in the Comptes Rendus for 
 1846 ; Mr Adams' papers in the Nautical Almanac for 1851, and the Astronomical Society's Memoirs, vol. xvi. ; Mr Airy 's singularly 
 curious and impartial Historical Account in the 7th vol. of the Astronomical Society's Monthly Notices ; M. von Lindenau's history 
 in Schumacher's Nackrichten (Erganzungsheft) (favourable to M. Leverrier) ; Grant's History of Physical Astronomy (advocating 
 principally the claims of Mr Adams). Sir J. Herschel 's Outlines of Astronomy contain a very valuable description of the scientific 
 part of the question. 
 
Chap. III., § 1.] 
 
 ASTRONOMY. — MASKELYNE — DELAMBRE. 
 
 35 
 
 were both distinguished by modesty, simplicity, and 
 love of truth. Of all their contemporaries of emi- 
 nence, few escaped so happily from the unprofitable 
 strife of rivalry and personal disputes, and none ex- 
 hibited a more impartial desire for the advancement 
 of the science to which they were devotedly attached. 
 Perhaps neither was a man of lofty talent, yet they 
 did not fail to secure deserved respect in their own 
 day, and far more gratitude from the posterity whom 
 they essentially benefited than falls commonly to 
 the share of men of higher pretensions in this re- 
 spect. Both their names are important links in the 
 history of astronomy. 
 (150.) Nevil Maskelyne, bom in 1732, and educated at 
 
 Maskelyne; Cambridge, was early attached to astronomical pur- 
 suits. After various minor services connected chiefly 
 with navigation and the discovery of the longitude, he 
 attained the honourable post of Astronomer Royal, 
 which he filled from 1765 till 1811 with distinguished 
 success. His immediate predecessor was Dr Bliss, who 
 held the office for but three years and without dis- 
 tinction. Practically, Maskelyne may be said to have 
 succeeded Bradley, probably the greatest astronomer 
 whom England has yet seen, whose discoveries have 
 been recorded in the last Dissertation, and whose 
 observations, through a variety of circumstances, were 
 destined rather for the benefit of the nineteenth cen- 
 tury than for his own. Maskelyne wisely recollected 
 that the observatory was mainly founded for the 
 improvement of navigation,^ and one of his earliest 
 labours was the establishment in 1767 of the "Nau- 
 tical Almanac," a work based on the best astronomi- 
 cal observations and of the highest service to seamen. 
 " During Maskelyne's long tenure of office he was 
 entirely devoted to its duties, making himself all the 
 most delicate observations, particularly those of the 
 moon, and rarely quitting the observatory except to 
 attend the meetings of the Royal Society. The per- 
 fect method and continuity of his observations give 
 to them a great value, especially for the correction 
 of the Lunar Tables, in which respect they are indeed 
 without a 'parallel. But the regularity of their 
 publication was not their least merit. Four large 
 folio volumes include the patient labours of a life 
 (for he had but one assistant). Delambre in his 
 character of Maskelyne says, that if through some 
 catastrophe the whole materials of science should be 
 lost, except these volumes, they would suffice to re- 
 construct entirely the edifice of modern astronomy ."^ 
 value of Jq fact, on Maskelyne's accession, the only methodi- 
 vations^rt ^^^ publication which had issued from Greenwich 
 Greenwich. Observatory was ithe " Historia Celestis" of Flain- 
 steed ; Halley's, Bradley's, and Bliss's observations 
 remained in manuscript. A like fate attended most 
 
 of the foreign astronomical observations ; labours 
 the most irksome and conscientious lie buried in 
 piles of MS. useless to science, and which therefore 
 might almost as well have never been made. This 
 is particularly the case with the Parisian observa- 
 tions (as the impartial Delambre records with pain), 
 commenced even before the time of Flamsteed ; but 
 which, owing to this cause principally, have remained 
 even to the present day (and it is forty years since 
 Delambre wrote his patriotic protest) without con- 
 tributing materially to advance astronomy. Let it 
 then be recorded to the honour of Maskelyne, that 
 this important step of regular and full publication 
 at the public expense was entirely due to him. His 
 places of the sun, moon, and planets, were the founda- 
 tion of the improved theories of physical astronomy, 
 then more ably cultivated on the Continent than in 
 Britain, and of the tables also chiefly furnished by 
 German and French computers. 
 
 Maskelyne's more important contributions to' (151.) 
 science may be briefly stated under these two heads ; 
 — The determination of the Lunar orbit from observa- 
 tion, and its application to navigation ; and the de- 
 termination of the local attraction of Schehallien and 
 of the density of the earth. 
 
 I. The determination of the Lunar Orbit from Ob- (152.) 
 servation and its application to Naviqation. — Though L""*'' ob- 
 astronomy owes (as we have already said) much to 
 Maskelyne in the exact determination of the places 
 of the sun, planets, and the most conspicuous fixed 
 stars, the comparison of the Lunar place with the 
 tables was by far the most arduous and the most im- 
 portant of his undertakings. It was the most ardu- 
 ous, because, from the extreme complexity of the 
 moon's motions, every part of its orbit must be nar- 
 rowly watched, requiring the astronomer's presence 
 at his instruments at all possible hours during the 
 course of a lunation, these motions being subject to 
 important changes which recur every nineteen years, 
 besides others of yet far longer duration. It was 
 Maskelyne's good fortune, and at the same time the 
 reward of his perseverance, to watch three revolu- 
 tions of the lunar nodes. He did not content him- 
 self, however, with making observations ; he contri- 
 buted in every possible way to the improvement of 
 the tables of the moon's motion. He was in con- 
 stant communication with Mayer, one of the ablest 
 astronomers of his day, and he directed the calcula-- 
 tion of Bradley's observations by Mason, for the far- 
 ther improvement of Mayer's Tables. Maskelyne's 
 own observations, to the number of at least 5000, 
 were used by Biirg in his excellent tables of the moon 
 which have even yet been hardly surpassed; but 
 their full value has only been tested recently by the 
 
 1 In the warrant appointing Flamsteed to be the Royal " Astronomical Observator," his duty is declared to be " to rectify the 
 tables of the motions of the heavens and the fixed stars, so as to find out the so much desired longitude at sea, for perfecting tha 
 art of navigation." 
 
 " From an article on Greenwich Observatory in the Edinhwrgh Review, written by the author of this Dissertation. 
 
 JP 
 
36 
 
 ASTEONOMT. — MASKELYNE — DELAMBRE. 
 
 [Diss. VI. 
 
 (153.) 
 The Jfau. 
 tical Alma- 
 nac. 
 
 (154.) 
 Attraction 
 of moun- 
 tains. 
 
 systematic reduction of all the lunar observations of 
 Maskelyne and Pond, and a comparison with Damoi- 
 seau's tables, under the direction of the present As- 
 tronomer Royal, Mr Airy. 
 
 But, for the application of the method of lunar 
 distances to navigation, farther aid than the con- 
 struction of good tables was required. This Maske- 
 lyne provided by obtaining the regular publication 
 of the Nautical Almanac, superintended by himself, 
 and containing the distances of the moon from the 
 principal fixed stars at predetermined hours for the 
 meridian of Greenwich, a comparison of which with 
 the distance observed by means of the sextant in any 
 part of the world enabled the seaman (after proper 
 reductions) to infer the exact Greenwich time of the 
 observation, and thence, by comparison with the local 
 time obtained by the usual methods, to obtain his 
 longitude. To this, long admitted to be the best 
 practical solution of the celebrated problem of " the 
 longitude at sea," Maskelyne contributed probably 
 more than any other person. His " Lunar Distances" 
 were reprinted in the French Almanac (Connaissance 
 des Terns) for a considerable number of years. 
 
 II. The determination of the Attraction of Sche- 
 hallien, and of the Earth's Density. — The deviation 
 of the plumb-line from the vertical by the neighbour- 
 hood of a mountain had been pointed out by Newton^ 
 as a direct consequence, and also as a test, of the 
 principle that gravity resides in every part of the 
 earth as well as in the earth as a whole. Bouguer 
 had the merit of pointing out the form in which the 
 experiment might be made, and of making the trial, 
 though in a rude and insufficient manner, in the 
 Peruvian Andes in 1738. He observed the effect of 
 the mountain on the south side only, but at two sta- 
 tions unequally distant from its centre of attraction. 
 The numerical result being (as the author himself 
 admitted) without value, Maskelyne proposed to the 
 Royal Society in 1772 to repeat the observation on 
 some British mountain. A " Committee of Attrac- 
 tion" was named, which, besides Maskelyne, included 
 Cavendish, Franklin, and Horslfey. Cavendish, as 
 might have been expected, took an earnest part in it. 
 The search for a suitable hill was confided to Mr 
 Charles Mason in 1773. Skiddaw and the York- 
 shire Hills were first thought of, but finally Sche- 
 hallien in Perthshire was preferred.^ Thither Mas- 
 kelyne himself proceeded in 1774, with his assistant 
 Burrows, and by these two, with the aid of a local 
 land-surveyor, the labour of the astronomical and 
 
 chief geodetical operations, including the measure- 
 ment of two base lines, was effected between the 30th 
 June and the 24th October, notwithstanding the 
 hindrances of a most unfavourable season. 
 
 The distance between the two stations obtained with (155.) 
 Eamsden's 9-inch theodolite, was 4364-4 feet, which Maske- 
 in the latitude of Schehallien corresponds to 42"-94 servation's 
 of latitude. The observed difference of latitude by at Sohehal- 
 337 observations with Sisson's 10-feet zenith sector lien, 
 was 54"-6.3 The excess, or U"-6, is the double at- 
 traction of the hUl drawing the plumb-line towards 
 itself at the two stations. The sine of this angle, or 
 rri'Sft represents the actual ratio between the double 
 attraction of the hill and the attraction of the earth. 
 But by the computation of the attraction which the 
 hill ought to exert, from its figure, as determined by 
 Maskelyne's gauges, were its density the same as that 
 of the globe generally, this ratio should amount to 
 ■^^■g-g, which can only be accounted for by assuming 
 the earth to be denser on the average than the hill 
 of Schehallien in the proportion of 17804 to 9933. 
 This deduction was made by Dr Hutton by means of 
 a troublesome calculation of the summation of the 
 attractive effects of a number of vertical prisms into 
 which the hill was imagined to be divided. The arti- 
 fices of calculation were, however, due to Cavendish 
 (who it will be recollected was on the " Committee of 
 Attractions,") as Mr Airy ascertained from his manu- 
 scripts. A careful lithological survey of the hill Earth's 
 enabled Professor Playfair to deduce the probable ^^^*y ^^ 
 mean specific gravity of the globe to be between 4-56 
 and 4'87, which was somewhat greater than Dr 
 Hutton assumed it. 
 
 This is the proper place to mention an experiment (156.) 
 on the density of the Earth perhaps still more re- Michell 
 markable, devised by the Rev. Mr Michell, who con- ^^^Caven- 
 structed the apparatus, but first put m practice by riment for 
 Mr Cavendish in 1797-8. It consisted in measuring the same 
 the force of gravitation between two spheres of such ®'"^' 
 small size that they could be moved by the hand 
 nearer to or farther from one another. The essen- 
 tial part of the invention was to contrive a balance 
 so delicate as to measure the almost inappreciable 
 tendency of such small bodies to unite. Newton had 
 shown that the attraction at the surface of any sphere 
 is directly as its radius, which he observed must 
 always be incomparably smaller than their tendency 
 towards the earth, that is, their weight. In the 
 largest and heaviest masses with which it has hither- 
 to been found practicable to operate, this tendency 
 
 1 De Mundi Systemate, § 22. Newton, in a very remarkable passage of the Third Book of the Principia (Prop. X.), con- 
 jectures that " the quantity of matter in the earth may be five or six times greater than if the whole were composed of water." 
 
 ^ A laughable mistake of Zach in his account of the Schehallien experiment ftn his Attraction dea Montagues) is commented 
 on by Playfair in the Edinburgh Review. In a note to the word Schehallien, Zach says, " Montague appelee dans le pays en 
 langue Erse Maiden pap, qui veut dire orage perpetuel." It is needless to add that these two alleged synonyms are different in- 
 terpretations given by Gaelic scholars of the word. " From this inaccuracy," adds his reviewer, " his residence in London 
 ought to have delivered him, for though he could not learn there what was Erse, he might have learned what was English." 
 
 ^ Zach obtained the same result exactly by including all the observations, as Maskelyne had provisionally obtained by using 
 only those stars on which he most depended. 
 
Chap. III., § 1.] 
 
 ASTRONOMY. — MASKELYNE — DELAMBRE. 
 
 37 
 
 amounts to only a very minute fraction of a grain. 
 
 How could such quantities be accurately estimated, so 
 
 as not only to leave no doubt of the phenomenon of 
 
 gravity thus acting on the small scale, but to deduce 
 
 its amount, and hence to weigh the globe % 
 
 »,, ^^^ "^ Michell imaginedfor this purpose the balance of tor- 
 
 The Torsion • i ■ i • ^ n u ^ i , / , , , , 
 
 Balance. «o«. which was re-mvented by Coulomb (who probably 
 
 first executed it) for the purpose of measuring electrical 
 forces. Michell's apparatus came first into the hands 
 of WoUaston.then of Cavendish, who made the experi- 
 ment. He used a very light rod of deal, six feet long, 
 suspended by a fine silver or copper wire, forty inches 
 long, within a wooden case to defend it from currents 
 of air. At each end of the lever was hung a ball of 
 lead, two inches in diameter, and by a simple con- 
 trivance a pair of leaden spheres, weighing, together, 
 348 pounds, could be brought simultaneously into 
 the neighbourhood of the balls (but outside the case), 
 on opposite sides, so that their attractions might con- 
 cur to swing the suspended lever out of the position 
 of repose which it had previously taken up, under 
 the action of the slight twisting force of the silver 
 wire. A new position of rest was thus established, 
 the small balls being pulled as much one way by the 
 attraction of the spheres as they were urged in the 
 opposite direction by the torsion of the wire. The 
 position of repose being observed from a distance by 
 a telescope (to avoid disturbance from the heat of 
 the observer's body), the great spheres were then 
 changed in position so as to act upon the opposite 
 sides of the small balls, from what they formerly did. 
 The deflection and new stable position would be as 
 much on the other side of the zero, and the arc de- 
 scribed would be an accurate measure of the double 
 deflection. The force of torsion for 1° of deflection 
 is known by the time of oscillation of the lever 
 and balls when free, and as the forces are exactly as 
 the angles, the force corresponding to any displace- 
 ment becomes known. Cavendish conducted the ex- 
 periment with his usual patience, judgment, and suc- 
 cess ; he found the joint attraction of the small balls 
 and large spheres to be about ^^Vxr "^ ^ gr^H) their 
 centres being 8-85 inches apart, and he thence com- 
 Result. puted the density of the Earth to be 5-48 times that 
 of water. Cavendish's paper is as usual a model of 
 precision, lucidity, and conciseness. The attraction 
 of the fixed parts of the apparatus is calculated and 
 allowed for. 
 (158.) It would-be diflBcult to mention in the whole range 
 
 Baiiy's re- of physics a more beautiful and more important ex- 
 "^'' periment. It has been repeated since by Reich of 
 
 Freiberg and Baily of London. The former obtained 
 5-44, the latter 5-66 for the Earth's specific gravity; 
 
 this last result being worthy of much confidence from 
 the extraordinary care taken to avoid errors and to 
 obtain independent values of the quantities sought.^ 
 
 Maskelyne continued his zeal for the promotion of 
 astronomy to the last. He superintended the publi- 
 cation of 45 annual volumes of the Nautical Alma- 
 nac. He left the whole of the observatory work in 
 perfect order, and the greater part printed. He had 
 the well-earned satisfaction of finding his observa- 
 tions in request in every civilized country, the bases 
 of the most useful tables, and the tests of the most 
 advanced theories. He cultivated the friendly cor- 
 respondence of astronomers in every country. Not 
 given to change, he preserved the instruments and 
 chief methods of the immortal Bradley ; but suffi- 
 ciently alive to the necessity of progress in the 
 sciences, he introduced many simple but practical im- 
 provements in the art of observation. Even in his 
 last years, satisfied that the celebrated quadrant of 
 Bird was no longer the best instrument for its pur- 
 pose, and was besides sensibly deteriorated by use, 
 he adopted the circle instead (then recently come into 
 notice, though first used more than a century before 
 by Rijmer), and directed the construction of that by 
 Troughton, though it was not placed at Greenwich 
 until after his death, which occurred in 1811, in the 
 79 th year of his age. His biographer Delambre 
 mentions, that a considerable number of his posthu- 
 mous memoirs were put into the hands of Professor 
 Vince for publication. They have not, however, ap- 
 peared. 
 
 Practical astronomy was on the Continent far be- 
 hind its state in England at the period of which we 
 speak. The various national observatories contri- 
 buted comparatively little to the progress of science ; 
 but there were of course exceptions, a few of which 
 we will here briefly notice. 
 
 The discovery of the four small planets^ Ceres, 
 Pallas, Juno, and Vesta, the first by Piazzi, the second 
 and fourth by Olbers, the third by Harding, gave cele- 
 brity to those astronomers, of whomPiazzi and Olbers 
 were farther distinguished by many important labours. 
 To the latter we owe the discovery of several comets, 
 and one of the best methods of calculating their or- 
 bits from observation. He was a person of much 
 simplicity of manner, made his observations with the 
 most unpretending means in the attic of his house, 
 and died at a great age generally respected. His 
 firmest friend was Baron von Zach, who had no slight 
 share in the discovery of the new planets, owing to 
 his having instigated the association of twenty-four 
 astronomers, chiefly in Germany, for the express pur- 
 
 (169.) 
 Maske- 
 lyne's im- 
 provements 
 at Green- 
 wich. 
 
 (160.) 
 Its superi- 
 ority to 
 Continent- 
 al observa- 
 tories at 
 that time. 
 
 (161.) 
 Astronomy 
 on the Con« 
 tinent. 
 Olbers — 
 Piazzi. 
 
 1' The experiments of Cavendish are related in the " Philosophical Transactions" for 1798 ; those of Reich in a separate small 
 work, entitled " Versuche Uher die mittlere Dichtigkeit der Erde," Freiberg, 1838 ; those of Baily in the " Memoirs of the 
 Astronomical Society," vol, xiv. A still more recent series of experiments by Reich gives 5'58, a close approximation to Baiiy's 
 result. — (PMl. Mag. March 1853.) From observations with a pendulum in Harton coal-pit in 1854, Mr Airy has obtained a 
 density higher than any of the above. 
 
 " In the Fifth Dissertation, page 789, Harding instead of Olbers is named as the discoverer of Vesta. 
 
38 
 
 ASTBONOMY. — MASKELYNE — DELAMBRE. 
 
 [Diss, VI. 
 
 (162.) 
 ]Jala,nde. 
 
 (163.) 
 French arc 
 of the me- 
 ridian. 
 
 (164.) 
 Delambre 
 his charac- 
 ter and 
 talents. 
 
 pose of ascertaining whether no planetary body filled 
 the void between Mars and Jupiter. To Piazzi, of 
 Palermo, we owe a most excellent catalogue of fixed 
 stars from observations with a moveable circle of 
 four feet radius by Eamsden. Oriani of Milan was 
 likewise one of the best informed practical astrono- 
 mers of his time. 
 
 In France, after the death of the celebrated La- 
 caille, perhaps Lalande (who was exactly Maskelyne's 
 contemporary) was the most active astronomer. To 
 him and his nephew we owe a very valuable catalogue 
 of 50,000 stars, lately edited by the British Associa- 
 tion. But practical astronomy was seriously neglect- 
 ed in France generally. The national observatory 
 was feebly superintended by the later members of 
 the Cassini family ; of the French expedition under 
 Maupertuis to measure the length of a degree in Lap- 
 land, the Abbe Outhier alone, it is said, knew how 
 to use a quadrant, and the celebrated Lagrange was 
 as ill informed until instructed by Lalande.^ 
 
 But the most important labours of the French 
 astronomers at the close of the last, and at the com- 
 mencement of the present century, were in carrying 
 out the measurement of the arc of the meridian from 
 Dunkirk to the Balearic Isles, with the more imme- 
 diate object of fixing the length of the metre, but con- 
 tributing to the solution of far more considerable pro- 
 blems connected with the figure of the earth. We 
 connect this labour with the respectable name of De- 
 lambre, who was more intimately associated with it 
 than perhaps any other person, though united with 
 such eminent men as Mechain, Biot, and Arago. 
 
 Delambre was the pupil of Lalande, who used to 
 say that his disciple was his best work. He first ob- 
 tained distinction as a computer of tables. Those of 
 the motions of the Sun, Jupiter, Saturn, and Uranus, 
 and of the satellites of Jupiter were deservedly 
 prized, and some of them are still the best of their 
 class. He was a man in whom the love of truth and 
 accuracy was conspicuous. Learned and patient, he 
 spared no pains in acquiring knowledge, and in using 
 it to the best purpose. As a calculator he was emi- 
 nent. Physical astronomy he did not cultivate, ex- 
 cept with a view to compare its deductions with facts. 
 He was intimately conversant with all properly as- 
 tronomical methods and formulae. He knew the his- 
 tory of every problem, and the details and modifica- 
 tions of every astronomical instrument. He has 
 embodied the results of this vast industry in a series 
 of works (forming six quarto volumes) on the his- 
 tory of his favourite science, which are without a 
 parallel for fulness and impartiality. He laboured 
 as conscientiously to ascribe the due credit to Hip- 
 parchus and Ptolemy as to hold an equal scale be- 
 tween the merits of French and British astronomers. 
 
 His critical knowledge of the ancient languages (for 
 he could speak Greek with fluency) was not more re- 
 markable than his complete freedom from national 
 prejudices. Both attributes qualified him pre-emi- 
 nently for the office of an historian. He published 
 also a large treatise on astronomy, and numerous 
 memoirs on practical subjects in the Connaissance 
 des Terns between 1788 and 1817. 
 
 Of his original labours the measurement of the ^P^^'^ , 
 FrenchArcof the meridian,of which he has givenafuU the French 
 account in his Base du Systeme Metrique Decimal, is Arc. 
 the most important. As some account of this un- 
 dertaking has been given in Sir John Leslie's Dis- 
 sertation, I shall state concisely a few particulars not 
 there mentioned. Not the least singular feature of 
 this gigantic work was the political crisis under 
 which it was conducted. So early as August 1790, 
 the French Constituent Assembly, on the motion of 
 Talleyrand, desired the king to write to the English 
 government, to represent the advantage of the two 
 nations uniting, to adopt a common unit or standard 
 of weight and measure, which it was proposed should 
 be done by a joint committee of the Royal Society 
 and the French Academy,^ This application was 
 probably never made, at least nothing came of it ; 
 but the Academy named their own committee, who, 
 after discussing three sorts of natural standards, — 
 the length of the pendulum in lat, 45° (first proposed 
 by Huygens in his Horologium Oscillatorium), the 
 length of a quadrant of the equator, and that 
 of a quadrant of the meridian from the equator to the 
 pole assumed to be elliptic, — adopted the latter, 
 and this labour was committed to MIchain for the 
 southern part, from Rodez to Barcelona (170,000 
 toises), and to Delambre for the northern, from 
 Rodez to Dunku:k (380,000 toises). The southern 
 arc was afterwards extended to Formentera in the 
 Balearic Isles, and the whole length of the arc was 
 found astronomically to be 12° 22' 12"-6. Two bases 
 were measured (both by Delambre), one at Perpignan 
 of 6006 toises, the other at Melun of 6076 toises 
 (each about 7'3 miles). When the length of the for- 
 mer was computed by triangulation from the latter, 
 the difference of the observed and inferred amount is 
 said to have been only ten or eleven inches. 
 
 But difficulties greater than physical obstacles pre- 
 sented themselves to the completion of this vast work. 
 The excited state of the public mind during the most 
 frenzied period of the French Revolution rendered 
 the simplest operations matters of suspicion. The 
 nearer to Paris that the survey was carried on, the 
 greater were the precautions necessary. Instruments 
 were seized, assistants arrested, and night signals had 
 to be totally dispensed with. " The coolness and in- 
 trepidity of Delambre, added to unexampled patience, 
 
 (166.) 
 Its difficul- 
 ties. 
 
 1 Both anecdotes are told by Moll, who had them from Delambre. 
 
 2 The two governments and their respective learned societies had already co-operated in 1784 for a survey to connect 
 Paris and Greenwich Observatories. 
 
Chap. III., § 1.] 
 
 ASTRONOMY . — MASKELYNE— DELAMBRE . 
 
 39 
 
 MSchain, 
 Biot, and 
 Arago. 
 
 (167.) 
 English 
 Arc. 
 
 ■were the principal means of extricating him from his 
 difficulties : but his danger was often imminent, and 
 he appears to have sometimes heard the dreadful words 
 which, as an eloquent author has expressed it, were 
 the last sounds that vibrated in the ear of many an 
 unhappy victim." The operations were actually sus- 
 pended for a time by a decree of Robespierre and his 
 colleagues, who deposedDelambre,alongwithLaplace, 
 Lavoisier, Borda, and others, from the Commission 
 of Weights and Measures, as being deficient in " re- 
 publican virtues and their hatred of kings." They 
 were, however, resumed, and Delambre had finished 
 his share of the work long before his colleague M6- 
 chain, whose shorter task was conducted amidst a 
 people rude and uneducated, indeed, yet far more to 
 be trusted than were then those of the north. Me- 
 chain was apparently wayward and impracticable, 
 somewhat too aged for so great a work, yet a really 
 good astronomer. The want of agreement to within 
 3" of two sets of observations for latitude atBarcelona, 
 the southern end of the arc at that time, led him to 
 the suppression of one of them, and he was tormented 
 ever after by the consciousness of the evasion, which 
 deprived him of the tranquillity necessary to resume 
 and complete his work, which was done chiefly by 
 Delambre after vexatious delays.^ The error, which 
 may be said to have cost Mechain his life, was pro- 
 bably owing to the instrument employed on this sur- 
 vey, the repeating circle of Borda, only fourteen 
 inches diameter, with a rather weak telescope. The 
 opinion generally entertained in Britain is, that the 
 repeating circle was quite inadequate to the prodi- 
 gious accuracy required of it, especially in the deter- 
 mination of latitudes. The errors of mere division 
 are often trivial compared to those inherent in other 
 parts of an instrument. Of these a deficiency of op- 
 tical power, and the want of absolute security of the 
 clamps, upon which the entire success of the princi- 
 ple of repetition depends, are amongst the most ob- 
 vious. The arc was finally prolonged from Barcelona 
 to Formentera by Biot and Arago in 1806. The 
 conclusion of the survey was not destitute of the ad- 
 venturous character of its commencement. The 
 French astronomers ran many risks, underwent much 
 suffering, and Arago narrowly escaped finishing his 
 days in the dungeons of Spain. 
 
 The English survey carried on by Roy and Mudge 
 has been also noticed in the previous Dissertation, 
 The arc from Dunnose to Burleigh Moor amounts 
 to 3° 57' 13"-1, the measured length to 1442953 
 feet. An arc of parallel was also measured from 
 Dover to Falmouth. We shall say something of its 
 later progress in the concluding part of this essay, 
 but we have still to regret the postponed publication 
 of the British Arc of the Meridian, which we have 
 no reason to doubt will bear a favourable compari- 
 son with the work of Delambre. The practical 
 
 appliances, the three-feet theodolite of Ramsden for 
 horizontal angles, and the eight-feet zenith sector 
 of the same artist for latitudes, were unequalled in- 
 struments, and contrasted in almost every respect 
 with the light and portable apparatus of the French. 
 By means of the former the spherical excess of terres- 
 trial triangles was first observed as a fact. The 
 results of the French and British arcs taken sepa- 
 rately concurred in showing a local curvature in this 
 part of the world altogether anomalous, the de- 
 grees rather shortening in the northern part of each 
 arc. This fact, which must be imputed either to 
 large local attractions, giving errors of several seconds 
 in the determination of latitudes, or (less probably) 
 to a local departure in our quarter ofthe world from 
 the general or mean figure of the earth, sufficiently 
 shows the futility of the proposed method of deter- 
 mining a natural, recoverable standard of length. 
 When combined with the measures of Bouguer in 
 South America and Lambton in India, and the revised 
 arc (measured in the beginning of this century) of 
 Svanberg and Melanderhjelm in Lapland, the French 
 and English measures give a general ellipticity some- 
 what under ^^,, which is probably as near the truth 
 as local inequalities admit of the determination being 
 made. 
 
 To Delambre was confided the drawing up of the 
 trigonometric formulee used in the calculations of the 
 survey, which were published in a separate work ; 
 De Prony conducting the laborious calculation of an 
 altogether new set of logarithmic tables, with the 
 aid of an immense staff of computers, the results of 
 whose labour (still in MS.) are preserved at Paris in 
 17 folio volumes. Delambre carried his personal 
 exertions so far as to compute his own triangles — 
 which were also independently calculated by Le- 
 gendre. Van Swinden, and Tralles. 
 
 As an acknowledgment of his merit, the highest 
 indeed in their power to bestow, the Institute of 
 France decreed to him in 1810 one of the Decennial 
 Prizes instituted by Napoleon. But the Emperor, 
 though professing to be the warm encourager of 
 science, suffered some meaner motive to interfere, 
 and refused to ratify the decision. " Ce fut," writes 
 Dupin, " un pas dans lal route qui le menait k sa 
 chfite." After the siege of Paris in 1814 Delambre 
 wrote a characteristic letter to his friend Moll. The 
 tranquil spirit which had braved the horrors of the Re- 
 volution was not to be moved by the sounds of the 
 artillery of the allied armies. In spite of the can- 
 nonade which he heard from his library, he laboured 
 from eight in the morning until midnight ; and, con- 
 scious of rectitude, he feared little the revolution of 
 circumstances, which changing dynasties might call 
 forth. " Labour," he says, " occupies all my time 
 and all my faculties." 
 
 As Secretary to the Academy of Sciences for the 
 
 French 
 trigono- 
 metric for- 
 mulae and 
 tables. 
 
 (169.) 
 Prize 
 
 awarded to 
 Delambre. 
 
 (170.) 
 
 1 The history is minutely given by Delambre himself in his Biography of M6ohain. — Astron. du XVIII. Siecle. 
 
40 
 
 ASTRONOMY. — SIE WILLIAM HERSCHEL. 
 
 [Diss. VI. 
 
 His impar- Mathematical Sciences, lie had to malce frequent re- 
 ''.*^'*y~ ports on the progress of those progressive branches 
 of knowledge, and to contribute memoirs of the most 
 eminent academicians, both native and foreign. Both 
 these duties he executed with his customary labour 
 and fidelity. His private character was as amiable 
 as his public career was distinguished. The tendency 
 of his writings was constantly to enforce the histori- 
 
 cal credibility of the Scriptures, especially with regard 
 to the most ancient astronomical records. The value 
 of his testimony is increased by his unusual skill in 
 philology. He died 19th August 1822, aged 73. _ 
 We reserve some farther remarks on the geodetic 
 results of this period, and especially on the pendulum 
 observations with which they were accompanied, for 
 the fourth section of this chapter. 
 
 (171.) 
 
 § 2. SlE William Hbrschel. — History of Siderecul and Telescopic Astronomy to- 1820. Her- 
 scJiel as an Optician. — Planet Uranus — Solar Spots — OrUts of Double Stars — NebulcB — The 
 Milhy Way — Sun's Motion in Space. 
 
 (172.) 
 Sir Wm. 
 Herscliel ; 
 
 (173.) 
 his exten- 
 sive works; 
 
 (174.) 
 early his- 
 tory. 
 
 The eighteenth century was not, generally speak- 
 ing, distinguished by original observations. The ex- 
 ceptions stand out with all the brighter lustre. 
 Amongst these, the discoveries of Sir William Her- 
 schel occupy perhaps the foremost place. Arago has 
 affirmed that Slough is the spot on the earth's sur- 
 face signalized by the most numerous discoveries, 
 and in a certain sense this is strictly true. No one, 
 before or since (with possibly the exception of Mr 
 Hind) has added so many new bodies to the known 
 planetary system, and this at a time when such 
 discoveries were rarer, more unexpected, and more 
 difficult than now. His researches on the fixed 
 stars are not of a nature to have their importance 
 numerically estimated. 
 
 Sir William Herschel's career was one of the 
 longest and of the most sustained labour in the history 
 of science. To have contributed papers — often several 
 in one year — to the Philosophical Transactions for 
 thirty-nine consecutive years, from 1780 to 1818, 
 with but two exceptions, is a feat of astonishing per- 
 severance ; but if we recollect that many of these 
 papers contain announcements of capital discoveries, 
 that every one of them is stored with original matter, 
 and that the author had already passed his fortieth 
 year when he commenced the production of this as- 
 tronomical library, we cannot withhold a tribute of 
 the warmest admiration, 
 
 England cannot claim Herschel as her own, except 
 by adoption. He was bom at Hanover in 1738, and 
 was one of a numerous family who supported them- 
 selves chiefly by their musical talents. William 
 Herschel, the third son, came to England in 1759 
 with his elder brother, and after struggling with many 
 difficulties, found himself in comparatively comfort- 
 able circumstances as an organist at Bath. In 1774 
 he had executed a reflecting telescope with his own 
 hands, and soon acquired so much dexterity as to 
 construct instruments of ten and twenty feet in focal 
 
 length. In 1780 he contributed his first paper on 
 the variable star in Cetus to the Royal Society, and 
 the following year (13th March 1781) discovered the 
 erratic body, which he at first took for a comet, but 
 which proved to be a planet exterior to Saturn ; the 
 first addition therefore to the number of the primary 
 planets since a period of an immemorial antiquity. 
 So fortunate a success made the name of Herschel 
 speedily famous, and he was effectively befriended by 
 (Jeorge III., who brought him to live near Windsor, 
 and gave him a pension.^ 
 
 Prom this brief sketch it will appear how great 
 were the obstacles which Herschel had to vanquish 
 before he became a man of science, and that, besides 
 the claims to distinction already enumerated, his 
 knowledge and his skill were acquired in spite of 
 every disadvantage. 
 
 Practical Astronomy naturally divides itself into 
 two great branches, that which depends upon the 
 use of the telescope merely ; on the telescope and 
 micrometer ; and that which determines the absolute 
 places of the heavenly bodies, and requires the aids 
 of divided instruments and a well furnished obser- 
 vatory. In the century to which he belonged Her- 
 schel is the type of the telescopic observer, Bradley 
 of the instrumental. The discoveries of Aberra- 
 tion and of Nutation by the latter may stand a com- 
 parison with any in the 'history of science, but the 
 resolution of Nebulae and the proof of the mutual 
 connection of stars in binary systems are not less 
 distinguished and original. Herschel would have 
 gained a great reputation as an optician, merely by 
 the wonderful improvement which he effected in the 
 dimensions and magnifying power of telescopes, and 
 by the skill with which he applied them to celestial 
 observations. He would have stood still higher as 
 an astronomer had he been merely the first observer 
 of a new planet and of eight secondary ones, as well 
 as of several comets, and the author of many nice 
 
 (175.) 
 
 (176.) 
 Dlvisioh of 
 Practical 
 Astronomy 
 into Tele- 
 scoplcand 
 Instru- 
 mental. 
 
 1 It may be doubted whether any other similar annuity was given at that period on scientific grounds alone, and it is difficult 
 to estimate the amount of benefit thus conferred on astronomy, for nothing short of the entire devotion of a lifetime could have 
 produced such results as we owe to Herschel. His proposal to name his planet after the Sovereign was a very natural expression 
 of his gratitude at a period when no rule whatever existed on the subject. See an interesting letter from Herschel to Sir 
 Joseph Banks (who was also a warm friend) in Weld's History of the Royal Society, ii. 146, note. Herschel was elected into the 
 Koyal Society 6th Dec. 1781. 
 
Chap. III., § 2.] 
 
 ASTRONOMY. — SIR WILLIAM HERSCHEL. 
 
 41 
 
 (177.) 
 
 (178.) 
 Herschel as 
 an optician. 
 
 (179.) 
 Magnify- 
 ing and il- 
 luminating 
 power of 
 telescopes. 
 
 <)bservations on the physical appearance and con- 
 stitution of the sun and planets ; but his great glory, 
 was in sidereal astronomy, of which he laid almost 
 the foundations, by means of discoveries which he 
 fortunately lived long enough to see confirmed and 
 enlarged beyond his reasonable hopes. 
 
 In this brief sketch of Herschel's achievements 
 (which in his own department may be said to embrace 
 those of his age, for he had hardly an imitator, and cer- 
 tainly no rival) we shall, in the first place, condense 
 into small compass what is to be said on the two 
 former heads — his merit as an optician and as a 
 planetary observer. 
 
 To construct good telescopes is itself no easy art, 
 especially if they are to be carried to a size and per- 
 fection previously unattained. To ascertain the best 
 composition, whether of glass or metal, to melt and 
 to cast it in the right way, is one branch of the art 
 which may be called generally the chemical part. To 
 fashion the lens or mirror correctly by grinding, and 
 to fit it for optical use by giving it an exquisite polish, 
 is a second step requiring a peculiar mechanical skill 
 and perseverance. To mount the telescope eflfec- 
 tively is another and entirely different problem in 
 mechanics ; and all these the amateur astronomer 
 must be prepared to accomplish with his own hands, 
 unless he command the services of practical opticians 
 to an extent rarely to be bought. Amateurs have 
 indeed seldom succeeded except with reflecting in- 
 struments, and Herschel acted very wisely in devot- 
 ing himself to their improvement at a time when the 
 success of DoUond with achromatic telescopes had 
 rendered the Newtonian form unfashionable. The 
 real secret of Herschel's success was his astonishing 
 perseverance ; his determination was to obtain tele- 
 scopes of twenty feet focal length or more, and of a 
 perfection equal or superior to that of the small ones 
 then in use. He himself relates, that whilst at Bath 
 he had constructed 200 specula of seven feet focus, 
 1 -50 of ten feet, and about 80 of twenty feet ; a proof 
 of extraordinary resolution in a man of limited means 
 and engaged in a laborious profession. By making 
 so great a number he could select those having 
 the most perfect figure, especially before he had con- 
 trived a method of obtaining mechanically a para- 
 bolic form, almost with certainty. This method was 
 not divulged. He was justified in keeping his secret, 
 whilst he made a handsome income from the manu- 
 facture of telescopes for sale. Lord Rosse and Mr 
 Lassell have had the merit of publishing their 
 methods, which by their results would appear to be 
 at least equal to Herschel's. 
 
 The usefulness of telescopes depends on two dis- 
 tinct qualities — magnifying power and illuminating 
 power. The former may be gained indefinitely by 
 
 diminishing the focal distance of the eye-glass ; the 
 latter can be had only by increasing the diameter of 
 the object-glass or speculum, so as to collect the rays 
 which fall upon a circle of large diameter from every 
 point of the object examined. But in order that 
 the whole light may be efiective, the magnifying 
 power of the eye-glass must be sufficient to condense 
 the emergent pencil within the diameter of the pupil 
 of the eye. The proportion in which these two 
 qualifications are requisite to obtain the best results 
 in astronomy is a matter involving nice questions 
 both of theory and practice. Sir William Herschel 
 did more than any one who preceded or fol- 
 lowed him to solve them. On the whole, the illu- 
 minating power is perhaps the most important, whilst 
 it is the most difficult of attainment ; but in truth 
 each class of telescopic objects have their own rule 
 in this respect. Brilliant objects, such as Venus, and 
 moderately bright stars, do not require large aper- 
 tures ; very feeble objects, as the remoter satellites 
 and the nebulae, require indispensably great illumina- 
 tion. Five satellites of Saturn were seen by Sir W. 
 Herschel in his great telescope by the naked eye alone, 
 that is, without the advantage of the magnifying 
 power of a lens. On the other hand, Sir John Her- 
 schel tells us that the satellites of Uranus cannot be 
 clearly made out without a magnifying power of at 
 least 300, whatever may he the aperture of the tele- 
 scoped 
 
 The mention of magnifying powers is calculated to (180.) 
 mislead rather than otherwise in comparing the efii- ^^agmfy- 
 cient means of different astronomers. The magnify- uaf d in 
 ing power used by Galileo did not exceed thirty-two Aetronomy. 
 times the diameter. Huygens, who used aerial tele- 
 scopes of immense length, pushed it to 163 times. 
 Auzout is said to have given a power of 500 to one 
 of these gigantic instruments of 300 feet in length ; 
 but it is easily understood that such achievements 
 were little more than nominal, the mechanical difl[i- 
 culty of managing these instruments being excessive. 
 Short professed to carry the magnifying powers of 
 his Gregorian reflectors to 1200,, but still they yielded 
 only trifling fruits to astronomy. It required that 
 such instruments should be made and used fami- 
 liarly, not as objects of luxury of which but one or two 
 were ever brought into actual use. Herschel applied 
 even to his seven-feet Newtonian (his favourite and 
 smallest working size, having 6'3 inches aperture) 
 powers exceeding 2000. To his largest instrument 
 (thirty-nine feet focus) was occasionally applied a 
 power of 6500. The highest powers usefully em- 
 ployed with the gigantic achromatics of Pulkowa and 
 of Cambridge (in America), do not exceed 1822 and 
 2004 times respectively. 
 
 The motion of the earth and the troubled state of (181.) 
 • Its limits. 
 
 ^ Struve found that witii a small telescope, magnifying three times, and having the same aperture with the pupil of the eye 
 (0-2 inch), he could count nearly twice as many stars (accurately 1-83 times) as with the naked eye. This result, interesting on 
 several accounts, deserves farther enquiry. — Etudes d'Astron. Stsllaire, p. 85 . 
 
42 
 
 ASTRONOMY. — SIR WILLIAM HERSCHEL. 
 
 [Diss. VL 
 
 the atmosphere, especially in these climates, impose 
 a speedy limit to the -increase of magnifying power, 
 unless in exceptional circumstances. The same ob- 
 jections do not apply to the increased aperture 
 and illuminating power of telescopes. This con- 
 sideration induced Herschel to construct his forty- 
 feet reflector, the funds being advanced by the king, 
 on the recommendation of the Royal Society. The 
 speculum had a useful surface precisely four feet in 
 diameter, the thickness three and a half inches, the 
 weight when cast above 2000 pounds. The second or 
 plane mirror having been dispensed with, the image 
 was thrown to one side of the object-end of the tube 
 by means of a very slight inclination of the speculum , 
 and was there observed directly by a common eye-piece 
 or single lens, the observer being thus stationed with 
 his back to the object he is viewing. This vast in- 
 strument collected a cone of rays from a distant point 
 between six and seven times larger than the twenty- 
 feet instrument commonly employed by Sir W. Her- 
 schel, of which the aperture was 18"8 inches. This 
 telescope was not frequently used, partly from the 
 rarity of sufficiently steady weather, and from the 
 difficulty of preserving the figure of the mirror under 
 changes of temperature.^ Its figure was also affected 
 by flexure under its own enormous weight, and it 
 has been found one of the greatest difficulties by those 
 who have followed Herschel's steps to avoid this 
 source of error. The forty-feet speculum has been 
 religiously preserved by the filial care of Sir John Her- 
 schel, in whose possession the writer of these pages 
 had the pleasure of seeing it, now many years since, 
 in a state of high polish. It remains in a deposit 
 hermetically closed, at Slough.* 
 (182.) Herschel made an ingenious determination of what 
 
 netratinff- ^® called the space-penetratingrpower of telescopes, by 
 power of which he discriminated the relative distances at which 
 telescopes, g, given fixed star would become invisible in his 
 several instruments. It was grounded on the as- 
 sumption that the visibility of the object depends, 
 first, on the density of its light reaching the eye, and 
 secondly, on the number of rays of that density 
 concentrated in the image. The former quantity 
 varies inversely as the square of the given distance, 
 the latter directly as the square of the aperture of 
 the telescope ; the limiting visible distance therefore 
 of the radiant body will be simply as the aperture. 
 To this he applied corrections depending on the loss 
 of light by reflection at the specula, and by trans- 
 mission through one or more eye-glasses. On this 
 scale the space-penetrating-power of the seven-feet 
 Newtonian being twenty, that of the twenty-feet tele- 
 scope (front view) was seventy-five, and the forty-feet 
 telescope 192. These estimations, as we shall see, 
 form an important step in Herschel's generalizations. 
 (183.) Of new bodies belonging to our system he dis- 
 
 covered Uranus and his six satellites, the two satel- 
 lites of Saturn next to the ring, and several comets. 
 He did not, so far as we know, even suspect the 
 planetary character of Uranus, which he believed to 
 be a comet. The honour of this appears to be due 
 partly to Saron- of Paris, partly to Lexell of St 
 Petersburg. Arago supposes that Laplace had 
 also a share, but the evidence on the whole matter 
 is somewhat obscure. Unquestionably it was an ex- 
 ceedingly difficult matter to fix upon a correct orbit 
 for a body moving with such extreme slowness within 
 the limits of the first few weeks after its discovery, 
 and its distance was far beyond what any one calcu- 
 lating a comet's path would readily assume. The 
 original discovery was also a fortunate one, for but 
 eleven days previously the planet was in a position 
 apparently stationary. It has led to results of still 
 higher interest by the prediction of the existence and 
 place of Neptune from the irregularities of Uranus. 
 The satellites move almost perpendicularly to the 
 ecliptic. Strange to say, they remained for, I be- 
 lieve, more than half a century, unseen by any eye but 
 that of their discoverer and his son : and two of them 
 still stand recorded on the single authority of Sir W. 
 Herschel. They are the least specks of light which 
 optical power has ever made visible. 
 
 Herschel made many observations on the physical 
 appearance of the sun, moon, and nearer planets, and 
 the times of their rotation. Into these details we 
 cannot now minutely enter. The papers which record 
 them are characterized (like all those of the same 
 author) by the faithful minuteness with which the ob- 
 servations are detailed,andbythemention of every in- 
 fluential circumstance by which the results might be 
 affected. In the case of observations so exceedingly 
 delicate as those of the planets, the astronomer has to 
 keep up an incessant struggle between the anxiety to 
 record all that he sees, and that of recording nothing 
 more than he really and perfectly sees. One or two 
 glimpses are not sufficient. Herschel at one time 
 imagined that the new planet had one or more rings 
 which unquestionably do not exist. His elaborate in- 
 vestigation of the figure, belts, and rings of Saturn, the 
 incredible tenuity of the latter, and the fact of their ro- 
 tation in lO'' 32", were amongst the most interesting 
 of his observations, and were illustrated by drawings 
 made with remarkable care. The edge of the ring was 
 seen in 1789, when it had totally disappeared in all 
 but his forty-feet telescope, and he estimated that its 
 thickness could not exceed 100 miles. How astonish- 
 ing the magnitude and thinness of this stupendous 
 circular plane, or rather series of flat rings ! Some 
 idea of it may be deduced from the fact that if the 
 thickness of the paper on which this is printed be 
 taken to represent that of the rings, their greatest 
 diameter would correspond to nine inches. Observa- 
 
 Herschel's 
 discovery 
 of TJranua 
 (or Georgi- 
 iim Sidue) ; 
 
 (184.) 
 observa- 
 tions on the 
 planets; 
 
 1 The Jim object viewed by Sir W. Herschel with his great telescope in 1789 was the nebula in Orion ; possibly it was also 
 the last, for he again observed it in 1811 (See Phil. Tr. 1811, p. 322). 
 '^ See Weld's History of the Royal Society, ii., 193. 
 
Chap. III., § 2.] 
 
 ASTRONOMY.— SIR WILLIAM HERSCHEL. 
 
 43 
 
 ass.) 
 
 on the Sun: 
 
 followed 
 Patrick 
 
 Wilson. 
 
 (186.) 
 Herschel'a 
 sidereal 
 discoveries, 
 
 tions on the other planets and on the moon we here 
 pass over for want of space. 
 
 I have reserved the observations on the nature of 
 the sun to this place, because everything leads us to 
 assimilate the nature of the sun and of the fixed stars. 
 The belief that the luminous disk of the sun is a photo- 
 sphere or luminous atmosphere of great tenuity sur- 
 rounding a globe of comparative density and dark- 
 ness, was long anterior to Herschel, and in fact due 
 to Dr Patrick Wilson of Glasgow, whose admirable 
 paper on this subject was published in the Philoso- 
 phical Transactions for 1774, in which he explains 
 the phenomena of the solar spots by apertures in the 
 luminous atmosphere, discovering the dark nucleus 
 below, and some shell or shells of intermediate 
 brightness which form the penumbra, l These con- 
 clusions were most clearly and ably deduced from a 
 careful observation of the changing aspect of the spots, 
 as they move by the solar rotation from the centre 
 to the edge of his disk. It is to be regretted that 
 Herschel does not more pointedly refer to the dis- 
 coveries of Wilson, which were more than twenty 
 years antecedent to his first paper on the subject, 
 and with which he could hardly fail to have been ac- 
 quainted. A similar remark applies, in a less degree, 
 to his papers generally, which rarely contain references 
 to the observations and speculations of his predeces- 
 sors. Herschel adopted Wilson's hypothesis almost 
 literally, and his long series of patient observations on 
 the sun, made with high powers and at an eminent risk 
 to his eyesight, enabled him to classify the singularly 
 varied appearances of that wonderful orb, and to 
 draw some probable conclusions from the excessive 
 rapidity and seeming tumult of the exterior portions 
 of it. That the photosphere is strictly gaseous he 
 rendered very probable, an inference confirmed by 
 the direct observations of Arago as to the un- 
 polarized character of its light. The singular dis- 
 closure of faint red prominences extending far beyond 
 the disk, and observed in the total eclipses of 1842 
 and 1851, shows that there is still much which re- 
 gards the mysterious nature of the sun within reach 
 of direct observation ; and the same may be observed 
 of the direct experiments lately made on the heat 
 and light of difierent parts of the disk, which diminish 
 to one-half between the centre and the edge, and 
 appear to attain a maximum at the solar equator. 
 
 A convenient, though not a strictly chronological 
 arrangement of Sir W. Herschel's more important 
 sidereal discoveries and speculations may be made 
 under the- following heads : — 
 
 I. Of double Stars and their mutual connection. 
 
 II. Of the Nature of Nebulae, and the so-called 
 Nebular Hypothesis. 
 
 III. Of the Grouping of the Stars generally in 
 space, and the significance of the Milky Way. 
 
 IV. Of the Motion of our System in space. 
 
 I. On Double Stars. Ducovery of Binary Sys- 
 tems. — Double stars were noticed as objects of curio- 
 sity even before the discovery of the telescope. The 
 group of the Pleiades attracted attention from the 
 earliest times. Amongst the earliest double stars 
 carefully observed were g Ursse Majoris (by Kirch, 
 1700) ; a Centauri in 1709 ; y Virginis and Castor 
 by Bradley (1718 and 1719) ; Mayer made a con- 
 siderable catalogue of double stars in 1756. But 
 Lambert first announced in 1761 (in his Lettres Cos- 
 mologiques) the probability of the mutual revolution 
 of suns, in these remarkable words (speaking of clus- 
 ters of stars), •' It will perhaps be decided whether 
 there are not fitxed stars which make their revolutions 
 in no long periods round their common centres of 
 gravity." Mitchell, in 1767 and 1784, maintained 
 the same views, but supported them by an applica- 
 tion of the then young science of probability, hazard- 
 ous in its principle, and unquestionably wrong in its 
 numerical solution.^ 
 
 Sir W. Herschel commenced his observations on 
 double stars with the hope of ascertaining the Annual 
 Parallax in the manner previously indicated by 
 Galileo and James Gregory ; but, as in many parallel 
 instances, whilst he failed of his main result, he dis- 
 covered unsought a phenomenon more unexpected 
 and probably more interesting. With the micro- 
 metrical means at his disposal, he entirely failed in 
 detecting any semi-annual fluctuation of the inter- 
 val between the members of the pair of stars, but 
 he found (in some instances) progressive and con- 
 tinually increasing changes both in the relative 
 position and distance of the two. He com- 
 menced his observations in 1779, but it was not 
 until 1802 that he thought himself entitled to an- 
 nounce with confidence his discovery of the circula- 
 tion of one sun round another, or rather of both 
 round their common centre of gravity. Herschel's 
 first list of orbital stars (Phil. Trans. 1803, where 
 this splendid discovery was first published*) includes 
 the chief examples now known ; and they have all 
 been confirmed. That of which the revolution is 
 most rapid is ^ Herculis, which has a period of 31J 
 years, and consequently has revolved twice round 
 since it was first observed, whilst the slow planet 
 Uranus has not yet returned to the position of its 
 first discovery. Herschel does not appear to have 
 received a medal or other public recognition of this 
 signal success. 
 
 Of the subsequent progress of this interesting in- 
 quiry we shall speak in the latter part of this chapter. 
 
 (187.) 
 DouWe 
 stars — or- 
 bital mo- 
 tion; 
 
 (188.) 
 failed to 
 discover 
 parallax. 
 
 (189.) 
 
 ^ Plamsteed appears to have entertained in 168 1 a somewhat similar opinion, as we find from a letter published (1855) in 
 Sir David Brewster's Life of Newton, vol. ii., p. 103. 
 
 * See art. (85) and note. 
 
 3 It was in fact distinctly though incidentally announced in his paper of 1802, though the proofs were given the following 
 year. See Phil. Trans. 1802. 
 
44 
 
 ASTKONOMY. — SIR WILLIAM HERSCHEL, 
 
 [Diss. VI. 
 
 (190.) 
 Nebulae. 
 
 (191.) 
 Classifica- 
 tion of ne- 
 bulae ; 
 
 (192.) 
 resolvable 
 and unre- 
 solvable. 
 
 Greaterprecision has beeninsomerespects attained, but 
 little, if anything, added to the theory :of double stars. 
 
 II. On NebulcB and the (so-called) Nebular Hy- 
 pothesis. — ^The cloudy patches of mild light which 
 are visible in clear but moonless nights in various 
 parts of the sky are called nebulse from their resem- 
 blance to light vapours moderately illuminated. 
 Some regions of the sky abound more with them than 
 others. The Milky Way presents to the naked eye 
 a nebulous appearance extending over large tracts, 
 and nebulae more or less dense are frequent within and 
 near its borders. These facts were well known from 
 an early period. Some conspicuous nebulje were 
 described in the sixteenth century ; that in Andro- 
 meda by Marius and the conspicuous nebula in 
 Orion by Huygens. Halley added several, but the 
 first descriptive catalogue of these objects was pub- 
 lished by Messier in 1783 (in the Connaissance des 
 Terns), and it forms the basis of the modern obser- 
 vations. 
 
 Sir W. Herschel took up the subject with his cus- 
 tomary zeal. In 1786 he published a catalogue of 
 1000 nebulae, which he had increased by 1802 to 
 2500. The first step to some appreciation of the 
 nature of these extraordinary appearances was of 
 course to classify them, and this. Herschel did with 
 such success that it may be affirmed that his classes 
 remain the best at the present time, as generally re- 
 presenting the phenomena. Without entering into 
 all his details, the following division embraces the 
 main facts : — 
 
 A. Clusters of stars. 
 
 B. Nebulae proper. , 
 a. Having a certain regularity, as 1 . Circular or 
 
 planetary nebulse ; 2. elliptic ; 3. annular. 
 )3. Wholly irregular, as the nebula of Orion, 
 the Magellanic clouds, &c. 
 
 C. Nebulous stars. 
 
 Remarks. A number of faint stars produces a 
 nebulous haze. This is a physiological fact. Parts 
 of the Milky Way which present this appearance to 
 the naked eye are at once shown by a telescope of 
 small power to be composed of stars. ^ Patches which 
 appear nebulous in such a telescope are shown by a 
 better one to be composed of small stars. This is 
 called the Resolution of a nebula. Such resolutions 
 become more and more numerous as the apertures of 
 telescopes are enlarged. Lord Rosse's telescope has 
 resolved severaL which withstood the highest power 
 of Herschel's. One inference might therefore be that 
 all nebulse are clustered stars, at a greater or less 
 distance. Such an opinion is very general, and very 
 plausible.' It may on the other hand be observed 
 that Herschel abandoned this his earlier inference, 
 
 whilst, at the same time, he proceeded diligently with 
 the resolution of successive nebulae, by means of his 
 powerful telescopes. He maintained on the contrary to 
 the last that nebulse belong to two classes, resolvable 
 and irresolvable. The latter he believed to be composed 
 of diffuse self-luminous matter, more or less con- 
 densed, whilst the milky light of the former is occa- 
 sioned by the blended gleam of numerous close stars. 
 With this difference, we find his views regarding the 
 changes in the sidereal system and the progress of 
 the condensation and breaking up of nebulse, nearly 
 the same in his earlier and later papers, particularly 
 those of 1785 and 1811. 
 
 The opinions of Herschel on these changes were 
 the following : — Having observed that the more 
 regular nebulae (whether with a central star or 
 not) presented almost invariably an appearance of 
 gradually increasing brilliancy towards its centre, 
 he was led to conclude that this is due to the aggre- 
 gation of the self-luminous parts in virtue of their 
 mutual gravitation; and the conclusion would so 
 far be the same, whether the parts thus coalescing 
 were in fact numerous distinct masses, or were like 
 a vapour diffused through space. This was the pro- 
 cess of condensation, which he inferred on the one 
 hand from the law of gravity, on the other from the 
 generally symmetrical arrangement of the luminous 
 matter in nebulae of the first class. In order to de- 
 tect, by actual observation, the progress of condensa^ 
 tion, he invented a simple and highly expressive 
 terminology, indicating the general brightness, the 
 amount of its gradation, and the law of its gradation 
 from the circumference towards the centre. In 
 whatever degree Lord Rosse's late observations may 
 be considered to deprive nebulae of the character of 
 symmetry which Herschel had conferred on them, 
 the general fact of an apparent condensation in a 
 great majority of instances cannot be denied. 
 
 The breaking up of nebulse (also described in his 
 paper of 1785, as well as in his later ones) is likewise 
 an inferred change anticipated in large irregular 
 nebulae, which usually exhibit bright spots or centres, 
 with irregular vacant spaces, which sometimes seem 
 like portions of a black and distant profundity seen 
 through the rents of a nebulous veil. Herschel sup- 
 poses that the luminous centres are also places of 
 greatest attraction, and must gradually draw away 
 the star-like substance from the rarer spaces. 
 
 It is curious that these speculations of Herschel 
 (which are substantially common to his papers of 
 1785 and 1811) had been at least imagined at a very 
 early period. Arago has pointed out that Tycho 
 and Kepler conceived the New Stars of 1572 and 
 1604 to have resulted from a sudden condensation 
 
 (193.) 
 Herschel 
 inferred 
 their pro- 
 gressive 
 condensa- 
 tion, 
 
 (194.) 
 and break- 
 ing up in 
 some cases. 
 
 (195.) 
 Early anti- 
 cipation of 
 this hypo- 
 thesis. 
 
 ^ The group of the Pleiades presents a peculiar instance. When the eye is turned full upon it, no more than six stars (as is 
 well known) can be counted, but when the eye is turned aside through 10° or 15°, by a peculiarity of indirect vision by means of 
 the lateral parts of the retina, the group appears a mass of nebulous light. This arises from an immense crowd of stars just 
 below visibility, which, probably from the greater sensitiveness of this part of the eye, make a sensible though somewhat Indis- 
 tinct impression. This observation as to the Pleiades, and the inference which explains by it the seeming countlessness of the 
 stars when viewed cursorily, were published by the present writer in Brewster's Journal for 1826. 
 
Chap. III., §2.] 
 
 ASTRONOMY. — SIR WILLIAM HERSCHEL. 
 
 45 
 
 (196.) 
 Herschel's 
 opinions 
 on the dis- 
 tance of 
 nebulae ; 
 
 (197.) 
 and their 
 changes of 
 form. 
 
 (198.) 
 Theory of 
 condensa- 
 tion. 
 
 of diffuse celestial matter, such as the Milky Way ex- 
 hibits, and Tycho alleged that the new star was sur- 
 rounded by an obscure space, half as large as the 
 moon's disk. The history of Science scarcely pre- 
 sents a more curious anticipation. 
 
 One practical difference between the earlier and 
 later views of Herschel on the nature of nebulse, was 
 as to their distance from our system. For if the milky 
 aspect be due to a confusion of small stars, it is 
 assumed that they must be almost incredibly distant. 
 In his memoir of 1785, he estimates this distance at 
 not less than 6000 or 8000 times that of Sirius. 
 If, on the other hand, the nebulous appearance be 
 due to a diffusion of starry matter, the distance may 
 be that of any order of fixed stars ; and this opinion 
 derives weight from the evident connection of some 
 nebulsB with stars round which they seem to cluster 
 or hang almost like a drapery. Thus in 1811 he 
 supposed that the nebula in Orion need not be more 
 distant than a star of the 7th or 8th magnitude. 
 
 It appears from his paper of 1802 (page 500), 
 that his ideas about nebulae were then wavering. Be- 
 tween that time and 1811 he elaborated the nebular 
 hypothesis, so far as it is due to him. He seems to 
 suppose that starry matter was once in a state of in- 
 definite diffusion. That during " an eternity of past 
 duration" (Ph. Tr., 1811, p. 287) it has been "break- 
 ing up" by condensation toward centres more or less 
 remote. That the Milky Way — or at least the nebu- 
 lous parts which it contained — and the dispersed ne- 
 bulse, are the relics of this former state of things. 
 That where condensation has gone on more energeti- 
 cally, we have nebulse with a gradually or rapidly 
 increasing brightness towards the centre; — if still 
 more energetic, a nucleus, or it may be a planetary 
 nebula ; — next a nebulous star, which he supposes 
 our sun to be, and the zodiacal light a relic of its 
 nebula (p. 311); — finally, the completely formed 
 stars may be assumed to be merely consolidated ne- 
 bulae. (See pp. 284, 285, 299, 310.) This conden- 
 sation, he believes, must be accompanied by rotation 
 due to the originally irregular distribution of the 
 gravitating particles (p. 312-319). 
 
 The proofs on which the whole of this cosmogony 
 rests are, \st, the gradation of appearances above 
 described, to be collected from distinct objects in the 
 heavens ; and, 'idly, supposed changes observed by 
 him in the nebula of Orion and others, during thirty 
 years, and even during intervals of a few years. As to 
 the last argument, it is admitted, we believe, by the 
 best authorities, to be without weight. The changes 
 of aspect of such curiously faint and graduated ob- 
 jects, even to the same eye using the same telescope, 
 are numberless, and may be due to the slightest at- 
 mospheric and physiological influences. This test 
 (as applied hitherto) is therefore generally rejected. 
 Against the first proof much might also be urged, for 
 
 '^ The most intelligible account of the nebular hypotheeis, in 
 Outlines ofAitronomy, Articles 870 to 872. 
 
 which we cannot afford space. Its idea is essentially 
 derived from the Natural History sciences, and I can- 
 not help thinking that Herschel must have derived it 
 from some one more conversant with these than with 
 mechanical physics. This opinion is confirmed by a 
 curious illustration which he uses in the same paper 
 of 1811. " There is perhaps not so much difference 
 between them" (viz., the whole group of nebular and 
 quasi-nebular phenomena), " if I may use the com- 
 parison, as there would be in an annual description 
 of the human figure, were it given from the birth of 
 a child until he became a man in his prime" (p. 271). 
 
 A theory or hypothesis in some respects similar (199.) 
 had been previously expounded by Laplace in the Laplace's 
 concluding chapter of his Systeme du Monde. M^^'^^^T^y 
 least it so far resembles it, that he puts forth Tycho's connected 
 notion of the star of 1672 being a condensation of a with Her- 
 widely-spread stellar atmosphere (without, however, ^'^^^^ ^• 
 naming Tycho), and supposes that our solar atmo- 
 sphere might also once have extended to the limit of 
 the system, and that the planets were thrown off suc- 
 cessively in the form of nebulous rings (subsequently 
 condensed into spheres) from the equatoreal parts of 
 this vast revolving mass during its contraction. He 
 ascribes to Saturn's ring a like origin. It required all 
 the authority of a name like that of Laplace to circu- 
 late a theory so bold, if not extravagant. He adhered, 
 however (at that time), to the old idea of the consti- 
 tution of nebulae, which he considered to be composed 
 entirely of stars, and to be at once the most distant 
 and the most massive aggregations of matter in the 
 universe. Herschel could hardly fail of being ac- 
 quainted in 1811 with Laplace's views, and they pro- 
 bably in some degree influenced his own, particularly 
 as to the cause of the rotation of his condensing suns. 
 But he prudently reserved his hypothesis for sidereal 
 objects, and did not deduce from it a planetary cos- 
 mogony. In the later editions of the Systeme du 
 Monde, Laplace quotes Herschel's observations in 
 confirmation of his views, adopts the notion of a dif- 
 fuse nebulous matter, and considers that an hypothesis 
 arrived at by a " remarkable coincidence" in oppo- 
 site directions, is thereby invested with a great pro- 
 bability. 
 
 Even Herschel's more limited conclusions have (200.) 
 been very dubiously received, and notwithstanding Doubts re- 
 the weighty adhesion of Humboldt and Arago toS*^^°gi*- 
 them, it may be afiirmed that natural philosophers 
 generally are content to leave the solution of this 
 cosmical problem to that distant posterity which 
 alone can hope to witness unequivocal evidence of pro- 
 gressive change in those wonderful objects.-' 
 
 III. Of the Grouping of the Stars generally in (201.) 
 Space, and the Significance of the Milky Way. — The ^''f consti- 
 earlier astronomers, and particularly Halley, had gt^j.™ j,g^. 
 the idea that the nebulae — ^which abound so remark- vens,andof 
 
 -the Milky 
 
 its least objectionable form, will be found in Sir John Herschel's Wayinpai^ 
 
 ticular. 
 
46 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Kant, 
 
 Lambert, 
 
 Wright. 
 
 (202.) 
 Hersohel's 
 " gaages." 
 
 (203.) 
 Plenitude 
 of stare in 
 different 
 regions of 
 the sky, 
 
 ably in the Milky Way, and wLich may in some sense 
 be almost said to compose it — are the parent-matter 
 of stars, whilst stars abound in their neighbour- 
 hood, or seem partly to compose them, in a state 
 of incredible aggregation. That the mass of sidereal 
 matter composing the Milky Way (which forms an 
 irregidar girdle round the whole heavens'^) has some 
 special reference in its locality to our solar system, 
 was also an early idea, which, towards the middle 
 of the 18th century, had attained to something like 
 a definite speculation in the miads of Kant, Lambert, 
 and other philosophers, chiefly those of Germany. 
 Its origin is perhaps traceable to Thomas Wright of 
 Durham^' (1742), who aflnrmed that the Milky Way 
 is a projection on the sphere of a stratum of stars, in 
 the midst of which our Sun and system are placed— 
 somewhat excentrically, however, towards Sirius. 
 
 I do not know whether Sir W. Herschel derived 
 his first ideas on the subject either from English or 
 German authors. His customary silence (which is 
 to be regretted) on the history of his discoveries, 
 leaves us ia doubt of his originality. Be this as it 
 may, he proceeded to test the reasonableness of the 
 speculation, in that definite and thorough manner 
 which was very characteristic of his genius. He pro- 
 ceeded to number the stars after a fashion which, if 
 the early attempt of Hipparchus was pronounced in 
 its day impious, might well have been accounted, 
 even in Herschel's age, impossible. To use his own 
 bold expression, he gauged the heavens, by counting 
 the whole number of stars visible in the field of his 
 20-feet reflector as many times as possible, and in 
 every region of the sky which was visible from 
 Slough, distinguishing the results of each region. As 
 it was impossible in one lifetime to accomplish the en- 
 tire survey (for the complete sphere contains 883,000 
 fields of 15' each in diameter), he took an average for 
 each region, and thus determined the general popula- 
 tion of the sky in all directions. The result more than 
 confirmed the suspicions of Wright and Lambert, 
 and demonstrated a remarkable, and, on the whole, 
 a steady law of decrease, from the central zone of the 
 Milky Way in opposite directions, until we reach two 
 poles, one ia the Southern, the other in the Northern 
 hemisphere, which are the localities poorest in stars. 
 This DISCOVERT (for it well deserves the name), 
 which assigns a Law to the distribution of the entire 
 visible bodies of the Universe in space, is surely one 
 of the greatest which man has ever attained. The 
 
 simplicity of the means by which it was reached, and 
 the amount of mere mechanical and arithmetical la- 
 bour which forms its sole basis, and constitutes its 
 essence, is a powerful lesson of how little mankind 
 has a right to scorn the humblest means of knowledge, 
 or to attach the prerogative of genius only to the 
 lofty flights of imagination and speculative philoso- 
 phy.^ This triumph belongs to Herschel alone ; his 
 successors have commented upon and scrutinized his 
 results ; his son has " gauged" the Southern Hemi- 
 sphere, with like results ; but the original result is 
 substantially confirmed. We may therefore antici- 
 pate so far as to quote the numbers denoting the 
 " plenitude" of stars as we recede from the equator 
 of the Milky Way in either direction, first, as calcu- as observed 
 lated by Struve* and Sir John Herschel, from Sir Wil- by Sir wn- 
 liam Herschel's observations in the Northern hemi- a.*"r*u "^ 
 sphere ; secondly, as calculated for the Southern he- Herschel. 
 misphere by Sir J. Herschel, from' his own observa- 
 tions at the Cape of Good Hope. 
 
 Limits of Zone, Average Nrnnier of Stan visible in 20-feet 
 reckoning from Reflector; Aperture 18'8 inches; Field 
 
 Equator of 15' diameter. 
 
 Milky Way, N. Hemisphere S. Hemisphere 
 
 (Magn. Power 157.) (Magn. Power 180.) 
 
 0°- 15° 53-4 69-1 
 
 15 - 30 24-1 26-3 
 
 30 - 45 13-6 13'5 
 
 45 - 60 8-2 9-1 
 
 60 - 75 5-4 6-6 
 
 75 - 90 4-3 6-0 
 
 This table shows the extreme condensation of the stars 
 round the " Galactic" equator ; indeed Struve carries 
 the average " plenitude" of the field as high as 122 
 stars in that plane itself. 
 
 According to Herschel's views, the whole visible fir- (204.) 
 mament of stars belongs to the nebula of the Milky 
 Way, of which our own system forms an infinitesimal 
 part. In his paper of 1785, on " the Constitution of 
 the Heavens," he inferred that the general form and 
 comparative limits of this cluster of stars might be 
 found from his " gauges," by supposing thai his tele- 
 scope brought into view every star between the specta- 
 tor and the surface of the cluster. Supposing the stars 
 to be uniformly distributed within the cluster, it is 
 easy to see that the number counted in a conical space, 
 having an angle of 15' at its vertex, would give the 
 height of the cone, or the depth to which the spectator 
 is immersed in the cluster, in that particular direction; 
 and thus he endeavours to assign the solid form of the 
 cluster and its dimensions, in terms of the distances 
 
 ^ Its plane is inclined about 63° to the Celestial Equator : its nodes are in O'' 47"" and 12'' 47™ of Eight Ascension. 
 
 2 In his Synopsis of the Universe, a rare work. See Professor De Morgan's account of Wright, in the Philos. Magazine 
 for 1848, xxxii., p. 241. Wright believed that the Milky Way was a congeries of stars of a particular form, which it owes to 
 a rotation of the whole round some central point. 
 
 3 Another remark, perhaps, deserves to be recorded. Had Hipparchus and his followers been deterred by the threatened 
 charge of impiety from making a catalogue of stars, how great the loss would have been, not to science alone, but to our esti- 
 mate of the order and magnificence of creation. The telescope only increased our knowledge of the number of worlds, without 
 really enabling us to approach to their limits : — the gauges of Herschel, which he at first supposed to reach to the boundary 
 of the visible firmament, proved to him at last that the wealth of creation was unfathomable by any measure he could apply to it. 
 " Numbers numberless" appeared in those regions where the stratum of the Milky Way is most extended. 
 
 * Etudes d'Astronomie Stellaire. 
 
Chap. III., § 2.] 
 
 ASTRONOMY. — SIR WILLIAM HERSCHEL. 
 
 47 
 
 (hypothetically uniform) between any two stars. But 
 in his later memoirs, Herscliel seems to have felt the 
 insecurity of his conclusions, and that there is no 
 reason, but the contrary, to believe in a uniform dis- 
 tribution of the stars ; that, at least in some direc- 
 tions, the Milky Way is unfathomable, or its limits 
 unattained even by the 40-feet telescope. (See his 
 Memoir of 1817.) He therefore judiciously recurs 
 to photometrical measures as the best criterion of the 
 distance of the stars. The estimate of "the space- 
 penetrating power" of his telescopes, already referred 
 to (182), enabled him to infer the relative distances at 
 ■which a star would become lost to vision aided by 
 each telescope. 
 (205.) Calling the distance of a star of the first magni- 
 
 Relative tude 1, and supposing that light takes three years to 
 
 fixed stars. ^"^^^'^'^^^ "' — „. .. 
 
 Dist. Light travels in 
 
 The distance of a star of the sixth mag- 
 nitude (the limit of unassisted vision) 
 will be 12 36 years. 
 
 Limit of 20-feet telescope (used in gaug- 
 ing) 900 2,700 ... 
 
 Limit of 40-feet telescope 2,304 6,912 ... 
 
 Limit of Lord Bosse's telescope (6 feet 
 
 diameter)... .3,436 10,308 ... 
 
 Yet none of these telescopes appear to touch the 
 boundary of our nebula in the direction of its greatest 
 extension, for fresh optical power still yields fresh 
 harvests of stars. 
 C206 ) ^^ * direction perpendicular to the plane of the 
 
 All visible Milky Way, not only is the paucity of stars remark- 
 stars be- able, but we seem to look out, as Sir John Herschel 
 long to the ,jgg(;j.i})gs jt^ jjj^q ^ starless region external to the stra- 
 the Milky turn. Sir W. Herschel concluded, in 1817, that the 
 Way. depth of the stratum in its least dimension is such as 
 
 to include all stars down to those three times more 
 distant than the naked eye perceives. His son, 20 
 years later, infers, from the investigation of the 
 southern hemisphere, that the distribution of stars is 
 comparatively independent of direction for all those 
 which are brighter than the 8th magnitude, and that 
 it is by the influence of the hosts of lesser brightness 
 visible in the 20-feet reflector, that the very remark- 
 able law of condensation towards the plane of the 
 
 (207.) 
 
 (208.) 
 Continua- 
 tion of 
 
 Milky Way takes effect. He is therefore disposed to 
 conclude that " our system is plunged in the sidereal 
 stratum constituting the Galaxy, reckoning from the 
 southern surface to a distance which corresponds to 
 the light of a star of the 9th or 10th magnitude." ^ 
 
 These great and arduous enquiries occupied Sir 
 William, Herschel during nearly the whole of his 
 scientific career, extending to almost half a century. 
 His first observations (Struve remarks) dated from 
 1774, his last observations on this subject which have 
 been published were of 1804, and his latest paper, 
 still on the same topic, was in 1821, when he was 
 almost on the verge of the grave. 
 
 Excepting the continuation of his laboiirs by his 
 illustrious son, little has been added to our know- 
 ledge of " the constitution of the Heavens" since his Herschel 't 
 death. We shall, therefore, hardly recur to the topic researches. 
 in the latter part of this chapter. Some German 
 astronomers of eminence have indeed tried to deduce 
 from an assumed distribution of the stars in the Milky 
 Way, the necessity of allowing that space is not per- 
 fectly transparent, and have even attempted to assign 
 the law of extinction of light through the sidereal in- 
 tervals ; but having examined their reasoning with 
 the best care I have been able to. give it, I am 
 bound to say that it appears to me very far short of 
 conclusive.^ 
 
 IV. Of the Motion of our System in Space. — That (2G9.) 
 the stars are not fixed, but have " proper motions," Proper mo- 
 not explicable by the gyrations of our earth round its *J°°^ °^ 
 centre of gravity (which produce precession and nuta- Halley. 
 tion), nor by its revolution round the sun (on which 
 aberration and parallax depend), was a fact first de- 
 tected by Halley from a comparison of ancient and 
 modern observations. Though small in amount, yet 
 as it continually increases in the same direction, this 
 Proper Motion becomes in the course of ages an im- 
 portant quantity. In 2000 years, Arcturus, /* Cas- 
 siopeise and 6 1 Cygni have moved 2J, 3 J, and 6 times 
 the moon's diameter. 
 
 In 1748, Bradley (in his paper on Nutation) stated (210.) 
 the probable explanation of these apparent motions 
 
 1 These startling results appear to be necessarily true, if the following assumptions be admitted : — (1.) That the stars have 
 on an average the same brilliancy in all regions of space. (2.) That the light received from a star is inversely as the square of 
 the distance ; or that the laws of radiation and of vii viva are rigorously true, and that there is no absorption of light in space. 
 (3.) That the visibility of a star is exactly as the quantity of light received from it in the telescope. Probably this last assump- 
 tion is the least sure. We know that magnifying power (independently of illumination) affects the result. 
 
 ® Cape Observations, p. 383. 
 
 3 I ought perhaps to state that in this passage I have referred to the reasonings of M. Struve, contained in the latter part of his 
 Etudes d'Astronomie Stellaire. Having taken some pains to follow the argument of that work, which professes to be " based en- 
 tirely upon observation, without any arbitrary hypothesis," I was reluctantly led to the conclusion that M. Struve's assumptions, 
 if tacit, were not the less arbitrary and questionable. Indeed it appears self-evident that no geometrical certainty can be at- 
 tained as to the relative distances of the stars composing the Milky Way, but from some fundamental hypothesis respecting their 
 magnitudes and distribution. I am persuaded that the popular writers and reviewers who have given additional publicity to 
 the most striking and positive of M. Struve's conclusions, have (very naturally) done so on the strength of the author's well-de- 
 served reputation as an observer, and without attempting to analyse his reasoning, which it must be owned is sometimes obscure. 
 My objections to M. Struve's argument were put in writing several years ago (1850), but not published except in my lectures. 
 It was only whilst correcting the proofs of these sheets (1855) that I saw for the first time a memoir by Professor Encke in the 
 Aitronomisohe Naehriehten, vol. xxvi.. No. 622 (published in 1848), maintainicg the same view of the invalidity of M. Struve's 
 reasoning, and questioning the hypotheses (of which M. Encke reckons^t;6)tacitly assumed by him. The Dutch Academy of Sciences 
 (Haarlem) has proposed the points at issue between MM. Struve and Encke as the subject of aprize question. 
 
48 
 
 MATHEMATICAL AND PHYSICAL SCIENCE; 
 
 [Diss. VL 
 
 system in 
 space — 
 Bradley— 
 Mayer. 
 
 direction 
 of motion. 
 
 Motion of to be the real displacement of our sun and system in 
 the solar space. In 1760 Mayer gave a list of 80 stars whose 
 proper motions he determined by a comparison of 
 Homer's observations. He conceived the possibility 
 of determining the direction of the solar motion by 
 the changing aspect of the constellations, keeping in 
 view, however, that the effect is complicated by real 
 independent movements of each individual star. 
 Lambert and Mitchell entertained similar views, but 
 carried them to no practical result. 
 (211.) Here, then, Herschel appears on the field. He 
 
 ^'vTj^^'" proceeded in 1783 to do what his predecessors had 
 mines the discussed the -possibility of doing. His own observa- 
 tions were not available in a problem like this. Tak- 
 ing the best values he could obtain of the Proper 
 Motions of only about 20 stars, he, with great saga- 
 city and success, divined that the solar system is 
 moving somewhere in the direction of X Herculis, a 
 point in the heavens whose right ascension is 257°, 
 and north declination 25°. This result he arrived at, 
 almost without calculation, by a mere consideration 
 of the changing perspective of a multitude of ob- 
 jects amongst which the spectator moves. Mayer had 
 compared the change to that seen when we walk 
 slowly through a grove of rather distant trees. Those 
 in front will seem to widen or expand as we approach, 
 those behind vrill condense towards the point we are 
 quitting. The greatest proper motions will be in the 
 • objects on our right and left as we advance. It is 
 not to be supposed that we find in the stars the exact 
 counterpart of this change of place. For each star 
 may by its own absolute movement in space either 
 conspire with or oppose the motion due to perspec- 
 tive. But a combination of the whole results will 
 make apparent the direction of that part of the motion 
 due to a common cause, that is, to the translation of 
 our system in space. A cleverer approximation than 
 Herschel's was never made. He returned to the sub- 
 ject in 1805, but there is reason to think that his 
 first result was the more correct. 
 (212.) As nothing essential has been added to Herschel's 
 
 Morerecentdiscovery of the direction of the solar motion, we 
 researches gjjali here refer once for all to the important confir- 
 subject. mations which it has since received. Professor Ar- 
 gelander, availing himself in 1835 of the improved 
 state of astronomy since Bradley's observations were 
 made, and since their reduction by Bessel, considered 
 the whole problem in a general and geometrical 
 manner, including every well-determined proper mo- 
 tion^ by means of appropriate equations of condition, 
 which, being resolved by the method of least squares, 
 
 give the direction of solar motion 261° 11' of right 
 ascension, and 30° 58' of north declination, differing 
 respectively about 4° and 6° from Herschel's first 
 numbers. Perhaps a still more convincing confirma- 
 tion was obtained by Mr Galloway [Phil. Trans. 1847), 
 from the proper motions of stars of the southern he- 
 misphere alone, which lead to a result nearly coin- 
 ciding with the above. 
 
 Sir William Herschel's leading discoveries in Side- (213.) 
 real Astronomy may therefore be reduced to these — Summary 
 the discovery of binary systems of stars and the orbits schel's dis- 
 of several revolving stars ; the discovery and classifi- coveries. 
 cation of a prodigious multitude of nebnl«; the law of 
 grouping of the entire visible firmament, and its con- 
 nection with the great nebula of the Milky Way; and 
 lastly, the determination of the fact of the motion of 
 our sun and system in space, and the direction of 
 that motion. Setting aside all that is valuable, in- 
 genious, and noble in his farther speculations, and 
 all that he contributed to the enlargement of our 
 knowledge of the system of sun and planets with 
 which we are more immediately connected, these po- 
 sitive discoveries will ever remain a magnificent tro- 
 phy of his perseverance and success as a natural phi- 
 losopher.2 
 
 When his increasing years rendered the relaxation .(2140 . 
 of his arduous course of telescopic observation ad- j P°y^'" 
 visable, whilst all his other faculties were in thevations. 
 highest vigour, he began to devote more attention to 
 physical enquiries less directly connected with astro- 
 nomy. The nature of the emanations of light and heat 
 proceeding from the sun was a matter on which he 
 was forced to speculate in connection with his ideas 
 of the sun's constitution ; and even the practical en- 
 quiry as to the kind of dark glasses best fitted for 
 defending the eye in observations of that nature, led 
 him, in conformity with his usual habit, to a large 
 series of experiments on solar heat, and its trans- 
 missibility through glasses of different colours, and 
 other bodies. In the progress of these he was led H^**'°S 
 to examine the heating power of the different rays o/ spectrum. 
 the spectrum, and consequently the refrangibility of 
 heat. He then arrived at the real discovery that the 
 place of greatest heat in a spectrum formed from the 
 sun's rays by a flint-glass prism is considerably be- 
 yond the extreme visible red ray. But we shall re- 
 turn to this result in connection with the history of 
 radiant heat. He also made some experiments on 
 
 1 A small star in Ursa Major (1830 of Groombridge's Catalogue) has an annual proper motion of 6"-97; the star 2151 Pup- 
 pis, is the greatest known, being 7"-87. 
 
 * No historian of science, or biographer of Sir W. Herschel, can fail to acknowledge with gratitude the important assistance 
 afforded by MM. Arago and Struve to a compendious acquaintance with his writings and discoveries; the former by his article on 
 Herschel in the Annuaire du Bureau des Zongitudee for 1842, the latter in his Etudes d'Astronomie Stellaire. While acknowledg- 
 ing my obligations to these works, I shall not be suspected by any careful reader of having dispensed with a reference to the 
 original memoirs ; still less of having adopted without examination the conclusions of these eminent authors, from whom, indeed, 
 on some important points, I differ entirely. 
 
Chap. III., § 3.] 
 
 ASTRONOMY. — BESSEL — MR AIRY. 
 
 49 
 
 the colours of thin plates, but to these he did not 
 attach much importance. 
 
 (215.) The philosophical character of Herschel is almost 
 
 Herechel's included in what precedes ; but we will endeavour 
 character; ^^ ^^^ j^ ^p -^ ^ f^^ words. He united in a re- 
 markable degree the resolute industry which distin- 
 guishes the Germans, with the ardour and constancy 
 of purpose which has been thought characteristic 
 of the Anglo-Saxon. From his native country he 
 brought with him a boldness of speculation which 
 has long distinguished it, and it is probable that he 
 had also a vigorous and even poetic imagination. 
 Yet he was ever impatient until he had brought his 
 conjectures to the test of experiment and observation 
 of the most uncompromising kind. He delighted to 
 give Lis data a strictly numerical character. Where 
 this was (by their nature) impossible, he confirmed 
 his descriptions by reiterated observation, in different 
 states of weather, with different telescopes, apertures, 
 and magnifying powers ; and with praiseworthy fide- 
 lity he enabled his readers to form their own judgment 
 of the character of his results by copious and literal 
 transcripts from his journals. On his claims to 
 originality we are unable in all cases to decide, owing 
 to almost his only literary fault, that of rarely al- 
 
 luding to the writings of his predecessors or con- 
 temporaries, even so far as to acknowledge their 
 existence. The discovery of binary systems is pro- 
 bably that which was most absolutely his own ; but 
 even supposing the speculations of Wright, Lambert, 
 and Mitchell were not unknown to him, this would 
 diminish but little the substantive merit of having 
 devised and executed the means of removing them 
 from the regions of almost metaphysical abstraction 
 to that of concrete reality. 
 
 His long and tranquil but ever active life corre- (216.) 
 sponded happily to the nature of his pursuits, which ^}^ lo°6 
 required an absolute devotion of his time, and the ' 
 means of instituting comparative observations after 
 an interval of many years. There are not many 
 philosophers who could have expected within their 
 lifetime to see at least one pair -of suns complete 
 their mutual orbit. 
 
 Herschel's career at length drew to a close. He (217.) 
 died peacefully at Slough, near Windsor, where he *°^ '^*" 
 had resided throughout the greater part of his 
 life, at the age of eighty-three, on the 23d August 
 1822, one year only after the publication of his latest 
 memoir in the Transactions of the then recently 
 formed Astronomical Society, of which he was the 
 first President. 
 
 3. Bessbl — Mr Airy — Modern Observatories. Fixed Star Catalogues — Planetary and Lunar 
 
 Observations. 
 
 (218.) 
 Modern as- 
 tronomical 
 details 
 since 1810. 
 
 (219.) 
 Practical 
 astronomy 
 in England, 
 
 As we approach the most recent period of the his- 
 tory of astronomy, I feel the increasing difficulty of a 
 due condensation and selection of the interesting mat- 
 ter which claims our notice. Astronomy has been so 
 generally and so zealously cultivated, that it seems 
 almost invidious to select a few names and a few lead- 
 ing discoveries as the topics of discussion. It is, 
 however, necessary to do so, and I shall be guided by 
 the single aim of trying to specify impartially those 
 individuals who have by their labours given most of 
 the impress of the age to the science which they re- 
 present. In a subject like this, of almost infinite de- 
 tail, the reader is not to expect a list of the names of 
 all discoverers and improvers ; it is not our business 
 here to dwell upon mere labours oi precision, to which 
 so large a part of the most useful industry of astro- 
 nomers is devoted ; but to show the spirit in which 
 these labours must be undertakrai, and the general 
 results by which they enrich the knowledge of the 
 passing generation. 
 
 In the first section of this chapter we have sketched 
 (in connection with the name of Maskelyne) the 
 state of accurate astronomy in fixed observatories, 
 down to about the year 1810. Since that period the 
 multiplication of observatories has been very great. 
 There has been a great improvement in instruments 
 and in the methods of using them. But there has been 
 an incomparably greater advance in the methods of ex- 
 
 tracting trustworthy results from observations made 
 with due care. The art of dividing instruments was 
 carried to great perfection in Great Britain by Graham 
 and Bird, but their preference of the quadrant to in- 
 struments of a circular form (introduced long before 
 by Ebmer) retarded the progress of astronomy. Fo- 
 reign observatories in the early part of this century 
 (as in the last) sought their divided instruments from 
 London ; Piazzi and Bessel worked with English 
 circles. Troughton was as an artist the worthy suc- 
 cessor of Eamsden; and even to the present time 
 British astronomers, at least, do not admit that the 
 nice contrivances and beautiful workmanship of Eep- 
 sold and of Merz in Germany, or of Gambey in 
 France, have produced instruments worthy of more 
 confidence than those which have been constructed 
 at home. In the improvement of object-glasses for 
 telescopes, however, Germany and France bear away 
 the palm, although for many years Dollond supplied 
 Europe with his achromatic telescopes. With regard to 
 constancy and fidelity of observation, whether in fixed 
 observatories or in maritime and geographical expe- 
 ditions, English astronomers have never been back- 
 ward ; and the reputation of Greenwich Observatory 
 in this respect (and also in the punctuality of pub- 
 lication) has, as we have stated elsewhere, earned the 
 approbation and gratitude of all Europe. 
 
 But here our praise of British astronomy must (220.) 
 
50 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Keduction pause. Until very recent times, with few exceptions, 
 ofobserva- our observers, however industrious, have merely 
 ions ong ygg^ mechanically the apparatus put into their hands 
 by intelligent and conscientious artists, who yet, 
 never having occasion to apply their own handiwork 
 to the purposes for which it was made, could not be 
 expected to detect deficiencies of construction, nor 
 to possess the mathematical knowledge required to 
 remedy them. To determine in a complete an(i inde- 
 pendent manner the errors, not only of adjustment, 
 but also of construction of the instruments, and to 
 correct them by calculations (deduced when neces- 
 sary from frequent observations of their amount) is 
 now felt to he the duty of the astronomer himself. 
 This improvement (though, as we shall see, already 
 partially practised even in England) was mainly due 
 to Bessel, whose name we have placed first at the head 
 of this section. But astronomy owes to him much 
 more than this. He first showed that it is part of 
 an intelligent astronomer's duty, not only to observe 
 stars and planets, but to undergo the vastly greater 
 labour of comparing his results with the best theories 
 of his time, and of improving as far as possible those 
 theories, so as to hand over each branch of science to 
 his successor in a more perfect state than that in 
 which he foimd it. In all these respects practical 
 astronomy commenced a new epoch in Germany, and 
 on this account principally we place the name of 
 Bessel in a conspicuous rank. 
 (221.) Fribdeich Wilhelm Bessel was born at Minden 
 
 Bessel— his qq t^e 22d July 1784. He was destined for a mer- 
 bou^ *" cantile career ; and it is an interesting fact that it was 
 the expectation of an appointment as supercargo on 
 a commercial voyage which led him to study naviga- 
 tion and astronomy, and finally induced him to de- 
 vote his entire energies to the latter science, in which 
 he received every encouragement from the amiable Gi- 
 bers, who fortunately inhabited Bremen, where young 
 Bessel was engaged in business. He commenced his 
 astronomical career by reducing Harriott's observa- 
 tions of the comet of 1607, and was thereafter ap- 
 pointed assistant to Schroter at the observatory of 
 Lilienthal. In 1 8 10 he was removed by the Prussian 
 government to the charge of the observatory about to 
 be erected at Kbnigsberg, where he spent the re- 
 mainder of his life, and which he very speedily raised 
 by his labours to almost the first rank of European 
 observatories. In fact, he possessed, in a singular 
 degree, the qualifications for directing a great obser- 
 vatory ; including a thorough acquaintance with the 
 use of instruments, with the theory of astronomy in 
 all its branches, with the higher mathematics, and also 
 the art and practice of calculation, as well as with 
 many allied branches of natural philosophy. 
 (222.) The work by which he is perhaps best Imown, the 
 
 His Funda- Pundamenta Astronomice, is not grounded on his own 
 tronomim : observations, nor even those made m the same cen- 
 tury, nor in his own country, -but, what may appear 
 singular, upon the observations of Bradley at Green- 
 
 wich in 1750 and some following years. In reality, — reduc- 
 no better observations had been then made. The in- *'°° °^ ^ 
 struments had undergone no material change during p^^^j,^^* 
 the long and industrious, though not splendid, career tions. 
 of Maskelyne ; and Bradley was beyond question the 
 most accomplished astronomer of the 18th century. 
 Let us record it as a fact for the encouragement of 
 conscientious labour in the service of science, that 
 these precious records of the state of the heavens, of 
 which the value seemed unknown to a whole succeed- 
 ing generation (so that they were not even printed 
 in a crude form until nearly fifty years after they 
 were made), were disinterred, so to speak, by an 
 illustrious foreigner, and in course of time made the 
 basis of what, in respect of precision and method, 
 might be called a new astronomy. Bessel was as- 
 sisted in this work by a grant from the British Board 
 of Longitude. 
 
 The observations especially considered by Bessel (223.) 
 are those of the fixed stars. To apprehend theirim- Special ob- 
 portance, we must recollect that the foundation of an^^^i" " 
 accurate knowledge of the orbits, and of the pertur- 
 bations of the Solar System, not to mention less ap- 
 parent but not less remarkable changes of place in 
 the stars themselves, consists in rendering perfectly 
 comparable observations of position at one time with 
 those made at another more or less remote. Now, 
 not only are our transit instruments and quadrants, 
 and circles, and clocks, affected with errors more 
 or less unknown, so that the registered figures re- 
 quire correction ; but, in consequence of Refraction 
 and Aberration, we see no body whatever exterior 
 to the earth in its real visual position ; and this 
 visual position, when found, is afiected by Parallax. 
 Besides all this, the grand points of reference in 
 the sky, the Pole and the line of Equinoxes, are 
 undergoing perpetual, though small, changes of po- 
 sition : — the first star of Aries had already, in the 
 time of Hipparchus, wandered from the point of in- 
 tersection of the Equator andEcliptic; — consequently, 
 longitudes and right ascensions have to be reckoned 
 from a directional line in space altogether imaginary. 
 The pole of the heavens wanders amongst the stars, in 
 consequence of Nutation — the obliquity of the Ecliptic 
 is itself changing ; and, to crown all these causes of per- 
 turbation and seeming unsteadiness, the stars called 
 fixed have (as we have formerly seen) peculiar and 
 individual displacements not accounted for by any of 
 the preceding causes of change. In short, nothing is 
 fixed and comparable, except our measure of time. 
 The length of the sidereal day is subject to no secular 
 variation. The bases of Astronomy, — the Funda- 
 menta Astronomice, — then, evidently consist in the 
 perfect evaluation of all these varying elements, so 
 that the stars, if not really fixed, may become, for us 
 at least, virtually so, — ^that by their aid the position 
 of the fundamental directional lines of the sphere 
 may at any time be found, and the relative positions 
 of the stars themselves. After this it is easy to 
 
Chap. III., § 3.] 
 
 ASTRONOMY. — BESSEL — MR AIRY. 
 
 51 
 
 refer the places of wandering bodies to standard 
 points. 
 (224.) Bessel's work includes a methodical reduction of 
 
 Results. ^}jg pij^ggg pf g^^j^g 3QQQ g^^yg observed by Bradley, 
 
 and an investigation of the sun's apparent path, to- 
 gether with a full discussion of the principles and 
 application of every correction, instrumental and 
 uranographical, which such observations require, and 
 which are applicable to all others of the same kind. 
 It includes, therefore, dissertations on some of the 
 most delicate points of Astronomy, and " Constants" 
 for the different corrections, which, with slight varia- 
 tion, have been since employed in every observatory; 
 Bessel devised also a remarkably simple mode of find- 
 ing for each star the varying corrections of its place. 
 The f roper motions of the stars were also determined 
 for the first time with approximate exactness, by 
 comparing Bradley's places with more modern ob- 
 servations. 
 (225.) In subsequent years (the Fundamenta were pub- 
 
 own obser- ^^^^^^ in 1818) Bessel contributed to the science of 
 vations. astronomy numerous and regular observations of the 
 heavenly bodies; the Annals of the KiJnigsberg 
 Observatory were regularly published from 1814, 
 being (I believe) the first foreign establishment 
 which followed the example set by Maskelyne at 
 Greenwich, with the important addition of systematic 
 reduction, 
 (226.) Of the subsequent labours of Bessel we must speak 
 
 His numer- shortly. The determination of the parallax of 
 
 ous works •/ •/ i 
 
 on astrono- the star called 61 Cygni, perhaps the most original 
 my. and important of these, we shall refer to another sec- 
 
 tion, where we shall compare it with the results ob- 
 tained by other astronomers. He made interesting 
 physical observations on Halley's comet at its return 
 in 1835; he prepared the materials for a very ex- 
 tended catalogue of fixed stars, arranged in zones, 
 more recently published by Professor Weisse. In 
 connection with the theory of the pendulum as a 
 measure of gravity, he repeated and extended Newton's 
 important experiments on the uniformity of the gra- 
 vitating force on all kinds of matter ; he applied a 
 new correction to the vibrations of the pendulum, and 
 improved the method of observing them correctly; 
 and he discussed with his habitual mathematical skill 
 and elaborate perseverance the figure of the Earth, 
 from the whole of the then existing observations; 
 whilst he also directed an operation for connecting 
 the Russian triangulations with those of western 
 Europe, — a delicate task, which he performed with 
 consummate skill. It will thus be seen that (vdthout 
 mentioning a host of minor works and memoirs) there 
 was hardly a great department of Astronomy in which 
 Bessel did not take a distinguished part. Even the 
 discovery of Neptune, by calculation from the irregu- 
 larities of Uranus, was contemplated as a practicable 
 problem by the veteran astronomer in his later years. 
 He died on the 17th March 1846 ; therefore only a 
 few: months previous to the publication of MM. Le- 
 
 verrier and Adams' discoveries, and their triumphant 
 consummation by M. Galle. 
 
 Even before Bessel's career as an astronomer had (227.) 
 properly commenced. Pond, in England, had antici- ^°"'^' *''® 
 pated, in a good measure, the improvements in prac- mer-Royal, 
 tical astronomy to which we have referred in the an excel- 
 beginning of this section. Already, in the earliest 1^°* °^' 
 years of this century, he had made observations at his 
 private residence with a comparatively small circular 
 instrument by Troughton, which led him to detect the 
 gradually increasing errors of Bradle/s quadrant still 
 in use at Greenwich, and to recommend the adoption 
 of complete circles (disused since the time of Romer) 
 and the specific examination of errors of division. 
 These principles he carried out at Greenwich, to which 
 establishment he was afterwards appointed. His very 
 indifferent health prevented that incessant activity 
 which the management of a first-rate observatory re- 
 quires; nevertheless, he is justly regarded as one of the 
 chief reformers of the practical astronomy of those 
 days. 
 
 His successor, Mr Airy, has distinguished himself (228.) 
 by a more active career. Endowed with very un- Succeeded 
 common abilities, and with great physical powers of ^j, ' 
 endurance, he has, from his youth, been ever foremost 
 not only in promoting, in every one of its departments, 
 his favourite science of Astronomy, ' but also many 
 other allied subjects, particularly Optics, to which we 
 shall have occasion to refer in another section. 
 
 Bom in the county of Northumberland in 1801, (229.) 
 Mr George Biddell Airt acquired great distinction ^'^ numer- 
 at Cambridge, where he graduated in 1823, and was °nph*ai°aT 
 appointed to the charge of the Observatory there in and practi- 
 1828, after the death of Professor Woodhouse, a per- «al astro- 
 son sincerely attached to gstronomy and well skilled in """"y* 
 it, yet one who did not succeed in imparting much in- 
 teresteither to its theoretical or practical departments. 
 Mr Airy engaged in the important investigation of a 
 new irregularity in the motion of the Earth and 
 Venus, to which I have referred in the chapter on 
 Physical Astronomy (114), and ap the same time he 
 imdertook to publish his own Observations in regular 
 annual volumes, including a complete comparison 
 of the results with the best tables, thus presenting 
 at a glance the existing errors of theory. This prac- 
 tice he introduced at Greenwich on succeeding Pond 
 there in 1835; and he has pursued it ever since. 
 But not contented with rendering the annals of the 
 National Observatory a correct reflection of the state 
 of the heavens in his own day, and also of the con- 
 dition of Astronomical Theories, he did not rest until 
 he had performed for the observations of his prede- 
 cessors the same service, and thus produced a series 
 of comparisons of the observed and calculated places 
 of the moon and planets, unexampled for extent and 
 accuracy. Beginniag with Bradley's Observations 
 in 1750, he investigated and applied all the instru- 
 mental and uranographical corrections to each, as 
 Bessel had done for the observations of the sun and 
 
52 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (230.) 
 The new 
 Greenwich 
 Transit 
 Circle. 
 
 (231.) 
 
 fixed stars, and then calculated the tabular places for 
 the same instants of time. This last, especially in the 
 case of the moon, was a truly formidable task. The 
 whole labour was methodically performed at the 
 expense of government by a staff of no less than six- 
 teen computers, under Mr Airy's vigilant superin- 
 tendence, and it extended, first and last, over the 
 space of a dozen years. The results, printed in the 
 most compendious form, fill 2200 quarto pages. One 
 consequence of this systematic reduction was, that 
 MM. Leverrierand Adams were separately provided 
 with the places and errors of the Tables of Uranus 
 necessary for their great investigations ; and the 
 Lunar Theory has been, enriched with Mr Hansen's 
 latest corrections through the same facilities. The 
 final corrections of the co-efficients of the Lunar 
 Tables are concisely stated by Mr Airy in a paper 
 addressed to the Royal Astronomical Society. 
 
 Like Bessel, Mr Airy is thoroughly acquainted 
 with the theory and practice of mechanics ; and he 
 has applied his knowledge both to the improvement 
 of clocks and of proper astronomical instruments. A 
 great and apparently successful experiment of the 
 latter description is now taking place at Greenwich. 
 A meridian circle (combining in effect a mural circle 
 and transit instrumept) has been erected, of great size ' 
 and optical power (6 feet circle and 8^ inch object- 
 glass). But the novelty of the apparatus is its great 
 weight and strength. Hitherto artists and astro- 
 nomers have sought to avoid the evils of unsteadi- 
 ness and flexure principally by the elaborate framing 
 and trussing of light materials (chiefly brass tubes), 
 and (in Germany especially) by an elaborate system 
 of counterpoises. The new Greenwich circular in-, 
 strument is constructed of as few pieces as possible, 
 of great strength and weight, and in great part of 
 cast iron. The whole was elaborated and prepared 
 for dividing in an engineering workshop, and with 
 the powerful and accurate tools which modem engi- 
 neers use. A man might stand upon the axis with- 
 out producing the smallest bad effect. It is xmder- 
 stood that the result is -perfectly satisfactory as to 
 steadiness and stiffness. Mr Airy has likewise in- 
 vented and erected a new and most ingenious zenith 
 tube (acting by reflection) for ascertaining the place of 
 y Draconis, a star which, at its superior culmination, 
 crosses the meridian of Greenwich almost in the zenith. 
 
 There are few projects for the improvement of 
 astronomy in the last twenty years in which Mr Airy 
 
 has not been a counsellor or participator. He has Introduc- 
 at all times given efficient aid to those engaged in the*'°".°*'g*l" 
 pursuit of science ; and has been himself thefirst to im- ^^^^ ^f p^, 
 port from America and to establish on a great scale servation at 
 the method of recording observations by means of a Greenwich, 
 galvanic pressure produced on a sheet of paper sur- 
 rounding a cylinder ; which cylinder is moved in a per- 
 fectlyuniform manner by means of a connection with a 
 clock producing uniform motion on the principle of 
 the conical pendulum. By means of a simple contri- 
 vance the tracer follows a slightly spiral line, so that 
 one barrel may include many hours of continuous ob- 
 servations. He has also established galvanically time 
 signals, and employed them for the determination of 
 longitudes. Besides all this, he has taken part in 
 furthering geodetical measures, in regulating the 
 national standards of length, and in promoting in 
 various ways the collateral sciences. He contributed 
 to the Encyclopoedia Metropolitana a most able 
 analysis of the methods for determining the Figure 
 of the Earth, and his conclusions have been very 
 generally adopted. In the same publication he has 
 given a theory of the Tides, already referred to (78, 
 82). The public and his own university are .indebted 
 to him for several very valuable text-books on mathe- 
 matical physics. 
 
 During his incumbency at Greenwich, Magnetical (232.) 
 and Meteorological Observations have been added ^*S^*Joal 
 to those of Astronomy, and engage the time of four teorologi- 
 regular assistants in that department. The astro- cal obser- 
 nomical assistants amount to six, besides occasional ''**"""• 
 computers. It may safely be affirmed that there is 
 not a public establishment in a more complete state 
 of efficiency than is Greenwich Observatory at this 
 moment; and that its traditional reputation, ex- 
 pressed in the emphatic eulogium of Delambre, Art. 
 (150), runs no risk of deterioration under the direction 
 of Mr Airy. 
 
 Our limits will not allow us to refer to the nu- (233.) 
 merous private observatories in England and public '^'*'^' "'!" 
 ones abroad which are contributing useful elements 
 to the promotion of astronomy. It is not too much 
 to say that the activity of Greenwich has set a gene- 
 rally good example. The observations at Oxford 
 and Edinburgh have long been reduced on a syste- 
 matic plan ; those at Cambridge had been already so 
 treated. The establishments where sidereal astro- , 
 nomy is particularly cultivated will be noticed in 
 another section. 
 
 § 4. BORDA— Kater — Baily. The Figure of the Earth from Pendulum Observations — " Reduc- 
 tion to a vacuum;" Mr Stokes. Colonel Everest — M. Struvb. Latest Measures of the 
 Earth. M. Foucault's Pendulum Experiment. 
 
 (234.) In tte first section of this chapter I have men- 
 
 Figure of tioned the progress made in determining the figure 
 resumed' ^"^ *^® ^^"^^^ ^^ measurements of its surface in the 
 early part of this century. I shall now advert 
 
 briefly to the employment of the pendulum for the 
 same purpose. 
 
 Clairaut had published in 1743 a very remarkable 
 theorem which connects the force of gravity in any 
 
 (236.) 
 
Chap. III., § 4.] 
 
 ASTRONOMY. — BORDA — KATER — BAILY. 
 
 53 
 
 Connection 
 of gravity 
 and the 
 figure of 
 the earth — 
 Clairaut's 
 Theorem. 
 
 (236.) 
 Early pen- 
 dulum ob- 
 servations. 
 
 (237.) 
 Borda im- 
 proves the 
 method of 
 making 
 them. 
 
 latitude with the compression of the terrestrial ellip- 
 soid.' The pendulum is the readiest and most accu- 
 rate means of determining variations in the force of 
 gravity ; the repetition of its oscillations enabling 
 the observer to ascertain their average duration with 
 extreme nicety. The more rapid the oscillation the 
 greater is the force of gravity, because the heavy 
 body is more quickly dravra into its lowest posi- 
 tion. Two sets of observations, made in different lati- 
 tudes, would, rigorously speaking, suffice to deter- 
 mine the polar compression, supposing the earth to 
 be a geometrical ellipsoid, and composed of homoge- 
 neous and concentric layers ; a larger number would 
 serve to test the accuracy of these assumptions, and 
 would, at all events, be imperatively required to 
 eliminate the errors of observation. 
 
 It might be supposed that to swing a pendulum, 
 count its vibrations, and measure its length, is a 
 very easy thing. Experience shows that a more 
 difficult practical problem can hardly be proposed. 
 Those persons, therefore, who have in a good mea- 
 sure overcome the difficulties, are to be regarded as 
 promoting materially an enquiry which has always 
 ranked amongst the most interesting connected with 
 astronomy. Some of the observations of the eight- 
 eenth century, especially those of Lacaille at the 
 Cape of Good Hope and of Phipps in the Arctic 
 Regions, appear to have been made with much care ; 
 but the French astronomer Borda seems to have 
 given the initiative to observations of a higher degree 
 of accuracy, and his methods were ably carried out 
 in connection with the great French meridian arc, 
 by M. Biot, who even extended his stations to the 
 Island of Unst in Shetland. 
 
 Jean Charles Borda, who was born in 1733 and 
 died in 1799, was devoted to the promotion of the 
 exact sciences, and contributed in an eminent degree 
 to the precision attained in physics and astronomy 
 towards the close of the last century. The name of 
 Borda deserves a record in the history of science, 
 since it has been said of him, by no less an authority 
 than Dr Young, that " he seems to have possessed a 
 ■considerable share of that natural tact and sagacity 
 which was so remarkable in Newton." His earlier 
 researches were connected with hydrodynamics, and" 
 the resisted motion of projectiles ; in later years he 
 was chiefly devoted to practical astronomy and geo- 
 desy. The portable repeating circle invented by him 
 
 has had a very great reputation in France. He was 
 one of the principal designers of the measurement 
 of the French arc, and was employed in its superin- 
 tendence, especially as regards the measurement of 
 the base. His experiments on the pendulum were 
 originally undertaken (I believe) in 1790, with a view 
 to making it the basis of the national measures, but 
 were afterwards subordinated to the greater scheme 
 of terrestrial measurement. Baily records a fact 
 connected with Borda, not unworthy of mention, as a 
 caution to observers : — the year in which many of 
 his experiments were made is not discoverable from 
 the account of them, though the day, hour, minute, 
 and second, are recorded with praiseworthy fidelity. 
 From this time pendulum experiments assumed an 
 astronomical and geodetical importance. The appa- 
 ratus of Borda consisted of a slender metallic wire, 
 attached at one end to a knife-edge suspension, and at 
 the other to a small brass cap, nicely fitted hy grifld- 
 ing to a sphere of platinum which formed the bob or 
 weight of the pendulum. The oscillations were counted 
 by the method of " coincidences," that is, by placing 
 the experimental pendulum in front of a good clock 
 with a known rate, and observing after how long a 
 time the two pendulums (having started in the same 
 direction) again coincided in their motions by one of 
 them having gained or lost exactly two vibrations ; 
 a method which has been used at least since the 
 time of Bouguer. The time of vibration being thus 
 known, the distance from the knife edges to the bot- 
 tom of the ball was measured by means of a scale ; 
 and due corrections for the position of the centre of 
 oscillation were then applied. 
 
 By English observers, an invariable pendulum of (238.) 
 the form of a flat bar, provided with a bob or weight, ^^ j"f„ * 
 has usually been preferred, and on the whole it ap- 
 pears to be more satisfactory. Such a pendulum, 
 after being compared with an astronomical clock at 
 Greenwich, or any other place of reference, is taken 
 to different stations and its rate of vibration deter- 
 mined, and it is then brought back and compared once 
 more at the point of starting. Important series of 
 observations of this kind have been made by Colonel 
 Sabine and Captain Foster, and also by Admiral Du- 
 perrey. 
 
 But the two individuals who have most studied „ (239-) 
 the practical determination of the length of the se- and febeo- 
 conds pendulum as a mechanical problem, are Kater lute mea- 
 . . sures. 
 
 Laplace 
 and Mr 
 Stokes on 
 the earth's 
 attraction. 
 
 1 Clalraut (besides giving a theorem which, in the case of an ellipsoid, connects the polar compression with the increase of 
 gravity there) showed that the increase of the force of gravity from the equator will vary as the square of the sine of the lati- 
 tude. This he proved to be true when the spheroid is homogeneous, or when it is composed of similar concentric layers of 
 varying density. Laplace confirmed the result by a different analysis, and farther showed, that if the earth be composed of con- 
 centric strata which are severally homogeneous, and nearly spherical, but otherwise arbitrary in form, and if the surface be that 
 of a fluid in equilibrium (as it practically is when we refer the earth's figure to the sea-level), there exists a necessary connection 
 between gravity and the superficial figure, which, in the case of an ellipsoid of revolution, leads to the same relation of the square 
 of the sine of the latitude. In this case, also, the strata are presumed to be concentric. But in a recent and remarkable paper 
 by Professor Stokes, it is shown that the law connecting the force of gravity and the figure of equilibrium still holds when no hypo- 
 thesis whatever is made as to the distribution of the matter within the earth, provided always that it be consistent with the observed 
 fact of the ellipsoidal figure of the earth's fluid covering. Thus the confirmation, by means of pendulum experiments, of Clairaut's 
 Theorems cannot be regarded as a proof of the concentric arrangement of the strata, nor (so far) of the primitive fluidity of 
 the earth. See Cambridge Transactions, vol. viii. ; and for a simpler proof, Cambridge and Dublin Math. Journal, vol. iv. p. 194. 
 
54 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (240.) 
 CaptaLa 
 Kater ; 
 
 his con- 
 vertible 
 pendulum, 
 
 (241.) 
 His CoUi- 
 mator. 
 
 (242.) 
 Francis 
 Baily ; 
 
 hia early 
 history 
 
 and Baily. As regards the determination of the 
 Earth's figure, the relative length of a pendulum vi- 
 brating seconds in different latitudes is all that is re- 
 quired ; but the absolute length in a given place is 
 necessary for finding the force of gravity there ex- 
 pressed by the acceleration of falling bodies in vacuo 
 in one second ; and as the British standard yard was 
 at that time made to depend on the length of the pen- 
 dulum vibrating seconds at London, this enquiry was 
 mixed up with the intricate one of National Standard 
 Measures. 
 
 Captain Henby Kater was a person of remarkable 
 mechanical skill and ingenuity, and his numerous pa- 
 pers in the Philosophical Transactions, between 1813 
 and 1828, refer chiefly to the accurate construction 
 and use of the Pendulum, the Balance, and certain As- 
 tronomical Instruments. He first applied to practical 
 use the beautiful theorem of Huygens respecting the 
 convertibility of the Centres of Oscillation and Sus- 
 pension of the pendulum. A metallic bar pendulum 
 was provided with two parallel knife-edges facing op- 
 posite waysj and upon either of which it might be 
 swung. They were so arranged that when either was 
 used as the point of suspension, the other nearly re- 
 presented the centre of oscillation, and by means of 
 a small adjustable weight, this condition might be ac- 
 curately fulfilled ; in which case (by Huygens' princi- 
 ple)the distance between the knife-edges corresponded 
 accurately to the length of an equivalent simple pen- 
 dulum. This elegant application was farther tested 
 by Mr Baily, but it was found liable to serious prac- 
 tical objections. Baily dispensed with the sliding 
 weight, and rendered the pendulum invariable : the 
 distance of the knife-edges was adjusted by grinding. 
 
 To Kater we owe the invention of the floating Col- 
 limator, for ascertaining the accurate zero or level 
 points of divided astronomical instruments. The op- 
 tical principle on which it depends is a very beau- 
 tiful one, and the invention of Kater, with several 
 improvements in point of form, has become the auxi- 
 liary of nearly every observatory in the world. It is 
 one of those small but happy improvements which 
 affect materially the progress of Science. 
 
 Francis Baily, whowas bom 28th Aprill774, and 
 who died 30th August 1844, was an instance of a 
 person not endowed with extraordinary talents, yet of 
 singular use in his generation. Those who knew Mr 
 Bailypersonally, and what he accomplished for Astro- 
 nomy, are best aware how rare and yet how estimable 
 are such qualifications as his. Born of parents of a 
 middle rank of life, educated at a country school, and 
 at an early age thrown into the vortex of commer- 
 cial life in the city of London, no probability could 
 have appeared more remote than that he should ac- 
 quire the respect of even the most accomplished As- 
 tronomers by his scientific acquirements and perform- 
 ances. He enjoyed the advantage, in the first place, 
 
 of a perfectly sound and uninterrupted state of health 
 until his 7 0th year. His intellect partook of the 
 equable tone of his bodily powers. Method, and an and charae- 
 ardour which, instead of acting by impulses, seemed *®'"' 
 inexhaustible and unvaried, were the secrets of his 
 success. Mr Baily never was hurried, and he never 
 was unemployed. He had always leisure to encourage 
 men of like tastes, and he was never unwilling to learn 
 from any one who had knowledge to communicate. 
 To do one thing at a time was his first principle. 
 When thoroughly accomplished, it was completely put 
 aside, and a fresh subject undertaken. Whether an 
 experiment or a calculation was found to require a 
 month or three years, it was pursued to a successful 
 completion, without stint or grudging. No amount 
 of contrariety and failure in such matters was ever 
 known to rufile his temper, or to make his persever- 
 ance falter. 
 
 Francis Baily was known, in the first place, as the (2*3.) 
 founder (in 1820) of the Astronomical Society of fj,"""*^^^^^^ 
 London, an institution of signal utility, which has nomical 
 ever since been conducted with great judgment and Society, 
 success. His accurate knowledge of past and current 
 astronomical history, and his personal acquaintance 
 with most European astronomers, enabled him to 
 conduct its affairs with great advantage. 
 
 Amongst his other acquirements, he studied his- (244.) 
 tory and chronology with his customary precision. A Writings 
 very able paper on the date of the celebrated Eclipse °"^ "sIIt^' 
 of Thales was his earliest scientific publication,^ and Catalogues, 
 the literature and phenomena of solar eclipses occu- 
 pied his particular attention ever afterwards. His ac- 
 counts of the Eclipse of 1820, of the Annular Eclipse 
 of 1836, which he observed at Jedburgh, and the Total 
 Eclipse of 1842, with its marvellous revelation of the 
 rose-coloured protuberances of the solar atmosphere, 
 are among the most interesting and classical of his 
 writings. He promoted greatly the formation and 
 publication of accurate Star Catalogues, and he in- 
 vented, independently of Bessel, constant numbers 
 for facilitating the calculation of Precession, Nuta- 
 tion, and Aberration, as affecting the places of parti- 
 cular stars. He also published a most useful collec- 
 tion of Astronomical Tables and Formulae, and an 
 elaborate and very curious life of Flamsteed, 
 
 I shall now proceed to notice his experiments on 
 the Pendulum, which are more particularly connected 
 with the present section. 
 
 Mr Baily's most important observations were on 
 a correction of the motion of a pendulum long mis- pendulum 
 understood. The corrections usually admitted were observa- 
 the following: — 1. For temperature altering theti*"^- 
 length of the pendulum. 2. For the height of the 
 station above the level of the sea. Dr Young showed 
 that this correction was commonly overrated, owing 
 to the sensible amount of the attraction of the ele- 
 vated land on which the experiment is made. 3. For 
 
 (245.) 
 
 . (246.) 
 Baily's 
 
 1 Phil. Trans. 1811, 
 
Chap. III., § 4.] ASTRONOMY. — BAILY — COLONEL EVEEEST— M. STRUVE. 
 
 55 
 
 to a va- 
 cuum. 
 
 the air's buoyancy. The mere resistance of the air 
 to the motion of the pendulum may be shown to pro- 
 duce opposite and compensating effects in the descend- 
 ing and ascending semi-vibrations : but the presence 
 of air, as of any other fluid, diminishes the total ef- 
 fect of gravity on the bob, and that in a degree de- 
 pending on the density of the air or atmospheric 
 pressure. But besides this obvious " reduction to a 
 vacuum," it appears that the air acts also in a dif-- 
 ferent way. Owing to its inertia and cohesion a 
 portion of air is shoved along with the pendulum, 
 or otherwise put in motion by it, and the force 
 thus spent in moving air is not compensated during 
 Reduction the two semi- vibrations. This effect was clearly as- 
 certained and measured by Dubuat about 1786, and 
 described in the second edition of his " Principes d'Hy- 
 draidique ;" but it appears to have been totally un- 
 observed by his own countrymen and others, who 
 (like Borda) were soon after actively engaged with the 
 same subject. The effect was experimentally re-dis- 
 covered by Bessel, and made the subject of an admi- 
 rable series of experiments by Baily, which were pub- 
 lished in the Philosophical Transactions for 1832. 
 He vibrated pendulums of different forms in vacuo 
 and in air (as Colonel Sabine had done to a more 
 limited extent shortly before), and he ascertained the 
 corrected " reduction to a vacuum" to be in many in- 
 stances double of the old correctidn, and to depend 
 materially on the form and density of the pendulum. 
 It ,even appeared that when a convertible pendulum 
 is swung in two positions in the manner of Kater, 
 the correction is different in the two cases, owing to 
 the want of symmetry, so that a pendulum convert- 
 ible in air of a given density is not convertible in va- 
 cuo, nor vice versa. 
 
 Bessel and Baily agree in imputing the effect to 
 the clinging of a mass of air to the metallic pendu- 
 lum, thus rendering it in effect a pendulum of much 
 less density, for which the ordinary correction for 
 buoyancy will have to be increased. This view is 
 probably rather a popular than an exact expression of 
 the fact, and the correction need not be always pro- 
 portional to that of buoyancy. Poisson has treated 
 the question mathematically, and Professor Stokes 
 has recently resumed the whole subject, both mathe- 
 matically and practically, and considers that he has 
 arrived at precise mathematical results in several 
 cases. The result may probably be a revival of inte- 
 rest in pendulum observations, which has manifestly 
 very much declined since the existence of this irregu- 
 larity has been fully established, and the incompe- 
 tency of existing rules for " reduction to a vacuum" 
 clearly shown. 
 
 In 1833, Baily deduced from the very elaborate 
 experiments of Captain Foster in both hemispheres 
 ^^ for the earth's compression. Colonel Sabine had 
 found it ^ from his own observations. The French 
 and Russian observers concur in obtaining a result 
 sensibly greater. Of these experiments, Captain Fos- 
 
 (247.) 
 
 Investi- 
 gated by 
 Bessel and 
 otliers. 
 
 Mr Stokes. 
 
 (248.) 
 Result as 
 to Barth's 
 oblateness. 
 
 ter's is by much the most extensive. Mr Baily's re- The Caven- 
 petition of Cavendish's experiment for determining ^.'^*' ^^P^" 
 tiie earth's density, has been mentioned in a previous 
 section. 
 
 In conclusion of the subject of the figure of the (249-) 
 earth deduced from observation, I shall now briefly ^3™°/;^^! 
 refer to the results of geodetical measures more re- measures : 
 cent than those noticed in the first section of this — Colonel 
 chapter, which comprehended the great French arc. ^^^0^'" 
 In a matter so much of detail, which will be bet- 
 ter appreciated from special articles in the Encyclo- 
 pcedia, I shall best fulfil the ends of this discourse, 
 by merely directing attention to the two most con- 
 spicuous and important of these measurements of 
 the earth, one in India, the other in central and 
 northern Europe ; the first directed by Colonel Eve- 
 HEST, the second by M. Stexjve, the eminent asfrono- 
 mer of Pulkowa. 
 
 The measurement of an arc of the meridian in In- (250.) 
 dia by Colonel Lambton in the early part of this cen- ^^ "g^"" 
 tury, has been mentioned in a former part of this rest's In- 
 Dissertation, as well as in Sir John Leslie's. But its dian arc. 
 value has been prodigiously increased by the exten- 
 sion of the same by Colonel Everest, who was at one 
 time the principal assistant and coadjutor of Colonel 
 Lambton. The arc of Lambton, extending from Punnae 
 (Lat. 8° 9' 35") to Damargida (Lat. 18° 3' 15"), was 
 measured after the model of the English trigonome- 
 trical survey, by means of a 100-feet steel chain for 
 the base, a 3-feet theodolite for the azimuths, and a 
 5-feet zenith sector for latitudes. Colonel Everest 
 pursued the triangulation in a northerly direction for 
 some years after the death of Lambton in 1823; 
 but losing his health, and being forced to return to 
 Europe, he was provided, by the princely munificence 
 of the East India Company, with an entirely new set 
 of instruments, and with two able assistants, Cap- 
 tains Waugh and Eenny. 
 
 He resumed operations in 1832, which were con- (251.) 
 tinned until 1840, and included an entirely new ^^^*^°^''^*'''' 
 measurement of an arc extending from Damargida, which it 
 where Lambton's arc terminated, to Kaliana (Lat. i^as exe- 
 29° 30' 48"), a space of 797 miles, covering an arc <="''«'^- 
 of 11° 27' 33". The latest geodetical improvements 
 were introduced. The bases were measured by Ge- 
 neral Colby's compensating bars, in which the effect 
 of temperature is self-corrected. The signals from 
 station to station were made during the day by he- 
 liotropes reflecting the solar ray parallel to the sides 
 of the triangles to be measured. The azimuths were 
 determined by a 3-feet theodolite of Troughton, in 
 addition to that of Carey used by Lambton ; the 
 astronomical observations were made with two circles 
 of large dimensions. The difficulties and annoyances 
 experienced in conducting so vast a work, requiring 
 such excessive accuracy, in so remote a situation, 
 can only be judged of by referring to Colonel Eve- 
 rest's graphic details contained in his elaborate ac- 
 
56 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 count of it, published at the East India Company's 
 expense in 1847. The heats and the rains, the 
 dull opake atmosphere of the Doab, with its bound- 
 less and densely-wooded flats, the jungle fever and 
 the wild animals, were natural impediments enough. 
 But Colonel Everest, whose conscientious anxiety 
 reached almost a nervous pitch, seems not to have 
 been satisfied with any one instrument which the 
 mechanicians of London could produce ; but to 
 have metamorphosed most of them, partly with his 
 own hands, partly by native aid. It says much for 
 his ability in this respect, that the results appear 
 entitled to compete with all the most exquisite of the 
 kind in Europe. His bases, for instance, about 7J 
 miles in length, when checked by intermediate trian- 
 gulation above 400 miles in extent, differed in one 
 instance by 4, in another by 7 inches from the pri- 
 mary measurement. The whole extent of Lambton's 
 and Colonel Everest's operations includes a continu- 
 ous arc of 21° 21' (1477 miles), by far the greatest 
 at that time executed. 
 (252.) It is indeed only rivalled in this respect by a vast 
 Russian arc operation very lately executed in Russia and other 
 ^y **• northern countries of Europe, by which an arc of 25° 
 20', extending from the banks of the Danube to the 
 shores of the Arctic Sea, near the North Cape, has 
 been measured under the general superintendence 
 and direction of that able astronomer M. Struve, 
 whose meritorious labours in other departments of 
 astronomy will be specified in a succeeding section. 
 The results are still incomplete, though the opera- 
 tions in the field were happily concluded just in time 
 to prevent their total frustration by the unhappy war 
 in which Russia has since engaged. 
 (253.) The arcs of India and of Russia include a space 
 Its extent, g.^^ j^^^ 3° to Lat. 71°, with the exception of only 
 about sixteen degrees, and are unquestionably the 
 most important which exist for the determination of 
 the earth's figure. When to them we add the French 
 arc of 12° 22' in a medium latitude, it will scarcely 
 be necessary to take, into account any other, at least 
 for the Northern Hemisphere. 
 (254.) The following brief details of the Russian arc are 
 taken from the provisional report of M. Struve (1852). 
 (255.) The southern extremity of the Russo-Scandinavian 
 
 the'E^'sso- ^^'^ i* ^^^^^ °^ ^^^ Danube (Lat. 45° 20'), the north- 
 Scandina- ern extremity is Fuglenaes on the island of Qualoe 
 vian Arc. in Finnmarken (Lat. 70° 40'). The interval from 
 Tornea to Fuglenaes (4"49') was measured by Swedish 
 and Norwegian engineers; all the remainder by those 
 of Russia, and, in particular, by M. Von Tenner, who, 
 with M. Struve, has since 1816 directed the whole 
 operation. The whole line is remarkably freefrom con- 
 siderable inequalities of ground, and from mountain 
 ranges, so that local attractions are probably incon- 
 siderable.' On the other hand, extensive forests ex- 
 
 tending over dead flats have, in the southern part of 
 the arc (as in India), occasioned great difficulties, and 
 compelled the erection of numerous temporary struck 
 tures to overlook the country. In the north the 
 extraordinary refractions have, as usual, created some 
 difficulties. Ten different base lines, all at a small 
 height above the sea, form part of the operations. 
 It is a very satisfactory circumstance, that by the 
 care of M. Struve and Mr Airy, the standards of 
 length used in the Indian and Russian arcs have 
 been directly compared. 
 
 The calculation of the figure of the earth from the (256.) 
 completed Russian arc, in combination with others, General re- 
 has not yet been made, but it is believed that it ^^^ Earth's 
 will indicate an ellipticity somewhat greater than eilipticity 
 that generally received.' The results obtained by Co* from geo- 
 lonel Everest, on the other hand, by comparing his ^'^ ' 
 arc with those of Europe, give generally small ellip- 
 ticities, that is under -gif,. The French and Indian 
 arcs, for instance, give ^{-g. Now Mr Airy had de» 
 duced 20 years ago from the best existing observa- 
 tions -^l-g ; Bessel, a few years later, obtained the al- 
 most identical result of ^J^; and Schmidt of ^ J j-- 
 The determinations by means of the pendulum are and from 
 somewhat larger. The extensive observations of Co- pendulum 
 lonel Sabine and Captain Foster concur in giving ^'^P®"" 
 an ellipticity of 5- J^ ; but the French experiments by 
 Duperrey and Freycinet lead to a result considerably 
 greater. The discrepancy between the geodetical and 
 pendulum results may of course be a real one de- 
 pending on local variations of density. The astro- 
 nomical determination from the lunar inequalities, 
 which might be expected to concur with the results 
 of the pendulum, gives (as we have seen in the chap- 
 ter on Physical Astronomy, Art. 63) ■^^3- at a mean. 
 
 I regret that my limits do not permit me to speak (257.) 
 of the measure of degrees of longitude or arcs of pa- British arc 
 rallel, as another test of the earth's figure. The rg-O^ P^'^'l^'- 
 suits, however, cannot compete in point of certainty 
 with those from arcs of the meridian. It may be sa- 
 tisfactory to add, that the British arc of parallel from 
 Greenwich to Valentia (west coast of Ireland) sen- 
 sibly accords with the earth's figure obtained inde- 
 pendently. 
 
 In connection with the subject of the pendulum (258.) 
 treated in the earlier part of this section, I shall here **• ^p"" 
 mention a very remarkable experimental observation 'Tt^ g™" 
 communicated to the Paris Academy of Sciences, on periment, 
 the 3d February 1851, by M. Leon Foucault, to 
 whom we also owe some ingenious experiments on 
 the velocity of light. It is not indeed connected with 
 the determination of the earth's figure, but it has a 
 connection with astronomy, inasmuch as it affords the 
 most remarkable and direct proof of the earth's rota- 
 tion round its axis. 
 
 ^ In India, on the contrary, the local attractions of the Himalaya must be very sensible ; indeed Mr Pratt has calculated them 
 to be so considerable, as to have given rise to a curious speculation by Mr Airy as to the circumstances which may tend to 
 diminish the attraction of mountain ranges. — {Phil.Trane, 1855.) 
 
Chap. III., § 5.] 
 
 ASTKONOMY. — M. FOUCAULT — M. ENCKE. 
 
 57 
 
 (269.) Suppose a considerable weight suspended by a wire 
 
 demon- of regular elasticity from a fixed point pr stand con- 
 ^^J^°^^g^nected firmly with the ground; and let us first ima- 
 ttttion. gine the place of the experiment to be exactly over 
 the North Pole. Let the wire pendulum be swung 
 so as to coincide with the plane of the meridian of 
 London. As the earth rotates, the wire and the ball 
 must evidently rotate too. But the motion of the 
 mass originally impressed parallel to a given plane 
 will continue in that plane, and consequently the 
 plane of motion will coincide in the course of 12 hours 
 with every meridian in succession, and the apparent 
 rotation will be entirely completed in a uniform man- 
 ner in 24 hours. In any other latitude than 90°, 
 but greater than 0°, a continuous and regular appa- 
 rent change of motion must also occur, since a me- 
 ridian of the globe does not preserve its parallelism 
 during diurnal motion, excepting only at the equator; 
 consequently, at all points of the earth's surface, ex- 
 cept at the equator, the plane of motion of the pendu- 
 lum will vary uniformly in azimuth — quicker, how- 
 ever, in high than in low latitudes. To find this 
 velocity, it is only necessary to decompose the rota- 
 tion of the earth round its axis into two, one of which 
 (which is alone efiective) is round the vertical of the 
 place of observation. The apparent angular motion 
 is thus proportional to the sine of the angle of lati- 
 tude. Thus, in an hour, it is 15° x sine lat. 
 
 M. Poucault's experiment was made, in the first in- (260.) 
 stance, with a pendulum of steel wire from -03 to -05 Corrections 
 inch in diameter, bearing a ball of 12 pounds weight, tended to. 
 It is desirable to make the pendulum vibrate in small 
 arcs, in consequence of the tendency to ellipticity in 
 the vibrations, which is necessarily accompanied by a 
 rotation of the major axis of the ellipse, which might 
 easily be mistaken for the influence of the earth's 
 motion. To take account of this disturbing force, 
 we have only to measure accurately the greater and 
 less axes of the ellipse described. Then a revolution 
 of the apsides (from this cause only) will be per- 
 formed in a time which will be found by multiply- 
 ing the time of a double vibration of the pendulum 
 by 8 times the square of the length of the pendulum,, 
 divided by 3 times the -product of the two axes of the 
 ellipse. This formula is due to Mr Airy. The theory 
 of M. Foucault's beautiful experiment has been 
 verified by numerous experiments in difierent la- 
 titudes. 
 
 Very recently the theory of the motion of a pen- (261. ) 
 dulum suspended by a thread or wire has been con- j^^g^y"^ 
 sidered in the most general manner by M. Hansen, gated by M. 
 the physical astronomer, with reference to the earth's Hansen, 
 motion.^ It is an intricate problem of analytical 
 mechanics. But the results show, as might have been 
 anticipated, that all the sensible results are those which 
 the geometrical treatment of the question indicate. 
 
 (262.) 
 Professor 
 Encke. 
 Periodic 
 Comets. 
 
 (263.) 
 Halley's 
 Comet — 
 period 76 
 years. 
 
 5. M. Encke. Cometary Astronomy — Periodic Comets of Halley and Encke. Gambart's anrf 
 Biela's Comet — Comets of 1811 and 1843. Mr Hind — New Planets or Asteroids. Mr Las- 
 SELL — Newly discovered Satellites. Mr Bond. 
 
 Professor Johann Franz Encke, Director of the 
 Observatory of Berlin, is one of the most eminent 
 physical and practical astronomers of the present day. 
 The author of many valuable observations and im- 
 portant memoirs, he is best known by those which 
 are connected with the motions and theory of Comets. 
 I shall therefore devote this section to an abstract of 
 the progress of this interesting subject, and more 
 particularly of M. Encke's discoveries and specula- 
 tions. I must premise, however, that, easy and 
 agreeable as it would be to introduce here a detailed 
 essay on Cometary Astronomy, the design and extent 
 of this discourse alike forbid it, and at the cost of 
 some self-denial, I will endeavour to confine myself 
 entirely to what is most new and characteristic in the 
 Cometary history of later years. 
 
 Halley's Comet. — Before proceeding to describe 
 the remarkable comet especially connected with the 
 name of Encke, it will be proper to resume the his- 
 tory of Halley's Comet where it has been left off by 
 Sir John Leslie in his Dissertation. That Comet — ■ 
 the comet of 1682 — must ever remain memorable, 
 perhaps the most so of its class, as being the first 
 
 whose return was confidently predicted, in firm reli- 
 ance on the Newtonian Theory of Gravity. Halley's 
 announcement — grounded not on vague analogies, 
 but on laborious computations — that it would reap- 
 pear early in 1759, was realized almost to the letter ; Its return 
 and Clairaut, whose surprising analytical ability often ^° ^^^^• 
 left but little to his successors to accomplish, calcu- 
 lated the perturbations with an accuracy which even 
 the present state of physical astronomy has hardly 
 exceeded. Indeed no general method for calculating 
 perturbations in highly elliptic orbits is as yet in use, 
 &nd though the methods of Clairaut have been super- 
 seded by those of Lagrange and Bessel and Lever- 
 rier, the summation of the efiiscts by the method of 
 " quadratures" is always used, — the periodic time of 
 the comet being divided into short intervals through- 
 out which the elements are considered invariable, and 
 during which the configurations and perturbing effects 
 of the principal planets are computed with much 
 labour. 
 
 The chief improvement in the calculation of per- (264.) 
 turbations is the introduction by Lagrange of the cele- 
 brated method of the Variation of the elements (44.) 
 
 1 Theorie der Pendelbewegung. Dantzig, 1853. 
 
58 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Itspertur- His successors have distinguished themselves chiefly 
 ''^*"Tt a ^y *^® praiseworthy minuteness and extent of their 
 by various calculations, which are amongst the most laborious, 
 astrono- if not indeed the most laborious, which occur in Phy- 
 mers. gjga,! Astronomy. The computers who calculated 
 the return of Halley's Comet in 1835 were four in 
 number, MM. Damoiseau, Pontecoulant, Lehmann, 
 and Rosenberger. Their memoirs are all considered 
 by competent judges to be excellent, but especially 
 that of Rosenberger, who calculated more fully than 
 the others the perturbations from 1682 to 1759, and 
 who has introduced a theoretical correction of some 
 importance. Some idea of the extent of these calcu- 
 lations may be formed from the fact, that in some 
 parts of the orbit the Elements were made to vary 
 for intervals of only two days. The Comet of Halley 
 was rediscovered at Rome on the 6th August 1835, 
 in the Jesuits' College. The error of Rosenber- 
 ger's Ephemeris was only seven minutes of arc, and 
 the perihelion passage took place on the 16tli No- 
 vember (civil reckoning), five days after the predicted 
 time. Bessel states the remarkable fact, that the coin- 
 cidence of the comet's path with the results of previous 
 calculation is as close as the use of five-place loga- 
 rithms in computing the perturbations would permit. 
 All this is very creditable to the state of Astronomy ; 
 still it is infinitely less remarkable than Clairaut's 
 approximation, only a little less close, made 77 years 
 before. It is a matter of regret that neither in the 
 matter of this comet, nor in any other point of theory 
 connected with Cometary movements, have our coun- 
 trymen made any considerable advance since the time 
 of Halley. 
 (265.) ^t itg return in 1835, this Comet was watched 
 in.l835. lentil May 1836, and in the course of its long visibi- 
 lity was made the subject of minute and admirable 
 telescopic researches, by Bessel in Europe, and by 
 Sir John Herschel at the Cape of Good Hope. Their 
 observations strictly confirmed a remark of M. Valz, 
 that the Tails of Comets, though evidently generated, 
 under the influence of the neighbourhood of the Sun, 
 yet commonly disappear at the period of closest ap- 
 proach. This, at least, was the case with Halley's 
 Comet. The tail began to grow on the 2d October, 
 two months after its discovery, and diminished after 
 the 15th (a month before perihelion). The comet re- 
 appeared in the end of January without any vestige of 
 a tail, and then dilated in absolute bulk with in- 
 credible quickness. But before its final disappear- 
 ance, on the 5th May, the tail is supposed to have 
 Its peculiar been reabsorbed into the nucleus, which presented 
 then a uniform circular outline. The evolution of 
 the highly-expansible luminous matter of the tail 
 took place from the nucleus in luminous fan-like 
 jets, directed on the whole towards the Sun, and 
 issuing on the side of the Comet exposed to that 
 body. The jets had a vibratory motion. The tail 
 
 (directed /rom the Sun) was formed by the abrupt 
 inflexion of these efiluent jets, in a manner resem- 
 bling electrical repulsion; and Sir John Herschel has 
 not hesitated to ascribe the phenomenon to the com- 
 bination of a repulsive force as respects the Sun, 
 (" of an energy very far exceeding the gravitating force 
 towards that luminary") with " a peculiar and highly 
 energetic attraction to the nucleus, differing from, 
 and exceptional to, the ordinary power of gravita- 
 tion."^ The opinion that polar forces resembling 
 magnetism or electricity are necessary to explain the 
 phenomena of Comets, has been for some time cur- 
 rent in G-ermany, and received, I believe, the coun- 
 tenance of Bessel. That there exist in the movements 
 of these bodies anomalies so great as to render the 
 sufiiciency and completeness of the Theory of Gravity 
 suspected by such high authorities, makes the state- 
 ment of them very important, though I confess a 
 great reluctance to share in the conclusion. 
 
 I shall terminate this notice of Halley's Comet" (266.) 
 with a table of the dates of its probable perihelion Jetonsf ''^ 
 passages, according to M. Laugier and Mr Hind.^ 
 The earlier appearances are deduced from the Chinese 
 Annals : — 
 
 features. 
 
 Date. 
 
 Interval. 
 
 Date. 
 
 IntervaL 
 
 B.C. 11-80 
 
 Tears. 
 
 
 Tears. 
 
 
 77-87 
 
 
 77-45 
 
 A.D. 66'07 
 
 
 A.D. 989-70 
 
 
 
 75-17 
 
 
 76-65 
 
 141-24 
 
 
 1066-25 
 
 
 
 77-02 
 
 
 79-06 
 
 218-26 
 
 
 1145-30 
 
 
 
 76-99 
 
 
 78-22 
 
 295-25 
 
 
 1223-52 
 
 
 
 78-59 
 
 
 78-29 
 
 373-84 
 
 
 1301-81 
 
 
 
 77-66 
 
 
 77-04 
 
 451-50 
 
 
 1378-85 
 
 
 
 79-34 
 
 
 77-69 
 
 530-84 
 
 
 1466-44 
 
 
 
 77-96 
 
 
 75-21 
 
 608-80 
 
 
 1531-65 (o. 
 
 s.) 
 
 
 76-00 
 
 
 76-14 
 
 684-80 
 
 
 1607-82 (n 
 
 s.) 
 
 
 75-64 
 
 
 74-88 
 
 760-44 
 
 
 1682-70 
 
 
 
 76-82 
 
 
 76-49 
 
 - 837-26 
 
 
 1759-19 
 
 
 
 74-99 
 
 
 76-68 
 
 91225 
 
 
 1835-87 
 
 
 The differences in the above periods are attributed to 
 the effects of perturbation. The extreme distance of 
 the Comet's path from the Sun is 35 J times the ra- 
 dius of the Earth's orbit, which is only one-sixth part 
 greater than the distance of Neptune, and therefore 
 nearly within the recognized limits of the planetary 
 system. 
 
 Comet of Enche. — Next in interest to the Comet (267.) 
 of Halley is that discovered by Pons of Marseilles ^^^f 
 in November 1819, which was first suspected,- then 
 proved by Professor Encke, to revolve in an elliptic 
 orbit of short period (considerably interior, in fact. 
 
 1 See Sir John Herschel's Ouflines pf Astronomy, and Mesulti of Obeervationi at the Cape of Good Hope, 
 3 Taken from Mr Hind's small work on Comets. 
 
Chap. III., § 5.] 
 
 ASTEONOMY. — M. ENCKE — GAMBART. 
 
 59 
 
 (268.) 
 Cometary 
 orbits de- 
 rived from 
 observa- 
 tion. 
 
 (269.) 
 M. Enclce's 
 researches 
 on the 
 comet of 
 1819— pe- 
 riod SJ 
 years. 
 
 to the orbit of Jupiter), and made the subject by 
 him of a series of investigations altogether peculiar. 
 On this account it bears the name of Encke, instead 
 of that of its discoverer Pons, although M. Encke 
 himself, with unaffected modesty, always describes it 
 as the Comet of Pons. 
 
 Newton gave, in the Principia, his celebrated so- 
 lution of the problem of determining a Comet's orbit 
 assumed to be parabolic, from three geocentric places. 
 This solution has been simplified and improved by 
 Lagrange and Boscovich, and also by Olbers. La- 
 place gave a method for an elliptic orbit, which may 
 represent any number of observations. Gauss, in 
 his Theoria MoHs Corporum Celestium, treated the 
 subject with great skill and generality. I am unable 
 to state who first attempted to discriminate an ellip- 
 tic from a parabolic cometary orbit, or to determine 
 the period in the former from observations at one ap- 
 parition only. It is evident that such outstanding 
 differences as are irreconcilable with a parabolic 
 orbit, will be most perceptible in the case of comets 
 whose orbits have a tolerably short major axis, or 
 whose period is not very great, and will be mate- 
 rially increased by watching a comet through a con- 
 siderable part of its orbit, which the assiduous appli- 
 cation of telescopes to every part of the heavens has 
 of late years rendered much more frequent than for- 
 merly. Amongst others, Bessel, who has signalized 
 himself by a capital performance in this, as in every 
 other department of Astronomy, applied rigorous me- 
 thods to determine the orbits of the comets of 1807 and 
 1815 ; the latter of which will very probably return 
 to its perihelion in 1887. It is undeniable, however, 
 that expert calculators have often been deceived in 
 assigning orbits, even when believed to be of short 
 period, founded upon a single apparition. 
 
 M. Encke, however, was more fortunate in the case 
 of the first comet of 1819. Using the methods of 
 Gauss, he showed that an Elliptic Orbit of about 3;^ 
 years must be admitted, and that the comet had pro- 
 bably been already observed in 1786, by M6chain, in 
 1795 by Miss Herschel.^ and in 1805 by Pons. He 
 investigated with great labour the effects of the planet- 
 ary perturbations on this body, which, in the case of 
 Jupiter, are occasionally very large, if that planet be 
 in the part of its orbit near the aphelion position of 
 the comet, when it approaches the orbit of Jupiter. 
 The careful calculations of M. Encke for the next re- 
 turn in 1822 were verified by the observations of Sir 
 Thomas Brisbane, at that time fortunately governor 
 of New South Wales, where he had, with character- 
 istic liberality, founded an Observatory. Since then, 
 this body, insignificant in its physical appearance 
 (being to all appearance a small cloud of vapour 
 without a solid nucleus), has been detected in one or 
 
 another part of the world at every revolution : — 
 namely, in 1825, 1828, 1832, 1835, 1838, 1842, Its appa, 
 1845, 1848, and 1852 ; so that the Comet has been"*^""'' 
 observed at fourteen (not all consecutive) returns. 
 
 The complete establishment of the existence and pe- (270.) 
 riodicity of a comet, quite in the interior of the planet- ^^^^^ ^^ 
 ary system (its greatest distance from the Sun being tion 
 four times the Earth's distance, and its least distance 
 but one-third of the Earth's), was a discovery in itself 
 highly interesting. But something yet remained be- 
 hind. Professor Encke, in comparing the earlier with 
 the later apparitions of the Comet, detected a gradual 
 acceleration of its movement, which amounted be- 
 tween 1786 and 1838, to 1-8 days, on a period of about 
 1211 days; being about 2|- hours per revolution. 
 Whatever may be the cause of this, the /aci is undis- 
 puted, even by Bessel, who was indisposed to accept 
 M. Encke's explanation. This fact, it will be observed, 
 is unique in Astronomy. The major axis and periodic 
 times of the planets and satellites have, as we have 
 seen in the chapter on Physical Astronomy, no secu- 
 lar variation. The moon's apparent acceleration has 
 been otherwise accounted for. M. Encke at once, attributed 
 and at an early period, attributed the acceleration of*" * ™'^8*" 
 
 . • XDS ins- 
 
 the Comet s mean motion to the effect of a slightly dium. 
 resisting medium, insensible in the case of the planets, 
 partly owing to their incomparably greater density (for 
 this Comet appears to be one of the most loosely ag- 
 gregated bodies known, being transparent to its very 
 centre); and also, to the circumstance, that the density 
 of the ether or resisting medium is assumed to dimi- 
 nish rapidly at a distance from the Sun. M. Encke 
 supposes it to decrease in density with thB square of 
 the distance, and only to affect the Comet sensibly 
 within 25 days preceding or following its perihelion. 
 That the effect of resistance is to accelerate the return 
 of the Comet is evident, by considering that the pro- 
 jectile force becoming gradually extinguished, the 
 Sun's attraction must be more available to pull the 
 body inwards at each revolution, thus shortening the 
 major axis of the ellipse, and diminishing the time. 
 
 In order satisfactorily to arrive at any such con- (271.) 
 elusion, it was of course necessary to estimate with P«'^'">'ba- 
 great accuracy the perturbing effects of the planets Encke's 
 on the Comet's motion; and it is not a little curious comet ap- 
 and satisfactory, that the movements of this insigni- P'^®? *" 
 ficant erratic body should have occasioned a niate-|^°ggg^Qf ^ 
 rial rectification of the masses of two of the Planets. Mercury 
 M. Encke very early suspected that the received ^^d Jnpi- 
 mass of Jupiter was too small, a fact clearly esta- 
 Wished afterwards by Mr Airy ; and in 1838 M. Encke 
 showed that the mass of Mercury (which, not having 
 a satellite, was little more than guessed at previously) 
 had been assumed nearly three times too great by La- 
 grange. The perihelion of the Comet approaches much 
 
 Miss Caro- ^ Caroline Liicretia Herachel, sister of Sir William and aunt of Sir John Herschel, deserves a passing notice, not only as the 
 line Her- independent discoverer of eight comets (of which five were first seen by her), but as the indefatigable and intelligent assistant of 
 schel ' ^'"^ William Herschel during the busiest years of his life. For this service King George III., carrying out his judicious liberality 
 to her brother, gfranted her a small pension. She died at Hanover 9th January 1848, aged 97. 
 
 I 
 
60 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 (272.) 
 Theory of 
 a resisting 
 medium not 
 altogether 
 favourably 
 received. 
 
 (273.) 
 and still 
 questioned. 
 
 (274.) 
 
 (275.) 
 M. Encke 
 on pertur- 
 bations. 
 
 more nearly to the orbit of Mercury than the aphelion 
 does to that of Jupiter ; consequently at times the 
 perturbations due to the former planet may be very 
 great, and though the gravitating mass of the Comet 
 is utterly unknown, yet since the momentary direc- 
 tion of its motion depends solely on the ratio of the 
 attractive force of the Sun and Mercury, its observed 
 course gives the means of estimating that ratio.^ 
 
 The theory of a resisting medium was, on the whole, 
 well received, especially in England, where some of 
 our first authorities gave it their adhesion. The then 
 recent establishment of the Undulatory Theory of 
 Light, was thought by many to receive a confirmation 
 from this evidence of something material filling the 
 planetary spaces. In Germany the hypothesis of re- 
 sistance received the complete opposition of Bessel's 
 high authority ; who declared that " a hundred other 
 reasons" might be found for the fact of the accelera- 
 tion, vjhieh he admits to be true. Encke, in reply, 
 reduces these IQO possible hypotheses to four, of which 
 we shall mention only one, as seemingly important, 
 namely, the forces exerted with so much intensity 
 witliin the body of the Comet itself, as indicated by 
 the projection of the tail. But he observes, with great 
 sagacity, that these forces, being apparently usually 
 excited in the line of the radius-vector joining the 
 Comet and the Sun, can hardly be supposed to afiect 
 the periodic time. It having also been objected that 
 Halley's Comet shows no trace of acceleration, but, if 
 anything, of the reverse, M. Eneke truly says, that 
 its perihelion distance does not lie witliin the assumed 
 limits of the denser ether. 
 
 Nevertheless, the theory of a resisting medium in 
 space is not perhaps very popular, except in England. 
 Althougl* M. de Humboldt appears to favour it, I 
 understand that the German astronomers in general 
 scarcely regard it as in any degree proved. 
 
 Yet, if not true, the cardinal fact remains unex- 
 plained. The anomalous phenomena of the Tails of 
 Coniets, considered by Herschel to be altogether inex- 
 plicable by the law of gravity, demand the closest 
 scrutiny ; and one can hardly help supposing that 
 the two diiSculties may be in close connection. As 
 the Newtonian law is now considered (since the dis- 
 covery of Neptune, and the latest corrections of the 
 Ltinar Tables) to be ahsolutely siufficient to account 
 for everything connected with planetary motion, the 
 Astronomy of Comets will be looked to with increas- 
 ing interest, as likely to reveal some laws of nature 
 not otherwise to be detected. In this respect. Pro- 
 fessor Encke's labours are likely to be more and more 
 important in their results. 
 
 With reference to this very eminent astronomer, 
 we have only to add, that he has for a great many 
 years been at the. head of the Observatory at Berlin, 
 and in that capacity has published an Astronomical 
 Ephemeris of first-rate excellence. It is as a phy- 
 
 sical astronomer, however, that he will be principally 
 remembered. Besides his admirable investigations 
 connected with the Comet, he improved the theory of 
 Vesta, and has very lately published a new Method 
 of Computing Perturbations, especially for orbits con- 
 siderably elliptical. Neptune was discovered at his 
 Observatory, by the assistant astronomer, M. Galle. 
 
 Gamhart's and Biela's Comet. — Jean Gambaet, (276.) 
 one of the most promising astronomers in France, died Gambart's 
 of consumption at a comparatively early age, I believe ^^^^^ 
 in 1836. He was director of the Observatory at Mar- 
 seilles, which, notwithstanding its very unfavourable 
 position in the midst of the town, has acquired con- 
 siderable celebrity as regards the discovery and obser- 
 vation of Comets. Pons, by whom Encke's Comet was 
 found, both in 1805 and 1818, conducted the Ob- 
 servatory ; but its mounting was as bad as its situa- 
 tion, and Pons used despairingly to describe his tele- 
 scope as rather 'paralytic than parallactic. To this 
 crippled establishment M. Gambart succeeded, and by 
 his skill in managing his defective instruments, and 
 by his patience in sweeping for Comets, he discovered 
 and subsequently computed the orbits of a number of 
 these bodies between 1822 and the period of his death. 
 Gambart was highly esteemed, both by French and 
 foreign Astronomers. Pons also deserves great credit 
 for his extraordinary diligence in the discovery of 
 Comets, and M. Valz, who still directs the Obser- 
 vatory of Marseilles has cultivated this and other 
 branches of the science with success. 
 
 Gambart's most remarkable discovery was the pe- (277.) 
 riodicity of the first Comet of 1826, having' detected Periodicity 
 that body independently at Marseilles, though it had '" ^^ J**" 
 been observed some days previously in Bohemia, by 
 Biela, an ofiicer in the Austrian service. It is most 
 usually called Biela' s Comet, though it might with 
 equal right be termed Gambart's, who assigned its 
 path and predicted its return. Clausen, about the 
 same time with Gambart, assigned it a period of about 
 7 years ; and it was identified with former appear- 
 ances in 1772 and 1805-6. Its period thus appeared 
 to be 2460 days, or 6f years ; its aphelion is a little 
 exterior to Jupiter's orbit, and its perihelion is not 
 much within the Earth's. This Comet's orbit very 
 nearly intersects in one place the orbit of the Earth, 
 so that had the earth been one month forwarder in 
 its annual course in 1832, a collision would have 
 taken place, or at least the Earth would have been 
 enveloped in a cometary haze ; for it is difficult to 
 imagine a collision with a body whose tenmty is so 
 excessive, that Sir John Herschel perceived through 
 its entire thickness (estimated at 50,000 miles) stars 
 of the most excessive minuteness (16th or 17th mag- 
 nitude) as seen by his 20-feet reflector. It is an in- 
 teresting circumstance, that the first predicted peri- 
 helion passage, in 1832, took place within some hours 
 of the time fixed by MM. Santini and Damoiseau, 
 
 1 On the Masses and Densities of the Planets, see Encke in ^stron. Nachrichten, vol. xix., col. 187. 
 
Chap. III., § 5.] 
 
 ASTKONOMY. — MR HIND — MR LASSELL. 
 
 61 
 
 (278.) 
 
 (279.) 
 Division 
 of the body 
 of the co- 
 met in 
 1846. 
 
 (280.) 
 Other 
 periodical 
 comets. 
 
 (281.) 
 Great 
 comets of 
 1811 and 
 1843. 
 
 though the perturhations of Jupiter were, as usual, 
 large. 
 
 Biela's Comet has been since recognised in 1846 
 and 1852, but it was not seen in 1839. It does not 
 appear to be admitted that it shows any acceleration 
 due to a resisting medium. Its perihelion distance 
 is, however, considerable. 
 
 At the apparition of 1846 an extraordinary cir- 
 cumstance occurred. When discovered in the end 
 of November 1845 it appeared round and single. 
 On the 19 th December it was observed by Mr Hind 
 to be elongated, and ten days, later was seen in Ame- 
 rica (and soon after at Cambridge and elsewhere) to 
 have divided into two seemingly distinct nebulous 
 parts.* These continued to subsist and move inde- 
 pendently throughout the remainder of the appari- 
 tion : the real distance of the centres being about 
 150,000 English miles. In 1852 the comet was 
 rediscovered at Rome ; the division into two still 
 subsisting, but the interval of separation being in- 
 creased about eight-fold. 
 
 Besides the comets of Encke and Biela, there are 
 several others which are suspected on good grounds 
 to have periods of from 5^ to 7^- years, their aphelia 
 all lying in tolerable proximity to the orbit, of Ju- 
 piter. But among these. the return of only one has 
 yet been verified by observation ; namely, the comet 
 of Faye, which, after passing its perihelion 17th 
 October 1843, returned to it 3d April 1851, within 
 an hour of the time predicted by M. Leverrier. The 
 motion of comets of short period seems to be inva^ 
 riably direct or conformable to that of the planets. 
 The inclination of their orbits to the Ecliptic is 
 usually moderate. 
 
 Great Comets of 1811 and 1843. — ^The finest 
 comets of the last hundred years were those of 1811 
 and 1843. The former was observed for a length of 
 time altogether unusual, having been visible from 
 March 1811 to August 1812. There is pretty good 
 reason to think that its period is not much less than 
 3000 years. The comet of 1843 was even more 
 splendid, but its flight was more rapid, and it was 
 not favourably seen in northern latitudes. It was 
 visible at many places in broad daylight when less 
 than 4° from the Sun, and at one time a tail 65° in 
 length could be traced. The circumstance which 
 distinguishes this comet from all others which have 
 been computed is the smallness of its perihelion dis- 
 tance, which was only ^^5 of the radius of the Earth's 
 orbit, or the comet approached the Sun's body within 
 one-seventh of his radius. The solar disk then sub- 
 tended an angle at the comet of 121^°, or the glare 
 was equal to that of 47,000 suns as seen by us ! 
 The heat to which the comet was exposed is supposed 
 
 to have exceeded 24 times that concentrated by our 
 most powerful burning-glasses by which even rock 
 crystal has been fused.^ 
 
 Mk Hind. — Discovery of New Planets. — ^We have i^ii.) 
 spoken in a former section (161), of the discovery of Discovery 
 four small planets or asteroids between the orbits of of new 
 Mars and Jupiter. They were found between the years ^'g^^"^* -^""^ 
 1801 and 1807. An interval of nearly forty years 
 elapsed without any addition to the members of our 
 system. In 1845 a new asteroid, Astrsea, was found 
 by M. Hencke ; the following year was distinguished 
 by the discovery of Neptune under unparalleled cir- 
 cumstances ; and since 1847 every year, down to the 
 present time (1855), has added to our knowledge of 
 the group of asteroids. 
 
 Among the discoverers of these planetary bodies „ ^ S,^^ 
 Mr Hind has been distinguished by frequent success, 
 under circumstances which appeared by no means 
 peculiarly advantageous. This indefatigable obser- 
 ver and computer commenced (I believe) his astrono- 
 mical career as one of the assistants at (Greenwich, 
 and afterwards had the sole charge of the private ob- 
 servatory of Mr Bishop, a wealthy citizen of London, 
 together with the use of a fine refractor equatoreally 
 mounted. It is within the Regent's Park, close to 
 the smoke of the metropolis, that Mr Hind has dis- 
 covered a larger number of planetary bodies than 
 any other person Uving. Next to him M. de Gas- **• ?® ^'^ 
 paris of Naples has been most successful. Unques- 
 tionably the impulse towards these new discoveries 
 has been given by the indefatigable industry of astro- 
 nomers (principally those of Germany), in constructing 
 minutely accurate star-maps. Mr Hind is also advan- 
 tageously known by the discovery of several comets, 
 and by his ingenious observations in sidereal astro- 
 nomy, especially on variable stars. I shall here 
 give a table of the asteroids in the order of discovery 
 
 as at present known (July 1855). 
 
 ^ List of the 
 
 Asteroids. 
 
 1 Ceres 
 
 1801 Jan. 1 
 
 Piazzi. 
 
 2 Pallas 
 
 1802 March 28 
 
 Olbers. 
 
 3 Juno 
 
 1804 Sept. 1 
 
 Harding. 
 
 4 Vesta 
 
 1807 March 29 
 
 Olbers. 
 
 5 Astrsea 
 
 1845 Dec. 8 
 
 Hencke. 
 
 6 Hebe 
 
 1847 July 1 
 
 Hencke. 
 
 7 Iris 
 
 Aug. 13 
 
 Hind. 
 
 8 Flora 
 
 Oct. 18 
 
 Hind. 
 
 9 Metis 
 
 1848 April 26 
 
 Graham, 
 
 10 Hygeia 
 
 1849 April 12 ' 
 
 De Gasparis. 
 
 11 Parthenope 
 
 1850 May 11 
 
 De Gasparis. 
 
 12 Victoria 
 
 Sept. 13 
 
 Hind. 
 
 13 Egeria 
 
 Nov. 2 
 
 De Gasparia. 
 
 14 Irene 
 
 1851 May 19 
 
 Hind. 
 
 15 Eunomia 
 
 July 29 
 
 De Gasparis. 
 
 16 Psyche 
 
 1852 March 17 
 
 De Gasparis. 
 
 17 Thetis 
 
 April 17 
 
 Luther. 
 
 18 Melpomene 
 
 June 24 
 
 Hind. 
 
 19 Portuna 
 
 Aug. 22 
 
 Hind. 
 
 1 A similar phenomenon is related by Seneca, See Grant's History of Astronomy, p. 302. 
 
 ^ See many other interestine particulars of this comet in Sir 31 Herschel's Outlines of Astronomy, arts. 589, &c. See also in- 
 teresting details on the subject of comets generally in Mr Hind's and Mr Milne's works on comets, and in Mr Grant's excellent 
 History of Physical Astronomy, 
 
'1 1 
 
 62 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss, VL 
 
 20 Massilia 
 
 21 Lutetia 
 
 1852 Sept. 19 
 Nov. 15 
 
 De Gasparis. 
 Goldschmidt. 
 
 22 Calliope 
 
 23 Thalia 
 
 Nov. 16 
 Dec. 15 
 
 Hind. 
 Hind. 
 
 24 Themis 
 
 25 Phoceea 
 
 1863 April 5 
 April 6 
 
 De Gasparis. 
 Chacornac. 
 
 26 Proserpine 
 
 27 Euterpe 
 
 28 Bellona 
 
 May 5 
 Nov. 8 
 1854 March 1 
 
 Luther. 
 
 Hind. 
 
 Luther. 
 
 29 Amphitrite 
 
 30 Urania 
 
 March 1 
 July 22 
 
 Marth. 
 Hind. 
 
 31 Euphrosyne 
 
 32 Pomona 
 
 Sept. 1 
 Oct. 26 
 
 Ferguson. 
 Goldschmidt. 
 
 33 Polyhymnia 
 
 Oct. 28 
 
 Chacornac. 
 
 34 Circe 
 
 1855 April 6 
 
 Chacornac. 
 
 35 Leucothsea 
 
 April 19 
 
 Luther. 
 
 Mr Lassell. — New Secondary Planets. — Mr Las- 
 sell of Liverpool deserves a more lengthened no- 
 
 (284.) 
 New Se- 
 
 Plan"^ tice than bur limits will permit, not only as a dis- 
 Mr Lassell. tinguished discoverer, but as one wliose success can- 
 not be too -widely made known as an' encouragement 
 to others. This gentleman, engaged in mercantile 
 pursuits in an eminently commercial town, possessing 
 little leisure and no enormous fortune, has contrived, 
 in the intervals of business, to construct with his own 
 hands telescopes which in accuracy of definition ap- 
 pear to rival any which art stimulated by national 
 liberality has yet constructed elsewhere, and to use 
 them with a degree of skill and success which has 
 not been exceeded (nor in some respects equalled) 
 by any astronomer whether professional or otherwise. 
 I speak, let it be observed, of accuracy of definition, 
 such as is necessary to display minute points of 
 light, like the satellites of Uranus. In respect of 
 the amount of illumination requisite for the display 
 of many difiuse faint objects among the nebulae, the 
 gigantic telescopes of Herschel and Lord Eosse are 
 of course superior. 
 
 Mr Lassel's observatory near Liverpool was erected 
 in 1840. The principal instrument is a reflecting 
 telescope of 24 inches aperture (completed, however, 
 only some years later), mounted equatoreally, an ar- 
 rangement requiring great mechanical skill, but, as 
 the results show, most effectually accomplished. The 
 speculum was worked and polished by machinery con- 
 structed by Mr Nasmyth, but principally devised by 
 Mr Lassell, after he had examined and tried Lord 
 Eosse's method. I should think it must be admitted 
 to be the most perfect optical work of its kind ever 
 made : for I believe there is no test object in existence 
 which Mr Lassell has not seen with it ; in fact he 
 has discovered the most delicate tests himself, — the 
 6th star of the group 6 Orionis (though not first seen 
 
 (285.) 
 His instru- 
 ments. 
 
 by him), a satellite of Neptune, an eighth satellite of 
 Saturn, and several satellites of Uranus. 
 
 Not many days had elapsed after the discovery of (286.) 
 Neptune, before Mr Lassell, directing his telescope He disco- 
 to it, perceived a satellite (as he believed) on Oct. T^y^ °f" 
 10, 1846. The discovery was fully made out in the Neptune, 
 following year, and was soon after verified by the 
 great refractors of Pulkowa and Western Cambridge 
 (U.S.) Its period is about 5'879 days,^ and its dis- 
 covery was of singular importance as leading to a 
 knowledge of the mass of the planet. 
 
 Till 1848 only seven satellites of Saturn were ad- (287.) 
 mitted. The two closest to the planet were detected and one of 
 by Sir "William Herschel in 1789, and have been^'""'^"- 
 seen by very few astronomers since. During five 
 years' residence at the Cape, Sir John Herschel never 
 but once obtained even a doubtful glimpse of the 
 closest with an 18-inch mirror. The third, fourth, 
 and fifth were discovered by Cassini in 1684 ; the 
 sixth and most conspicuous by Huygens in 1654 : the 
 outermost by Cassini in 1671. To these an eighth 
 satellite, intermediate in position between the two 
 last, was added by Mr Lassell on the 19th September 
 1848. By a singular coincidence, it was recognised 
 as a satellite the very same evening by Mr Bond of 
 Cambridge (in America) with the great Munich re- 
 fractor. The new body was called Hyperion, in con- 
 formity with Sir John Herschel's suggestion of distin- 
 guishing the satellites as well as the planets by mytho- 
 logical names. On the 22d November 1850 Mr Las- 
 sell saw at once Saturn with his whole train of eight 
 satellites — ^a glorious spectacle probably enjoyed by no 
 other astronomer. In the same month of November Faint ring 
 Mr Bond discovered a faint or dusky ring of Saturn °f Saturn 
 interior to the two long known. It is probably ne- ^'^"^7"^ 
 bulous, for by Mr Lassell' s observations and Mr Bond. 
 Jacob's it appears to be transparent. 
 
 Sir William Herschel thought that he recognised (288.) 
 six satellites of Uranus. The second and fourth of^^'^'^""" 
 his table have been observed by several astronomers, 
 particularly Sir John Herschel and M. Lamont. 
 Their periods are 8<i 17*' and 13* \l\ To these Mr 
 Lassell, aided by the fine climate of Malta (to which 
 for two seasons he removed his tel'escope), has con- 
 clusively added two more : one, appearing to coin- 
 cide with the closest of Herschel's, of which the 
 period is 4^ Z^ 28™, and one still nearer the planet 
 revolving in 2'' 12"^ 29^, the shortest orbital revolu- 
 tion in the solar system. Mr Lassell doubts se- 
 riously the existence of any other satellite.^ 
 
 1 From Mr Lassell's observations at Malta, 1852-3. 
 
 * See Astrm. Society's Notices, xiii. 151 ; and xiv. 133, 
 
Chap. III., § 6.] ASTRONOMY. — M. STRUVE — SIR JOHN HERSGHEL. 
 
 63 
 
 § 6. Sidereal Astronomy since 1820. — M. Struvb — Double Stars. Observatories of Dorpat and 
 Pulkowa. Sir John Hersohel — Orbits of Double Stars. Magnitudes of Stars. Variable 
 Stars. Earl op Rosse — His Telescopes. Nebulce. Hendersok and Bessel — Parallax of 
 Stars. 
 
 (289.) As it is absolutely necessary to bring this chapter 
 
 Continua- to a speedy close, and as I have already anticipated, 
 tion of the -^ ^.j^^ account of Sir William Herschel's discoveries, 
 
 nistory ot pit i i. i. i 
 
 Sidereal P*''* of what relates to the recent history of the As- 
 Aatrono- tronomy of the Fixed Stars, particularly the " Con- 
 ™y" stitution of the Heavens," and the motion of our 
 
 system in space, I shall condense within brief com- 
 pass a few leading facts connected, in the first place, 
 with the Orbits of Double Stars, the Brightness of 
 Stars, and the constitution of Nebulae, and these sub- 
 jects I shall connect with the names of the elder M. 
 Struve, Sir John Herschel,and Lord Rosse; the second 
 topic shall be the Parallax and distance of the fixed 
 stars, as ascertained more particularly by the late 
 professors Henderson and Bessel. 
 (290.) Friedrich Gbobg Wilhelm Strttve has been the 
 
 M. Struve. j^Qgt assiduous observer of double stars since the time 
 of Sir William Herschel. No discovery in this de- 
 partment can for a moment compete with the great 
 one of the orbital revolution of one star round an- 
 other. But M. Struve, by devoting his chief energies 
 during the most active years of his life, since 1813, 
 to the assiduous continuation of Herschel's observa- 
 tions, has added immensely to our knowledge of these 
 systems, and has earned the reputation of one of the 
 most skilful of modern practical astronomers. His 
 most elaborate observations were made at the Rus- 
 sian Observatory at Dorpat, with a noble refractor by 
 Fraunhofer, nearly 10 inches aperture, and 13^ feet 
 in focal length. He has published three works on the 
 subject of double stars, one in 1824, one in 1837, 
 and one in 1852, besides minor papers. The second 
 of these works contains the particulars of about 3000 
 double stars, deduced from a survey of the heavens, 
 in which at least 120,000 stars were examined. 
 (291.) M. Struve's papers are distinguished by the ela- 
 
 His re- boration of the reductions, and of the statistical re- 
 double suits deduced from them. In his last publication he 
 stars. has made an interesting estimate of the number of 
 
 true double stars in the heavens, which, it appears, 
 is much greater in proportion to the whole number 
 than is usually believed. But it is first necessary to 
 distinguish those which are physically double from 
 those which are merely apparently or optically so. 
 The criteria on which he principally depends are — 
 (1.) the fact of observed orbital revolution ; but as 
 this is established in comparatively few instances, he 
 very reasonably admits (2.) a common proper motion 
 of the two components as a proof of their connection. 
 He thus finds the evidence for physical duplicity to 
 be much stronger for the closer double stars, and also 
 for brighter or nearer stars, as compared with those of 
 less magnitude. On the whole he concludes, that of 
 
 1973 double stars, 1702, or six-sevenths of the whole, 
 are physically connected, and that, amongst at least 
 the brighter stars, the number of compound systems 
 is to that of isolated stars in a ratio not less than 1 
 to 3, perhaps even 1 to 2. 
 
 M. Struve has also determined with extreme care (292.) 
 the places and proper motions of the double stars ;^' S**'"^® 
 
 *■ L L OH proper 
 
 and he has formed a decided opinion, that the proper feiotione. 
 motions diminish on the whole regularly with the order 
 of magnitude, — thus confirming the criterion of in- 
 creased distance from diminished brilliancy, by that 
 of the apparent displacement of the stars by the mo- 
 tion of our system. 
 
 Besides these important works on Sidereal Astro- (293.) 
 nomy, M. Struve is well known as the head and di- Directs the 
 rector of perhaps the best organized observatory in ^^^y ^f 
 the world, that of Pulkowa near St Petersburg, of?iilkowa. 
 which he has published a very interesting descrip- 
 tion. Besides other noble instruments, it contains 
 the finest refractor in Europe, that by Merz, 1 5 inches 
 in diameter, and 22 feet focal length. The observa- 
 tions with this noble telescope are chiefly made by his 
 son M. Otto Struve, the author of many good papers. 
 We have seen in a former section (252), that we owe 
 in great part to M. Struve the conduct of the most 
 extensive trigonometrical operation ever undertaken. 
 
 Sir John Frederick William Herschel, son of (294.) 
 Sir William Herschel, whilst conversant with almostsir John 
 every branch of science, has devoted himself with re-f:®^^'; "" 
 
 111 1 1 • . t. r^. 1 1 A hisastrono- 
 
 markable success to the cultivation of Sidereal As-^ical ca- 
 tronomy. " Bearing a name honoured and reveredreer. 
 by all, his career at Cambridge reflected upon it fresh 
 lustre ; the variety and extent of his acquirements 
 gave him a reputation amongst his college contem- 
 poraries, afterwards fully confirmed by the not more 
 impartial voice of mankind at large." He was senior 
 wrangler in 1813. " Since that time he has been 
 indefatigable as an author : — first, in systematizing 
 the higher mathematics, and in forwarding their study 
 in his own university ; — afterwards by treatises con- 
 tributed to the Encyclopmdia Metropolitana on Sound, 
 Light, and Physical Astronomy, which still rank 
 among the clearest, completest, and most philoso- 
 phical in our language. About the same time he 
 wrote experimental essays on different branches of 
 Chemistry, Magnetism, and Optics, and commenced 
 his purely astronomical investigations, chiefly on 
 nebulsB and double stars, partly in conjunction with 
 Sir James South, of which the details are given in 
 difierent volumes of the Astronomical, and of the 
 Royal Society's Transactions. These memoirs collec- 
 tively include a complete revision of the objects of 
 the same description catalogued and classified by Sir 
 
64 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Sir J. Her- 
 schel's ob- 
 servations 
 at the Cape 
 of Good 
 Hope. 
 
 (295.) 
 His high 
 character 
 amongst 
 bis contem- 
 poraries. 
 
 (296.) 
 On the or- 
 bits of 
 double 
 
 stars. 
 
 William Herschel."^ But the most considerable 
 monument to Sir John Herschel's love of science is 
 the record of his four years' labours for the advance- 
 ment of Sidereal Astronomy at the Cape of Good 
 Hope, where he applied his father's methods of ob- 
 servation to the southern hemisphere. His Results 
 of Astronomical Observations, which fill a large quarto 
 volume, and which include " the completion of a 
 Telescopic Survey of the visible Heavens, commenced 
 in 1825," form one of the most considerable and 
 most interesting works of our time. The instruments 
 employed were a 20-feet reflector, of 18 J inches aper- 
 ture, and a 7-feet achromatic, with 5 inches of aper- 
 ture. With these the nebul» and double stars of 
 southern skies were examined and measured, and that 
 wonderful " Gauging of the Heavens" completed, of 
 which I have spoken in the account of Sir William 
 Herschel (201). There is an admirable chapter on 
 the apparent magnitude of the stars, to which I shall 
 refer presently, and one on Halley's comet, besides 
 other matters of interest. 
 
 Since his return to England in 1838, Sir John 
 Herschel has withdrawn from the labours of practi- 
 cal astronomy, but he continues to advance different 
 branches of science, and to expound them by his able 
 and lucid writings in a way which has made his au- 
 thority equally respected by philosophers and by men 
 of the world. The career of Sir John Herschel has 
 been marked by an almost total absence of the ele- 
 ment of ambition, so often a powerful excitement in 
 the pursuit of discovery. Had he sought notoriety 
 and posthumous fame, he would have confined his 
 efforts within a more circumscribed range. But his 
 versatile talents sought their appropriate exercise in 
 all departments of exact science, and even (it is be- 
 lieved) in pursuits widely distinct from these, in 
 natural history, ielles lettres, and the fine arts. In 
 all this he no doubt considered simply the useful 
 and pleasurable employment of his mental activi- 
 ties. Truth seemed to him as desirable whether at- 
 tained by the labours of others or by his own ; and 
 in his numerous writings he has expounded these 
 with a zest which a less generous spirit might have 
 reserved for his peculiar achievements. What he 
 may have lost in future fame by this enlargement of 
 his sympathies and interests, he has gained in the re- 
 spect and good-will of all his contemporaries. Sir 
 John Herschel recently filled the post of Master of 
 the Mint, to which, like his illustrious predecessor 
 Newton, he devoted a considerable share of his time. 
 His general eminence as a man of science has been 
 acknowledged by his nomination in 1855, to the dis- 
 tinguished honorary position of one of the eight fo- 
 reign Associates of the French Academy of Sciences. 
 
 Orbits of Double Stars. — Though not absolutely 
 the first to apply calculation to the orbits of double 
 stars, this step in their theory may not unfitly be con- 
 
 nected with the name of Sir John Herschel, from the 
 ardour of his researches and the neatness of his 
 methods. To Savary of Paris is due the merit of 
 ascertaining the form and position of the orbit of f 
 Ursse Majoris in 1827, which was followed by a 
 more purely analytical method by M. Encke, and 
 one chiefly graphical by Sir J. Herschel,^ in which 
 angles of position of the component stars are used 
 nearly to the exclusion of the more doubtful measures 
 of distance. On the whole, these investigations not 
 onlyconfirm Sir William Herschel's anticipations, but 
 render it highly probable that the relative orbits are 
 really ellipses, and consequently that the law of force 
 is that of the inverse square of the distance. The 
 reader will find in Sir J. Herschel's Cape Observa- 
 tions a very curious discussion of the orbit of y Vir- 
 ginis, a remarkable double star, whose interval was 
 in 1783 five seconds and two-thirds, which diminished 
 till 1836, when the two stars appeared united in one, 
 as seen even in the best telescopes. This was the 
 perihelion passage of these two suns, and the angle 
 of position must then have varied (could it have 
 been measured) at the rate of 70° per annum, or 1° 
 in 5 days. The following are some of the best as- 
 certained periods of sidereal revolutions in years : — 
 t, Herculis 36^-4 ; g Ursse Majoris 61^-5 ; a Centauri 
 77'' ; p Ophiuchi 80 or 90^; 6 Coronas Borealis 600 
 or 700^. M. Madler, Admiral Smyth, and Mr Hind, 
 have added much to our knowledge of this interest- 
 ing subject. 
 
 Brightness of Stars, and Variable Stars, — Sir John (297.) 
 Herschel has attempted by an elaborate system of^° *® 
 inter-comparison to assign the correct relative bright- j,"^j° 
 ness of the stars, and to give precision to the ordi- 
 nary terminology of Magnitudes. His " Method of 
 Sequences" described in his Cape Observations, ap- 
 pears to be one of the happiest specimens of generali- 
 zation which experimental science affords. Whilst 
 regretting the impossibility of here giving even the 
 slightest sketch of it, I cannot but recommend it to 
 the student of natural philosophy as a model of re- 
 search. Having ascertained, in a way independent 
 of every sort of hypothesis, the relative brightness 
 of the stars upon the scale of Magnitudes usually 
 adopted, but which is wholly arbitrary. Sir J. Her- 
 schel proceeds, by properly photometric methods, to 
 give a scientific precision to this notation ; and he 
 arrives at this singular and fortunate conclusion, that 
 by adding a small and constant correction to the re- 
 ceived scale of Magnitudes, the numbers will repre- 
 sent the distances of the respective stars from our 
 system on the supposition of an intrinsic equality in 
 the brightness of the stars themsehes. 
 
 This subject naturally includes that of Variable (298.) 
 Stars, which may be divided into those which under- ^°'''^°'''^* 
 go periodic or irregular fluctuations, and the latter 
 class may embrace new stars, and stars which have 
 
 QiUarterly Seview, vol. Ixxxv., p. 2. 
 
 ^ Aetronomical Society't Memoirs, vol. v. 
 
Chap. III., § 6.] ASTRONOMY. — LORD ROSSE — HENDERSON AND BJESSEL. 
 
 65 
 
 disappeared. The last two hundred years hare not 
 presented any such astonishing phenomena as the 
 new stars recorded in the sixteenth and seventeenth 
 centuries ; hut singular variations in the hrightness 
 of some of the most conspicuous stars, as a, Orionis 
 and rj Argils, have been discovered by Sir John 
 Herschel. Several stars of short and irregular 
 periods of varying brightness were recorded towards 
 the close of last century. But upon this very in- 
 teresting subject I must content myself with refer- 
 ring to the details given by Professor Argelander in 
 the third volume of Humboldt's Cosmos. 
 
 (299.) Earl of Rosse. Latest observations on Nebvlce 
 
 LordRosse j^ |g g^ remarkable circumstance, that as the reflect- 
 flecting ''I'S telescope was a British invention, so the more 
 telescopes, important improvements and applications of it have 
 been almost confined to the United Kingdom. It is 
 also worthy of notice that the manufacture has pros- 
 pered more in the hands of amateurs than of regular 
 opticians. Sir William Herschel appeared at one 
 time to have brought the invention to its highest per- 
 fection, but the Earl of Rosse has made an important 
 step farther ; not only by constructing a larger tele- 
 scope than had been made before, but by adapting 
 machinery driven by steam power, to the grinding 
 and polishing of the mirror ; so that the largest 
 speculum may be finished with nearly the same ac- 
 curacy and expedition as the smallest. The chef 
 cPceuvre of Lord Rosse is a telescope of 6 feet aper- 
 ture, and 53 or 54 feet of focal length. It was com- 
 pleted in the latter part of 1844, and erected at Par- 
 sonstown in Ireland. 
 (300.) Let me here record the important fact, that neither 
 
 Difficulties Yojik nor wealth could absolve Lord Rosse from those 
 tered. toils and disappointments which attend all new and 
 original efforts. Thereisnoroyalroadtosuchtriumphs. 
 The Irish nobleman owes his success entirely to his 
 unwearying perseverance and mechanical skill. Even 
 his assistants were countrymen instructed by him- 
 self in his own workshops, where the very steam-en- 
 gine which drives the polisher was fabricated. His 
 labours to improve the telescope date from 1828 
 (when he was Lord Oxmantown), or even earlier, and 
 they appear to have been unremitting until 1 844 ; in- 
 deed I might say until the present time. Com- 
 mencing with a variety of ingenious attempts to cor- 
 rect spherical aberration, and to overcome the ex- 
 treme difficulty of procuring large castings of so ex- 
 cessively brittle a material as speculum-metal, they 
 terminated in the rejection of all minor helps and 
 expedients, and in the fortunate completion of im- 
 mense mirrors at a single casting, and of correctly 
 parabolic figure when ground and polished. The 
 speculum of his largest telescope weighs four tons. 
 It was polished in six hours, and its surface is con- 
 
 siderably more than twice as large as that of Sir 
 William Herschel's forty-feet instrument. 
 
 We cannot enter into the details of the methods, (301.) 
 which evince no small mechanical skill and scientific Methods of 
 ingenuity, together with a perseverance admirable in jj^^ 
 itself.^ I will only mention how the upper and 
 lower surfaces of the casting were made to cool nearly 
 equally fast. To effect this the lower surface of the 
 mould (which naturally retains the heat more than 
 the upper) was made of iron, a good conductor, whilst 
 the upper surface was made of sand. This effected 
 the purpose; but it being found that air bubbles 
 entangled in the fluid metal could not escape beneath, 
 and injured the casting, the iron bed was constructed 
 of hoops set on edge and closely packed, the crevices 
 allowing the escape of air, whilst the cooling pro- 
 ceeded as before ; and this ingenious contrivance was 
 perfectly successful. 
 
 Many difficulties in detail have been found in the (302.) 
 mounting and use of so gigantic a mass, particularly 4??'"^^ 
 on account of the distortion of the mirror by flexure. ^^^^ ^^^ 
 But these have gradually been surmounted by Lord its results. 
 Rosse. His published observations (Philosophical 
 Transactions, 1850) relate almost entirely to objects 
 of the class of nebulje ; and as I cannot enter into 
 details, I may state the general results in two or three 
 sentences. (1.) As might have been expected, many 
 nebulse which resisted the power of former telescopes 
 (for, except in rare instances, nothing greater than 
 eighteen-inch apertures have been directed to theiri) 
 have been "resolved'' into stars by the six-feet specu- 
 lum. (2.) The aspect of a great number of nebulae 
 described by the two Herschels is materially modified 
 by the power of the telescope to embrace the fainter 
 prolongations of these singular objects. In general, 
 the symmetrical forms are very much cut up and 
 confused, and in many cases vanish altogether. 
 (3.) Instead of these, a certain species of symmetry, 
 of a vague yet very remarkable description, has been 
 detected by Lord R,osse, probably for the first time. 
 It is a spiral arrangement of the nebulous coils 
 round a centre, resembling somewhat the spiral 
 emanations of revolving fireworks. The well-known 
 nebula No. 51 of Messier's Catalogue shows this 
 in a remarkable manner. 
 
 Some observations have been made upon the moon. (303.) 
 It is much to be desired that these were continued, 
 and that the planets could also be observed ; but I 
 believe that the climate of Parsonstown affords but 
 few nights favourable to observation. 
 
 Henderson and Bessel. Parallax and distance (304.) 
 of the Fixed Stars. — Thomas Henderson, at one ^^".'^^':^°" 
 time government astronomer at the Cape of Good ~a ^ifarac-" 
 Hope, and subsequently professor of practical as-ter. 
 tronomy in the university of Edinburgh, and his 
 
 ^ For a comparison of Lord Rosse's and Messrs Naysmith and Lassell's (subsequent) methods of mechanical grinding and 
 polishing, see Astron. Soc. Notices, vol. ix. p. HO. In Lord Rosse's apparatus every stroke of the polisher is almost a straight 
 line ; in Mr Lassell's it never is. 
 
66 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 Majesty's astronomer for Scotland, was born at 
 
 Dundee, in Scotland, 28tli December 1798. He died 
 
 at Edinburgli 23d November 1844. His career was 
 
 an instance of the conquest of disadvantages of many 
 
 , kinds by a patient, devoted, and conscientious spirit, 
 
 and of the attainment of a station of great eminence 
 
 in the world of science by singleness of purpose, and 
 
 an ardent love of knowledge. 
 
 (305.) He was fortunate in halving Mr Duncan (now of 
 
 ender- g^ Andrews) as his instructor in mathematics at 
 
 sonsscien-^ ■- .'. ... . . ,, , 
 
 tific pro- Dundee, and it was " while employed as an attorney s 
 gresa. clerk in a provincial town that he laid the founda- 
 tions of that extensive acquaintance with astronomy 
 for which he was afterwards distinguished." It was 
 his good fortune to attract in Edinburgh the discern- 
 ing notice of Sir James Gibson-Craig and his family; 
 through whose influence, probably, he obtained pro- 
 fessional employments of a kind which permitted 
 him considerable leisure, and even gave him an op- 
 portunity of forming scientific acquaintances in Lon- 
 don. His early tastes were towards the practical cal- 
 culations of astronomy, such as occultations and 
 ephemerides ; and from his merits alone he was 
 commended and patronized by Dr Thomas Young. 
 Had that great man lived, his promotion to a scienti- 
 Appointed fie post Would have probably been earlier. As it was, 
 Obltrvrr ^e obtained in 1831 an honourable, and, for him, 
 tory. lucrative appointment as astronomer at the Cape ; at 
 
 the sacrifice, however, of quitting his native country. 
 In the thirteen months during which he held that 
 situation, he performed an amount ot/lrst-rate work 
 in practical astronomy which may bear a comparison 
 with any similar efibrt. Charged with an instrument 
 notoriously defective (Jones's circle), he had to 
 examine its errors and their compensations ; and 
 it is no small credit to him to say that with such 
 an indifferent tool he carried off a prize which 
 had been the aspiration of so many astronomers 
 before him — the determination of the parallax of a 
 fixed star. 
 (306.) We must not go back to the history of this pro- 
 
 The paral- -blem previous to the nineteenth century, when alone 
 lax of fixed . . "^ , « i-ijj.- li 
 
 stars instruments were so tar perfected as to give results 
 
 by which a parallax, or displacement by perspective 
 
 of a star in consequence of the earth's motion had a 
 
 chance of being discovered, since it certainly does not 
 
 amount to above a second or two, probably never 
 
 attains even the former amount. 
 
 (307.) The earlier part of this century witnessed a memor- 
 
 had been j^|jjg goptest on this Subject between Mr Pond, the 
 
 galed by Astronomer-Eoyal, and Dr Brinkley, afterwards Bi- 
 
 Pond and shop of Cloyne ; the former founded on observations 
 
 Brinkley. 
 
 at Greenwich, the latter at Dublin, both with instru- 
 ments of great power, being meridian circles of the 
 largest size. It is suflBcient here to note that Dr 
 Brinkley attributed to some of the brighter stars, 
 such as a LyrsB, a parallax of 2"* 5 (which, how- 
 ever, he afterwards reduced to little more than 1"), 
 whilst Mr Pond could arrive at no such result. There 
 is no doubt that Mr Pond was correct.^ ■ 
 
 The first case of parallax which was determined with (308.) 
 some certainty by the use of ordinary meridional in- Henderson 
 struments was that of « Gentauri, a bright star of the ^;^^^ ^f^ 
 southern hemisphere, which was deduced by Hender- Centauri. 
 son from his observations at the Cape long after they 
 had been made, and what is perhaps still more satis- 
 factory, made without reference to this particular 
 question. The result, which gave to this star an 
 annual parallax of 0-91 of a second, is believed to be 
 correct, because it has been confirmed by Mr Maclear, 
 Henderson's successor at the Cape. It may, however, 
 be not unreasonable to desire that the observations 
 should be repeated in another locality, and with a 
 difierent instrument ; for it has not been imusual (as 
 in the case of Brinkley) to obtain under the same 
 circumstances perfectly consistent, yet erroneous, and 
 therefore inexplicable results. 
 
 The very considerable amount of parallax in this (309.) 
 instance, corresponding to a large proper motion 
 (3"'6), gives a strong independent probability that it 
 is not materially erroneous ; and in this respect the 
 most competent and impartial historians of science 
 have given full credit to Mr Henderson for having, 
 by superior skill in the use of his instruments, and 
 the happy choice of an object, made a discovery which 
 so many eminent observers had long sought for in 
 vain. 
 
 Subsequent to the date of Henderson's observa- (310.) 
 tions, but before their publication, Bessel (whose Bessel's 
 biography we have given in Section 3 of this chap- "io^ng on'gi 
 ter) determined the parallax of the star 61 Cygni, in Cygni. 
 a difierent way. It was a happy suggestion of Galileo, 
 that if two stars be selected apparently near one 
 another, but really disconnected, and having very un- 
 equal magnitudes (therefore probably at very dif- 
 ferent distances from our system), — and if the ap- 
 parent angular distance between the two stars be 
 measured from opposite parts of the earth's orbit, 
 it must sensibly vary by an obvious effect of per- 
 ' spective. It was in pursuit of this happy idea 
 that Sir W. Herschel discovered the fact that the 
 connection of such pairs of stars is often real, not 
 ap'jparent — but it was Bessel who, guided in his 
 choice of an object by the critical character of the 
 
 Notice of 
 Brinkley, 
 Bishop of 
 Cloyne. 
 
 1 John Brinkley, Bishop of Cloyne, was born in England, and educated at Cambridge, where he was senior wrangler in 1788. 
 He acted for a short time as Maskelyne's assistant at Greenwich, and was subsequently appointed Professor of Astronomy at 
 Dublin, where he made many excellent observations, especially those on Ifutation and Aberration. Brinkley ought to have 
 been mentioned in Art. (30) of this Dissertation, as having contributed materially to the progress of the study of the Continental 
 Mathematics in the 0nited Kingdom. 
 
Ghap. IV., I 1.] 
 
 MECHANICS.— WATT. 
 
 67 
 
 considerable proper motion of an otherwise un- 
 conspicuous star, first reduced Galileo's theory to 
 successful practice. The details of this elaborate in- 
 vestigation have been considered by competent judges 
 as among the happiest specimens of astronomical in- 
 duction ; and like Professor Henderson's, they have 
 also had the advantage of subsequent and still more 
 independent corroboration. Professor Johnson of 
 Oxford, using, like Bessel, a divided object-glass 
 micrometer (or heliometer, as it is not very appro- 
 priately called, never being applied to the sun), has 
 obtained results for the parallax of a Cygni almost 
 identical with Bessel's, which was 0-35 of a second. 
 I am sorry that my limits will not allow me to 
 explain more particularly the details of Bessel's 
 
 method, "which, however, may be found in several 
 modern works on astronomy. 
 
 M. Peters of the Observatory of Pulkowa has an- (311.) 
 nounced several additional parallaxes, all determined ^- Patera, 
 with the aid of a meridian instrument. He has even 
 attempted to infer the mean parallax of stars of the 
 1st, 2d, &c. magnitudes, which M. Struve has com- 
 pared with his estimate of relative distance derived 
 from other considerations ; but the numbers of as- 
 certained parallaxes, as well as their amount, are too 
 smkll, and the anomalies still too apparent (as in 
 the case of the star No. 1830 of Groombridge's 
 Catalogue), and the parallactic distances too often 
 inverted on the scale of brightness, to allow us to 
 attach piuch importance to these generalizations. 
 
 CHAPTEE IV. 
 
 MECHANICS OP SOLID AND FLUID BODIES, CIVIL ENGINEEEING, AND ACOUSTICS. 
 
 § 1. Watt. — Condition of Practical Mechanics previous to the time of Watt. His genius for the 
 application of Science to Practice. His successive Improvements on the Steam- Engine. Steam 
 Navigation. 
 
 (312.) 
 James 
 Watt. 
 
 (313.) 
 Relation 
 of engi- 
 neering to 
 physics. 
 
 (314.) 
 State of 
 mechanics 
 in the 
 seven- 
 teenth cen 
 tury. 
 
 James Watt may be considered as the most dis- 
 tinguished practical man of science of the last cen- 
 tury, or even for a much longer period. But this is 
 not all. Few men achieve such a reputation as his 
 without having done more than originate a great in- 
 Afention for the use and benefit of mankind in all ages : 
 — He also taught men to raise the useful arts to a new 
 dignity, — to marry them to genuine, unpretending, 
 and inductive science, — to disparage ignorance and 
 empiricism, and to render the labours of the work- 
 shop subservient to intellectual progress. 
 
 I have attempted, in the first chapter of this Dis- 
 sertation, to place the scientific part of engineering in 
 its due relation to pure physics, and I have compared 
 the relation between them to that subsisting between 
 Mathematics and Physics — the one as an instrument, 
 the other as an end. Now it was this, in particular, 
 which made Watt the important character he really 
 was. He brought out the dependence of the former sub- 
 jects, as Newton and others had successfully taught 
 and demonstrated that of the latter. 
 
 To appreciate Watt's merit, we must compare the 
 purely mechanical contrivances of the period preced- 
 ing the date of his improvements on the steam-engine 
 with those of a similar space of time succeeding it. 
 In the former we find multitudes of contrivances on 
 paper — ^ingenious, indeed, but many of which could 
 not be executed ; the greater part of the remainder 
 could not be carried into efiect through want of know- 
 ledge in the inventor. We have large promises of 
 
 " semi-omnipotent engines," perpetual motions, 
 " quintessences of motion," and the like, mingled 
 with trivial mechanical toys ; or we have elaborate 
 diagrams of mill-gearing, lathes, fountains, and saw- 
 ing machines without end, illustrated with showy and 
 expensive plates, but destitute, for the most part, of 
 the slightest novelty of principle, or truly mechani- 
 cal skill in application. Here and there, no doubt, 
 elegant and appropriate contrivances for communi- 
 cating or sustaining motion occur ; but nearly all 
 the best forms of elementary machinery were of re- 
 mote antiquity, excepting those connected with clock- 
 work, which, including the great and truly scientific 
 application of the principle of Ispchronism, formed 
 the only considerable step in philosophical mechanics 
 for very many years previous to the conception of 
 the steam-engine. The statical part of mechanics 
 had made more progress. Masonry and Carpentry 
 had attained a degree of perfection in many respects 
 admirable, under the Italian and i^orman architects ; 
 but the really difficult theory of machinery in motion 
 was little understood before Watt's day, and the 
 knowledge which then existed was unassociated with 
 practical skill or commercial enterprize. It could 
 be found only in profound treatises of theoretical 
 mechanics, and in experimental courses of natural 
 philosophy. The sources of power were almost ex- 
 clusively those derived from simple gravity and the 
 impact of fluids. It was not, indeed, the good for- 
 tune of Watt to be the first to employ the admirable 
 
68 
 
 MATHEMATICAL AND PHYSICAL SCIENCE, 
 
 Piss. VI. 
 
 properties of steam as a source of power ; but he was 
 almost the first to study them as a philosopher, and 
 to apply, with exemplary patience and skill, princi- 
 ples sought in the laboratory, to make available the 
 most convenient of all motive forces. This was done 
 by means of a series of contrivances so ingenious — 
 so strictly connected by scientific relations — as to be 
 a model of experimental research, quite as much as 
 a triumph of mechanical art. 
 (315.) Such combinations of theory and practice have now 
 
 Ta'l'iTrit''' ^®'=*'™^ f^i" fro"i '■^re. They have followed the march 
 infused in- °f physical learning, they have borrowed from it, 
 to practical and they have contributed to it. But it was Watt 
 h'^'w^^r^ who chiefly gave the happy example. Himself by 
 education and habit strictly a mechanic, he had the 
 peculiar merit of apprehending the value of theory, 
 and of acquiring a kind of knowledge then altogether 
 uncommon amongst persons of his profession. He 
 was no doubt a successful speculator, and a shrewd 
 ingenious man besides ; and this, his ostensible cha- 
 racter, constituted possibly in the eyes of many his 
 world-wide celebrity. But such considerations were 
 little likely to influence the opinions of contemporary 
 scientific men well qualified to judge, and least of all 
 of eminent foreigners, who generally regard with little 
 partiality the presumed commercial character of their 
 insular neighbours. Dr Black, who was by no means 
 prodigal of praise, termed the steam-engine, as im- 
 proved by Watt, " an invention which is in its pre- 
 sent state the master-piece of human skill," not 
 " the production of a chance observation, but the 
 result of deep thought and reflection, and really a 
 Estimate present by philosophy to the arts.'' ^ Professor Eo- 
 of Watt's bison, who knew Mr W^^ intimately, was even more 
 genius. enthusiastic in his appreciation of his genius ; and 
 Sir Humphry Davy, in a speech manifesting a just 
 estimate of his peculiar merits, did not hesitate to 
 place him on a level with Archimedes.^ But a tes- 
 timony more authoritative and unbiassed than any 
 of these, is the fact that Watt was elected first a 
 corresponding member of the French Institute, and 
 finally one of the eight foreign Associates of the Aca- 
 demy of Sciences. This honour, to which so few can 
 attain, which Newton once owned, and which now 
 graces or lately graced the names of Young, Hum- 
 boldt, Oersted, Brewster, and Kobert Brown, is a 
 sure passport to scientific immortality. Here, at 
 least, no utilitarian pride, nor even the laudably pa- 
 triotic emotion of gratitude to one who had proved, 
 in more ways than one, his country's benefactor, can 
 be supposed to have influenced in the remotest de- 
 gree his election. 
 (316.) Having said thus much on the position to which 
 
 Watt's inventions entitle him in the narrative of the 
 history of science, we may refer with brevity to the 
 generally well-known improvements of the steam- 
 
 engine, in which they mainly consist. In Sir John 
 Leslie's Dissertation, a space of but a few lines has 
 been devoted to them, which seems inadequate to 
 their importance. For details, however, we must 
 refer to the articles in the Encyclopaadia where they 
 are explained at full length. 
 
 No doubt we cannot in strictness call Watt the (317.) 
 inventor of the steam-engine. The grand principle .i"^™ "^ 
 of rendering the heat contained in steam available as engine, 
 an economical source of moving power may be traced 
 so far back that we lose the clue altogether in the 
 obscure, or impracticable, or simply puerile shapes 
 in which the idea was contained. Even in the time 
 of Worcester (1663) we must be allowed to doubt 
 whether the history of the steam-engine had out- 
 grown the mythical stage ; Papin, indeed, proposed 
 a piston and cylinder in which the vacuum was pro- 
 duced by steam instead of by the air-pump (as already 
 suggested or practised by Guericke) ; but Savery 
 (1698) was the first who constructed a steam-engine, 
 and applied it to the drainage of mines. His inven- 
 tion included the two capital properties of steam, its 
 power of producing a vacuum by coudensation, and, 
 its elastic force at high temperatures. A few years 
 later the piston-form was introduced or re-invented 
 by Newcomen and Cawley, as well as the valuable 
 expedient of producing condensation by a squirt of 
 cold water injected into the cylinder ; and in this 
 condition the Atmospheric Engine remained with 
 slight improvement for above half a century, doing 
 the work for which it was invented, — the pumping 
 of water out of shafts (the pump being moved by a 
 chain attached to the end of a horizontal oscillating 
 beam),. — wherever economy of fuel was unimportant. 
 Such was the case at coal pits, but in other mines, 
 usually situated remote from coal, it was of compara- 
 tively little u^e, on account of the enormous con- 
 sumption of fuel. 
 
 James Watt was born at Greenock in 1736, and, (318.) 
 owing to feeble health, seems to have enjoyed little James 
 advantage from regular tuition of any kind ; which ^*j** ! . . 
 was, however, to a great extent made up for by the tory, 
 intelligent spirit with which he acquired knowledge 
 without assistance on a great variety of subjects. At 
 the age of nineteen he proceeded to Loudon, where 
 he learned mathematical-instrument making, but he 
 soon returned to Scotland, intending to pursue that 
 business in Glasgow. Here he met with obstacles, 
 but finally, by the patronage of Dr Adam Smith, Dr 
 Black, and other professors, he was established as 
 instrument-maker to the university within the college 
 buildings. I mention these details because they show 
 that Watt, as early at least as 1757, had been favour- 
 ably noticed by the most celebrated professors then 
 in Glasgow, and had received a special pledge of their 
 good will.' It is evident that the professors of Che- 
 
 1 Lectures, i., 181. " Speech at Freemasons' Hall, preserved in Arago's Eloge of Watt, and in Davy's Works, vol. vii. 
 
 3 It appears from Mr Muirhead's work on The Origin and Progress of the Mechanical Inventions of James Watt (published since 
 
 the greater part of the text of this section was written), that Watt's introduction to the college took place " through the instru- 
 
Chap. IV., § 1.] 
 
 MECHANICS.— WATT. 
 
 69 
 
 tion with 
 Dr Black, 
 
 andoonnec-Tnistry and Natural PHlosophy (Dr Black and Dr 
 * ' Dick), who had obtained for him his appointment, 
 must have been also his chief academical employers ; 
 and we may safely conclude that Watt constructed 
 much of Dr Black's apparatus, as he was certainly 
 admitted to intimate and confidential intercourse with 
 that great and amiable man. Dr Black removed to 
 Edinburgh in 1766, but the friendship which he had 
 extended to the young mechanic remained unaltered 
 during their joint lives, although their personal in- 
 tercourse must have been extremely slight after that 
 time. Now Watt's first thought of improving the 
 steam-engine dates (as we shall see) from the session 
 1763-4, the last but one of Black's stay in Glasgow ; 
 their intimacy was therefore fully established by that 
 time ; and we find Watt acknowledging his " obliga- 
 tions to him for the information received from his 
 conversation, and particularly for the knowledge of 
 the doctrine of latent heat ;"^ and we also find that 
 during Watt's experiments on steam subsequent to 
 the last-mentioned date, Black was cognizant of them, 
 and assisted in their contrivance.* Moreover, Watt 
 admits Dr Cullen's well-known experiment of redu- 
 cing the temperature of ebullition under the air-pump 
 to have been one of his starting points in the im- 
 provement of the steam-engine.' Yet this experiment 
 was not published until 1770,* and Watt must have 
 heard of it from Black himself, or from some one 
 attending his lectures, where the fact was almost cer- 
 tainly mentioned. Whether formally a student of Dr 
 Black's chemistry class or not, it is therefore evident 
 that Watt enjoyed advantages in the prosecution of 
 experimental physics which nineteen-twentieths of 
 enrolled students never attain. He had the privilege 
 of unreserved personal intercourse, amounting at last 
 to intimate friendship, with the first authority of the 
 last century on the subject of Heat, and one of the 
 
 most cautious and accomplished of inductive philo- 
 sophers.^ Watt's eminent merits, and doubtless his 
 merits alone, gained him this happy position ; but 
 had he remained either at Greenock, or with the op- 
 tician in Cornhill, he might have failed to combine 
 so admirably as he did the character of the practical 
 man and the philosopher. His place in science was His poei- 
 well typified by his position in Glasgow. His was *'°" '° 
 " the workshop within the College." Whilst the la- cou^e' 
 boratories of the classes of Chemistry and Natural 
 Philosophy must have been his familiar resort, his 
 own rooms were frequented by the most intelligent 
 students, including his contemporary Dr E-obison, 
 where subjects of science particularly connected with 
 mechanics were diligently canvassed. The extent of 
 his knowledge and the variety of his resources were 
 fully tested, and the result, as stated by the generous 
 pen of Eobison, was a conviction of the superiority of 
 Watt in these respects to any of his contemporaries. 
 
 It is a fact worthy of note that the immediate oc- (319.) 
 casion of Watt's improvements was the commercial Watt's first 
 consideration of economy. In 1763 or 1764, being ^gP^''^^^ 
 called on to repair a model of the Atmospheric En- steam, 
 gine in the Natural Philosophy class at Glasgow 
 (which model is still preserved), he found the amount 
 of steam expended in heating the cylinder at each 
 stroke to be so great that the boiler was insufiicient 
 to supply it properly. He then commenced experi- 
 ments on the amount of steam thus consumed, and on 
 the means of diminishing it. Though the primary ob- 
 ject was the repair of a model, it is not to be doubted 
 that Mr Watt had in view the practical improvement 
 of the engine on the great scale, with the use of which 
 in the coal-fields of the west of Scotland he was pro- 
 bably familiar, having the intention of becoming 
 himself a civil engineer, and being already acquainted 
 with the writings of Desaguiliers and Belidor.^ 
 
 mentality of his mother's kinsman Mr George Muirhead, who had then (1764) just exchanged the professorship of oriental lan- 
 guages for that of Latin." It will be seen that this refers to a period antecedent to his journey to London. 
 ^ Letter to Dr Brewster in Kobison's Mechanical Philosophy, ii., p. v. 
 
 * Roblson's Mechanical Philosophy, ii., 115, note (by Mr Watt). 
 ^ Ibid., p. vii., and 114, note. 
 
 * In the Mdinburgh Physical and Literary Essays, vol. ii., Dr Black (who was intimate with Cullen) knew of it at least in 
 1757. Lectttres, i., 525. 
 
 6 It is perhaps unfortunate that Mr Watt, when on the verge of fourscore, contrary to his ov n intentions, but yielding to " the 
 representation of friends," recorded a complaint that his best friends, Black and Uobison, had refused him his due share of merit 
 in the improvement of the steam-engine, and disclaimed, as injurious, the appellation of " a pupil of Dr Black'' (letter to Dr 
 Brewster in Robison's Mechanical Philosophy, vol. ii., p. v.) Admitting (as he does on the same page) that the doctrine of latent 
 heat was due to Dr Black, and that he first learnt it from him, he adds, " this theory did not lead to the improvements I after- 
 wards made in the engine," p. viii. No one ever ascribed to Black the beautiful invention of a separate condenser, but even 
 Watt's most ardent eulogists (Lord Brougham and M. Arago) admit that the theory of latent heat " forms the key to the econo- 
 mical appreciation of the steam-engine." So far was Watt from being independent of Dr Black's assistance in this matter, that 
 he himself tells us twice over, in substantially the same language, that when in the course of his experiments on the model engine 
 in Glasgow College in 1764 he was " at a loss to ■understand'how much cold water could be heated by so small a quantity in the 
 form of steam," he "applied to Dr Slack, and then first understood what was called latent heat" (Robison, ii., p. v.; also p. 116, 
 note). Mr Watt might have been the discoverer of latent heat, and the solver of his own dilemma, had not Dr Black been at 
 hand. It is the highest compliment we can pay him to say that such aij achievement was not too much to expect from him. 
 
 [These conclusions are fully substantiated by the interesting documents lately published by Mr Muirhead in the Correspondence 
 of Watt on the Composition of Water, p. 6, and in his Mechanical Inventions of James Watt, vol. i., p. Ixxxi. ; vol. ii. pp. 116, 118, 
 119, 275. In the last-cited passage Watt himself fixes the date and manner of his receiving from Dr Black his knowledge of the 
 doctrine of Latent Heat. Be Says, " I myself never attended his (Dr Black's) lectures ; but the doctor explained his doctrines 
 to me about the year 1763."] iVoJe added during printing. 
 
 ^ See Mr Watt's own narrative in Robison's Mechamical Philosophy, ii., 113, note; and in Mr Muirhead 's Mechanical Inventioiu 
 of James Watt, vol. i. 
 
70 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (320.) 
 Imperfec- 
 tions of at- 
 mospheric 
 engine. 
 
 (321.) 
 Watt's 
 principle 
 of separate 
 condensa- 
 tion. 
 
 When Watt discovered by means of his model that 
 the condensation and loss of steam in the cylinder at 
 every stroke of the piston exceeded that which is use- 
 fully employed in producing the vacuum, he proceed- 
 ed very methodically to ascertain the chief numerical 
 data or constants upon which the working of steam- 
 engines depend ; as, the bulk of steam of given elas- 
 ticity compared with that of the water producing it, the 
 elasticities of steam at different temperatures, espe- 
 cially above the boiling point, the evaporating power 
 of a pound of coals, and finally, the expenditure of 
 steam and of injection-water for a single stroke. The 
 l^st, the amount of cold water required effectually to 
 condense the cylinderful of steam, appeared so very 
 large that it at once betrayed the source of the waste- 
 ful expenditure of fuel. All the heat which was ab- 
 stracted by the injection-water had to be supplied 
 afresh at a vast expense of steam, and consequently 
 of coal, before a fresh stroke could be made. The 
 mere amount of steam necessary to fill the cylinder 
 and elevate the piston was a trifle in comparison. He 
 naturally ascribed it to the absorption of heat by the 
 material of the cylinder, which no doubt was an im- 
 portant element ; and he tried cylinders of different 
 materials, and ascertained (in most instances for the 
 first time) the speciAc heats of the substances used. 
 But still the amount of injection-water remained un- 
 accounted for, and the regulation of it was the great 
 difficulty of the old engine. If a tolerable vacuum 
 was desired, the cylinder must be flooded with cold 
 water, and all the heat abstracted must be restored 
 before the next stroke was produced. If, on the other 
 hand, the injection was imperfect, so that the con- 
 densed steam and water together retained a high 
 temperature, an atmosphere of vapour so elastic 
 spoiled the vacuum, and in many cases the working 
 efficiency of the engine was reduced to about half of 
 the atmospheric pressure. 
 
 The theory of latent heat, showing that steam con- 
 tains as much heat as if the water yielding it had 
 been raised through 1000° of temperature, gave a 
 clear explanation of the enormous amount of injec- 
 tion-water necessary. How to escape from the diffi- 
 culty was another question, which was solved solely 
 by Mr Watt, who, early in 1765, first conceived the 
 idea of retaining the cylinder always at the boiling 
 heat, and effecting condensation in a separate vessel 
 kept constantly as cold as possible, in which injection 
 should also take place, and into which the steam of 
 the cylinder would spontaneously rush, on a commu- 
 nication being opened at the proper instant. The suc- 
 cess of this device was complete, and it was speedily 
 followed by a series of admirable and mutiially de- 
 
 pendent improvements which Watt introduced. To 
 keep the cylinder as warm as possible, it was first 
 provided with a cover, through which the piston-rod 
 passed by means of a stuffing-box. Then steam it- 
 self was employed to press down the piston, instead 
 of atmospheric air which cooled the cylinder injuri- 
 ously. 
 
 Having thus steam on each side of the piston, the (322.) 
 step was easy to make the engine a double-acting Double-act- 
 one ; so that the volume of steam which by its elas- '°S engine, 
 ticity impelled the piston during its descent, being 
 thrown into the condenser, produced the vacuum 
 necessary to make the ascending stroke equally ad- 
 vantageous.^ But in pumping-engines, which had 
 hitherto been the main employment of steam, or /ire 
 engines (as they were then called), it was sufficient 
 that the power was produced in one direction, that 
 is, to lift the pump-rods ;^ but the double action of a 
 pushing and pulling force was evidently applicable 
 to every sort of machinery by the use of a crank and 
 fly-wheel. A difficulty, however, was experienced in 
 applying this push-and-puU movement to the oscil- 
 lating beam which had so long formed a part of the 
 atmospheric engine, and which it was so convenient to 
 use. Mr Watt obviated it with his customary saga- Parallel 
 city, and succeeded in inventing a connection of rigid motion, 
 jointed links which effectually united the piston-rod 
 with the end of the beam, the former moving in a 
 vertical straight line, the latter in a circular arc, so 
 that pressure was transmitted in the manner of either 
 push or pull without the slightest practical incon- 
 venience. No doubt the locus of the motion of the 
 piston-rod head is not rigorously straight. It is, when 
 fully developed, a curve of the fourth order, resem- 
 bling a very elongated figure 8 ; but the portion of 
 the curve in use is practically straight. This happy 
 solution, the most elegant perhaps in the science of 
 pure machinery, or kinematics, was not the result of 
 a formal mathematical research, but presented itself 
 to the mind of Watt, as he tells us, almost intui- 
 tively. It became from henceforth an important ele- 
 ment of mechanical combinations. 
 
 Other methods of producing direct rotation oc- (323.) 
 curred to the ingenious mind of Watt, and many of Expansive 
 them were shown to be practicable by being actually -^"''^"'g- 
 executed in model size. But the next great practi- 
 cal improvement introduced by him was the princi- 
 ciple of expansive working, whereby a saving of steam 
 is produced (particularly in single-acting engines), 
 second in importance only to the result of the sepa- 
 rate condensation. This consists in allowing the 
 steam to flow in upon the piston during only the first 
 part of the stroke ; the rest being completed partly 
 
 1 This happy idea seems to have been suggested by Dr Small of Birmingham in a letter to Watt, of date 5th November 1769. 
 
 " I see no reason why you should not condense at both ends of your cylinder, and drive all before you, baclt stroke and 
 
 fore stroke." — Mechanical Inventions of James Watt, i. p. 81. The uncommon sagacity of Dr Small, and the important services 
 which he rendered in many vifays to Watt, come out clearly for the first time in this work. 
 
 " So associated were these engines with the operation of raising water, that we find they were at one time used to supply 
 common water-wheels with a constant stream, and thus to produce continued motion for mill-work, &c. 
 
Chap. IV., § 1.] 
 
 MECHANICS. — WATT. 
 
 n 
 
 by the inertia of the moving machinery, but chiefly 
 by the continuous though constantly diminishing 
 elasticity of the steam as it expands and fills the en- 
 tire cylinder.^ It is evident that, in the extreme case, 
 the ■work required (in pumping) will be accomplished 
 if the piston reach the end of the stroke just as its 
 momentum is exhausted, and that, on the other hand, 
 if the pressure of the steam remain constant through- 
 out, the velocity will be a maximum just when the 
 work being done by the machine is suddenly com- 
 pleted, and so much moving power will be wasted. 
 A medium distribution produces the most favourable 
 result in practice, and it depends entirely upon the 
 ratio between the resistance and the effective pres- 
 sure of the steam what this most favourable propor- 
 Cornish tion will be. In the single-pumping engines of Corn- 
 engines, -wall, in which the economy of fuel is carried to the 
 highest perfection, it frequently happens that not 
 more than one-eighth of the stroke is performed un- 
 der the full pressure of the steam, which acts expan- 
 sively during the remainder of the stroke ; but these 
 engines, though condensing, are moved by steam of 
 four times the elasticity of the atmosphere. The 
 Cornish engines have been very elaborately perfected, 
 and they have been more carefully tested in respect 
 to performance than any others. It is perhaps not 
 too much to say that they do not contain a single 
 contrivance of any importance (beyond of course 
 what they have in common with the atmospheric 
 engine), which was not the unaided invention of Mr 
 Watt. 
 (324.) Iji the Cornish engine we see the Energy of Heat 
 
 i.-!!!-^^'" rendered available to an extent which the inventor 
 himself would at one time have thought scarcely cre- 
 dible. The combustion of a bushel of coal which in 
 a Newcomen's engine improved by Smeaton was 
 capable of raising 3,000,000 pounds through one 
 foot, in Watt's improved pumping engine raised 
 20,000,000 pounds the same height. But by the 
 indefatigable skill and perseverance of engineers the 
 Cornish pumps now yield at least five times the last 
 amount. This, however, is not the place to enter 
 upon these details, nor can we stop to particularize 
 the other and various mechanical inventions intro- 
 duced by Watt in the form of valves, governors, and 
 steam-indicators. Still less can we enlarge upon the 
 endless and still multiplying applications of this ad- 
 mirable moving power, which is as capable of super- 
 seding the greatest natural forces hitherto applied by 
 man to the useful arts, as it is adapted by its easy 
 regulation to replace human industry in the most 
 delicate operations ; " the trunk of an elephant, 
 which can pick up a pin or rend an oak, is as nothing 
 to it."' 
 
 feotion. 
 
 Of the applications of the steam-engine with which (325.) 
 Mr Watt was less immediately connected, its adap- tion of*" 
 tation to locomotion in the case of ships in the last steam to 
 century, and in that of railway trains in the present, navigation, 
 have been the most striking, and fraught with con- 
 sequences the most important to mankind. Of the 
 latter we shall have occasion to speak in a future 
 section ; of the origin of steam navigation we may 
 here say a very few words. Passing over projects 
 which never were realized, of moving barges by steam, 
 or other inanimate power, against wind and tide, — 
 such as those of Worcester, Papin, and Hulls, — we 
 find that the first experiment entitled to be called 
 successful was made by Mr Miller of Dalswinton in Miller- 
 Scotland, conjointly with Mr James Taylor, tutor in Taylor, 
 his family, who together formed the project of mov- 
 ing vessels by means of paddle-wheels driven by a 
 steam-engine, and realized it with the aid of Sym- 
 ington, a practical engineer. As we shall also fifld 
 in the case of steam-carriages, the idea of the applica- 
 tion of the steam-engine to move ships was already 
 a familiar one to the minds of many persons about 
 the middle of the last century. To put it in practice 
 with advantage was the step required. Mr Miller's 
 first boat was launched on Dalswinton Loch in Dum- 
 friesshire, in October 1788, and attained a speed of 
 five miles an hour. The subject was pursued by 
 Symington and others. In 1789 a larger vessel was 
 propelled on the Forth and Clyde Canal. Subse- 
 quently, however, the invention languished. The 
 want of co-operation, of capital, and ingenuity, na- 
 turally extinguishes many valuable inventions. Watt 
 himself was only rescued from the same difficulty by 
 the unusual intelligence of Boulton and Small, his 
 coadjutors at Birmingham. Symington was less for- 
 tunate, as well as probably less meritorious ; and 
 though it is well established that Fulton, who passes 
 on the other side of the Atlantic for the inventor of 
 steam-ships, had seen the relics of Symington's second 
 experiment, we must do the Americans the justice to 
 say that the application of steam to navigation first 
 flourished in the United States. In 1807 Fulton Fulton, 
 started a river boat with an engine of Boulton and 
 Watt. In 1813 the example was tardily imitated on 
 the Firth of Clyde. The subsequent improvements 
 need not here be specified. They have been very 
 great and striking, but with the exception of the recent 
 substitution of the screw-propeller for paddle-wheels, 
 they scarcely involve any new principles.^ 
 
 We may briefly close what we have to say of Mr (326.) 
 Watt personally. His health was feeble from child- P^"""*! 
 hood, but being blessed with much calmness of tem- ^f vfan 
 per he prolonged his life to a great age, and "passed 
 through its struggles, though they were to him con- 
 
 1 The double-acting engine was planned in 1774 or 1775. The expansion principle was first used in 1776 ; the parallel motion 
 was patented in 1784. — Watt's Notes on Dr Robison's Article. Eobison's Mech. Phil., vol. ii. 2 Lord Jeffrey. 
 
 " For farther details on the history of Steam Navigation, see that article in the Encjclopa;dla ; and Mr Bennet Woodoroft's 
 work on the subject, London, 1848. 
 
72 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (327.) 
 Personal 
 character 
 of Watt, 
 continued. 
 
 siderable, without serious injury. Vexatious law- 
 suits connected with his valuable patent rights af- 
 forded him but too much occupation and anxiety. 
 He wrote little, and he did not covet fame. He was 
 fond of chemistry as well as mechanics, and was well 
 acquainted with the theory and practice of that science 
 as it then existed. He put forth opinions on the 
 chemical constitution of water which, in the judg- 
 ment of some, entitle him to contest priority in the 
 discovery with Cavendish. He must have been 
 versed in mathematics in his early years, as we learn 
 from his friend Dr Kobison, but there is no evidence 
 that he ever attempted a strict theory of his own engine. 
 Nor were his successors in this respect more fortu- 
 nate. The best practical writers on the steam-engine, 
 up even to a late period, gave most rude and inac- 
 curate rules for computing its effects ; and it is to a 
 Frenchman, M. de Pambour, that we owe the first 
 philosophical, and, at the same time, elementary 
 analysis of this noble machine. 
 
 Much light has been thrown upon the character of 
 Watt by the recent publication of his correspondence 
 by Mr Muirhead.^ We there see the pressure of phy- 
 sical infirmity, and mental despondency and indif- 
 ference, under which he laboured from boyhood. We 
 learn the accumulated difficulties, arising from the 
 backward state of the mechanical arts in his time, 
 which delayed for years the successful prosecution of 
 his happiest, and what would appear in our day 
 most easily realized, conceptions. We see him at 
 times ready to abandon fame and profit for the en- 
 joyment of the humblest competence with tranquil- 
 
 lity. We find him, mechanic though he was, shrink- 
 ing from possible collision with the opinions or in- 
 terests of others, and in his early as in his latest 
 days, solicitous to avoid responsibility. He had, in 
 a word, throughout, the finely strung susceptibility of 
 a man of genius, sitigularly at variance with the 
 necessity he was under of pushing his way in the 
 world, and of turning his inventions to the best com- 
 mercial account. Proyidentially he was thrown in 
 the way of friends to whom, by his private character, 
 he was greatly endeared, and who supplied the ele- 
 ments necessary to the successful prosecution of his 
 schemes. The sanguine zeal of Roebuck, the com- 
 mercial sagacity of the capitalist Boulton, and not 
 least, the sympathizing friendship of Dr Small, who 
 was well fitted by his character and attainments to 
 mediate between Watt and the other two, were all 
 essential to the realization of the improved steam- 
 engine. 
 
 When Mr Watt was finally relieved of the oppres- ^25) 
 sion and chicaneries of his opponents in the courts Close of hi 
 of law, he was settling down into a peaceful old age. ^'^^• 
 He probably hoped to live over again some of the 
 scientific passages of Ms youth in sympathy with his 
 second son, Gregory, who possessed a decided taste 
 for science, but was unfortunately early cut ofi". Re- 
 spected and beloved by a large group of friends, many 
 of whom survived him, and admired by a far wider 
 circle, he died at Heathfield, near Birmingham, 25th 
 August 1819. Statesmen, philosophers, and men 
 of the world, united in extolling the worth of his 
 character and the greatness of his genius. 
 
 § 2. RoBisON. — Application of Statical Principles to Engineering — especially to Practical 
 Masonry. CouLOMB. — Friction — Force of Torsion. 
 
 (329.) 
 Kobison a 
 practical 
 philoso- 
 pher. 
 
 The name of Robison may perhaps not appear to 
 be sufiiciently identified with any great discovery to 
 merit a place in this condensed sketch of the pro- 
 gress of science biographically illustrated. Were 
 there no other claim, I should consider it a sufficient 
 one to entitle him to at least a brief notice, that he 
 was by far the most important, and, as M. Arago 
 has justly called him, " most illustrious contributor" 
 to the earlier editions of the EncyclopeBdia Britan- 
 nica. But he was also a philosopher in a high 
 sense of the word. His knowledge was multifarious 
 in no ordinary degree. He had little of pretension 
 to originality, yet he brought to bear upon matters 
 of science an unfailing amount of excellent common 
 sense, and his personal acquaintance with the Arts 
 which may be called Philosophical far exceeded, I 
 imagine, that of any man of his time. Though not 
 without his prepossessions, he was generous in the 
 highest degree in his estimation of others, who in 
 
 some sense might have been considered his rivals ; 
 he was eminently patient in his study of the works 
 of his contemporaries, and in his published writings 
 he laboured to render the results generally accessi- 
 ble to ordinary readers, by means of laborious ab- 
 stracts, intermingled often with highly original views ; 
 and he explained them with conscientious energy 
 in his lectures to the students of Natural Philo- 
 sophy, whom for thirty years of his life it was his 
 pride and pleasure to instruct. Amidst these con- 
 genial labours he found little time for making pro- 
 longed original trains of experiment, though the spe- 
 cimens which he has almost incidentally left us give 
 the fullest proof of his ability in this respect ; and 
 the explanation is, I have no doubt, to be found in 
 the peculiar circumstances of his early life. Until 
 his settlement in Edinburgh, he passed his time in a 
 series of active pursuits, having much more of the 
 character of stirring practical life than of literary re- 
 
 ^ The Origin and Progress of the Mechanical Inventions of Jvmes Watt. 3 vols, 1855. 
 
Chap. IV., § 2.] 
 
 MECHANICS. — KOBISON. 
 
 73 
 
 (330.) 
 Hie emi- 
 nent ser- 
 vices as an 
 expositor 
 of science. 
 
 (331.) 
 His early 
 life and 
 friendship 
 with Watt, 
 
 pose or scientific contemplation. He was thirty-five 
 years old •when he began to lecture in Edinburgh ; 
 and though an excellent working age, it is rare indeed 
 to find that the talent of discovering new truths has 
 been formed and developed so late in life. A major 
 part of the great steps in science have been taken at 
 even a much earlier period. 
 
 That Eobison possessed all the elements of an 
 original thinker we shall presently endeavour to 
 show ; but had his excellences consisted alone in 
 those we have specified, he would have been a per- 
 son eminently useful in forwarding the march of 
 science. In fact, a few more such authors in every 
 generation would be cheaply purchased by the post- 
 ponement of some second-rate discoveries. Men — and 
 we include men of science — are in too great a hurry 
 to push on (actuated often by a morbid love of praise) 
 to acquire something they may call their own, whilst 
 they are little acquainted with the important contri- 
 butions of their rivals in the race of fame, and of the 
 predecessors to whom they really owe so much of 
 what they may choose to consider their peculiar 
 property. To methodize knowledge from time to time 
 — to present discoveries in a form difierent from that 
 in which they were first published, and thus con- 
 nect them with what is already known and what re- 
 mains to be clearly proved — these are real services 
 to science which contribute in a very essential 
 manner to its progress. Eobison was a teacher, not 
 only to the youth of his native country, but to the 
 men of science and of practice of all countries, and 
 of many succeeding years. 
 
 John Robison was born in 1739, entered the Uni- 
 versity of Glasgow at the early age of eleven, and gra- 
 duated at seventeen. His early tastes were directed 
 . towards Natural Philosophy. He studied Mathema- 
 tics (as in after life) chiefly with reference to its appli- 
 cations. Whilst at Glasgow he formed the intimate 
 acquaintance of James Watt, then a practical instru- 
 ment maker. In a passage of a private paper, pub- 
 lished first in Arago's Eloge of Watt,^ Robison, with 
 his characteristic generosity, describes his mortifica- 
 tion when "yet a young student" at finding him 
 much his superior in mathematical and • mechanical 
 knowledge ; but M. Arago has omitted to state that 
 Watt was, at least, three years the senior, which at 
 such an age, and on such subjects, might make all 
 the difference between a beginner and a proficient. 
 But the truth is, that with a rarely generous rivalry 
 in excellence, each esteemed the other most ; for we 
 find Watt bearing a similar testimony to the supe- 
 
 riority of his friend and junior : " I was happy to 
 find in him [Robison] a person who was so much 
 better informed on mathematical and philosophical 
 subjects than I was."* It "was by Robison that 
 Watt had his attention first directed to the steam- 
 engine ; their correspondence appears to have been 
 frequent during their joint lives ; and near the close 
 of his life Watt acknowledged " his obligations to 
 him for very much information and occasional assist- 
 ance in his pursuits ;" and in the Edinburgh professor 
 he found not only the zealous defender before a court 
 of law of his rights as an inventor, but also the first 
 who expounded methodically the principles and de- 
 tails of the steam-engine in a manner which, at least 
 until lately, had not been superseded. 
 
 In 1758 he left Glasgow, and the following year 
 he went to Sea as tutor to a son of Admiral Knowles. 
 His life in a man-of-war, during which he saw some 
 active service in Canada, was favourable to the de- 
 velopment of his practical turn of mind, and doubt- 
 less gave him an interest in seamanship, naval archi- 
 tecture, and other subjects, which he afterwards 
 turned to good account ; and a subsequent expedi- 
 tion to Jamaica, for the trial of Harrison's Time- 
 keeper, exercised him in some of the practical parts 
 of astronomy. He returned, however, to Glasgow 
 in 1761, and attached himself with such success 
 to the study of Chemistry under Dr Black that he 
 taught the Chemical Class in the university for seve- 
 ral sessions.' But his active life was not at an end. 
 In 1770 he accompanied his first patron. Admiral 
 Knowles, to Russia, and for some years was em- 
 ployed, first as his secretary, superintending im- 
 provements in the marine establishment, and after- 
 wards as professor of Mathematics in the naval 
 school of Cronstadt. He spoke and wrote the 
 Russian language with facility,* and performed his 
 duties to the satisfaction of all. But in 1774 he 
 could not resist the honourable invitation which he 
 received to fill the chair of Natural Philosophy in 
 the University of Edinbui^h, where he spent the 
 remainder of his life, which terminated in January 
 1805, amidst incessant literary occupation, even 
 when repeated attacks of a painful disorder had pre- 
 vented him from personally continuing his lectures. 
 
 This brief sketch^ of a career rather unusual for 
 a man of science throws light upon Robison's pecu- 
 liar merits. He had extensive, and then uncommon, 
 opportunities of acquiring information, of seeing vari- 
 ous countries, and of noticing their physical peculiari- 
 ties ; of being introduced to their societyand literature; 
 
 (332.) 
 His adven- 
 tures ; 
 
 and his ap- 
 pointment 
 to the Uni- 
 versity of 
 Edin- 
 burgh. 
 
 (333.) 
 Character 
 of his ar- 
 ticles in the 
 
 poedia £ri- 
 tannica. 
 
 ^ And since, in sxtenno^ in Muirhead^s Mechanical Inventions of James Watt, vol. i., p. xli. 
 
 2 Ibid., vol. ii., p. 293. 
 
 3 The MS. of these lectures, written with curious care, hut with the use of continual abbreviations of the larger words for 
 the sake of compression, is now in my possession, having been given to me by his son, the late Sir John Robison. I have also 
 many others of his MSS., which for the most part seem to have been printed in some form or other. Dr Robison was an indefa- 
 tigable penman, and wrote and re-wrote his lectures with great labour. He also made elaborate analyses of his reading, but the 
 bad habit of contracting words remained with him through life. 
 
 * The private marks on his MSS. are often in the Russian character. 
 
 * A much fuller one will be found in Playfair's Works, vol. iv. 
 
74 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss, VI. 
 
 (334.) 
 Hisilfe- 
 ekanical 
 Philoaophy, 
 
 Sound 
 practical 
 
 of tating part in the actual execution of scientific 
 designs ; of studying foreign languages ; and of 
 methodizing his knowledge for the purposes of in- 
 struction. Every one of these influences may be 
 clearly traced in his writings, which will challenge 
 comparison with those of any English writer, except 
 perhaps Dr Thomas Young, for variety and fulness 
 of information, and for the general soundness and 
 strongly practical character of the mechanical know- 
 ledge with which they abound. They would also 
 doubtless have appeared to far greater advantage had 
 they been the product of his most vigorous days ; but 
 he was little known as a writer until the year 1793, 
 when he commenced a series of important contribu- 
 tions to the Encyclopcedia Britannica, embracing 
 at least forty-six articles, all scientific, some of great 
 length and elaboration, which were published during 
 the succeeding eight years, a period when he was seri- 
 ously afflicted with chronic disease. They embraced 
 disquisitions on general philosophy, as in the articles 
 Philosophy and Physics ; of strict science, as in 
 Astronomy, Dynamics, Projectiles, Pneumatics ; of 
 the more experimental sciences, as in Magnetism, 
 Electricity, Sound ; of the art of music (with which 
 he was practically conversant), in Temperament, 
 Piano, &c. ; — but his great strength lay in the ar- 
 ticles in which just mechanical principles were ap- 
 plied successfully, and often with marked originality, 
 to practice, as in Arch, Roof, Carpentry, and Strength 
 of Materials ; Resistance, Rivers, and Waterworks ; 
 Seamanship, Steam and Steam-Engine ; Machinery, 
 Telescope, and Watchwork. 
 
 The last-named articles (most of which have been 
 collected in a compilation, edited by Sir David 
 Brewster, in four thick volumes, entitled Robi- 
 son's Mechanical Philosophy) constitute a body 
 of knowledge in civil engineering which has not 
 yet been surpassed in clear exposition of physi- 
 cal principles and their application — in the ex- 
 tensive acquaintance it shows with the details of 
 practice — and in proofs of elaborate and impar- 
 tial study of authors, both British and foreign, on 
 the subjects of which it treats. Several of these 
 articles have been resorted to by the most accom- 
 plished engineers of our own time as stores of sound 
 experience, and they have been lavishly borrowed from 
 by some writers on similar subjects, occasionally with- 
 out acknowledgment. The original matter which 
 they contain is not always easily separated from that 
 which is compiled. In every instance Dr Robison 
 lays claim to less than his own share, and is so 
 scrupulous in quoting the names of other authors, 
 that he has unquestionably received less reputation 
 from these Essays than he deserves. He writes like 
 a man who has himself used the saw and hammer, 
 who has had the responsibility of success or failure. 
 
 who might have been called upon for a scientific 
 opinion (of far more weight than what generally goes 
 by the name) on almost any practical subject upon 
 which he might have been consulted ; and that not 
 merely in its general outlines, but in its strictest de- 
 tails ; not only the design for a roof or a centre, 
 but the scantling of the timber to be used ; the mi- 
 nutiae of a pump or hot-air stove ; the curvatures of 
 an achromatic object-glass ; the temperament of a 
 piano ; or the angle for the pallets of an escapement. 
 In such matters nothing important either in the 
 theory or the practice of his times escaped him. His 
 opinions were very generally formed on original con- 
 siderations, supported by experiments equally well 
 devised and carried out. His method of finding 
 mechanically the relation between the intrados and 
 extrados of a properly balanced arch by means of 
 suspended pieces of chain is as ingenious as it is 
 elementary ; but his observations on the manner in 
 which stone arches, when overloaded, break up, es- 
 tablished on direct observation and experiment, un- 
 questionably gave a just foundation to the theory 
 of masonry, till then so generally and erroneously 
 treated of by mathematicians with the preposterous 
 abstraction of the forces of friction and cohesion, 
 the action of which in many instances vastly exceeds 
 the direct effect of gravity. 
 
 But on this we must not dwell. Robison's articles 
 on Electricity and Magnetism are deserving of nearly 
 equal praise with reference to the state of knowledge 
 of the time. Probably there was not one author of 
 merit on these subjects, whatever his country or lan- 
 guage, whose works he had not laboriously consulted 
 and analysed the conclusions ; whilst a multitude of 
 ingenious experiments give evidence of the skill and 
 patience of the writer. To Dr Robison we are, indeed, 
 indebted for the approximate knowledge of the pri-' 
 mary law of electric attractions and repulsions ; for 
 a careful consideration of those beautiful curves 
 formed by iron filings round magnets,^ to which such 
 an enlarged importance has since been given by the 
 beautiful generalizations of Mr Faraday ; and I be- 
 lieve likewise for the first suggestion of combining 
 the voltaic elements in a pile or column.^ Dr Robi- 
 son, though for many years secretary of the Royal 
 Society of Edinburgh, published little in its Transac- 
 tions, and almost nothing, so far as I am aware, in 
 any periodical work. Hence his admirable adapta- 
 tions of pxperiments were little known beyond his 
 own class and friendly circle. 
 
 Of his more abstract mathematical vrritings we 
 need say little. He was thoroughly acquainted with 
 the works and methods of Newton, and with nearly 
 all those of the same school, particularly of Bos- 
 covich. He laboured incessantly to reduce the de- 
 monstrations of the higher mechanics and astrono- 
 
 (335.) 
 
 Writings 
 on elec- 
 tricity and 
 magnetism. 
 
 (336.) 
 His exten- 
 sive read- 
 ing and 
 mathe- 
 matical ac- 
 quire- 
 ments. 
 
 ^ Indirectly we owe to him also the first exact determination of the mathematical properties of these curves, made at his 
 request by Mr Playfair. — Robieon's Mech. Phil., iv. 350. 
 2 See the Fifth Dissertation (by Sir John Leslie), p. 739. 
 
Chap. IV., § 2.] 
 
 MECHANICS. — ROBISON— COULOMB. 
 
 75 
 
 my to their simplest and most geometrical elements. 
 But the result (as might have been foreseen) was in 
 many cases a wearisome prolixity; and originality 
 could not be expected in these departments without 
 applying the continental improvements in analysis : 
 not that Dr Eobison overlooked these ; but he took 
 little pleasure in them ; and as regards Physical As- 
 tronomy he adhered to the older methods. Having 
 been so long at St Petersburg, the writings of Euler 
 must have been familiar to him, as indeed they evi- 
 dently were as far as regards all subjects connected 
 with mechanics : he justly, however, considered Euler 
 as a superficial natural philosopher, though an in- 
 comparable mathematician. 
 (337.) As a lecturer in his own department, Bobison was 
 Eobison as the most eminent of his time, at least in Britain. That 
 " ""^ ^' his courses were not considered popular will easily be 
 understood from a slight inspection of his writings. 
 The demonstrations were long and copious, but too 
 rapidly delivered. "The singular felicity of his 
 own apprehension," says Mr Playfair, " made him 
 judge too favourably of the same power in others." 
 The lectures must have abounded in practical details, 
 which ordinary students rarely appreciate ; and they 
 were deficient in experiments, which unquestionably 
 arose from no want of the ingenuity necessary either 
 to invent or execute them. On the other hand, the 
 effect of his discourses was greatly enhanced by 
 his striking and energetic delivery, and by the stores 
 of his memory, which often recalled the incidents of 
 the stirring life in which he had once been engaged ; 
 and to the more thoughtful and philosophic they 
 were rendered at once attractive and elevating in no 
 ordinary degree by the strain of fervent thought by 
 which they were accompanied, and the impress which 
 they frequently bore of the pure morality and ex- 
 alted piety of' their author.' 
 (338.) Apart from his local usefulness as a professor, we 
 ^'^ P''*!"" regard Dr Eobisoh's place in science as eminent 
 character chiefly on account of the sagacity with which he ap- 
 plied knowledge to practice, and analysed complicated 
 effects of force as manifested in engineering con- 
 structions. This he did so ably as to guide future 
 practice, and to reflect much light on the theory of 
 solids more or less elastic and tenacious, and subject 
 to the intricate strains which gravity produces. The 
 difficulty and merit of these investigations will best 
 be gathered from the slow progress of his successors 
 in the same field. The criticism with which his 
 writings abound on the theories of even his more 
 celebrated contemporaries and predecessors show re- 
 markable acuteness, patience, and independence of 
 thought. We may perhaps sometimes think him pre- 
 judiced, but his decisions are never uttered without an 
 
 elaborate statement of reasons, nor ever sullied by the 
 suggestions of jealousy or self-conceit. Had he been 
 an accomplished analyst he must have been less dis- 
 tinguished in the equally important walk in which 
 he stood pre-eminent. The limits of human life and 
 faculties prevents universal attainment, but he was 
 surely no mean philosopher of whom the sexage- 
 narian James Watt could say, " He was a man of 
 the clearest head and the most science of anybody I 
 have known." ' 
 
 Amongst the contemporaries of Eobison was one (339.) 
 whose acquirements were in many respects v,ery si- ^°^^°^|'g„ 
 milar to his own, and who contributed, in a degree g^^jp^ggiye 
 second to no other philosopher of his day, to pro- strength, 
 mote sound views in the very same branches of 
 science. Charles-Augustin Coulomb (born 1736, 
 died 1806) was, like Eobison, addicted through life 
 to practical enquiries, and was intimately acquainted 
 with all the details of the civil engineering of his 
 day. To him we owe a correct knowledge of the 
 laws of friction in most ordinary cases, and the right 
 application of them to the theory of machines, and 
 to that of the stability of structures. In a very re- 
 markable paper, published in 1776, he analysed, from 
 the basis both of theory and lexperiment, the manner 
 in which columns of masonry give way under longi- 
 tudinal pressure ; not, as had previously been sup- 
 posed, by flexure under the imposed weight, like a 
 steel spring or a rod of deal, but by the sliding of 
 one portion of the column over another, at an angle 
 determined by the cohesion of the stone, and capable 
 of being reduced to a problem of maxima and mi- 
 nima. This important principle is now known to 
 apply to wrought and cast iron, and many other sub- 
 stances. 
 
 One of Coulomb's happiest investigations was on (340.) 
 the force of torsion, or the resistance of wires to 0° torsion, 
 twisting ; which he showed to vary directly with the 
 angle of torsion, inversely as the length of the wire, 
 and directly as the square of its section. These me- 
 chanical principles he applied with address to deter- 
 mine the viscosity of fluids, and with still more con- 
 summate skill and success to the measurement, of 
 electrical and magnetical forces by the construction 
 of a Torsion Balance, similar in principle but ante- 
 rior to that employed by Michel 1 and Cavendish for 
 estimating the force of gravity. 
 
 Coulomb's researches on electricity (which have (341.) 
 been only partially published) will be made the sub- ^'^ ^^- 
 ject of discussion in another chapter of this Disser- resembled 
 tation ; they were the most sustained and elaborate Roblson's. 
 of his investigations, and display very considerable 
 mathematical resources. In this respect he had a 
 superiority over Eobison, who, as we have seen, cul- 
 
 ^ See Br Chalmers' Life, vol. i. That great man had a peculiar veneration for Dr Bobison, and is understood to have received 
 impressions from attending his lectures which materially influenced his future life. 
 " Mechanical Inventions of James Watt, it, p. 290. 
 
76 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 tivated precisely the same branclies of science whict 
 gave distinction to the career of Coulomb. When we 
 compare the two philosophers, we find that the former 
 was the more discursive reasoner and experimenter, 
 and was diverted, perhaps by the copiousness of his 
 erudition, and the attention with which he studied 
 the works of others, from doing full justice to his 
 own original powers. The latter excelled as a ma- 
 
 thematician ; he concentrated his efforts more me- 
 thodically,- and displayed the results to the world (so 
 far as they were published) in a more consecutive 
 and lucid form. In uprightness of character and 
 high morality, the two philosophers bore a marked 
 resemblance. They were both sufferers from bad 
 health, and they died within about a year of each 
 other, at nearly the same age. 
 
 3. Thomas Young — Strength of Materials, and Art of Construction (continued), — Telpoed 
 — Introduction of Iron into permanent Structures. Suspension Bridges. — Tredgold; Mr 
 Hodgkinson ; M. Navier. — Mr Robert STEPHEH'SOir — Tubular Bridges. 
 
 (342.) 
 Difficulty 
 and impor- 
 tance of 
 the enquii-y 
 into the 
 mechanical 
 propertiea 
 of solids. 
 
 (343.) 
 Progress 
 during the 
 eighteenth 
 century. 
 
 (344.) 
 Thomas 
 Young. 
 
 It is a circumstance not uninstructive as to the 
 progress and achievements of science, that the 
 greatest modern philosopher who preceded Newton 
 — Galileo — and one of the most eminent, if not 
 the most eminent, of his successors — Young — should 
 have laboured with minute and practical care, and 
 with corresponding success, on a subject apparently 
 so humble and mechanical as the Strength of Mate- 
 rials, and the Resistance of Beams to fracture. 
 Newton himself condescended to swing pendulums, 
 and to observe the collisions of eilastic worsted balls. 
 It is sufiicient here to advert to the exceeding inte- 
 rest of enquiries which throw so much light upon 
 the internal constitution of bodies, and in some 
 instances intimately connect them with the laws of 
 vibration of elastic media, to which so much of 
 Modern Physics is intimately allied. 
 
 The eighteenth century was in this, as in so many 
 other departments of science, sluggish and mechani- 
 cal, or else abstract and ultra-geometrical. The 
 learned labours of Euler and the Bernouillis on 
 elastic curves, and the strength of pillars, were for 
 the most part elegant mathematical amusements, 
 and with the exception of the experiments of Mus- 
 schenbroek in the earlier half of the century, and the 
 skilful but more limited researches of Coulomb at 
 its close, little valuable in the way of precise theory or 
 of accurate data derived from practice had been added 
 to this important branch of mechanical engineering. 
 
 Eobison, indeed, with the peculiar tact and skill 
 which I have already ascribed to him, wrote several 
 papers (contributed to an early edition of the Ency- 
 clopeedia Britannica, and printed in his collected 
 works) full of acute observation and reasoning, 
 adapted to the imperfect experiments of his time, 
 and connected by sound scientific deductions, which 
 are still well worthy of careful perusal ; but it was 
 to the penetration of Dr Thomas Young,' who par- 
 took strongly of Robison's mechanical tastes, whilst 
 he surpassed him in facility of mathematical resource, 
 that we owe a great revision of the doctrine of the 
 strength of materials. In the " Syllabus of Lec- 
 
 tures" (1802), into which he condensed, in a manner 
 peculiar to himself, an incredible amount of positive 
 knowledge ; in the Lectures themselves (1806), with 
 the admirable " Catalogue of References ;" and in 
 the articles on " Bridges," and the supplementary 
 propositions on " Carpentry,'' which he contributed 
 to this Encyclopsedia — we find (stated, as usual, 
 not without some obscurity) a multitude of theorems 
 and problems embracing the whole principles of 
 construction, and based upon mechanical laws and 
 the most probable interpretation of experiments. 
 
 The forces tending to alter the figure or dimensions (346.) 
 of substances usually called solid may be thus clas- ^^^^^ 
 sified: (1.) Extending forces, or such as produce force to 
 elongation in a body when applied in a direct man- solids.— 
 ner. (2.) Compressive forces. (3.) Force produ- ^^*^°™°- 
 cing detrusion, or the slipping of one portion of the 
 substance over another. (4.) Force producing flexure. 
 (5.) Torsion or twisting force. The resistance of bo- 
 dies to extension was examined by Hooke and Grave- 
 sande, and is held to be directly as the area of section 
 of the body, and to increase directly as the amount of 
 elongation produced, at least within certain limits. 
 The measure of this resistance Young termed (not 
 very happily) Modulus of Elasticity, expressing the Modulus oj 
 force required to produce unit of elongation (or to -Etoficjiy. 
 double the length) of a prism of the substance un- 
 der experiment. This quantity may be measured 
 either by the length of a depending prism of the 
 substance which would produce the requisite strain, 
 or more simply by the strain expressed in pounds 
 or tons, which, supposing the elongations to increase 
 without limit as the extending forces, would double 
 the length of the prism under experiment. Thus, 
 in round numbers, a bar of vn-ought iron an inch 
 square will be extended twVtt^ P^^* hy a pressure 
 of one ton— -hence the modulus of elasticity is about 
 10,000 tons. The elasticity of wrought iron remains 
 perfect to about half the breaking weight, after which 
 the elongations appear to double for each addition 
 of about y'ir or ^V of the breaking weight. Thus, in 
 a recent experiment by Mr Edwin Clark, a bar of 
 
 1 1 reserve to the chapter on Optics a fuller account of Young and his writings. 
 
Chap. IV., § 3.] 
 
 MECHANICS.-— YOUNG — TELFOED. 
 
 77 
 
 beams. 
 
 wrought iron, one incli square and ten feet long, ex- 
 tended x^l^T of i's length for every ton of weight 
 up to 12 tons, from which point the extensions nearly 
 doubled successively for every two tons of load, and 
 the bar was finally torn asunder by 23 tons. 
 (346.) The compression of bodies proceeds (Uke the ex- 
 Compress- tension) at first uniformly with the load. Some bo- 
 ^ ■ dies resist compression more than extension (as cast 
 iron); some the reverse (as wrought iron). Sub- 
 stances give way imder compression after different 
 fashions. Hard bodies divide into prisms parallel to 
 the compressing force ; slender elastic bodies bend 
 laterally ; soft bodies bulge horizontally ; bodies of 
 a medium hardness divide into wedges, and the sur- 
 faces slide along the plane of spontaneous fissure. 
 Detrusion. Detrusion marks more particularly the mode of giv- 
 ing way by the sliding of surfaces in the interior of 
 solids. Though seldom due to force directly applied, 
 it is an important element in most cases of the rup- 
 ture of semiductile solids. 
 (347.) The force of flexure is that by which the resist- 
 Flexure of ance of the greater number of solids is most easily 
 overcome, but which it is of most importance to re- 
 sist ; as when a beam is fastened by one end into a 
 wall, and loaded at the other, or when it spans a 
 horizontal space. It had not escaped the notice of 
 James Bemouilli, Duhamel, and other writers of the 
 earlier part of the 17th century, that the fibres on 
 the concave side of a loaded beam are in a state of 
 compression and not of extension, and that there is 
 therefore a point, or rather a line, in every beam, in 
 which the fibres are neither extended nor compressed. 
 But the clear modification of the theory prevalent 
 in the time of Leibnitz and Marriotte which this 
 consideration introduced, was probably first deve- 
 loped by Coulomb, Robison, and Young, who in their 
 respective publications insisted upon it with great 
 judgment ; and it is difficult to overrate its import- 
 ance in mechanical engineering, although the first 
 great canon of Galileo remains still true, that the 
 ultimate strength of a solid rectangular beam varies 
 as the breadth and as the square of the depth. 
 The writings of Young and Robison did not im- 
 mediately attract the attention of practical men, 
 and Coulomb, who was by far the ablest French 
 experimenter on subjects of mixed mechanics, 
 seems to have done less on the theory of strains 
 producing flexure than in the case of torsion, which 
 he studied with so much success, and applied to 
 such excellent purpose. Nevertheless in his memoir 
 on the Resistance of Masonry, in the 7th vol. of the 
 " Memoires Presentes" (1776), he had already laid 
 down very clearly the effect of compression on abeam.^ 
 
 It is, however, to Young that we owe the application 
 of these principles in unfolding their legitimate conse- 
 quences. In a series of remarkable propositions con- 
 tained in the writings I have quoted (344), he assigns 
 numerical relations between the flexure of a beam 
 under almost every supposable circumstance, and 
 the resistance of the material to direct strains. These 
 results have been extensively used by all subsequent 
 writers. They are not equally verified in all classes of 
 substances. This, however, is not wonderful ; flexure 
 is not due to direct compressive and extending strains 
 alone ; deformation may take place in a solid without 
 appreciable change of density, thus giving rise to 
 some of the nicest questions in molecular physics. 
 
 The laws of Torsion, as laid down by Coulomb, (348.) 
 have been mentioned in the last section (340). Torsion. 
 
 The mathematical investigations of Young on— (349.y~ 
 mechanical problems were conducted with bold di- Young's j 
 rectness and in defiance of the generalizing methods "rj^yngs" ' 
 and symmetrical notation of foreign writers on such " / 
 
 subjects. But his pre-eminent sagacity in laying hold 
 on the salient points of the questions he discussed, 
 and in conducting his argument to a practical con- 
 clusion, was unequalled, and deserves imitation.^ , --' 
 
 A great revival in the study of the properties of (350.) 
 elastic matter, as regards strength, took place about General 
 the year 1820, probably in consequence of the in-"°® ,. 
 troduction of wrought iron into the construction of iron, 
 suspension bridges, which has been attended with 
 important results. 
 
 Thomas Telford, though neither the contriver of (351.) 
 suspension bridges, nor the introducer of them into Telford ; 
 Britain,^ deserves notice from the superior boldness ^^P^"^'"" 
 and solidity of the noblest work of the kind which 
 has yet been executed — ^the Menai Bridge, Telford 
 (and the same may be said of his contemporary 
 Rennie) was more distinguished as a man of judg- 
 ment, integrity, and experience, than as eminently 
 original or philosophical. In this respect both yield 
 to Smeaton, who, with Watt, was the founder (each 
 in his own department) of modem engineering. But 
 the beautiful and truly workmanlike structure of the 
 Menai Bridge inaugurated the era of the extensive 
 introduction of that admirable material, wkought 
 IRON, into great permanent structures exposed to 
 heavy strains. Cast iron had been used much ear- 
 lier, as in the bridge erected at Colebrookdale in 
 1777 by Mr Derby, and in the very beautiful arch 
 at Sunderland, which dates from 1796. The span 
 of the Menai Bridge is 580 feet, the whole quantity 
 of iron used was 2186 tons, the transverse section 
 of the suspending chains or bars was 260 square 
 inches, supporting a strain of 1094J tons. This 
 
 ^ Eeprinted in the Flieorie des Machines Simples, Paris, 1821. 
 
 * A copious selection from Young's mechanical writings may be found in his Miscell. Works edited by Dr Peacock, vol. ii. 
 
 ^ Captain Samuel Brown erected the first considerable chain bridge in this country across the Tweed in 1819. 
 
78 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 was a work quite unexampled at the time of its 
 erection (1826), and showed a sagacious confidence 
 in the employment of a material then comparatively 
 little trusted. 
 (352.) Telford never made extensive experiments on the 
 2)a«a of re- resistance of solids. Some special ones were indeed 
 Bistance. made under his direction on wrought iron in par- 
 ticular, but in general he seems to have relied upon 
 „ , , , the old ones of Musschenbroek and Buifon. The 
 Barlow.and two persons who first in recent times vigorously 
 Hodgkin- applied themselves to the practical determination 
 ^°°' of the data of resistance so long deficient, were Tred- 
 
 gold, a private engineer, and Professor Barlow of 
 Woolwich. The data they obtained have since been 
 generally used, not only in this, but in other coun- 
 tries. Tredgold's works (on Carpentry, Strength of 
 Timbel:, &c.) show a very great aptitude in applying 
 the results of science to practice, and an acquaintance 
 with both which is rarely attained. Mr Eaton Hodg- 
 kinson has made many valuable additions to Tred- 
 gold's work, and has contributed an excellent paper 
 on the strength of pillars to the Philosophical Trans- 
 actions (1840.) 
 
 To Mr Hodgkinson we are also indebted for a 
 useful investigation (in the Manchester Transac- 
 tions) into the figure assumed by the chains of sus- 
 pension bridges. The elegant properties of the 
 simple or geometrical catenary were fully investi- 
 gated a century and a half since by the Bernouillis 
 and by David Gregory, but the application of sus- 
 pended structures of immense weight to purposes of 
 utility suggested new problems. Amongst these, 
 perhaps the most interesting was the catenary of 
 uniform strength, in which the section of the sus- 
 pending chains is made everywhere proportional to 
 the strain which they have to resist at that particu- 
 lar point. Its equation was investigated by Mr Da- 
 vies Gilbert in 1826. An elegant and valuable con- 
 tribution to the geometry of catenarian curves was 
 made by the late Professor Wallace of Edinburgh,' 
 with particular application to curves of equilibration 
 for bridges of masonry after the ingenious manner 
 of Robison mentioned in Art. (334). 
 (■354 ) In connection with suspension bridges, and also 
 
 M. Navier. Tfith researches on the yielding of elastic materials, 
 we must record the name of M. Navier, a very 
 eminent French, engineer and writer on practical, 
 and theoretical mechanics. His work on suspension 
 bridges (1823) is one of the earliest and best. He 
 is also well known for his physico-mathematical re- 
 searches on the yielding of elastic solids to pressure 
 
 (353.) 
 
 Geometry 
 of the 
 catenary. 
 
 under given circumstances, in the course of which he 
 came into collision with Poisson, who gave a some- 
 what different theory. The subject is one of ex- 
 treme difficulty, owing io our ignorance of the 
 molecular constitution of bodies ; and it is believed 
 that all these investigations were so far erroneous 
 that they were based upon the assumption of a single 
 constant to represent the resistance of bodies to 
 change of form and dimension. These (form and 
 dimension) are two very diflerent things, and require 
 distinct treatment.^ British mathematicians have 
 lately paid much attention to these enquiries, with 
 the prospect of a solid improvement in engineering 
 theories.^ 
 
 The art of bridging over great spaces has been (355.) 
 pushed, by the requirements of the railway system, to *'"■ Robert 
 an astonishing extent, and under circumstances of ^^^^ ^°" 
 peculiar difficulty. I shall connect these improve- 
 ments with the name of Mr Robert Stephenson, 
 the inventor of the Tubular Bridge, a work which, 
 in its very simplicity, is a triumph of art, and being 
 nothing more than a hollow beam of somewhat pecu- 
 liar construction, supported at the ends, it is an ad- 
 mirable instance of a structure of which the stability 
 may be easily reduced to calculation. 
 
 The wooden bridges of Switzerland were for a long (356.) 
 time unequalled as skilful works of carpentry. During 1,^°^ ^ "j^ 
 the last century the Rhine at Schaffhausenwas crossed Switzer- 
 by two spans of 171 and 193 feet. At Trenton, inland and 
 America, the river Delaware is crossed by a wooden ■*-"*™*- 
 bridge, of which one arch is 200 feet in span. It is 
 on the how principle, an elastic wooden arch, convex 
 upwards, being skilfully braced and united to a level 
 roadway passing through the spring of the arches. 
 The American lattice bridge, very simply and skil- 
 fully contrived, has great firmness, owing to the depth 
 of the framing, and exercises no horizontal thrust on 
 the piers. The widest spanned wooden bridge in the 
 world, 340 feet, across the Schuylkill, at Philadel- 
 phia, designed by Wernwag, combines the bow and 
 lattice principle. 
 
 In these we might see foreshadowed in some faint (357.) 
 degree the principle of the Tubular Bridge, the The tubular 
 greatest discovery in construction of our day, But'''''^se- 
 in reality the idea of it arose from a different con- 
 sideration. 
 
 During the first ten or fifteen years of railway ex- (358.) 
 perience, engineers had gradually acquired a correct ^^^J 
 perception of the manner in which cast and wrought bridges, 
 iron may most effectually and economically be formed 
 
 ^ Edinburgh Transactions^ vol. xiv. 
 
 2 About twenty years ago, the present writer showed that India rubber, which possesses to such a remarkable extent the 
 quality which may be termed cubical flexibility, is yet scarcely at all compressible-^in fact, just as much as water, and no more. 
 Though not otherwise published, he has been in the habit of demonstrating this in his annual course of lectures. 
 
 3 Professor Stokes in Cambridge Transactions, vol. viii. ; Mr Clark Maxwell in Edinburgh Transactions, vol. xx. Mr M. 
 Eankine in Cambridge and Dublin Math. Journal for 1851 and 1852. Experimental data are still deficient; but M. Wertheim 
 has lately published some valuable ones (which are still in progress) in the Annales de Chimie. 
 
Chap. IV,, § 3.] 
 
 MECHANICS. — ME, STEPHENSON. 
 
 79 
 
 into girders or beams supported at the ends, and 
 adapted for sustaining enormous loads. Such beams 
 were constructed, often of single castings, so as to in- 
 clude three portions ; an V-Tp-per flange, alovrev flange, 
 and a web, or thinner vertical plate connecting the two. 
 The relative section of the upper and lower flange was 
 made to vary with the material. In cast iron, which 
 yields far more easily to tensile than to compressive 
 strains, the lower flange should be almost incom- 
 parably greater than the upper ; in wrought iron a 
 slight predominance should be given to the upper 
 flange for the converse reason. 
 (359.) Hence it will be easily understood how, when Mr 
 The idea of Robert Stephenson was desired to construct a rail- 
 bridee de-'^^^y bridge across the Menai Strait, — subject to the 
 rived from onerous condition imposed by the Admiralty, that it 
 them. should (even at the abutments) be without lateral 
 struts or diagonal pieces below the roadway, — he 
 should have entertained the idea of a gigantic girder 
 with a top and bottom flange of proportionate extent, 
 with a deep web uniting them, or rather of two such 
 girders placed side by side, thus forming square 
 tubes, of which the lower flanges should constitute 
 the bottom, the upper flanges the top, and the two 
 webs the sides. 
 (360.) It is not for me in this place to explain how, step 
 Progress of by Step, the idea of a tubular bridge of wrought iron 
 the inven- assumed the practical shape, now to be seen at Con- 
 way, and near Bangor, in North Wales. It is un- 
 fortunately notorious that there has existed an un- 
 happy rivalry as to the share of merit due to the 
 several persons who of necessity were jointly con- 
 cerned in the completion even of the design of these 
 astonishing works. Unfortunately for Mr Stephen- 
 son's tranquillity, the tremendous responsibility of 
 this novel, gigantic, and costly experiment, was 
 thrown upon him during the very height of the com- 
 mercial and engineering excitement (not unjustly 
 called mania) which prevailed in 1845 and 1846, on 
 the subject of railway projects. Instead of the un- 
 interrupted leisure which he required to superintend 
 his preliminary experiments, to consider his plans, 
 and perform his calculations, Mr Stephenson, as well 
 as every other engineer of eminence was at that time 
 engaged all day and a great part of the night in the 
 unparalleled worry of Parliamentary contests. As a 
 matter of course, much was trusted to able, confi- 
 dential, and highly paid assistants. The experiments 
 on models of different forms, which alone cost many 
 thousand pounds, could not all be conducted in the 
 presence of the chief engineer. Yet he alone was 
 responsible for the failure or success of the plan. 
 (361.) The comparatively great strength of tubes was 
 The cellu- a fact known from the time of Galileo. Their de- 
 ar top. fgj.^ ^g^g g^ liaWUty to crumple or pucker. Bound, 
 oval, and rectangular tubes were tried, and the last 
 (Mr Stephenson's original conception) were, as might 
 -be supposed, found to be stronger than the other 
 two. When supported at the ends, and loaded in 
 
 the middle, model tubes of this form invariably gave 
 way at the top. How to strengthen the top against 
 compressive strains was the question. The exces- 
 sive stiifness of corrugated iron and zinc plates (long 
 previously used for roofs) came to the engineer's 
 assistance. A combination of two longitudinally cor- 
 rugated or goffered wrought-iron plates running 
 along the top of the model, and forming long and 
 nearly cylindrical cells, was found to give the re- 
 quired stiffness with the least increase of weight. 
 Ultimately a square arrangement of cells was adopted, 
 principally to give facility for painting and repair. 
 The tubes were hindered from racking by means of 
 numerous wrought-iron frames employed to stiffen 
 them, whose section resembled the letter T, and which 
 were called T irons. Suitable diaphragms were also 
 inserted at short distances along the tubes. The 
 widest spaces to be spanned at the Menai Strait were Dimensions 
 460 feet, there being two intervals of this width, and and 
 two of 230 feet. The tubes are 30 feet high and 14 'f/°f*^ f 
 broad, containing a transverse section of about 1500 
 square inches of wrought iron. The weight of one 
 principal tube is about 1450 tons, and its strength, 
 measured by the breaking load at the centre, above 
 2300 tons. This last number is calculated from the 
 experiments on the breaking weight of models, one ot 
 which was on no less than a sixth of the true scale. The ' 
 boiler-plates, of which the tubes are composed, are 
 united by mechanical pressure by means of hot rivets; 
 and it may safely be affirmed that without this ingeni- 
 ous and perfect method of combination (which is due 
 to Mr Fairbairn, who had previously obtained a patent 
 for it), the structure would have been impossible. 
 
 The success of this astonishing piece of engineer- (362.) 
 ing has been complete ; the stiflhess of the tubes, I*^ 0°™- 
 whether under constant pressure or during the rapid ^^^^^ ^"°' 
 transit of trains, is ajmost incredibly great. 
 
 To Mr Robert Stephenson is clearly due the credit (363.) 
 of undertaking, on his sole responsibility, a project Mr Ste- 
 of equal boldness and novelty, and of contriving, not ^ gl^^n^^ie 
 perhaps in every detail, but in its totality, the means inventor ; 
 by which so signal a triumph of art and of science was 
 carried into effect, an honour to his own age, and a 
 lesson to posterity. To Mr Fairbairn and Mr Hodg- assisted by 
 kinson, his assistants, selected by himself, much praise ^^f^F^. 
 is also due for the manner in which the experiments g^„^ Hodg- 
 were managed, and the principles established by these kinson. 
 educed. Mr Fairbairn, a practical engineer of Man- 
 chester, well known for his experience and sagacity, 
 gave to Mr Stephenson, as a matter of honour, the 
 full benefit of both ; and his confidence in the result 
 helped no doubt to sustain the manly courage of his 
 principal amidst a storm of oppositioil. Mr Hodg- 
 kinson, well known for his able enquiries into the 
 strength of pillars and girders of ditierent forms, 
 conducted the mathematical enquiries, and deter- 
 mined the relative strengths of the models. His con- 
 fidence in the result was less encouraging than that 
 of his coadjutor, which serves to show the greatness 
 
80 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (364.) 
 Commis- 
 sion on 
 railway 
 bridges. 
 
 (365.) 
 
 of the responsibility of the engineer-in-chief. As 
 neither Mr Fairbairn nor Mr Hodgkinson could have 
 incurred any just blame had the vast structure when 
 on the eve of completion doubled up under its own 
 weight, and blocked up, perhaps for ever, the navi- 
 gation of half the Menai Strait, so neither can they 
 possibly claim more than a subordinate share in the 
 success of the undertaking.'- 
 
 I shall here only refer to the work of Mr Edwin 
 Clark, the resident engineer of the Britannia Bridge, 
 for farther details of its principles and construction, 
 and to the report of a royal commission (published 
 in 1849) on the application of iron to railway struc- 
 tures, for many curious researches connected with the 
 subject of this section. In particular, we find a theo- 
 retical and practical solution of the very delicate pro- 
 blem of the influence of the speed of passing loads on 
 the deflection of bridges, to which Professors Willis 
 and Stokes, and ColonelJames,R.E>,are contributors. 
 
 Mr Robert Stephenson is the son of Mr George 
 Stephenson, who will be mentioned in a succeeding 
 
 section. He was born in 1803; educated (in part) at Other 
 the University of Edinburgh, under Leslie, Hope, and ^^^ "^ 
 Jameson ; he long occupied the chief position in the phenson. 
 locomotive factory established by his father at New- 
 castle, having in the first place constructed under 
 his direction the celebrated " Rocket" engine which 
 gained the prize at the opening of the Liverpool 
 and Manchester railway. To his own exertions, 
 both before and after that period, the locomotive 
 owes much of its present perfection. He surveyed 
 and principally carried through the London and Bir- 
 mingham railway, the second great line in the king- 
 dom ; and he has been engaged in a large proportion 
 of the most remarkable engineering works connected 
 with railways, both in this country and abroad. He 
 has personally superintended the construction of 
 railways amidst the blowing sands of Egypt, and in 
 Norway with its heavy winter snows and deeply frozen 
 soil. Ilis high personal character, both for skill and 
 integrity, has everywhere procured him the respect 
 and confidence of his profession and of the public. 
 
 § 4. Brunel. — Self-acting Machinery. — The Thames Tunnel. — Mr Babbage's Calculating 
 
 Engines. 
 
 tart Bru- 
 nei. 
 
 (366.) Sir Marc Isambart Brunei, bom at Hacqueville 
 Marc Isam- jn Normandy on the 25th April 176 9, was one of the 
 most inventive mechanicians and engineers of his day. 
 As his genius gave a strong impression to contem- 
 porary art, we associate his name with the progress 
 of civil engineering in the earlier part of the pre- 
 sent century, particularly in connection with me- 
 chanism. Like most of his eminent coevals in the 
 same profession, he had not the benefit of a scien- 
 tific education ; but he more than most of them sup- 
 plied its defects by a singular capacity for correct 
 induction and by great mechanical ingenuity. Though 
 a native of France, it was in Great Britain that his 
 talents were to find their full scope, and it became his 
 thoroughly adopted country. 
 
 Disgusted by the horrors of the first revolution, 
 he quitted France in 1793 in the capacity of a com- 
 mon sailor, a position far below that which either his 
 birth or his intellect entitled him to hold, yet in 
 which he made himself remarked by his excellent 
 disposition and mental superiority. His destination 
 was New York, where in 1794 he commenced his 
 
 (367.) 
 
 His early 
 history. 
 
 career as a civil engineer, his boyish tastes having 
 already indicated this as his natural calling. He exe- 
 cuted some considerable works, and planned many 
 more ; it is stated that he there devised the essential 
 parts of his block machinery. About 1799 he decided 
 on settliug in England, 
 
 It is probable that his talents and ingentiity alone 
 recommended him to a government employment at a 
 time when the mere fact of his being a Frenchman 
 must have acted as a powerful obstacle to his suc- 
 cess. Those who recollect the vivacity and bright 
 intelligence of even his later years, will imderstand 
 that in his more active days it must have been difii- 
 cult to refuse Brunei at least a hearing. And it is 
 to the credit of Lord Spencer, then one of the Lords 
 of the Admiralty, and of General Sir Samuel Ben- 
 tham, inspector of naval works, that Brunei was en- 
 gaged in 1802 to superintend the erection of his cele- 
 brated block machinery. 
 
 The invention of self-acting machinery to super- 
 sede the work of artisans was of course not new. 
 The saw-mill and the spinning-jenny were already in 
 
 (368.) . 
 Employed 
 by the Eng- 
 lish go- 
 vernment. 
 
 Self-acting 
 machinet'y. 
 
 1 It has been alleged that Mr Stephenson's original proposal to allow the suspension chains (which were primarily intended to 
 be used in putting together the tubes in their final positions) to remain in aid of the rigidity of the structure, manifested a 
 want of confidence in his own great idea. But a dispassionate consideration of his evidence before the committee of the 
 House of Commons would alone clearly show (independent of Mr Stephenson's declarations on the subject) that he was 
 forced into the admission that the chains might give an ulterior guarantee against miscarriage of the whole plan, simply to save 
 the bUl from being thrown out by the not unnatural incredulity of those to whom a proposal so new, so gigantic, and aflfeoting the 
 lives of so many persons, as well as so great pecuniary and other interests, was for the first time and suddenly proposed. Be- 
 sides this, even his own coadjutors did not aU entirely support him. Mr Hodgkinson, whose character for scientific know- 
 ledge carried great weight with the committee, recommended in his report the ultimate additional security of chains. 
 
Chap. IV., § 4.] 
 
 MECHANICS. — BKUNEL — MR BABBAGE. 
 
 81 
 
 (370.) 
 The block- 
 machineij 
 
 its results. 
 
 (371.) 
 Crave an 
 impulse to 
 mechanics. 
 
 (372.) 
 Introduc- 
 tion of me- 
 chanism 
 into work' 
 shops. 
 
 use, but tte invention of Brunei was not less im- 
 portant as creating an epoch in art. Not only is 
 it possible to execute in a comparatively short 
 time, and with a prodigious economy, objects such as 
 blocks and pulleys, which are required in vast num- 
 bers and precisely alike, but the nicety and accuracy 
 of the manufacture is thereby increased, and owing 
 to the facility with which inanimate force may be 
 concentrated on machinery, works which transcend 
 the power of unaided muscular labour are as surely 
 and exactly executed as those of smaller dimensions. 
 For example, by no enlargement of the common 
 turning-lathe would it be possible to construct an 
 accurately turned iron steam-cylinder 8 feet or more 
 in diameter, which is yet readily executed under the 
 direction of a very ordinary workman by means of 
 steam power and self-acting machinery. 
 
 The block-machinery at Portsmouth consists of a 
 series of engines impelled by steam, and by means of 
 ' which thematerials of wood and metal employed in the 
 construction of ships' blocks are reduced to exact forms 
 in graduated sizes, and are finally put together with 
 very little manual labour. These machines, with the 
 exception of the turning-lathe and circular saw, were 
 wholly new, and, it is stated, were devised in part by 
 General Bentham, who gave to Brunei at least the 
 benefit of his advice and previous experiments. In 
 some of them we have the first germ of implements 
 now used by every machine-maker in the kingdom; 
 and the ingenuity of the movements, and the variety 
 of effects produced, earned for this great invention a 
 just celebrity. Such a beginning could not have 
 been made without the aid of government. To con- 
 struct the tools was an expensive and troublesome 
 business, and to start the manufactory cost L.53,000, 
 which was speedily saved by the economy of the pro- 
 cess. In the course of a year 140,000 blocks of no 
 less than 200 different patterns were produced, and 
 the number of workmen was diminished in the pro- 
 portion of about 11 to 1. As a reward, Mr Brunei 
 received L.16 ,000, being two-thirds of the first year's 
 saving, itself a sufficient proof that he was the bona 
 Jide inventor of this admirable apparatus, whatever 
 hints he may have received from his immediate su- 
 perior. 
 
 So successful an experiment produced ultimately, 
 though with characteristic slowness, its effect on the 
 mercantile world ; nearly twenty years elapsed before 
 such a splendid example of ingenious economy and 
 artistic precision was at all generally imitated. Yet 
 before his death. Sir Marc Brunei saw the fruit of his 
 ingenuity almost indefinitely miJtiplied in the work- 
 shops of London, Manchester, Glasgow, Newcastle, 
 and Binningham, and highly appreciated if less ex- 
 tensively imitated abroad. 
 
 The more we reflect on the comparative state of the 
 arts now and a century ago, the more we shall find 
 reason to estimate highly the introduction of correct 
 and scientific ideas of machinery and of tools for con- 
 
 structing other machines and structures. It was, in 
 fact, the necessary complement of the invention of 
 the steam-engine. Watt contrived the mighty Heart 
 which was to give a new impulse to social life, Bru- 
 nei and others of the same stamp added limbs and 
 muscles, whereby its energies were rendered tho- 
 roughly pi?actical. The sixteenth, seventeenth, and 
 part of the eighteenth centuries, had given to the 
 world designs for countless mechanical contrivances, 
 often highly original and ingenious. But many 
 were grounded on fallacies, and others belong to 
 the class of elaborate trifles. At that period the 
 slide-rest of the turning-lathe, the planing machine, 
 and the circular saw, were practically unknown ; at 
 least the two former, which are incomparably the 
 most important inventions of their class, and which 
 belong to no certain author, having almost imper- 
 ceptibly come into use — the slide-rest about the Slide-rest 
 end of the last century, the planing machine as f"^ P^*°" 
 lately as about 1820. The former of these readily ^^?j"*' 
 forms surfaces of revolution with geometrical accu- 
 racy, the latter plane surfaces, and in either case 
 the application to metals is most important. The 
 circular saw and slide-rest form part of Brunei's 
 series of machines, and he afterwards constructed the 
 former on a very great scale for the manufacture of 
 wooden veneers. To them he added the mortising 
 machine, and these, it will be seen (together with the 
 planing engine), form the staple of the magnificent 
 and varied apparatus with which, driven by the gi- 
 gantic power of steam, our mechanical factories are 
 now so generally provided. We again repeat that 
 the triumphs of art in which our generation glories, 
 our railroads, our locomotives, our crystal palaces, 
 and our steam navies, would have been impossible 
 feats but for the improvement of tools and the substi- 
 tution of steam for muscular power. 
 
 Every one is, however, aware that Brunei owed Ms (373.) 
 reputation to other achievements as well as his im- TheThamea 
 provements of mechanical tools. The Thames Tun- T""°ei. 
 nel will ever be considered as his most arduous tri- 
 umph. It is a structure of exquisite firmness laid 
 in a qtdcksand. It will endure like the cloacee of 
 regal Rome, when the palace and the cathedral have 
 crumbled to dust. Yet here also we perceive that 
 it was Brunei's exquisite mechanical tact and inge- 
 nuity which enabled him to succeed. The problem 
 of the tunnel is not one of balancing vaults ; the sta^ 
 tical conditions of stability are simple enough, and 
 it was not in the solution of such that Brunei pecu- 
 liarly excelled. The practical problem was to intro- 
 duce a rigid tube of brick horizontally into the 
 middle of a quaking mass of mud ; and the solution 
 was the invention of a tool which should enable men 
 to make the excavation and to proceed with the 
 building in safety. It was the shield which carried The shield. 
 the tunnel under the Thames, — a moveable vertical 
 frame of cast iron, provided with thirty-sis cells, in 
 each of which a man was placed with a pick to ex- 
 
82 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (374.) 
 Completion 
 of the tun- 
 nel. 
 
 cavate the area required for the construction of the 
 tunnel. By a simple but most ingenious contrivance, 
 every part of tlie face of unstable clay was firmly 
 supported by boards which leaned upon the frame or 
 shield, which, in its turn, pressed against the part of 
 the brickwork of the tunnel already completed. Each 
 workman could remove one or more of these small 
 boards at pleasure, and excavate a short way into 
 the yielding mass before him, then advance the boards 
 and sustain the slippery face. When the whole face 
 had thus undergone piecemeal excavation, the frame 
 or shield was moved bodUy forwards by powerful 
 screws, and the bricklayers brought up the masonry 
 behind, which was then beyond the reach of injury. 
 
 The idea of the shield was derived, it is stated, from 
 a specimen in the arsenal at Chatham, showing the 
 operations of a testaceous worm which bores under 
 water, and which nature has provided with a protec- 
 tive covering. But the analogy is certainly indirect, 
 since water could hardly retard the operations of 
 such an animal. Repeated irruptions of the Thames 
 several times drowned the work, which was as often 
 abandoned and renewed, but every difficulty was met 
 by fresh resources on the part of the engineer. The 
 failure of funds was a far more serious obstacle, and 
 government at last came to the aid of an undertak- 
 ing of such consummate ingenuity that its comple- 
 tion was deemed due to the honour of the nation. 
 The tunnel was commenced on the 2d March 1825, 
 and finished 25th March 1843. Brunei survived the 
 completion of his great work above six years, dying 
 on the 12th December 1849, aged 81. 
 
 We have not in this brief sketch glanced at one 
 half of his ingenious projects and successful enter- 
 prizes. Scarcely any branch of his multiform pro- 
 fession but received some improvement at his hand. 
 The discovery of the condensation of several gases in 
 1823, by Mr Faraday, suggested to Brunei their ap- 
 plication as a moving power ; and his want of suc- 
 cess did not arise from any deficiency on his part of 
 skiU or forethought. He was one of the first to con- 
 struct a roof of extreme lightness, somewhat resem- 
 bling those now in use for railway stations. He 
 erected a suspension bridge in the Isle of Bourbon 
 on an original plan ; and he pointed out with cha- 
 racteristic shrewdness how much of the stability of 
 arches depends upon the cohesion of the parts, so 
 that the vault may in some cases be entirely dis- 
 pensed with. 
 
 It will be understood that we have selected Sir 
 Marc Brunei as the representative of a class, the 
 eminently mechanical engineers, a class now exten- 
 sively multiplied, and amongst whom his son, Mr 
 Brunei, occupies an eminent position. 
 
 (377.) It cannot be expected in an essay like the present 
 
 Calculat- t}ia,t I should enter into the details of the variety of 
 
 chfnes^of mechanical inventions which have now become so 
 
 Mr Bab- numerous, and which have been marked by every 
 
 Death of 
 Brunei. 
 
 (375.) 
 Variety of 
 his works. 
 
 (376.) 
 
 gradation of originality and resource. But as illus- 
 trating a class of contrivances altogether different 
 from those of Brunei, though like them tending to 
 produce a great influence on the improvement of the 
 mechanical arts, I will briefly refer to the Calcu- 
 lating Machines of Mr Babbage, which have at dif- 
 ferent times excited the interest of the public and of 
 scientific men. 
 
 Mr Babbage was a fellow student at Cambridge (378.) 
 with Sir John Herschel and Dean Peacock, and along '^^Jf^^ 
 with them he contributed by his writings and per- «""*°S'°*- 
 sonal efforts to introduce into that university the 
 improved Continental mathematics. A few years after 
 leaving college he originated the plan of a machine 
 for calculating tables by means of successive orders 
 of differences, and having received for it in 1822 and 
 the following year the support of the Astronomical 
 and Royal Societies, and a grant of money from go- 
 vernment, he proceeded to its execution. It is be- 
 lieved that Mr Babbage was the first who thought 
 of employing mechanism for computing tables by 
 means of differences ; the machine was subsequently 
 termed the difference engine. In the course of his 
 proceedings Mr Babbage invented a mechanical no- 
 tation (described in the Philosophical Transactions 
 for 1826), intended to show the exact mutual rela- 
 tions of all the parts of any connected machine, how- 
 ever complex, at a given instant of time. He also 
 made himself acquainted with the various machines 
 used in the arts, with the tools used in constructing 
 them, and with the details of the most improved 
 workshops. Employing Mr Clements, a skilful me- 
 chanist, a portion of the calculating machine, very 
 beautifully constructed, was brought into working 
 order, and its success so far answered the expecta- 
 tions of its projector. But, notwithstanding several 
 additional grants from government, the outlay on 
 this most expensive kind of work soon exceeded them. 
 The part actually constructed is now placed in the 
 Museum of King's College, London ; it employs 
 numbers of nineteen digits, and effects summations 
 by means of three orders of differences. Though 
 only constituting a small part of the intended engine, 
 it involves the principles of the whole. The inventor 
 proposed to connect with it a printing apparatus, so 
 that the engine should not only tabulate the num- 
 bers,- but also print them beyond almost the possi- 
 bility of error. 
 
 At this stage (1834) Mr Babbage contrived a ma- (379J 
 chine of a far more comprehensive character, which The anaJy- 
 he calls the Analytical Engine, extending the plan "."'*' ®°' 
 so as to develop algebraic quantities, and to tabu-° 
 late the numerical value of complicated functions 
 when one or more of the variables which they con- 
 tain are made to alter their values. Had this engine 
 been constructed, it would necessarily have super- 
 seded what had already been done. Government were 
 not unnaturally startled by this new proposal, and 
 as about the same time Mr Babbage's relations to 
 
CHiP. IV., § p.] 
 
 MEOHANIOS— TREVITHICK — G. STEPHENSON. 
 
 83 
 
 Mr Clements were broken off, the difficulties of the 
 affair became insurmountable, and the construction 
 of either engine has for some years been in abeyance. 
 The opinions of men of science are not unanimous 
 as to the great practical importance of calculating 
 tables by machinery, but the improvements of me- 
 chanical contrivance which the joint skill of Mr 
 Babbage and Mr Clements introduced into engi- 
 neering workshops are unquestionably of great impor- 
 tance to the arts. Though the details of Mr Bab- 
 bage's plans have not been published, there can be 
 no doubt that, whether economical or not as sub- 
 stitutions of machinery for human labour, they were 
 devised with remarkable skill and ingenuity, and even 
 on this account merit preservation.^ 
 (380.) Recently (1855) attention has been directed in 
 
 M.Scheutz Loudon to a simple and effective Difference Engine 
 engine. constructed and patented by M. Scheutz, confessedly 
 on the principles of Mr Babbage, though without an 
 acquaintance with his mechanical contrivances. The 
 result is stated to be satisfactory. The engine deals 
 with fifteen digits or figures, and with four orders of 
 differences. Only eight figures are preserved in the 
 result, the others being reserved to prevent errors 
 
 arising from the accumulation of still lower digits 
 omitted. The engine not only computes with facility 
 and accuracy, but, by means of steel punches impress- 
 ing lead, provides for the perpetuation of the num- 
 bers in the form of stereotyped plates. The work- 
 manship of the whole requires no particular nicety 
 of execution, is not liable to derangement, and can by 
 scarcely any contingency produce inaccurate results. 
 
 Before closing this section, we may advert to im- (381.) 
 provements in the theory of machines by those who Foreign 
 have regarded it rather from the geometrical side^"^^"^"" 
 than from that of routine practice. Our French of ma- 
 neighbours have been distinguished in this respect, chines. 
 Carnot and De Prony, MM. Hachette, Poncelet, and 
 Morin, have been or are accomplished mechanists in 
 this respect ; and in the French repertories we must 
 look for some of the earliest good scientific descrip- 
 tions of machinery, even when of English invention. 
 , In England, besides Mr Babbage, Professor "Willis (382.) 
 of Cambridge has shown a peculiar aptitude in this English 
 
 S.Iltill01*S 
 
 department, and has published a very valuable work 
 on machinery, regarded in a strictly geometrical sense.^ 
 To Mr Moseley we are likewise indebted for some va- 
 luable contributions to the theory of engineering. 
 
 §5. Trevithick.- 
 
 -George Stephenson. — The Locomotive Steam-Engine.- 
 of Railways. — M. de Pambour on Locomotives. 
 
 -Rise and Progress 
 
 (383.) 
 The loco- 
 ■motive en- 
 gine and 
 railway. 
 
 (38i.) 
 Early anti 
 cipation 
 of steam- 
 carriages. 
 
 Of all the inventions which have powerfully af- 
 fected the interests of mankind, none have been more 
 slowly perfected, or can be less certainly traced to a 
 single individual as the inventor, than those of the 
 Locomotive engine and the Railway. These two great 
 and essentially connected portions of the greatest 
 mechanical and commercial effort of any age or 
 . country had their origin in obscurity. Each ap- 
 peared several times to be rising into the import- 
 ance it deserved, but failing the concurrence of 
 the fortunate circumstances which are necessary to 
 give permanence to invention, was once more for- 
 gotten and was left for re-discovery at a happier 
 epoch. 
 
 With regard to Steam-Carriages, passing over still 
 earlier speculations, we find that Dr John Robison, 
 at the age of twenty-one, published a design for a 
 steam-carriage in the Universal Magazine for No- 
 vember 1757, and that he also directed Mr Watt's 
 attention to the steam-engine in the same year, with 
 a view to this very application. The cylinder of the 
 proposed machine was an inverted one, and Watt ac- 
 tually made a rude model on Robison's suggestion.^ 
 From this time the steam-carriage seems never to have 
 
 been long lost sight of by mechanical speculator?. 
 It was included in a patent by one Moore, a linen 
 draper, in 1769.* In the same year it is stated that 
 Cugnot, a native of Lorraine, actually constructed 
 a steam-carriage, which, like the nearly contemporary 
 but unsuccessful efforts of his countrymen to effect 
 steam navigation, fell speedily into oblivion, About 
 1773 Edgeworth of Edgeworthstown urged the con- 
 struction of steam-carriages, and at a later period ex- 
 pressed, in terms of unequivocal anticipation, the 
 triumph arising from their connection with railways. 
 " 1 have always thought," he wrote in 1813, "that 
 steam would become the universal lord, and that we 
 should in time scorn post-horses. An iron railroad 
 would be a cheaper thing than a road on the com- 
 mon construction." At Soho the movement of car- 
 riages as well as of boats by steam never was or could 
 be forgotten. In Watt's patent of 1784 the steam- Watt and 
 carriage forms the seventh article, and in the same **'^^yg°'*' 
 year^ Mr William Murdoch, a member of Boulton 
 and Watt's establishment, made a model, acting by 
 high-pressure steam, which drove a small waggon 
 round the room. Hence it required no prophetic 
 power in Darwin, the intimate friend of Watt, to 
 
 ^ For historical details connected with Mr Babbage's engine, see Weld's History of the Royal Society, vol. ii. An account of 
 the principles and action of the Difference Engine may be found in the Edinburgh Review for July 1834 ; and those of the Ana- 
 lytical Engine in Taylor's Scientific Memoirs, vol. lii. 
 
 ^ Principles of Mechanism. Camb., 1841, 3 Mechanical Inventions of James TFa«, ii. 294. 
 
 * Mechanical Inventions of James Watt, i. 52. 5 Translation of Arago's Eloge of Watt, p. 120, note. 
 
84 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 , write those often quoted lines in the Botanic Garden 
 (canto i. line 290) : — 
 
 " Soon shall thine arm, unconquered Steam, afar 
 Drag the slow barge, or drive the rapid car." 
 
 (385.) A somewhat longer pause now occurs. But in 
 
 Trevitbick 1802 we find Richard Trevithick, a Cornish " cap- 
 vian ■ their ^^^^ " °^ ^ mine, taking out a patent along with Vi- 
 patent in vian for the high-pressure steam-engine, and apply- 
 1802. ing it specifically and practically to the movement 
 
 of carriages or waggons along a railway at Merthyr 
 Tydvil in South Wales. Mr Muirhead informs us 
 that Trevithick saw Murdoch's model at Eedruth in 
 Cornwall. But admitting this, it is plain that the 
 idea was much older still, and also that many years 
 elapsed without its ever being brought practically 
 to bear until the year 1804, when Trevithick's loco- 
 motive was actually used. 
 (386.) Richard Trevithick appears to have been one of 
 
 Account of the most ingenious men of his time ; but (from the 
 revithic . ggj^jj).y notices which I have been able to collect') to 
 have been also of an inconstant speculative disposi- 
 tion, which prevented him from bringing any of his 
 numerous inventions to perfection. Yet he had the 
 good fortune, which so many inventors have missed, 
 of meeting with partners able and willing to assist him 
 in carrying out his designs. Amongst these was 
 Andrew Vivian, with whom in 1802 he took out the 
 patent already mentioned for the construction of high- 
 pressure engines, and their application to the move- 
 ment of carriages along rails or common roads. As 
 Applies the first practical employer of high-pressure steam of 
 '^ "P"^ 60 to 80 lb. pressure on the square inch, Trevithick 
 to looomo- deserves especial notice. He borrowed the notion of 
 tives on it, as well as the ingenious invention of the four-way 
 1804°^^° "^ cock, from an old scheme of Leupold's, but he over- 
 came for the time the iirejudicc which had always 
 existed even in the mind of Watt against its adop- 
 tion. His earliest engine is stated to have been con- 
 nected with a common stage coach which ran on the 
 streets of London ; but his more successful and im- 
 portant effort was made in dragging waggons along 
 the Merthyr Tydvil railway in South Wales, which 
 was successfully tried on the 21st February 1804, 
 when the engine drew carriages containing ten tons 
 of bar iron for a distance of nine miles at the rate of 
 five miles an hour. This was unquestionably the 
 first successful example of this modern species of 
 locomotion. 
 (387.) If y^e look more closely at the means by which it 
 
 his engine ^^* accomplished, we find still more reason to com- 
 mend the sagacity of the inventor, and to wonder at 
 the interval of nearly thirty years which elapsed be- 
 fore the general adoption of his plan. " A square 
 iron case containing the boiler and cylinder was placed 
 behind the large or hinder wheels of the carriage, and 
 was attached to a frame supported from the axles of 
 
 those wheels. The cylinder was in a horizontal po- 
 sition, and the piston-rod was projected backwards 
 and forwards in the line of the road towards the front 
 of the carriage. Across the square frame, supported 
 by the wheels of the carriage, an axle was extended 
 reaching a little beyond the frame on each side ; this 
 axle was cranked in the middle, in a line with the 
 centre of the cylinder, and a connecting-rod passing 
 from the end of the piston turned this axle round, 
 and produced a continued rotatory motion of it when 
 the piston was moved backwards and forwards in the 
 cylinder; upon both ends of this axle cog-wheels 
 were fixed, which worked into similar cog-wheels 
 upon the axles of the wheels of the carriages, so that 
 when a rotatory motion was produced in the cranked 
 axle by the piston-rod it was communicated to the 
 axle of the larger or hinder wheels of the carriages, 
 and these wheels being fixed upon and turning round 
 with the axle, gave a progessive motion to the car- 
 riage. Upon one end of the axle was fixed a fly- 
 wheel to secure a rotatory motion in the axle at the 
 termination of each stroke." ^ 
 
 We here find the cranked axle and the horizontal (388.) 
 cylinder of modern locomotives, both of which were 
 departed from by Trevithick himself, probably in 
 consequence' of difiiculties of execution. When we 
 add to this plain description, that the fly-wheel was 
 furnished with a break, that the boiler had a safety- 
 valve or a fusible plug beyond the reach of the engi- 
 neer, and that the patent includes the production of 
 " a more equable rotatory motion by caus- 
 ing the piston-rods of two cylinders to work on the 
 said axis by means of cranks at a quarter of a turn 
 asunder," it is scarcely too much to say that nothing 
 material was added to the design of the Locomotive 
 until the invention of the tubular boiler in 1829. 
 
 The Merthyr locomotive blew up, and the preju- (389.) 
 dice against high-pressure steam revived. The in- Trevi- 
 ventor, in the meantime, diverted his attention to .J^g "^_ 
 other schemes, and continued his profession as apiodes. 
 Cornish mining engineer. 
 
 A singular circumstance opened for Trevithick a (390.) 
 new sphere. A Spanish-American gentleman named Hia subse- 
 Uville, who was engaged in working the silver mines 1"''°* "?" 
 of Peru, came to England in 1811, with a view to ^igappoint- 
 discover an engine fit for draining those mines whose ment. 
 high elevation rendered condensing steam-engines 
 working under atmospheric pressure comparatively 
 inert. In London he met accidentally with a model 
 of Trevithick's engine, and having carried it to the 
 heights of Pasco in Peru, and being satisfied with its 
 work, he did not rest until he had returned to Eng- 
 land and transported nine high-pressure engines in 
 1814 to the scene of operations. In 1816 Trevi- 
 thick himself followed, with coining engines and pu- 
 rifying furnaces of his own contrivance. Had he 
 
 * It is stated that the Society of Civil Engineers have in vain proposed a medal for a biography of Trevithick. 
 ^ Wood on Railways. This description corresponds with Trevithick's specification and drawings. — Repertory of Arts, &c., Se- 
 cond Series, vol. iv. 
 
Chap. IV., § 5.] 
 
 MECHANICS. — GEORGE STEPHENSON. 
 
 85 
 
 been a prudent man his fortune was now made ; but 
 it is stated that about 1827 he returned to this 
 country impoverished and disappointed. I am un- 
 acquainted with his further history. 
 (391.) In ^ijg meantime the locomotive engine, which 
 
 Trevithick had long abandoned to its fate, was be- 
 coming known in the hands of a man perhaps of less 
 genius but of greater sagacity and perseverance. 
 (392.) George Stephenson, civil engineer, was born in 
 
 phenfoif-^' ^'^^^ ^^^^ Newcastle, of respectable persons in the 
 humblest rank of life. His father was either a com- 
 mon pitman or otherwise employed aibout the collier- 
 ies of the district, and young Stephenson, without 
 any advantages of education, began to labour for his 
 bread at an early age. His work appears to have 
 been always connected with the machinery of the pits 
 above ground, and not with their excavation. Thus 
 he rose gradually to be an engine-man at the wages 
 ?«! **r'^ °^ twelve shillings a week. This was at Killingworth 
 ' near Newcastle, where he showed considerable me- 
 chanical ingenuity, and gradually gained the confi- 
 dence of his employers. Having married in 1802, 
 he had a son born the following year, the present 
 Mr Robert Stephenson, M.P., whom he brought up 
 with the tenderest care, and whom he ever and justly 
 regarded with a father's pride. In order to bestow 
 upon him the advantage of that education of which 
 he had himself felt the want, it is stated that he made 
 money at extra hours by mending his neighbours' 
 clocks and watches, and finally, in more prosperous 
 days, sent his son to complete his education at the 
 University of Edinburgh. George Stephenson never 
 acquired much book-learning himself, but by natural 
 sagacity and observation he attained to a sound 
 knowledge of mechanical principles. We do not 
 claim for him, however, the character of great inven- 
 andcharac-tiveness. His skill rather lay in perceiving how far 
 **'■• methods and contrivances already known might be 
 
 pushed to an advantageous result. He possessed 
 that shrewd decision which ingenious persons often 
 want, enabling him to detect what is truly valuable 
 in the numerous mechanical schemes which at any 
 time are afloat, and to devise the means of realizing 
 them. He also possessed that confidence in his own 
 judgment which is necessary to carry out principles 
 to their legitimate extent, but from which feebler or 
 legs practical minds usually shrink. 
 (393.) j^ot to interrupt the principal topic of this section, 
 
 e con- J ^jjj j^ ^jjj mention that in 1815 he set about 
 tnves a , , pip- • i i 
 
 safety inventing a safety lamp for mines at a time when the 
 
 lamp; recent heavy loss of life in his own neighbourhood 
 had excited general attention ; insomuch that Sir H. 
 Davy had been specially invited, by a meeting of per- 
 sons interested, to propose a remedy. I shall in an- 
 other place speak of the result ; but in the meantime 
 I may state, that George Stephenson made some expe- 
 riments of his own, which, leading him in the same 
 track which Davy followed, that of admitting the foul 
 air to the lamp through long narrow tubes, might in 
 
 the end have led him to a construction analogous 
 to that of the safety lamp. As matters stood, it 
 is not surprising that his efforts, though highly me- 
 ritorious, led him slowly and uncertainly towards 
 the goal which Davy, having once sighted, arrived at 
 with that rapid instinct in which he has never been 
 surpassed. Stephenson was left behind, but was 
 rewarded by a handsome gift offered by his local 
 admirers, who, in doing so, naturally rather consi- 
 dered the difficulties' overcome by their humble 
 neighbour than the strictly comparative merit of the 
 two inventions. 
 
 But it is of the locomotive and of the railway that (394.) 
 we have here to speak. 
 
 The former, we have seen, had been brought to (395.) 
 considerable perfection by Trevithick. An engine on studies the 
 his plan had been constructefflRd used by Mr Blackett °^°^° .'"* 
 of Wylam in Northumberland, near the place where 
 Stephenson resided, and was the basis of his im- 
 provements. Blackett's engine had two cylinders, an 
 addition often ascribed to Stephenson, but which, as 
 we have said, was included in Trevithick's patent. 
 What he saw of the performance of this machine ap- 
 pears to have convinced Stephenson, once for all, of 
 the groundlessness of an opinion which then and for 
 long after haunted the minds of railway engineers. 
 This opinion was, that the adhesion between the 
 wheels of a locomotive engine and the smooth iron 
 surfaces of the rails must be insufficient to allow the 
 impulsion of the train, at least with any degree of 
 velocity, or up the smallest inclination. Trevithick dismisses 
 had a scheme for increasing the adhesion, and this tlie fear of 
 ideal improvement was the subject of repeated pa- insufficient 
 tents, some of a singular nature, between 1802 andjjjgp^^j™ " 
 1824, one of which, Blenkinsop's, provided a cog- 
 wheel in the engine working into a rack on the rail, 
 which was actually in use down at least to 1830. It 
 is rather a singular thing that men spurning theories, 
 as was the fashion of the engineers of that day, and 
 especially those of Smeaton's school, should have 
 thought as little of an appeal to experiment on so 
 simple a matter as did the followers of Aristotle in 
 the seventeenth century, when Galileo offered to con- 
 vince them that light and heavy bodies fall equally 
 fast. Forgetting that direct friction is always large, 
 and that it varies in proportion to the pressure, these 
 practical men could not get over their first impres- 
 sion, that iron must slide on iron long before a heavy 
 train could be set in motion. It was characteristic 
 of Stephenson's decision of character, that he dis- 
 missed all doubts on the subject so soon as his obser- 
 vations seemed distinct, and that he did not hesitate 
 to carry out his belief to its consequences, and to 
 maintain his confidence in the locomotive engine 
 against all antagonists. 
 
 I shall not stop to particularize Stephenson's first (396.) 
 improvements on the locomotive, which were rather ^- Stephen 
 in detail than in principle. He saw clearly all along °°° ^ '"" 
 that if it was to work at high speeds he must in every menta. 
 
86 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 Piss. VI. 
 
 possible way diminish the vibrations and strains to 
 which it was subject, and which would otherwise ra- 
 pidly wear out the machinery. For this purpose he 
 proposed to connect the engine with its carriage by 
 means of steam acting on six pistons in lieu of springs. 
 But perhaps his most material improvement con- 
 sisted in the very simple one of throwing the waste 
 The steam, higb-pressure steam as a blast into the chimney, 
 Wast. which was found to increase enormously the force of 
 
 the fire, and the evaporating power of the boiler. 
 Engines having this improvement, and with two ver- 
 tical cylinders, as constructed in 1818, are, or were 
 lately (1854), still atwork on the Killingworth railway 
 dragging coals at the rate of five or six miles an hour. 
 (397.) One of Steplienson's clear practical opinions was 
 
 Rejects the this, — that the locomotive and the railway are part 
 steam-car- ^f ^^^^ mechanism, and must be adapted to one an- 
 riage on o • n 
 
 roads. other. He was not a iriend to steam-carnages on 
 
 common roads, and the event proved his sagacity. 
 (398.) If the idea of a locomotive belongs to no one man, 
 
 Origin of still less does that of a railway, which being one of 
 railways, ^.j^g most elementary of mechanical contrivances, 
 may be traced, under some modifications, almost inde- 
 finitely backwards, as a means of conveying heavy 
 loads with facility. Hence it was at first confined 
 chiefly to quarries and collieries, especially in under- 
 ground passages or drifts. The gauge of these sub- 
 terranean railways, or tramv/ays, was only about 18 
 inches. The material of the rails was first wood, then 
 cast iron, finally wrought iron, as being less liable 
 to wear and to accident. The wrought iron rail, 
 though not absolutely new, was first generally intro- 
 duced in 1820. About the same time, or rather 
 sooner, the rails began to be made plain, that is, 
 without any vertical guide or flange to prevent the 
 wheels of the carriages from leaving the rail, and the 
 flange was transferred to the wheels of the locomo- 
 tive. Even this was not new, for it had been used 
 by Jessop in 1789. The weight of the rails has 
 been constantly on the increase. The original cast- 
 iron rails weighed only 15 lb. a yard ; the malleable- 
 iron rail in 1821 weighed about 28 lb., then 35, 
 afterwards 64, and now rails of 80 lb. a yard are 
 generally used. 
 (399.) One of Stephenson's first cares was to make his 
 
 Stephenson railways solid and level, and to prevent jerks at the 
 th^'^'t th junction of the rails. The gauge he adopted, or the 
 locomotive, interval between the rails (now generally used, except 
 on the Great Western Railway and its branches), was 
 4 ft. 8-| inches; and was derived from the accidental 
 width of the parent railways in Northumberland. 
 Like Watt and all other innovators, his great diffi- 
 culty was to get the machinery of his locomotives pro- 
 perly made, and the gTeat railway movement of 1825 
 was anticipated by the establishment in 1820 of 
 an engine factory at Newcastle, which, till after the 
 
 opening of the Liverpool and Manchester Railway in 
 1831, remained the onlj/ one, and for long afterwards 
 the best of its class. The cranked axle contrived by 
 Trevithick, and abandoned because it could not be 
 properly welded, was now restored ; the heavy loco- 
 motive was placed on strong but easy steel springs, 
 wrought iron was skilfully introduced into the wheels 
 of the carriages, and the whole machinery was made 
 to work with precision, and to combine a degree of 
 resistance never before anticipated with comparative 
 lightness. The factory was established in 1821, and 
 the first passenger locomotive was started on the Dar- 
 lington and Stockton Railway in 1825. 
 
 I ought, perhaps, to apologize for these details, (400.) 
 but they illustrate so well the exceedingly gradual 
 progress of mechanical invention, that I have thought 
 them worthy of mention here."^ The subsequent his- 
 tory of the locomotive and the railway is more gene- 
 rally known. From the date of 1825, both grew and 
 flourished ; the railway first and most steadily ; the 
 locomotive was introduced more cautiously, and met 
 with much opposition ; its triumph was almost en- 
 tirely due to the steadiness of George Stephenson. 
 
 The year 1825, so fertile in speculation, produced (401.) 
 a series of projects for railways to an extent not com- ^i^^ilway 
 monly known, since few of them came into existence fP™V 
 
 If 1 rrn tions of 
 
 or were even commenced for many years later. Thei825. 
 projected capital of these companies amounted to not 
 less than L.30,000,000 or L.40,000,000. But the 
 only considerable undertaking which was at that time 
 seriously supported was the railway from Liverpool 
 to Manchester, and on that battle-field were fought 
 the great questions of the superiority of railways to 
 common roads, — of high to low velocities of trans- 
 port, — and of locomotives to fixed engines. 
 
 On these three important points, George Stephenson (402.) 
 was in advance both of the science and of the prac- ^apenority 
 tice of his age; and, accordingly, backed chiefly by^^^^j^^^^ 
 commercial men, who had entire confidence in hispoads. 
 sagacity, he had to maintain the conflict almost single- 
 handed against general and professional prejudice. 
 With respect to the Railway, he had long decided in 
 his own mind against the use of steam-carriages on 
 common roads. This conclusion was scientifically 
 based on his own experiments on the friction of wag- 
 gons on railways made in conjunction with Mr Ni- 
 cholas Wood, civil engineer at Newcastle, as far back 
 as the years 1 8 1 5 and 1816. A simple dynamometer stephen- 
 of Stephenson's invention was used, and by means of^™'^ ^^P^" 
 it the two fundamental propositions were established, J'j^™^"^^?"^ 
 that the friction is directly as the pressure, and that it of trains, 
 is quite independentof velocity (at leastwhen the speed 
 was moderate). It may be said that these proposi- 
 tions were already known ; but, besides that probably 
 Stephenson and Wood were equally unacquainted 
 with the writings of Coulomb, they could not have 
 
 1 I have found many curious details of the early history of railways in a series of articles on the life of George Stephenson 
 in the CivH Engineer Journal for 1848 and 1849. I am indebted to Mr Robert Stephenson, M.P., for many interesting parti- 
 culars respecting his father's inventions. 
 
Chap. IV., § 5.] 
 
 MECHANICS. — GEORGE STEPHENSON. 
 
 87 
 
 dispensed with verifying his results under circum- 
 stances so peculiar as those of a railway and a train of 
 carriages. The necessity of doing so was manifested 
 by the opposition, and even ridicule, with which the 
 idea of friction being in this case independent of ve- 
 » locity was received, showing, as has been correctly 
 observed, " how small was the amount of science at 
 that time blended with engineering practice." The 
 friction of even the indifferent railways of those days 
 amounted to only 10 lb. per ton of load ; consequently 
 an incline of only 1 foot in 100 would increase by 
 one-half the resistance to the motion of a carriage on 
 a railway. Hence Stephenson determined to con- 
 struct railways having only the smallest inclinations, 
 and to u,se fixed engines for higher slopes. With re- 
 spect to common roads, he showed by powdering 
 even a level railway with sand, that the most power- 
 ful locomotives then in use speedily came to rest ; 
 this, with the previous objection, overruled in his 
 mind the possibility of advantage in that case. 
 (403.) With low gradients and small resistances, together 
 
 bilitv of" ^'*^ ^^® proved invariability of friction with speed, 
 high velo- there necessarily came into Stephenson's mind the 
 cities on practicability of using high velocities. Ataveryearly 
 rai ways, period (1816) he spoke in one of his patents of con- 
 veying goods " at nearly double the rate at which 
 they were then usually carried along railways," in 
 other words, at 10 or 12 miles an hour, and this he 
 states " with no hesitation, speaking from experi- 
 ments already made," referring, no doubt, to those 
 on friction made along with Wood about this time. 
 Yet after nine years of farther experience, his old 
 coadjutor Wood deserted him on this grand point, 
 and in the first edition of his book on Railways (1825, 
 p. 290) he disclaims the "ridiculous expectation"' 
 that locomotives will be seen to travel at " 12, 16, 
 18, or 20 miles an hour," and scorns " the promulga- 
 tion of such nonsense." Even in 1829 he reported to 
 Messrs Walker and Rastrick, who were referees on 
 the Liverpool and Manchester Railway, " that no lo- 
 comotive engine should travel more than 8 miles an 
 hour." If at this comparatively late period perhaps 
 the most practised railway engineer in England held 
 these opinions, and that with the full knowledge of his 
 friend Stephenson's matured convictions (which it is 
 difficult to believe were not pointed at in this para- 
 graph), we may imagine the opposition which the 
 plans of the latter were likely to meet with from in- 
 terested or even indifferent persons. 
 (404.) At last a company was formed, and funds pro- 
 
 The Man- yjijed to construct the Liverpool and Manchester 
 Liverpool Railway. It is unnecessary to state how successfully 
 Railway. Stephenson conquered the engineering difficulties of 
 the line, and refuted the predicted impossibility of 
 crossing the Chat Moss. In every respect this rail- 
 way became a model for those which succeeded, and 
 
 in essentials very little has been added by 25 years' 
 experience on lines of the same gauge. But now came 
 the struggle as to how this beautiful road was to be 
 worked ; — with horses, — by means of fixed engines, 
 — or by locomotives. It was not without a struggle 
 that Stephenson gained his point. Even in 1829 
 the prejudices of the engineering profession were still 
 strong against the locomotive. And it is curious to 
 read in the contemporary documents with what dis- 
 trust they were regarded. The clumsy expedient of 
 a series of stationary engines 1 J miles apart, dragging 
 the trains by ropes, would probably have been adopted 
 to the disgrace of the age, but for the energy of Ste- 
 phenson and his commercial friends. A competition The loco- 
 of locomotives was at last agreed to, which took ™o*'^«. 
 place on October 6, 1829, on a level piece of rail- °"^"'^^f'" 
 way at Rainhill near Liverpool. Though the makers 1829 at 
 of engines had their energies hampered by various itainhiU, 
 needless conditions (particularly as regards the weight 
 of the engines, under the mistaken notion, that velo- 
 city could only be combined with lightness), several 
 excellent engines appeared; but the "Rocket" made 
 at Stephenson's factory at Newcastle, not only gained 
 the prize, but far exceeded in its performances the 
 limits assigned in the programme. It weighed 4J 
 tons, and dragged a gross load of 17 tons, at the 
 rate of 15 miles an hour, but moved itself with a 
 velocity of 35 miles an hour. The "Novelty" of 
 Messrs Braithwaite and Ericson was also very suc- 
 cessful. The prize was awarded to Stephenson, and 
 this success was mainly due to the admirable inven- 
 tion of the multi-tubular boiler, imagined by Mr 
 Booth, and carried out by Stephenson. To distribute 
 ih^ water of the boiler in tubes, and allow the heat of 
 the furnace to act around them, was an idea as old 
 as the time of Watt, but it did not succeed. To carry The mnlti- 
 the-hot air of the furnace through tubes surrounded *"^"l'''" 
 by water, was the more successful arrangement of 
 Booth and Stephenson, to the right working of which 
 the draught occasioned by the steam-blast in the 
 chimney was essential. The idea, it is said, had oc- 
 curred both in France and America, but it certainly 
 remained practically inefficient, perhaps on account 
 of the want of draught. 
 
 This invention, by increasing almost without limit (405.) 
 the evaporating power of the boiler, which is the ^®P^""_ 
 key to the efficiency of a locomotive, completed for eess 
 the time the skilful improvements on locomotives 
 and railways, which, as has been seen, we owe mainly 
 to Stephenson. The comparatively trifling- ameliora- 
 tions which have occurred in either, and the stereo- 
 typed character of even the minor arrangements, such 
 as those of stations and of passenger carriages, show 
 how much the sagacity of the engineer had antici- 
 pated the accommodation of the public.^ (406.) 
 
 I here close my account of Mr Stephenson and of g" g'^g°°°" 
 
 ^ I do not overlook dt course the modifications introduced in the broad-gauge system of the Great Western Railway. Mr 
 Brunei indeed tried to show how far he could deviate without positive injury from Stephenson's plans ; in some points, perhaus, 
 he did so with advantage, yet, on the whole, the results do not shake Stephenson's position as the commanding engineer of his time. 
 
88 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss, VI. 
 
 the railway system. The locomotive engine will ever 
 remain as an invention entirely distinct from those 
 created by the genius of Watt. It is in reality in- 
 dependent of his great principle of separate conden- 
 sation. It has a power of adaptation and a perfection 
 of performance more astonishing than any contrivance 
 of our time, except perhaps the electric telegraph. 
 In 1552, Jerome Cardan took twenty-three days to 
 travel from London to Edinburgh; that the same 
 should be done 300 years later in eleven hours, and 
 every day, is a fact as striking as any which the pro- 
 gress of science presents. Whilst to Trevithick and 
 George Stephenson we are mainly indebted for these 
 results, the theory of the steam-engine is still in ar- 
 
 rear. To M. de Pambour we are indebted^ for by M. de Pam- 
 far the best account of the elements of force contained °P^^ °° ^f"® 
 in the locomotive, and of the resistances which they locomo- 
 have to overcome ; but it is not to be doubted that tivea. 
 much yet remains to be done in this direction. 
 
 George Stephenson died 12th August 1848, at the (407.) 
 age of sixty-eight, and generally respected for his ^J^P^^°son 
 private character as well as for his talents. His son jg^g_ 
 had the honour of completing the second great railway 
 work in Britain, from London to Birmingham, and 
 by the invention of the tubular bridge, described in 
 a previous section, he has added the most important, 
 as well as the most scientific auxiliary to the exten- 
 sion of railways since 1830. 
 
 § 6. Hydrodynamics, DtJBUAT, Venturi, Professor Stokes. — Friction and Resistance, of Fluids. 
 MM. Weber, Mr Scott Russell. — Propagation of Waves. Influence on Canal Naviga- 
 tion. MM. FouRNEYROif ancZ PONCELET. — Improved Hydraulic Machines ; Turbine. Reference 
 to the subject of Capillary Attraction, 
 
 Hydrodj' 
 namics. 
 
 (408.) There are few subjects less adapted for the kind 
 
 Progresa of of discussion which I have adopted in this Disserta- 
 tion than Hydrodynamics, whether in its abstract or 
 practical form. Not only is it difficult to fix upon 
 individuals who, in the more recent progress of the 
 subject, have attached themselves to it in so especial 
 a manner as to have impressed the science with the 
 individual character of their own minds, but the pro- 
 gress made in either branch has been of a remarkably 
 fragmentary kind, usually bearing upon the solution of 
 individual problems, and tending to the improvement 
 of particular machines. It must be owned, too, that 
 however important in practice may be the efficiency 
 of a water-wheel or the discharge of a pipe, the so- 
 lution of such problems does not present the attrac- 
 tive interest which attaches to many less difficult ones 
 in Natural Philosophy. As regards more general pro- 
 blems of which a direct solution from first principles 
 might appear possible, it has been found that these 
 are as yet so limited as to give a character (which is 
 generally admitted) of great barrenness to the theo- 
 retical investigations. 
 
 WhUe, then, I shall endeavour, in conformity with 
 my general plan, to preserve something of the bio- 
 graphical character in the history, suppressing details 
 and many minor and even some important steps, 
 this section will necessarily have somewhat of a frag- 
 mentary character, and its deficiencies must be sup- 
 plied by a reference to the numerous articles of the 
 Encyclopsedia which treat more or less fully of these 
 subjects and their history. 
 
 (409.) 
 
 1, Friction and Resistance of Fluids. — The first 
 name I shall mention is that of the Chevalier Du- 
 who has the signal merit of having attri- 
 
 (410.) 
 Dubuat — 
 Friction 
 and resist- 
 ance of buted due importance to, and of having considered 
 fluids. — — — 
 
 with much sagacity, the effects of the friction of 
 fluids against their own particles, and against the 
 sides of the solid bodies used to confine them. He 
 had the full advantage of an acquaintance with the 
 Abbe Bossut's excellent experiments and judicious 
 writings, but he was, I believe, the first who suc- 
 ceeded in ascribing to the diflferent forces which act 
 on fluids in a state of uniform motion their effective 
 share in determining their velocity. I refer particu- 
 larly to the discharge of pipes and of rivers. Du- Theory of 
 buat showed that when the motion of water in such''"^'*" 
 circumstances becomes uniform, the accelerating force 
 which acts is the measure of the total resistances to 
 the fluid motion, whether arising from the inequali- 
 ties of the bed or the viscosity of the fluid. These re- 
 sistances are assumed to be proportional to the square 
 of the velocity. Since they are exactly in proportion 
 to the length of the pipe or channel, and since the 
 moving pressure increases in the same proportion, the 
 velocity is independent of the length of the pipe, whilst 
 the inclination remains the same — a simple result not 
 previously noticed. In the case of a pipe the head 
 or superincumbent pressure may be divided into two 
 parts ; one, requisite to force the water into the tube 
 with the requisite velocity, which is independent of 
 the distance to be travelled; the other, which balances 
 the resistance due to the length of the pipe, which 
 for a given diameter varies as the length, or if the 
 slope be constant is independent of the length. 
 
 The relation of the area of the stream to the peri- ^^^\^ 
 meter or rubbing surface of the channel is then taken araulio 
 into account. This ratio is called by some writers the depth. 
 mean hydraulic depth. The manner in which Dubuat 
 derives his formula (which I shall not here set down) 
 from direct experiment, guided by a few general no- 
 tions of theory, is a very good specimen of this kind 
 
 1 The Theory of the Steam-Engine (1839), and A Practical Treatise on Locomotive Engines (1840), by the Comte P. M. G. de 
 Pambour. 
 
Chap. IV., § 6.] MECHANICS (OF FLUIDS.) — DUBUAT — VENTUKI — MR STOKES. 
 
 89 
 
 (412.) 
 Dabuat's 
 formulae 
 improved^ 
 
 (413.) 
 Viscosity 
 of fluids. — 
 Venturi — 
 Coulomb. 
 
 (414.) 
 Three cases 
 of fluid re- 
 sistance to 
 moving 
 solids. 
 
 of induction, without any pretence -whatever of pro- 
 ceeding upon the mathematical theory of fluids in 
 motion. The same views were ably expounded and 
 enlarged by Dr Robison in his excellent article on 
 Rivers and Resistance in this Encyclopsedia, through 
 which principally the theory of Dubuat became known 
 in this country. Indeed, viewed apart from the tech- 
 nical value of the enquiry, the research as to the na- 
 tural economy of rivers is a wonderful and striking 
 branch of terrestrial physics, and one which had long 
 afforded a subject of anxious and perplexing enquiries 
 to Italian engineers from the time of Leonardo da 
 Vinci, though comparatively little studied elsewhere. 
 The collected treatises of Italian authors form an 
 important body of hydraulic information.' The rivers 
 of the north of Italy, like those of Holland, conveying 
 vast masses of water charged with mud under very 
 feeble slopes to the sea, present a formidable difficulty 
 which compels attention, — vast territories being in- 
 creasingly subject to inundation, as the beds of the 
 rivers are raised by deposition above the general level 
 of the soil. 
 
 Dubuat's formulas have been modified, and made 
 to represent experiments better, bysubsequentwriters, 
 particularly by De Prony, Langsdorf, Eytelwein, and 
 Thomas Young ; and the discharge from mere orifices 
 has been discussed by numerous authors who have 
 given empirical co-efficients to represent the pheno- 
 mena. But little has been added to a philosophical 
 view of the real laws which govern the fluid motion 
 in this case. Nevertheless Savart and Magnus have 
 made some ingenious observations on the constituent 
 parts of effluent streams. 
 
 The viscosity or imperfect fluidity of water is the 
 property most difficult to be taken into account in 
 these and other hydraulic problems. It is that which 
 causes the velocity of a stream to diminish from the 
 surface to the bottom, and from the centre to the 
 sides ; these proportions were also sought by Dubuat. 
 Each layer of water in motion exerts a dragging or 
 " tangential force" upon other layers, which from 
 any cause are comparatively quiescent ; and the ex- 
 periments of Venturi about the end of the last cen- 
 tury, showing that a stream in motion draws towards 
 it the particles of still water with which it may be in 
 contact, with a force sufficient to overcome consider- 
 able hydrostatic pressure, attracted much attention. 
 About the same time Coulomb, with his usual ad- 
 dress, made experiments on the friction of fluids by 
 observing the rapidity with which cylinders oscillat- 
 ing by means of torsion in different fluids had their 
 original motion destroyed. 
 
 Intimately connected with the friction, and conse- 
 quent mutual action of fluids, is the resistance which 
 they offer to the passage of solid bodies through them, 
 
 and this favourite problem of mathematicians was 
 treated by Dubuat, in his inductive way, in an able 
 and practical manner. Three cases may be specified 
 on account of their theoretical or practical import- 
 ance: — 1st, In the case of a body oscillating like a 
 pendulum, with small velocities, the body being im- 
 mersed in a resisting medium ; 2dli/, The resistance 
 to vessels floating on and propelled through water ; 
 3dfo/, The resistance of the air to projectiles whose 
 velocity is very great. 
 
 Under the first head Dubuat made those ingenious (415.) 
 experiments long overlooked, but lately brought into Motion of 
 notice, which I have mentioned in the section on the P^""^"'"™*' 
 Pendulum in the chapter on Astronomy, Art. (246). 
 The cause of the neglect of these striking and original 
 observations has probably been correctly stated, by 
 saying that in them the pendulum was made subser- 
 vient to hydraulic experiments, and not the theory of 
 fluids to the improved use of the pendulum ; and they 
 were therefore overlooked by those whose studies were 
 connected with the pendulum and its applications. 
 The fact observed by Dubuat was, that a large mass 
 of air (or of water in the corresponding case) is car- 
 ried along with a pendulum in motion, and affects 
 in a sensible manner the time of vibration, quite in- 
 dependent of the diminution of gTavity due to the 
 buoyancy of the pendulum. The moved mass of air 
 was proved by hanging a film of worsted from an 
 arm a foot long in advance of the moving sphere, 
 when it was found to be but slightly driven by the 
 inertia of the air through which the pendulum moved. 
 Dubuat significantly calls the mass of moved air " the 
 prow" of the moving body, and it is easy to antici- 
 pate the sort of effect which such a graduated con- 
 dition of the surrounding air from motion to absolute 
 rest would produce. 
 
 But the most surprising thing is, that mathema- (4i6.) 
 ticians should have attempted to compute the effect. Professor 
 or should have been in any degree successful in doing Stokes's eo- 
 so; yet after the preliminary efforts of Poisson andg^g A 
 Green, Professor Stokes has introduced for the first 7niiea! of 
 time a correct definition of the " index of friction" of/™*'""- 
 a fluid, and after great labour has succeeded in find- 
 ing exact expressions for the motions of a solid sphere 
 and cylinder. This investigation may be found in a 
 very elaborate paper in the Cambridge Transactions,^ 
 in which he solves the equations found by him in a 
 previous paper, ^ in the cases of pendulums having 
 the forms just mentioned. Another interesting re- 
 sult of his investigation is the immense effect of fluid 
 friction in retarding the fall of minute rain drops, 
 which he states to be such as to explain satisfactorily 
 the suspension of clouds. In the second part of the 
 paper I have first cited Mr Stokes proceeds to com- 
 pare his theory with the observations on the pen- 
 
 ^ Raocolta di Autori che trattano del moto deW acque, 10 vols., 1822-26 ; and Nuova Raccolta, 7 vols., 1823-45. See also the 
 admirable methodized catalogue of writers on Hydraulics in the second volume of Young's Lectures on Natural Philosophy, 
 ^ Vol. ix. part ii. — On the effect of the internal friction of Fluids on the motion of Pendulums, 
 ^ On the friction of Fluids in motion. Camb. Trans., vol, viii., part iii. 
 
w^ 
 
 90 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (417.) 
 Kaval ar- 
 chitecture. 
 
 (418.) 
 Kesisted 
 molion of 
 projectiles. 
 
 (419.) 
 Experi- 
 ments on 
 waves in 
 "water. 
 
 (420.) 
 Observa- 
 tions of 
 MM. We- 
 ber on the 
 form of 
 vraves. 
 
 dulum mentioned in Art. (246), and the agreement 
 appears satisfactory. "With reference to Coulomb's 
 experiments on oscillating disks there remains some 
 doubt whether the theory applies satisfactorily to 
 viscid fluids such as oil. 
 
 On the very difficult and still empirical subject of 
 naval architecture as regards forms of least resist- 
 ance, I shall not here speak; but one very interesting 
 case of the resistance of fluids in canals will be noticed 
 in the course of this section — Arts. (422), &c. 
 
 The theory of military projectiles has perhaps re- 
 ceived no improvement so considerable during the 
 last 100 years as by the previous experiments of 
 Robins, and the invention of the Ballistic Pendulum 
 referred to in the preceding Dissertation ; though the 
 experiments of Borda in France, and of Hutton in 
 this country, have of course increased the technical 
 precision of artillery. Poisson has considered, in a 
 mathematical way, some of the simpler cases of pro- 
 jectiles moving with a moderate velocity. 
 
 II. Experiments on Waves. — MM. Webek — Mr 
 Russell. — Whilst the theory of the dilated and com- 
 pressed waves which constitute sonorous vibrations 
 in elastic fluids was being successfully investigated 
 by Lagrange and Laplace, the case of waves in water, 
 due to a disturbance of hydrostatic pressure only, 
 was attacked by the same mathematicians with far 
 less success. It is generally allowed that the more 
 recent and abstruse researches of Poisson and M. 
 Cauchy, though very valuable as improvements in 
 pure mathematics, have been also singularly barren 
 of valuable results admitting of the very desirable 
 confirmation of direct experiment. The greatest of 
 all hydrodynamical problems, -that of the Tides, is, as 
 has been seen in the second section of the chapter on 
 Physical Astronomy, Art. (69) &c., so excessively 
 complex as to be the last, instead of the first, which 
 analysis might have, been expected to resolve. 
 When, on the other hand, we see the light which has 
 been thrown even upon it by experiments on a com- 
 paratively small scale, we learn to value them in 
 proportion to their rarity. 
 
 The brothers Ernst Heinrich Weber and Wilhelm 
 Weber, known for many ingenious experiments in 
 physics, and particularly in magnetism, are the authors 
 of a useful book on waves.^ They made experiments 
 on the velocity of waves in glass troughs, by means of 
 which they determined in several cases the velocity 
 of the wave with different depths of fluid ; they also 
 ascertained mechanically the form of the wave, which 
 they found to be that of the curve of sines. But the 
 most important of the Webers' experiments is pro- 
 bably the determination of the motion of individual 
 particles of the water, which they ascertained by 
 watching from the exterior of the glass trough the 
 
 curve described by minute floating particles as the 
 wave passed over them. The usual form of the trajec- Trajectory 
 tory is an ellipse having the greater axis horizontal, the °. ,* '""'' 
 whole ellipse being described when the wave includes 
 a ridge followed by a depression of the surface ; but 
 if there be only an elevated wave propagated, then a 
 semi-ellipse is described in the direction in which 
 the wave moves, 'and the particle returns to rest in a 
 new position ; if the wave be a hollow one the con- 
 verse takes place. The limits of oscillation diminish 
 with the depth of the fluid, particularly the vertical 
 limits ; consequently at some depth the motion of 
 the particles is nearly in a short straight line. The 
 rapidity of the degradation of the individual motions , 
 depends on the relation between the length of a wave 
 compared to the depth of the fluid : where the wave 
 is very short compared to the depth of fluid, the el- 
 lipses near the surface become circles, and the mo- 
 tion rapidly disappears beneath ; when the length of 
 the wave is great compared to the depth of fluid, 
 the motion of tlie particles is nearly the same from 
 top to bottom. The conclusions of theory are on the 
 whole confirmed by these experiments. 
 
 The experiments of Mr John Scott Russell, so (421.) 
 far as we shall notice them, refer to two closely con- ^ j," 
 nected subjects : — the transmission of waves, and experi- 
 the resistance of water to vessels propelled through ments on 
 it as afiected by waves. They are principally to be ^*'"«8. 
 found in the Edinburgh Transactions, vol. xiv., and 
 the British Association Report for 1837. The velo- 
 city of waves in troughs of diiferent depths and sec- 
 tions was ascertained by allowing the wave to be re- 
 flected at either end of the trough, which does not in 
 any way affect the time of its propagation, and gives 
 great facility for ac9urate observation, as the distance 
 travelled over may thus become large, at the same 
 time that all casual and interfering waves are gra- 
 dually eliminated. The instant of the passage of 
 the wave was ascertained by reflecting the light of a 
 candle vertically upwards from its horizontal sum- 
 mit. T|he length of the trough was 20 feet, but 
 since the wave was made to traverse it as often as 
 60 times, a distance of 1200 feet was really ob- 
 served. The waves were single or "solitary" 
 waves, either "positive" produced by a gush of 
 water from behind a sluice, or " negative" by with- 
 drawing water suddenly. Mathematicians seem not 
 agreed as to whether or not the " solitary" waves of 
 Mr Russell are to be treated as a species apart.^ 
 Unquestionably it has long been known that a par- 
 tial wave either positive or negative may be propa- 
 gated without any farther disturbance of the fluid. 
 Theory also shows that the velocity of a w^ve long in 
 proportion to the depth of the water is nearly as the 
 square root of the depth ; but it does not clearly ap- 
 
 1 Wellenlehre auf experimente gegriindet, oder fiber die Wellen tropf barer Flussigkeiten mit anwendung auf die Schall und Licht- 
 wellen. Iieipzig, 1825. 
 
 " Compare Mr Airy in the article " Tides and Waves," Encycl. Metropolitana ; 
 and Mr Earnshaw in Cambridge Trans., vol, viii. 
 
 Prof. Stokes in British Assoc. Report for 1846, 
 
Chap. IV., § 6.] MECHANICS (OF FLUIDS). — MR EUSSELL — M. FOURNEYEON. 
 
 91 
 
 Compared 
 with theory 
 by Mr Kel- 
 land and 
 Mr Airy. 
 
 (422.) 
 Peculiar 
 effect of 
 wave tranS' 
 mission on 
 canal navi- 
 gation. 
 
 (423.) 
 Practical 
 results. 
 
 pear whether the disturbed or undisturbed depth is 
 to betaken., The analysis of Mr Airy seems to show 
 that a depth somewhat greater than that due to the 
 utmost effect of disturbance is to be preferred. Mr 
 Russell also made experiments on the propagation of 
 waves in channels of different forms of section. Pro- 
 fessor Kelland has given a very simple expression 
 for the velocity of the wave in this case,^ which on 
 the whole agrees with experiment. 
 
 Sometime about the year 1830, attention was 
 drawn to a singular fact connected with the resist- 
 ance of water in the case of canal navigation. It 
 was first noticed I believe in Scotland, probably on 
 the Forth and Clyde Canal. It amounted to this, 
 that whereas at moderate or rather slow velocities, 
 the resistance to a boat increases with the square 
 of the velocity, — after a certain point, not differing 
 very much from 7 miles an hour, the resistances not 
 only cease to increase according to the same rapid 
 law, but actually dimmish to some extent when the 
 speed is greater. Different experiments were made 
 by the canal proprietors with a view to meet in some 
 degree the active competition by railways, then com- 
 mencing. Mr Russell was employed by the directors 
 of the Forth and Clyde Canal, and to his experiments 
 we now refer. It appears from his tables that the 
 resistances increased on the whole faster than the 
 squares of the velocities up to 7^ miles an hour, 
 when they suddenly diminished between 7^ and 8^ 
 miles an hour by one-fifth part in one experiment, 
 and by no less than one-third in another.^ It was 
 not until about 12 miles an hour, that the resistance 
 reached the same amount as at 7i- miles. 
 
 The occurrence of this singular transition was at- 
 tended with a phenomenon easily noticeable. In 
 every ordinary case a boat in a canal drives a wave 
 before it, which is in fact a heap of water resisting 
 the boat by increasing the prpssure against its bows, 
 which wave may be called a forced wave, having this 
 peculiarity that it travels with the speed of the boat 
 and never quits it ; whilst a free wave, by whatever 
 cause excited, is propagated at a rate depending only 
 on the dimensions of the canal, particularly its depth. 
 Now the dimirtished resistance takes place when the 
 boat is by the force of traction partly drawn out of the 
 water, and lifted up upon the wave to which its own 
 motion gives rise. It is said to ride upon the wave, 
 and the head of water pressing against its bows is 
 visibly diminished. The most advantageous rate of 
 transport was found to be about one-third greater than 
 that required merely to mount the wave, which last 
 depends principally on the depth of the canal. Thus 
 on three different canals, S^-, 5J, and 9 feet deep, 
 the most advantageous velocities were 8, 11, and 
 15^ miles an hour. The actual velocities of the 
 free wave were ascertained by Mr Russell in an in- 
 
 genious and satisfactory manner. When the boat is 
 dragged to most advantage, the draught of water is 
 less at the stem and stern than in the centre. All 
 these circumstances have been very ingeniously and 
 satisfactorily explained by Mr Airy in his paper on 
 Tides and Waves, articles (404-411). 
 
 Many persons (amongst whom are Colonel Henry (424.) 
 Beaufoy, Mr Scott Russell, and the American ship- ^o"°8 of 
 builders) have bestowed much attention on the forms ^ '^'' 
 of vessels for ensuring speed, especially by the avoid- 
 ance of waves of various kinds generated by steam- 
 vessels in motion. Every one who can compare the 
 performance of such vessels during the last twenty 
 years, and the still surface which waters navigated 
 by steam vessels now present, as if they were merely 
 cut open and closed again before and after the passage 
 of the ship, instead of being tossed into dangerous bil- 
 lows consuming uselessly the propelling force, will 
 readily admit that, however imperfect the theory, prac- 
 tical art has made real progress in this direction. 
 
 III. Improved Hydraulic Machines — Turbine. — (425.) 
 Before concluding this section, I will refer to the Improved 
 most considerable improvement made of late years hydra"!"! 
 in the application of hydraulic pressure to motive ^^^ Tur-~~ 
 purposes, and I shall couple it with the names bine, 
 of two French engineers, MM. Fourneyron and 
 PoNCELET, the former the inventor of the Turbine 
 (the machine referred to), at least in its improved 
 practical form ; the latter an important contributor 
 to the useful application of hydraulics, an accom- 
 plished mathematician, and the author of several 
 standard works connected with industi-ial mechanics. 
 
 The defects of common vertical water-wheels, (426.) 
 whether overshot or undershot, are so great and Defecfe of 
 
 so notorious, that only their simplicity, and the <^°'°™™ 
 
 . ' •' r J ' water- 
 tact that m very many cases water-power costs wheels 
 
 next to nothing, and may be squandered with im- Barker's 
 punity, could justify their use. The advantage of ™'^^' 
 using the simple pressure of a fluid as a moving 
 power had been foreseen in that application of re-ac- 
 tion caWedi Barker's JfiK; which, though well known 
 in models, was seldom if ever applied in practice. 
 Mathematicians were, however, aware that it offered 
 important advantages. Of late years a patent has been 
 taken out in Scotland for a modification of it, which 
 is found, I believe, to work well. But the Turbine 
 or horizontal water-wheel imagined by Burdin and 
 Fourneyron, and brought to a high state of perfection 
 by the latter about the year 1833, appears to exhaust 
 all that is valuable in this mode of applying water. 
 
 Referring to other parts of the Encyclopsedia (427.) 
 for the details, I may here explain generally that Poumey- 
 the Turbine consists of two parts, one a fixed cy- "^ ^ *"'" 
 linder or drum of small height compared to its 
 diameter; the other a portion of a cylinder ex- 
 terior to the former, and moveable round it, so that 
 
 1 Velocitv = V ^ ^ ; where A is the area of section of the canal, 6,the breadth of the water at the surface, and g the accele- 
 ' ■ 
 
 rating effect of gravity. Edinburgh Trans, vol. xiv. 
 '- J^din. Trans. ^ vol. xiv., p. 48. 
 
92 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (428.) 
 Principle 
 of greatest 
 advantage 
 in water- 
 wheels. 
 
 (429.) 
 Power of 
 adaptation 
 of the tur- 
 bine. 
 
 the inner surface of the moveable cylinder is all but 
 in contact with the circumference of the fixed cylin- 
 der. Further, water under a greater or less hydro- 
 static pressure, and moving with the consequent velo- 
 city, is introduced at the centre of the fixed cylinder, 
 and conveyed to its circumference by channels of a 
 peculiar form constructed by means of vertical parti- 
 tions or guides of continuous curvature, from which 
 the water is discharged against float boards within 
 the external cylinder, which are also curved, but the 
 curvature is turned the other way so that the parti- 
 tions in the first cylinder are where they terminate 
 nearly perpendicular to the internal surface of the 
 moveable or second cylinder where they commence. 
 These latter partitions or float-boards terminate ex- 
 teriorly in a direction nearly tangential to the outer 
 cylindric surface where the water emerges. 
 
 The hydraulic principle of greatest possible advan- 
 tage to which these Turbines are made as nearly as 
 possible to approximate is this, that the water shall 
 enter the moveable apparatus without shock, and shall 
 quit it without velocity, being simply left behind by 
 the wheel as it escapes from it. Since both these con- 
 ditions cannot absolutely be fulfilled, the first part of 
 the condition is left imperfect. Some secrecy is, I 
 believe, still maintained as to the forms and dimen- 
 sions of these machines ; but their actual efiicicncy 
 has been most thoroughly tested by means of De 
 Prony's Friction Dynamometer^ by Colonel Morin, a 
 most competent authority. His experiments leave no 
 doubt of the admirable qualities of these machines. 
 In particular, the useful effect compared to the theo- 
 retical effect represented by the fall of water expended 
 rises higher than probably in any other hydraulic 
 machine, being under favourable circumstances about 
 eighty per cent. Now water-wheels moved princi- 
 pally by the shock of the fall seldom, in the most 
 advantageous conditions, realize thirty-five percent., 
 often not seven per cent. This superiority of action 
 of the Turbine is due entirely to the approximation 
 which it gives to the theoretic condition above men- 
 tioned of perfect efficiency. 
 
 But what is not less striking in the performance 
 of this machine, is the variety of circumstances under 
 which it acts advantageously; however great may be 
 the variation in the size and velocity of the wheel, the 
 height of fall, and the power disposable. Turbines 
 have been made of as small diameter as 2 feet with the 
 enormous fall of 350 feet, making 2300 revolutions 
 per minute. They work with nearly equal advantage 
 (relatively to the power expended) whether the supply 
 of water be small or great. They may be completely 
 
 (430.) 
 
 (431.) 
 
 drowned or buried under water to a considerable 
 depth without any sensible variation in their effi- 
 ciency, thus preventing any inconvenience from floods. 
 
 It is remarkable that, with these manifest advan- 
 tages, the Turbine has been so sparingly introduced at 
 least in this country. No doubt the first establish- 
 ment of it is attended with considerable expense. 
 
 M. PoNCELET, an active and' intelligent officer of 
 Genie, and member of the Institut, is favourably M. Ponce- 
 known by his hydraulic observations and inventions, fT^'^^ 
 as well as by his skilful investigation of the effects breast- 
 of machines, and his excellent works and memoirs wheels, 
 on several subjects. He has investigated with much 
 patience and geometrical nicety the form and dis- 
 charges of spouting fluids, and was one of the first 
 to improve materially the ordinary water-wheels, by 
 introducing a kind of breast-wheel (which thirty-five 
 years ago was scarcely known in France) in which 
 the water is conveyed without shock into compart- 
 ments on the descending side, from which again it 
 was allowed to escape with all its acquired velocity 
 spent, or nearly so. The eSiciency of these wheels is 
 equal to aboi(t two-thirds of the power expended. 
 Before the Turbine had been finally improved by M. 
 Fourneyron, M. Poucelet had invented an engine on 
 the same principle, in which the water enters at the 
 circumference of the horizontal wheel, and is deli- 
 vered at the centre. 
 
 I am aware how imperfect this section remains as C432.) 
 a history of Hydrodynamics. But I must again Capillary 
 refer to special articles on the subject, the plan of***™"*'"" 
 the Dissertation not admitting of farther detail. As j ?"°^ 
 nothing material has been added to the doctrine of place. 
 Capillary Attraction since the publications alluded 
 to in Sir John Leslie's Dissertation (although M. 
 Poisson has written a treatise on the subject), I will 
 for the sake of compression not enlarge upon it. I 
 do so vrith the less regret, because I cannot regard 
 the excessive mathematical illustration which it has 
 received as altogether justified by the certainty and 
 due. appreciation of the physical principles involved, 
 such as can alone give to applied mathematics their 
 distinctive value. The theory of Laplace, so far 
 as it was based on novel grounds, was anticipated 
 by Dr Young, and gave rise to several controversial 
 articles by that most eminent philosopher, of which 
 all account will be found in Br Peacock^s Life of 
 Young, pages 199-210, as well as a most excellent 
 review of the subject of Capillary Attraction, which, 
 indeed, by its candour and completeness, supersedes 
 anything which I should have felt disposed to say 
 on the subject. 
 
 1 Gaspard de Prony, born in 1765, was an eminent engineer, especially in the department of hydraulics, and the author of a 
 \ol\iTa'mooB work entitled Noumlle Architecture Hydraulique ; but his originality was not great enough to authorize his being 
 placed among the leaders of his age. His simple invention of the Frein Bynamometrique, or friction dynamometer, is the one 
 by which perhaps he will be longest remembered. It consists of an iron collar with tightening screw, which may be clasped 
 on a horizontal wooden arbor connected with uniformly revolving machinery. A lever, to which a weight may be applied, is 
 attached so as to form part of th^ collar. The clasping screw being moderately tightened, the collar and lever are of course 
 carried round by the machinery until a weight is applied sufficient to check the velocity, and to generate an amount of friction 
 which is in fact the useful effect of the machine for that velocity, and which is determined by the momentum of the weight over- 
 come in one second. De Prony was a most amiable man, and died in 1839, in the 84th year of his age. 
 
Chap. IV., § 7.] MECHANICS (ACOUSTICS). — CHLAI/NI — SAVART. 
 
 93 
 
 § 7. Progress of Acoustics. Chladni — SavART. I^place's Correction of the Theory of Sound, 
 Vibrating Plates and Acoustic Figures:' Cagniard de la Tour's " Sirlne." 
 
 (433.) The mathematical theory of the propagation -6f 
 
 Mathema- sound, considered as a branch of analytical m^tha- 
 of the OTo^'^^*'^' "^^^® ^^^ greater progress during the eighteenth 
 pagation Century, in harmony with the general character of 
 of sound, the science of that period, than the inductive doc- 
 trines of acoustics. Newton here, as in other de- 
 partments, overstepping the limits of knowledge of 
 his day, left a legacy of toil to his immediate suc- 
 cessors. Lagrange had the most distinguished good 
 fortune in reducing the theory of aerial tremors under 
 their most general conditions to the laws of mecha- 
 nics by the calculus of partial differentials ; and La- 
 place supplied the link which was wanting to recon- 
 cile the result with the known mechanical properties 
 of air. As the former of these matters belongs more 
 properly to the period of the previous Dissertation, 
 Laplace's and as the beautiful discovery of Laplace has been 
 correction more especially touched upon by Sir John Leslie, 
 theory ^* ^^^ ^^ sufficient here to recall the fact that the 
 spring of air, or the effort by which it tends to re- 
 expand under sudden compression or to contract to 
 its former bulk when suddenly dilated, is increased 
 by the heat extricated in the former case, as well as 
 by its absorption in the latter. And as sonorous 
 pulsations are held to consist of a series of com- 
 pressed and rarified waves whose velocity is affected 
 by the recoil of air, it appears certain that the velo- 
 city must be increased by this circumstance, though 
 it is difficult to determine experimentally the exact 
 amount. 
 (434.) The revival of experimental acoustics is due to 
 
 Chladni Eknst Chladni a native of Saxony, but of Hungarian 
 of experi- extraction, born in 1756. Little had been done in 
 mental this department since the time of Sauveur, who as- 
 acoustics. certained the nature of the harmonic vibrations of 
 strings, and that of Daniel Bernouilli, who considered 
 the analogous case of organ pipes. We are indebted 
 to Chladni for two classes of original experiments — 
 his measure of the velocity of sound in a variety of 
 bodies by peculiar and ingenious methods ; and his 
 observations on the vibrations of plates by means of 
 the ingenious expedient of strewing them with sand 
 and other powders. 
 
 We shall say a few words under each of these 
 
 heads : — 
 
 (435.) I. Chladni observed the velocity of sound in air 
 
 Velocity of p£ different densities, and in different gases, by using 
 
 different ^ Aute of metal which was sounded by means of the 
 
 media ; elastic fluid required, and the resulting note enabled 
 
 him to determine by an easy calculation the speed of 
 
 propagation of the tremor. This method (using an 
 
 organ pipe) has been more lately resorted to by 
 
 Dulong for the purpose of deducing the properties 
 
 of different gases with respect to heat, by ascertain- 
 ing from experiment the co-efficient in Laplace's 
 correction for the velocity of sound. Chladni was 
 also probably the first to notice the longitudinal os- 
 cillations of strings and rods which always yield a 
 note immensely sharper than the lateral vibrations. 
 By means of the former he ascertained the velocity 
 of sound in a variety of woods and metals, in some 
 of which it is no less than seventeen times greater 
 than in air. These observations are not only inte- 
 resting in themselves, but as throwing light on the 
 constitution of solid bodies. To Chaldni we like- 
 wise owe a knowledge of the twisting vibrations of 
 rods, which exhausts the modes of vibration of such 
 bodies. To connect theoretically the periods of these 
 different kinds of movement, has been a favourite 
 problem with recent mathematicians, but has not even 
 yet been quite successfully performed. 
 
 The determination of the velocity of sound in (436.) 
 water, an experiment by no means difBcult, was re- ^'^ ^^'ter. 
 served for MM. Colladon and Sturm, who ob- 
 served it on the Lake of Geneva, and found it to be 
 4708 English feet per second, a result closely con- 
 forming to the theoretical amount deduced firom 
 Oersted's observation on the compressibility of water. 
 
 II. But Chladni' s experiments on the vibrations (437.) 
 of plates are of still greater interest and originality. Chladni on 
 Though it has been affirmed that Galileo strewed , . ® ^'J"^*" 
 sand or light substances upon the sounding boards plates. 
 of musical instruments,^ Chladni deserves the entire 
 credit of rendering this an exact method of ascertain- 
 ing the nodal lines or points of rest in bodies vi- 
 brating in a stable or permanent manner. He first 
 applied it to plates round, square, or of different 
 figures, supported horizontally and caused to vibrate 
 by applying a violin bow to their edges. Dust or fine 
 sand strewed or sifted uniformly over such a plate, 
 arranges itself in a variety of beautiful figures, being Acoustic 
 tilted from the greater part of the surface, and heaped figures- 
 up on those parts which are at rest in consequence of 
 the vibratory motion of adjacent parts taking place 
 simultaneously in opposite directions ; just as the 
 nodal points of a string vibrating harmonically are 
 without motion on the same account. The number 
 and variety of figures thus producible in the same 
 plate is very great, and corresponds, as Chladni 
 clearly saw, to different simple harmonical vibrations 
 of the elastic plate, being accompanied by their ap- 
 propriate notes ; or by the superposition of several 
 such modes of vibration, and of the corresponding 
 sounds. The tract published by him in 1787 en- 
 tituled, Entdeckungen vher die Theorie des Klanges, 
 contains numerousfigures of these appearances, which, 
 
 ^ This, however, is very doubtful. See Dove, Bepertorium, dii. 106. 
 
94 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 (•438.) 
 In bodies 
 possessing 
 unequal 
 elasticity. 
 
 (439.) 
 Chaldni on 
 meteoric 
 bodies. 
 
 (440.) 
 Young — 
 Bobison. 
 
 (441.) 
 Savart. 
 
 Propaga- 
 tion of 
 sound in 
 masses of 
 air, &c. 
 
 more recently, Savart found the means of presei^ving 
 by transferring them to sheets of gummed paper. 
 There are few experiments in physics of a mora, 
 striking character, or which so plainly reveal minute 
 and complex motions so small and so rapid as to 
 he difficultly appreciated otherwise. Mr Faraday 
 and Mr Wheatstone have pursued the same enquiry 
 experimentally, and the latter has satisfactorily de- 
 duced the figures of Chladni's square plates from the 
 mechanical superposition of simple modes of vibra- 
 tion which are symmetrical and isochronous. {Phil. 
 Trans. 1833.) By so doing he has succeeded better 
 than the mathematicians, whose results on this sub- 
 ject have been very little practical. 
 
 Chladni was the first to make experiments on the 
 vibrations of bodies whose elasticity varies in dif- 
 ferent directions. Thus he cut plates outof difierent 
 kinds of wood, and found the nodal curves unsym- 
 metrical in difierent directions depending on the 
 course of the fibres. The experiments were naturally 
 afterwards employed to illustrate the theory of ellip- 
 soidal waves on the undulatory hypothesis of Optics. 
 
 The experiments of Chladni procured for him the 
 especial notice of Napoleon, by whose wish one of 
 his works was translated into French. He died in 
 1827, and besides his acoustical discoveries, he will 
 be remembered by the sagacity and boldness with 
 which he maintained the popular opinion of the 
 fall of- heavy meteors from the sky, contrary to the 
 prevalent scepticism of philosophers. Chaldni's suc- 
 cess in establishing this important fact in natural 
 history is due, like his other physical inductions, to 
 the constancy and simple-mindedness with which he 
 attached himself to a strictly definite enquiry. 
 
 We must not here enlarge upon the ingenious and 
 important investigations of Dr Thomas Young con- 
 nected with acoustics. Being chiefly connected with 
 his admirable Theory of Light, they will be noticed 
 in the chapter on Optics. The peculiarly practical 
 and sagacious views of Dr Kobison connected with 
 the Theory of Musical Instruments and Acoustics 
 generally, must also be passed over. 
 
 In Felix Savart we find a man like Chladni who 
 was especially devoted to a single and circumscribed 
 branch of science — acoustics. Hispublishedresearches 
 are almost all detached notices in the Annales de 
 Chimie, with a few memoirs in the publications of the 
 Institute; and whilst they are very interesting, exact, 
 and instructive, I doubt whether it would be possible 
 to place the results in a connected and comprehen- 
 sive view before the reader. They are therefore rather 
 to be sought in the special articles of the Encyclo- 
 psedia devoted to the subject. In general they may 
 be stated to refer to the following topics : — (1.) To 
 the manner of propagation "of sound through the 
 air and through liquids, with an attempt to explore 
 the manner in which sounds spread in apartments 
 of different forms ; an enquiry as difficult as it is 
 important ; (2.) To the generation and audibility of 
 
 musical notes. Previous authors (for example, 
 Chladni, Biot, and WoUaston) having differed mate- 
 rially as to the range of audibility of repeated equi- 
 distant impressions which affect the human ear as 
 mnsical notes, Savart used a simple method, no 
 doubt original to him, but anticipated I believe by 
 Kobisofl, in which a card is held near or touching 
 a revolving wheel, and the number of impulses 
 (each double) given to the air by every tooth as 
 it passes the card, is readily measured. He thus 
 found that a note occasioned by 24,000 double vi- 
 brations in a second is perfectly audible; and, at 
 the other limit of the musical scale, from seven to 
 eight equidistant beats constitutes a sound having 
 a distinct pitch. According to Savart, two conse- 
 cutive double impulses of whatever duration are suf- 
 ficient to convey to the ear the sensation of pitch. 
 But a more elegant and accurate instrument for 
 the numeration of sonorous pulsations is the Sirene 
 of M. Cagniard de la Tour, unquestionably one of 
 the most exact and satisfactory additions lately made 
 to our experimental apparatus. In it a current of 
 air is repeatedly interrupted and renewed, giving 
 rise to a series of impulses similar to those of the 
 toothed wheel ; and this apparatus is ingeniously 
 contrived, so as to maintain its own motion, and 
 record its indications. It is by far the most accu- 
 rate known method of ascertaining the pitch of a 
 given note. It may also be worked with water. 
 Eobi'son had also the merit of the primary idea of 
 the Sirene, by making a stopcock revolve rapidly 
 whilst applied to a tube emitting a blast of air. (3.) 
 Savart extended the researches of Chladni by means 
 of sand to many new cases, and with interesting 
 results ; in particular he exhibited the effects of the 
 unequal mechanical elasticity of crystals cut in dif- 
 ferent directions. He has also examined with great 
 care and ingenuity, the nature of the vibrations which 
 occasion the accumulations of sand on the nodal 
 lines of plates, and he comes to the conclusion that 
 they are determined by simultaneous transverse and 
 longitudinal movements (the latter of which are pa- 
 rallel to the surface of the plate). In proof of this 
 he shows that in long rods or hollow cylinders, the 
 position of the nodes is intermediate and opposed 
 upon the contrary sides of the rod or hollow cylinder. 
 Savart made many experiments on the communica- 
 tion of vibrations from one body to another ; showing 
 that the molecular movements generally preserve 
 their parallelism, so that a longitudinal vibration of 
 one body may give rise to transversal movements in 
 another ; and he applies this to the theory of musi- 
 cal instruments. 
 
 Savart was born at Mezi^res in the department of 
 Ardennes, on the 30th June 1791 ; and died some- 
 what prematurely on the 16th March 1840. He 
 had some peculiarities of temper, amongst which 
 was his unconquerable prejudice to everything Eng- 
 lish. He did not even acknowledge the intimation 
 
 On the pro- 
 duction of 
 musical 
 notes. 
 
 Sirene of 
 M. Cagni- 
 ard de la 
 Tour. 
 
 Savart on 
 the vibra- 
 tion of 
 solids. 
 
 (442.) _ 
 Biographi- 
 cal notice 
 of Siivnrt 
 
Chap, v., §1.] 
 
 OPTICS. — YOUNG. 
 
 95 
 
 of his election as a foreign member of the Royal 
 Society of London. It is to be regretted that Savart 
 never published a connected account of his obser- 
 vations. He had caused to be collected at the College 
 de France, where he was professor, an unequalled col- 
 lection of acoustical apparatus, a great deal of which 
 was contrived by himself, and where he delivered 
 extensive courses of lectures on this subject alone. 
 
 Several English philosophers, in particular Pro- (443.) 
 fessor Willis, Mr Hopkins, and Mr Wheatstone, have 0*er_ 
 written several important detached memoirs on par- experi- 
 ticular practical points, for which we must refer to ments. 
 special treatises.' The first and last of these gentle- 
 men, together with some Germans, have approxi- 
 mated in some degree to the formation (on empirical 
 principles) of a speaking machine. 
 
 CHAPTER y. 
 
 OPTICS. 
 
 1. Thomas Young. — The Undulatory Theory of Light. — Its history from the time of Hooke 
 and Huygens. — The Law of Interference. — Its application to Diffraction — to the Rainbow 
 — and to other subjects. — The Theory of Polarization referred to another section. 
 
 optics in 
 the 18th 
 century. 
 
 (444.) The history of Optics in the eighteenth century is 
 
 Small pro- One of the blankest pages of scientific story ; at least 
 gress of if ^g allow Bradley's discovery of aberration to be (as 
 it really is) rather an astronomical than an optical 
 discovery. The most notable advance was unques- 
 tionably the invention of the achromatic telescope 
 as narrated in the Fifth Dissertation,^ founded on 
 the proof of Newton's oversight in the matter of dis- 
 persion. The construction of refracting telescopes 
 made rapid advancement in the workshop of Dollond, 
 whilst reflecting telescopes, in the hands first of Short, 
 but far more conspicuously, of Sir William Herschel, 
 were shown to be capable of making unimagined dis- 
 coveries. The geometrical theory of optical instru- 
 ments was also greatly improved ; but all this led 
 to little increased knowledge concerning Light itself. 
 If we except the valuable though imperfect treatises 
 of Bouguer and Lambert on the subject of photo- 
 metry, and a paper by Mr (now Lord) Brougham in ' 
 the last years of the century, recalling attention to 
 the inflexion of light, the history of Physical Optics 
 (as that part of the science touching more imme- 
 diately the nature and qualities of light is now usu- 
 ally termed) is almost a blank from the publication 
 of the Optics of Newton in 1704 to that of Young's 
 papers almost one hundred years later. 
 
 It is not therefore from overlooking Young's pre- 
 decessors that we open our review of the recent pro- 
 gress of optics with his discoveries. We here meet 
 
 ' (445.) 
 Thomas 
 Young. 
 
 with a man altogether beyond the common standard, 
 one in whom natural endowment and sedulous cul- 
 tivation rivalled each other in the production of a 
 true philosopher ; nor do we hesitate to state our 
 belief that since Newton, Thomas Young stands un- 
 rivalled in the annals of British science. 
 
 He was born at Milverton in Somersetshire on the (446.) 
 13th June 1773, and his biographers dwell with com- His early 
 placency on the prodigies of his youth, uncertain as •education 
 such attainments confessedly are in stamping the ments. 
 greatness of the future character. At the age of 
 fourteen he had learned (principally for amusement) 
 seven languages besides his own, and besides had 
 made a point of mastering every subject, whether in 
 science or miscellaneous knowledge, which he had 
 once determined upon prosecuting. Thus, whilst 
 studying botany he resolved to learn how to make a 
 microscope, but finding in Martin's Optics the nota- 
 tion of fluxions, he became his own preceptor in that 
 branch of analysis. " He acquired a great facility 
 in writing Latin. He composed Greek verses which 
 stood the test of the criticism of the first scholars of 
 the day, and read a good deal of the higher mathe- 
 matics. His amusements were the studies of botany 
 and zoology, and to entomology, in particular, he at 
 that time paid great attention. "^ Dr Young's edu- 
 cation was almost completely private. Having been 
 brought up according to the tenets of the Society of 
 Friends, he had not thought of going to Cambridge 
 
 ^ See also Herschel on St}und (Eneyc. Metrop.) ; and Whewell's Histortj of the Inductive Sciences, vol. ii. 
 
 ^ It may be mentioned, however, that the credit usually ascribed to Dollond must be divided, at least, with Mr Hall, a pri- 
 vate gentleman of Worcestershire, who not only imagined but constructed achromatic telescopes as early as 1733 (Gentleman^ 
 Magazine, 1790, and Phil. Mag., vol. ii.) The improvement by Dr Blair of Edinburgh has been alluded to in Sir John Leslie's 
 Dissertation. It consisted in enclosing fluids in the object glass, of such composition as to disperse the several rays of the spec- 
 trum in the same 'proportion to one another (though not to the same absolute amount) aa the glass with which it was combined • 
 thus rendering the achromatism more perfect. 
 
 3 Memoir of the Life of Thomas Young, M.D. 8vo, 1831. The present section of the Dissertation was written shortly be- 
 fore the publication of the Life and Miscellaneous Works of Br Tkomas Youn^, for which the public is indebted to Dr Peacock 
 Dean of Ely, the possession of which would have materially facilitated my task. Wherever Dr Peacock's information has 
 
96 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Residence 
 
 at Edin- 
 burgh ; 
 
 (447.) 
 at Gottin- 
 gen and at 
 Cam- 
 bridge. 
 
 (448.) 
 Character 
 of his in- 
 vestiga- 
 tions. 
 
 (which would have been his natural destination), and 
 entered the university of Edinburgh as a medical stu- 
 dent at the age of twenty-one. He had already de- 
 clined the overtures of such distinguished patrons as 
 Windham and Burke, resolving to devote himself to 
 the pursuit of science, for which a medical education 
 seemed to him a fit entrance ; — his studies being made 
 under the more immediate advice of his uncle, Dr 
 Brocklesby. He attended Black's lectures in Edin- 
 burgh ; whether he was known to Eobison I am not 
 aware, though I should be inclined to infer that he 
 was from the terms in which Kobison speaks of 
 Young when criticising his strictures upon Smith's 
 Harmonics. Eobison disagreed with him on this 
 point, and also about the nature of light, yet he 
 speaks of Young and of his paper on Sound with 
 very rnarked respect. More than a year before his 
 enrolment at Edinburgh (which took place in autumn 
 1794), he communicated to the Royal Society of 
 London a paper on vision, of which we shall pre- 
 sently give some further account ; and was elected a 
 fellow of the Society when just of age. 
 
 From Edinburgh he proceeded to Gottingen where 
 he graduated ; acquiring the German language, and 
 leaving a vivid impression of his astonishing versa- 
 tility of talent and powers of memory. Early in 
 1797 he returned to England, and soon after en- 
 tered himself at Emmanuel College, Cambridge, in 
 order to comply with the requisitions of the London 
 College of Physicians, and thus to obtain a license 
 to practice. For the next few years his time was 
 divided much between Cambridge and London. He 
 was now twenty-three years of age, and his mental 
 habits too much formed to bend to the rules of Cam- 
 bridge study. When the master of his college intro- 
 duced him to the fellows, he is reported to have said, 
 " I have brought you a pupil qualified to read lec- 
 tures to his tutors," and such, no doubt, was the fact. 
 We hear little of his occupations at Cambridge, but 
 we can hardly doubt that his private studies then 
 ranged over the vast fields of erudition which he af- 
 terwards proved that he had made so completely his 
 own ; and we cannot doubt that he was then preparing 
 the groundwork of his theory of optics, although his 
 discovery of interference was certainly not made at 
 Cambridge, and probably in London after his settle- 
 ment there in 1800. ^ His first paper on sound and 
 light is dated from Cambridge in July 1799. 
 
 I have entered into these details because they 
 throw light on the peculiarities of Young's cha- 
 racter and attainments. He was to a great degree 
 self-educated ; and his studies in consequence may 
 be called desultory, though none would dare to call 
 
 them superficial. Mathematicians may consider his 
 acquaintance with their science as not technically 
 complete, yet one of them admits that " he could 
 make a small amount of mathematics go farther than 
 any one else." Had he been a consummate analyst 
 it is unlikely that we should have had in him the 
 author of the undulatory theory, the difficulties of 
 which in its earlier stages made it unpalatable to 
 Laplace, Poisson, and the most considerable French 
 mathematicians. Having thought out for himself 
 every one of the multifarious subjects with which he 
 grappled, his writings have a striking force and ori- 
 ginality, and his reports of the labours of others are 
 almost invariably drawn from a study of their original 
 works. His earliest principle was, that what one 
 man has done another may accomplish ; and one of 
 the many respects in which he resembled his great 
 predecessor Newton, was unbounded confidence in 
 the powers of " patient thought." Not that he con- 
 fined the desire to excel to purely intellectual matters. 
 What he found it worth while to do at all, he thought 
 it worth doing well. He chose to be first-rate in 
 dancing and in equitation ; — his penmanship was (in 
 his early days) as 'scrupulously elegant as his scho- 
 larship. 
 
 In 1801 Young was appointed Professor of Natu- (iiS.) 
 ral Philosophy at the Eoyal Institution, where he was T*"J°^ ^ 
 the colleague of Davy. Young had not the qualifi- Natural 
 cations of a popular lecturer, and the most important Philosophy. 
 result of his short connection of two years with the 
 Royal Institution was the publication in 1807 of his 
 Lectures on Natural Philosophy, in two large quarto 
 volumes. It is a work peculiarly characteristic of the 
 author ; and is rather adapted for reference by the 
 scholar, than to be studied as an elementary trea- 
 tise. Its condensation is such as to render it in 
 many places obscure ; though when read by one 
 conversant with the subject, its comprehensiveness 
 and precision are surprising. It is a truly admi- 
 rable monument of labour and genius combined. 
 Embracing the arts as well as the whole of natural 
 philosophy, it seems to include the mention of every- 
 thing connected with his vast subject from the 
 simplest tool of the artisan to the highest specu- 
 lations of Newton and Lagrange ; and yet it is evi- 
 dent, by the masterly manner in which he handles 
 it, that the author had made all this mass of know- 
 ledge completely his own. The catalogue of refer- 
 ences with which it closes indicates an extent of bib- 
 liographical research which would have done honour 
 to any one who had made that an exclusive object of 
 study. Even the plates are drawn with a studious 
 care, betokening well his own mechanical talent. 
 
 enabled me to improve the text I have not hesitated to use it. The facility of consultation afforded by the collection of Dr 
 Young's widely scattered writings is a most important aid to all future students of science, and one which cannot fail to raise 
 still higher the great reputation of their author. ' 
 
 ^ See Sect. vii. of the article Polarization in this Encyclopaedia, where, in a bracketted interpolation by the translator, 
 Dr Young, he speaks of this fundamental experiment being made " in the room and at the table on which he is now writing." 
 This must have been in Welbeck Street, London, 
 
Chap. V., § 1.] 
 
 OPTICS.— YOUNG. 
 
 97 
 
 Many of the figures, though of hackneyed subjects, are 
 represented in a novel manner ; there seems not a 
 line drawn at random. Such figures often illustrate 
 hetter than pages of description, the clearness with 
 which an author has conceived to himself the neces- 
 sary results of his own principles. An example of 
 this may be found in Plate XXX., fig. 442 of the 
 first vol'ume, which, as Arago relates, served to de- 
 monstrate to him, when he visited Dr Young in 
 1816, that he and Presnel had been anticipated on 
 one point more than they believed.^ 
 (450.) The absence of algebraic formulae from this work 
 
 was as characteristic of Dr Young as their copious 
 introduction into articles which he subsequently con- 
 . tributed to the Quarterly Review. He had decided 
 upon writing a book without symbols, and he wrote 
 it, though it gave additional trouble both to himself 
 and the reader. 
 451.) We shall now proceed to trace the progress of the 
 
 undulatory theory of light, the greatest physico- 
 mathematical discovery of our time, in the establish- 
 ment of which Young acted the leading part. 
 (452.) Undulations of Light — Hooke and Huygens. — 
 
 The undu- rpjjg j^gg^ ^f accounting for the efiects and modi- 
 theory of fications of luminous impressions by disturbances 
 light— propagated through a very elastic medium was by 
 no means new at the, commencement of the present 
 century. We do not, indeed, attach much impor- 
 tance to the so-called anticipations of Grimaldi and 
 Hooke in the seventeenth century. The former, 
 amongst his valuable experiments on the deflection of 
 light and fringes of shadows, had used an expression 
 as to illumination being diminished by the addition of 
 light, which is true in fact, and is a correct deduction 
 from the law of interference as we now understand it. 
 Hooke, in his Micrograpkia, asserts light to consist 
 in " quick, short, vibrating motion ;" but his expla- 
 nation of refraction by it is altogether erroneous ; 
 and his application of it to the doctrine of the colours 
 of thin plates, though admitted by the candid Young 
 to be an anticipation (unknown to him at the time) 
 of his own, has in it no more than a germ of truth 
 (like so many of Hooke' s ingenious hints, afterwards 
 claimed by him as discoveries), which yet only ex- 
 plains the fact on which it is founded by means of 
 an additional and gratuitous assumption. The germ 
 of truth in Hooke's writings is this, that the colours 
 in question depend upon a mixture of the, light re- 
 flected at the first surface of the thin plate with " a 
 kind of fainter ray " propagated from the second sur- 
 face backwards : the gratuitous assumption is, that 
 " this compound or duplicated pulse does produce on 
 the retina the sensation of a yellow ;" why it does so 
 
 Hooke. 
 
 is not explained. Thiswasiu 1664, before even New- 
 ton was acquainted with the analysis of white light, 
 Hooke's idea that yellow, or any other colour, was 
 the result of the conflict of pulses simultaneously 
 reaching the eye, was an assertion, admissible, per- 
 haps, at that time, as expressing a fact ; but surely 
 not a proof of interference producing reinforcement 
 or annihilation of light, as taught by Young. I am 
 not aware that Hooke ever even reiterated his opinions 
 on this subject after Newton had' analysed the phe- 
 nomena experimentally, and shown that the colours 
 of thin plates result from the superposition of bright 
 and dark rings of different prismatic hues, each with 
 its appropriate diameter. It was then apparent that 
 colour was only an indirect effect of interference. 
 
 But whatever may be thought of the theories of (453.) 
 Hooke, those of Huygens deserve a far more eminent Huygens 
 place in fiistory. Having already been succinctly ad- j^jaiere. 
 verted to in Professor Playfair's dissertation, we T*ill 
 only observe that the TraitS de la Lumiere (1690) is 
 an admirably composed and reasoned treatise on the 
 phenomena of light on the undulatory hypothesis. 
 The uniformity of its propagation through the celes- 
 tial spaces, its rectilinear course in ordinary circum- 
 stances, the laws of its reflection and refraction, are 
 there explained with a degree of elegance and preci- 
 sion which ought to have excited (we must think) 
 general attention and assent, but for the ascendancy 
 of Newton's authority, and the astonishing and beau- 
 tiful nature of the experiments on which his theories 
 were based ; whereas Huygens referred to few expe- 
 riments except those of the simplest kind, and the 
 phenomena of colour were (for good reasons) left 
 chiefly out of view.'^ Such being the case, Huygens 
 may fairly be considered as the author of the undu- 
 latory theory, which he supported by such convincing 
 proofs. 
 
 The fundamental principle of the Huygenian (454.) 
 doctrine was the same as that which Hooke ad-^^P^^"''- 
 mitted, which was probably far older than his time, *'™ ?^ , 
 
 11 11 -IT . • ' Simple and 
 
 namely, that a;il space, including the interior of double re- 
 transparent bodies, contains an ether whose pulsa- fraction, 
 tions communicate the sense of light to the eye, as 
 waves in air convey to the ear impressions of sound. 
 To this he added the assumption, that in refracting 
 media, such as glass, the pulsations are retarded ; 
 whereas in Newton's theory, as is well known, the 
 propagation of light is assumed to be fastest in dense 
 media. The " law of the sines " in refraction, is de- 
 duced as a consequence ; and one of the prettiest ap- 
 plications made of it is to the phenomena of atmo- 
 spherical refraction. But the most important features 
 of the whole investigation are these two — (1), the 
 
 ^ The reference of Arago, in his original iloge of Young, is to p. 387 of the Lectures, obviously by mistalce. In the first 
 volume of his (Arago's) collected works it is corrected into p. 787, which is as certainly correct. I have supposed fig. 442 to be 
 more probably the one referred to than 445, to which Dr Peacock refers (Life of Young, p. 389).' 
 
 ® Nevertheless the Huygenian Theory of Light was propounded as the subject of a thesis at St Andrews by David Gregory, 
 whilst professor of mathematics there, within about a year of its publication (including also the Newtonian doctrine of gravity), 
 — a pleasing proof of the activity which then reigned in that university. Principal Lee possesses the original programme. 
 
98 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 principle that the impression of a wave of light 
 on a screen is to be found by considering the simul- 
 taneous effect of the wavelets propagated from all 
 the points disturbed at any previous moment (which 
 points form what is called the front of a wave). 
 It is only when these partial impressions concur 
 that they are strong enough to affect the sense of 
 vision ; — (2), the representation of the phenomenon o^ 
 double refraction by a wave of two sheets, or the 
 simultaneous propagation of spherical and spheroidal 
 waves in one and the same medium. Of the last of 
 these doctrines I shall speak in the next section in 
 connection with the discoveries of Malus. "With re- 
 spect to the former I may here observe that it gives 
 the only satisfactory explanation of the primary diffi- 
 culty of the undulatory hypothesis^ — namely, that a 
 beam of light admitted by a hole in a screen pursues 
 a rectilinear course afterwards, instead of spreading 
 sideways, as do waves in water, and waves of sound. 
 Huygens shows, on elementary and convincing prin- 
 ciples, that the lateral impressions of the wave are 
 rapidly extinguished by the want of concurrence of 
 the impulses which they communicate to the ether. 
 This is necessarily true when the breadth of the aper- 
 ture is such as to exceed vastly the length of a wave ; 
 and such is always the case with light, but rarely in 
 any other instance. It is, in short, only imme- 
 diately in front of the aperture that the disturbances 
 originating in every part of the front of the original 
 wave embraced within the aperture, c6ncur in pro- 
 ducing an accordant movement on the ether. 
 (455.) This principle, more fully stated, by which every 
 
 The prin- luminiferous disturbance of the ether is considered 
 "ffuvoms ^^ ^^® resultant of all the pre-existing disturbances 
 to which it is due, constitutes what is sometimes 
 called the principle of Huygens, of which I shall 
 have more to say hereafter. 
 (456.) Neither at the time of its publication, nor for 
 
 Newton's more than a century afterwards, was the value of 
 the "lature" ^^^^^ reasonings understood. It would be beside 
 of light. our present object to discuss Newton's opinions ; but 
 it is too certain that he did not allow Huygens' argu- 
 ments on the undulatory nature of light to have any 
 weight with him. Not that he was averse (as is 
 often supposed) to the presence of Ether as modify- 
 ing the corpuscular theory of light; on the con- 
 trary, in many of his minor writings he speaks of 
 its existence as all but certain, and as a requisite 
 adjunct to the corpuscular hypothesis to which he 
 had been led by the facts of reflection and refrac- 
 tion. ^ But he never adjusted the terms of a compro- 
 
 mise, and must be held, we think, to have left behind 
 him no substantive theory of light worthy of the 
 name. The question never perhaps very seriously 
 engaged his attention after the publication of Huy- 
 gens' book -j^ and we know that about that time his 
 intellectual energies received a shock which left him 
 indisposed for the fatigue of constructing new theories, 
 and still more disinclined to publish them. 
 
 Euler, though he professed to defend an undula- (457.) 
 tory theory of light, treated the subject in a point of Euler. 
 view chiefly mathematical, and betrayed that uncon- 
 cern about physical theories which characterized a 
 mind steeped in geometric abstractions. He even 
 retrograded ; for he did not maintain the Huygenian 
 explanation of the cause of definite shadows. 
 
 Young on the Undulatory Theory — Diffraction. (458.) 
 — -One hundred and ten years after the publication of^°""So° 
 the Traits de la Lumiere of Huygens, Dr Thomas ^ory theory 
 Young re-opened the theory of light or "Physical Op — Diffrac- 
 tics," as he termed it. His experiments and reasonings *'""• 
 will be found in a series of papers in the Philoso- 
 phical Transactions for 1800, 1801, 1802, and 1803.' 
 These memoirs are of no great length, and deserve 
 the most careful study. They are perhaps among the 
 clearest and plainest of Young's writings, although 
 blamed at the time for defects precisely the reverse. 
 They are eminently marked by penetration, profound 
 induction, and candour of argument. Starting from 
 his studies in acoustics, the transition to optical 
 questions is extremely gradual. Young was, cha- 
 racteristically, a good musician in practice, as well as 
 a profour(d one in theory, and his paper of 1799 is 
 principally acoustical. . In it he attaches conse- 
 quence to showing that the divergence of sound from 
 the direction of its emission is slower and less com- 
 plete than it is commonly believed to be, and he applies 
 theanalogy to the existenceof ray.? of light and definite 
 shadows. In one short section he sums up the chief 
 points of optical doctrine which lead him to prefer 
 the theory of Huygens to that of Newton. Amongst 
 the facts better explained by waves than corpus- 
 cles, we find reckoned Inflection and the Colours of 
 thin plates. But all this is stated in a very general 
 way, evidently rather as a conclusion towards which 
 his mind had for some time been tending, than as the 
 result of demonstrative proofs. In his paper of 1801 
 the undulatory doctrine is methodically expounded in 
 a series of propositions, accompanied by proofs'. The 
 accurate definition of shadows is shown to be possible 
 and natural on that theory, as well as the usual phe- 
 nomena of reflection, refraction, and total reflection. 
 
 1 Thus Newton writes in 167^5 :— " "Were I to assume an hypothesis, it should he this, if propounded more generally, so as not 
 to determine what light is farther than that it is something or other capahle of exciting vibrations in the ether ; for thus it will 
 become so general and comprehensive of other hypotheses as to leave little room for new ones to be invented." And again, — 
 " Do not the most refrangible rays excite the shortest vibrations [of the retina], the least refrangible the largest ?" — Birch's Hint, 
 of the Royal Society, quoted in Young's Lectures, ii. 615, 617. Sir D. Brewster {Life of Newton, 1855, vol. i. p. 148) considers 
 that some passages in the later editions of Newton's Optics show that he had departed from any tlieory of undulations. 
 
 2 The Optics, though published in 1704, had been written principally in 1675 and 1687 (see Preface). 
 
 3 They may be more conveniently consulted as reprinted in the second volume of his Lectures on Natural Philosophy, and in 
 his Miscellaneous Works, vol. i. 
 
Chap. V., § 1.] 
 
 OPTICS.— YOUNG. 
 
 99 
 
 Optical 
 parados. 
 
 (459.) 
 The Erio- 
 
 meter. 
 
 (460.) 
 Fundamen- 
 tal law of 
 interfe- 
 
 The partial reflection which always accompanies re- 
 fraction is strongly and justly insisted on as an ob- 
 vious consequence of the theory, while it requires a 
 separate hypothesis on Newton's. But the chief 
 weight is claimed for the evidence from the colours 
 of heated surfaces, of thin plates, and of diffracted 
 shadows, all of which the author explains by the 
 mixture of two portions of light conveying to the 
 same particle of ether at the same time either ac- 
 cordant or opposing motions, thus redoubling or 
 destroying the light. Of these the splendid iri- 
 descent colours reflected by surfaces having fine 
 equidistant lines drawn upon them, admit of the 
 most elementary and striking explanation. The 
 reflected image of a luminous point viewed in a 
 mirror thus cut up by parallel lines, consists of one 
 common reflection and numerous lateral images 
 which are coloured, and in which the angles of inci- 
 dence and reflection are not equal, thus contradicting 
 one of the axioms of common optics. Young showed 
 that the scattered waves of light recover the faculty of 
 appearing when the surface of the plate is seen under 
 such an angle that foreshortened intervals between 
 the scratches amount severally to the length of one 
 undulation or a multiple of it; for then the waves of 
 light scattered by the reflecting surface will not come 
 entire to the eye, but each will have a part systema- 
 tically suppressed by the non-reflecting space of the 
 groove, so that the remainders being nearly in one 
 phase, concur in making a general impression. This 
 experiment, therefore, literally presents us with the 
 paradox that 6y suppressing half the light, the re- 
 mainder is not suffered to be extinguished by it. The 
 difierent colours appear reflected at different angles, 
 because the obliquity must vary in order to be ac- 
 commodated to their several wave-lengths, and each 
 colour undergoes several repetitions corresponding 
 to breadths representing the successive multiples of 
 a wave-length. 
 
 Precisely similar in their origin are the coloured 
 rays scattered by fibrous substances when held be- 
 tween the eye and a small point of light. If they be 
 numerous and all of the same diameter, such fibres 
 will suppress symmetrically portions of waves, and 
 suffer the oblique effect to be perceptible. Dr Young 
 most ingeniously applied this principle to construct 
 an Eriometer or measurer of the fineness of fibres. 
 The diffracted light of any order and colour from a 
 distant flame will be seen at an angle with the prin- 
 cipal or white image about four and a half times 
 greater when viewed through the down of the beaver, 
 than in the case of Southdown wool ; being the in- 
 verse proportion of the diameters of the fibres which 
 compose them. 
 
 Fundamental Law of Interference. — But the cri- 
 tical and characteristic experiment of interference in 
 its simplest shape was published two years later, in 
 
 the Bakerian Lecture for 1803.^ A small hole 
 being made with a needle point in a piece of paper 
 applied to a window- shutter, and a sunbeam being 
 directed upon it by means of a mirror from with- 
 out, a cone of light is thrown into a darkened room. 
 A slip of card one-thirtieth of an inch wide being 
 held in the sunbeam, its shadow was observed on 
 the opposite wall or on a moveable screen. There 
 were seen fringes of colour exterior to the shadow 
 on each side, such as Newton had described, and on 
 which Mr Brougham and others had made experi- 
 ments. But besides these, the narrower and less 
 conspicuous fringes seen in the interior of the shadow, 
 and first described by Grimaldi, were found by Young 
 to have this remarkable property, that they disap- 
 peared the moment that the light passing either edge 
 of the card was intercepted, whilst the exterior fringe 
 was not at all affected by that circumstance excepting 
 on the side where the light was stopped. 
 
 Young at once perceived the significance of this ^61.) 
 admirable fact. The existence of light within the ^'^''^'^ 
 shadow at all, was evidently due to the bending of explained, 
 the wave round the opaque edge ; but the alternation 
 of light and dark spaces required the union of the 
 two lights from opposite edges, which, immediately 
 behind the centre of the obstacle, must have de- 
 scribed exactly equal paths, and therefore united in 
 the same phase ; but a little way either to the right 
 or left of the centre the phases were discordant, and 
 complete and effectual annihilation of the light re- 
 sulted. In fact, when the experiment is performed 
 under favourable circumstances, the result of the 
 union of the light is perfect blackness in these places, 
 but if half the light is stopped the dark spaces be- 
 come luminous ! 
 
 This splendid paradox may also be demonstrated (462.) 
 without any bending round the edges of bodies, and Mixed 
 consequentlv without any inflexion in Newton's sense l^gMs pro- 
 
 ... 1. Q1IC6 QEirk 
 
 of the word ; and this simplifies the conditions mate- ^ands. 
 rially. In order to effect this, Fresnel (many years 
 after) produced interference bands by allowing light 
 emitted from a very small luminous point (an image • 
 of the sun formed by a lens of short focus) to fall 
 upon two mirrors touching at the edge, and inclined 
 to one another at an angle very little less than 180°. 
 By the- common principles of reflection there will be 
 a space beyond the mirrors where the light reflected 
 from the respective mirrors overlaps, and except in a 
 single line within that space, the paths of the two 
 rays meeting in any point will be different. When 
 this difference amounts to a whole number of undu- 
 lations, an exalted brightness results ; when the un- 
 dulations arrive in opposite phases or the centres of 
 one set of waves concur with the ends of the other, 
 blackness results. The experiment may even be 
 made with a single mirror which a ray of light just 
 grazes, and after reflection mixes with the direct light 
 
 1 Miieell. Works, toI. i. p. 179. 
 O 
 
100 
 
 (463.) 
 Length of 
 the waves 
 of coloured 
 light. 
 
 Number of 
 vibrations 
 in a second. 
 
 (464.) 
 Opposition 
 to 5foung's 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. piss. VI. 
 
 which had in the first instance passed clear of the took to crush at once the theory of Young and his 
 
 mirror.' Here evidently we have the required con- reputation as a philosopher, and this (in singular 
 
 dition of double illumination with difference of paths, contrast to its avowed principles), not by argument, 
 
 The same effect is obtained without either Inflexion but by an appeal to the weight of prescriptive autho- 
 
 or Reflection by refraction through an excessively rity in favour of the Newtonian hypothesis, conclud- 
 
 flat prism. ing with an admonition to the Royal Society to cling 
 
 It is an easy matter (comparatively) to assign the to its old standards and old celebrities, and to save 
 
 lengths of a wave of light, from the intervals of the its Transactions from degenerating into volumes of 
 
 interference lines, or still better from the elongations miscellanies. This attack, paltry as it was, seriously 
 
 of the coloured images produced by striated surfaces, prejudiced the reception, or even the dispassionate 
 
 the intervals of the strise being given, Newton's consideration of Young's views. His anxious vin- 
 
 measures of the intervals between the lenses pro- dication put forth in a separate pamphlet was unread, 
 
 ducing coloured rays, gave Dr Young the following and the doctrine of interference was first understood 
 
 for the number of undulations contained in an inch and relished in France ten years later, 
 
 producing each colour : Theory of the Rainbow. — It is a matter of interest 
 
 ^ , _ , o-, nAn in several points of view that the phenomenon of the 
 
 Extreme Red 37,640 . K. ^^ a j. ■■ e ix. 
 
 Boundary Red and Orange 40,720 rambow, which gave the first suspicion of the vary- 
 
 Orange and Yellow. 42,510 ing refrangibility of light, and which, when explamed 
 
 Yellow and Gfreen 45,600 a,nd reduced to calculation by Newton, so convin- 
 
 Green and Blue 49,320 . , j ^.t x j.i e x\. j j. • i xt. 
 
 Blue and Indigo 52,910 cingly proved the truth of thedoctrme of the compo- 
 
 Indigo and Violet 55,240 site nature of white light, was destined in the hands 
 
 Extreme Violet 59,750 of Young and of his successors to yield one of the most 
 
 Now the velocity of b'ght is known, that is, the rate refined evidences of the extensive application of the 
 of propagation of a disturbance in ether ; but the doctrine of interference. The general fact of the ar- 
 duration of an impulse, or rather the interval between rangement of colour in the primary and secondary 
 two successive impulses striking the eye and pro- bows Newton accounted for. But the spurious or 
 ducing the effect of colour, is the time that an impulse supernumerary bows occasionally seen within the 
 takes to travel over the length of a wave. It is easy primary, and far more rarely beyond the secondary, 
 to see how almost infinitely short this must be : 460 consisting of reddish and greenish bands, remained 
 millions of millions of such impressions in a second unexplained. The brilliancy of any given portion of 
 of time go to make up the sensation of redness, 735 the rainbow depends upon the deviation of the sun's 
 millions of millions that of violet light. rays by two refractions and one reflection, approach- 
 It might be supposed that Young's discovery and ing to a limit which it cannot overpass. But except at 
 its application excited the notice and applause of all this precise limit an amount of scattered light will 
 persons interested in optics. This was very far from reach the eye, which, though not reflected under the 
 being the case. Though he brought it several times most favourable circumstances, yet is still sufficiently 
 in succession and in different forms before the Royal intense to be visible. This light must be composed, as 
 Society of London, there is no evidence, so far as I at Young showed, of two portions, entering the eye in 
 present know, of his having then obtained a single ad- the same direction, but which have pursued different 
 herent. Davy was no optician ; Wollaston was too paths within the drop, and which never coincide except 
 cautious to commit himself, though probably giving at the extreme geometrical limit before mentioned, 
 a tacit assent ; Cavendish was aged, and besides had When one of these paths differs from the other by the 
 attended less to this subject than to most others ; Sir length of half a wave of the particular kind of light 
 William Herschel had only lately taken up phy- considered, darkness will result, but a feebler maxi- 
 sical optics, and that with reference to the qualities mum will be again attained when the interval rises 
 of the spectTuin least connected with Young's obser- to a whole wave-length, or to two or more. Hence 
 vations. At the Royal Institution Young vainly at- these consequences follow — -Jirst, that the bright part 
 tempted, in the elaborate course of lectures which he of each colour is limited by its self-destruction to a 
 there delivered for two years (1801-3) on natural narrow band, and thus the purity of prismatic colour 
 philosophy and the arts, to arouse a popular inte- So striking in a well-formed rainbow is preserved ; 
 rest in the unveiling of these mysteries. The ab- secondly, that each colour may attain (by interference) 
 struseness of his discourses scared that mixed audi- a second and a third maximum, corresponding in fact 
 ence, and his colleague Davy, in a letter, incidentally to the position of the spurious bows ; thirdly, that 
 observes that Young would be satisfied if any one these phenomena of perfect definition of the primary 
 would even offer criticisms on his opinions. Criticism and secondary bows, and of repeated maxima in the 
 of a certain kind, however, he soon got in abundance, supernumerary bows, depend essentially on this condi- 
 The Edinburgh Review, in its second number, under- tion, that the drops of falling rain shall approach to 
 
 1 This experiment is usually (arid justly) ascribed to an eminent and amiable British philosopher. But it had already been 
 performed by Fresnel with a special object. See Ann. de Ohimie et de Physique, second series, xv. 382. 
 
 (465.) 
 Theory of 
 the rain- 
 bow incom- 
 plete with- 
 out the 
 doctrine of 
 interfe- 
 rence. 
 
 Spurious 
 bows. 
 
Chap. V., § 1.] 
 
 OPTICS. — YOUNG. 
 
 101 
 
 a general equality of size. For the effects of inter- 
 ference depend on the precise diameter of the drop ; 
 if these be very various the resulting positions of 
 maxima and minima will be altogether confused. 
 Dr Young pointed out that to accord with the phe- 
 nomena the falling drops must be about -^ of an 
 inch in diameter, 
 (466.) I have merely indicated the nature of an argu- 
 
 ,..*"?"^° mentof extreme interest and beauty. Itwould be diffi- 
 menon of cult to Cite (except perhaps m the science of physical 
 the rain- astronomy) a more complete specimen of gradual in- 
 Ik)w as a ^uctive research. Here is a phenomenon — the rain- 
 Theory. ^^^ — ^s familiar as it is beautiful. Even a partial in- 
 sight into its cause confers a certain reputation upon 
 one individual (De Dominis), its farther explication 
 gave Newton one of his most popular triumphs. It is 
 then found that the rainbow is not so simple a fact 
 as was supposed, and that Newton's theory accounts 
 for only its broader features. Then, as in the theory 
 of gravity, a long period of uncertainty ensues ; but 
 observations are continued. A perfect rainbow is 
 found to be one of the rarest of natural phenomena, 
 instead of the commonest. Not above two or three 
 individuals have ever seen, or at least described one. 
 Then comes Dr Young, with his theory of interfe- 
 rence and diffraction. This theory not only accounts 
 for the spurious bows, but for the precise appearance 
 of the principal ones, which, but for it, would have 
 been different from what Newton supposed. Finally, 
 after being canvassed for more than two centuries, 
 the theory of Young is carried out into its rigorous 
 consequences by Mr Airy^ and Professor Stokes^ 
 (who must first invent a new mathematical method 
 for the purpose) and illustrated by the ingenious ex- 
 periments of M. Babinet and Professor Miller ;' until 
 at last we begin to believe that we understand this 
 matter completely. 
 _ (*67.) Exterior Fringes of Shadows. — I have men- 
 
 fring"s'of *i<"^^^ oi'ly generally Young's application of his 
 shadows ; theory to the coloured fringes observed by Grimaldi 
 and Newton to surround the outline of bodies, as 
 thrown in shadow by a luminous point upon a dis- 
 tant screen. I have done so because Young's ex- 
 planation was imperfect, not to say incorrect. But as 
 it would be inconvenient to discuss the subject here, 
 I shall briefly indicate its history and result. Dr 
 Young expresses himself more obscurely in his paper 
 of 1801 on this point than on any other, indicating 
 three possible explanations. In 1803, however, he 
 distinctly adopts the opinion that the periodical 
 colours in question are due to the interference of 
 direct light passing near the opaque edge with a por- 
 tion of light very obliquely reflected from that edge ; 
 and he enters into calculations to show that such a 
 theory represents sufiiciently well Newton's measures. 
 But it is unaccountable that Young should have been 
 satisfied with the belief that the screens employed 
 
 should in every case have reflected ah appreciable 
 quantity of light (or indeed any light at all) in the 
 required direction. It might be conceivable in the 
 case of a cylindrical wire or a cylindrical hair ; but 
 how could a film of gold-leaf or a slip of paper re- 
 ceiving the light on its broad side furnish such a de- 
 gree of oblique illumination 1 It is wonderful that 
 Young's intuitive sense did not perceive that the por- 
 tion of a luminiferous wave passing near an opaque 
 edge, is deficient on one side of the interfering wave- 
 lets which are necessary to make the boundary of 
 the shadow definite, and to extinguish the laterally- 
 spreading light. In short, he did not allow to Huy- 
 gens' principle (see art. 455) the full breadth of its 
 application — a discovery made some years later by 
 Fresnel, who has the credit of first explaining these 
 exterior fringes. 
 
 That great philosopher (the worthy rival of Young (468.) 
 in this career of discovery) found the means of com- ^"^\ e^pla- 
 puting, on strict geometrical principles, the sum total them due 
 of the disturbance produced at any point of a screen to Fresne). 
 by the whole effective portion of a luminiferous wave 
 partially stopped by an obstacle of a given form. 
 The principle of the calculation is simple enough. 
 The origin of the light being distant, the front of the 
 wave is considered as flat when it breaks against the 
 opaque body. Its front is then divided (in thought) 
 into small elementary portions, each of which is con- 
 sidered as the source of a disturbance propagated as 
 from a new origin. The effect of each wavelet is cal- 
 culated in terms of the co-ordinates of its origin, and 
 of the point where its effect is to be considered. The 
 sum of all these simultaneous effects is collected by 
 integration, a process which unfortunately is only 
 rigorously possible in a limited number of cases. 
 Some of these cases were solved with great ingenuity 
 by Fresnel, and compared with observation. The re- 
 sult was extremely satisfactory. Yet it is curious to 
 observe that Young's explanation, if it had had a 
 sufiicient physical basis, leads to nearly similar re- 
 sults. In the case of an indefinite opaque body with 
 a straight edge, the illumination precisely at the 
 boundary of the "geometrical" shadow is, on Fresnel's 
 theory, one-fourth of what it would have been were 
 the body removed. Within this line the light dies away 
 gradually, having no maxima or minima. Without it, 
 a series of dark and light bands occur, which rapidly 
 blend into a uniform illumination. The same theory 
 leads to results as to the position of the interior bands 
 which are also somewhat different from the simpler 
 calculation of Young, and still more conformable to 
 experience. Amongst the most singular of these re- 
 sults is this (which is perfectly confirmed by obser- 
 vation), that the shadow of a small round opaque 
 body (as a spot of tin foil) is illuminated by a 
 speck of diffracted light at its centre precisely 
 as bright as if the disk were removed ! How, aftCT 
 
 1 Camb. Trans., vol. vi. (1838.) 
 
 ' Ibid., vol. Ix. (1850.) 
 
 ' Ibid., vol. vu. (1842.) 
 
102 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 this, can we talk of light as moving in straight lines 
 only ] 
 (469.) We must now advert to the peculiar and disadvan- 
 
 Young's tageous manner in which Dr Young laid his farther 
 farther re- researches before the world. The optical papers in the 
 chiefly^^ Philosophical Transactions, ending with 1803, were 
 anony- the last which he published connected with his theory 
 mous. JQ that work, although he continued to be Foreign Se- 
 cretary until his death twenty-five years afterwards, 
 and although during all that time he never ceased to 
 extend and perfect his views on the subject of his predi- 
 lection. The explanation of this paradox is to be found 
 principally in the strictness with which he interpreted 
 the allegiance which he owed to the medical profes- 
 sion. He had determined to be a practical physician ; 
 his early principles of action prevented him from 
 doing anything by halves ; and all experience affirmed, 
 that to gain confidence as a physician in the metropolis 
 he must cultivate sparingly, and as it were by stealth, 
 the studies of abstract science and of philology in which 
 he delighted. Unquestionably he was also disgusted 
 by the absence of one single supporter amongst the 
 members of the great society referred to, — ^by the in- 
 jurious petulanceof the then popular critical journal, 
 — and by the impossibility under which he laboured 
 of communicating orally his knowledge to a general 
 audience in an interesting and acceptable manner. 
 The result of all this was the suppression of many of 
 his opinions, and the publication of others in so con- 
 cealed and uninviting a form that they remained 
 for years nearly buried and unknown to men of 
 science. He contributed a series of articles on sub- 
 His articles jects connected with light to the Quarterly Review ; 
 In the and we may well smile at the abstruse and really ob- 
 ^arterly g^^j-g dissertations on detached points of science — 
 ' often unmercifully loaded with algebra — thus inter- 
 spersed with articles of popular criticism for the enter- 
 tainment of the reading public. From some of these 
 papers we may readily gather the soreness which he 
 felt at the cold reception of his discoveries. Farther 
 and still more important original speculatit)ns were 
 contained in a series of anonymous papers (sixty- 
 three in pumber) on a vast variety of subjects, both in 
 science and philology, contributed to the Encyclo-poe- 
 and Ency- dia Britannioa. It is not in a work such as this that 
 elop(edia y^^ usually look for the /Irst publication of great and 
 rm . jjj.jg^jjg^][ views : the articles being anonymous could 
 only very gradually attract notice by their intrinsic 
 merit ; and the obscurity of some of those vrritten by 
 Young rendered this difficult enough. But it is most 
 fortunate that he was induced thus to write : many of 
 his most original thoughts must have been lost but for 
 these concealed repositories. In the articles in the 
 Quarterly Review, for example, we watch with interest 
 the impression which contemporary discoveries made 
 upon his mind. The spheroidal wave of extraordinary 
 refraction is explained by unequal elasticity of the 
 
 crystal in different directions ;' the discovery of polar- 
 ization by reflection is received with characteristic can- 
 dour, as giving a temporary blow to the undulatory 
 theory ;2 whilst in a later paper the cause of chromatic 
 polarization is convincingly deduced from the prin- 
 ciple of interferences, and in the space of two lines 
 the peculiar coloured laminaa occurring in Iceland 
 spar, which had been noticed by several experi- 
 menters, are accounted for. ^ 
 
 From about 1815 the optical discoveries of Young (470.) 
 were so intimately connected with those of his younger '^^^°'7°^ 
 friend and rival Presnel, that it seems best to defer ughi de- 
 our account of them until we consider (in § 3 of this ferred to 
 chapter) the peculiar researches of Fresnel, which § 3- 
 ultimately rendered the phenomena of polarization 
 the most impregnable position of the partizans of the 
 undulatory theory. The first great step was the con- 
 ception of transversevibrations of ether, asconstitutmg 
 polarization. This, as we shall see, was first pub- 
 lished by Young. It is to be regretted that the tardy 
 and imperfect publication of Fresnel's memoirs on 
 the one hand, and the resolution of Young to adhere 
 to an anonymous and indirect mode of announcing 
 his discoveries, on the other, render the history of 
 the subject sometimes obscure. The correspondence 
 between them, first fully published by Dr Peacock, 
 throws some light upon it; but several important 
 letters have not been recovered. 
 
 I had intended devoting a portion of this section to (471.) 
 Dr Young's important and ingenious researches on the Physiology 
 physiology of vision. But the length to which it has al- °^ '"*""' ' 
 ready extended obliges me reluctantly to omit it. I also 
 refer to the chapter on mechanics (Art. 344, &c.) for 
 some notice of his masterly reasonings on the princi- 
 ples of carpentry and the flexure of elastic substances. 
 They are characterized by directness of purpose and 
 a consummate command of ordinary mathematics, 
 unaccompanied by any pretension to symbolical dis- 
 play ;— it might be added too, by the obscure concise- 
 ness of Dr Young' s habitual style. His researches (pre- 
 ceding and anticipating those of Laplace) on capillary 
 attraction have also been referred to (432), as well as 
 his masterly investigation of the tides (80, 81). Itinterpre- 
 does not belong to this treatise to speak of his disco- '^*^™ "*' 
 very of the interpretation of hieroglyphics in certain pi,icg 
 cases which gave the first real impulse to this obscure 
 but interesting subject. The successes of ChampoUion, 
 Rawlinson, and others, in similar undertakings, must 
 logically be connected with the first great step of de- 
 cyphering the polyglot stone of Rosetta. It may safely 
 be affirmed that no philologer ever before made such 
 a discovery in science as the law of interference, and 
 that no natural philosopher ever made such a step 
 in the interpretation of a lost tongue as the forma- 
 tion (up to a certain point) of an Egyptian alphabet. 
 
 We cannot close this imperfect sketch of one of (472.) 
 the greatest ornaments of our age and nation, without 
 
 1 Quart. Rev,, vol. ii. 
 
 ^ Ibid., vol. iii. 
 
 3 Ibid., vol. xi. 
 
Chap. V., § 2.] 
 
 „OPTICS. — MALUS. 
 
 103 
 
 Young's adding, that in private life Dr Young was exemplary ; 
 
 personal endued with warm aifections, philosophic moderation, 
 ' and mgh moral and religious principles. His ofBce 
 as secretary to the Board of Longitude (the only 
 public promotion he received), was attended not only 
 with immense labour in editing the Nautical Al- 
 manac, but with vexatious contentions, which in his, 
 as in so many other cases, tended to diminish his 
 usefulness and even shorten his life. To the petty 
 persecutions with which he was assailed, it was owing 
 that the health which the unbroken study of fifty 
 years had ijot impaired, at length gave way, and he 
 
 and death, aied yet in the prime of intellect, the 10th May 
 1829, within a few months of his honoured asso- 
 ciates and friends, Wollaston and Davy. He had 
 been elected two years previously one of the eight 
 foreign associates of the Academy of Sciences of 
 Paris. 
 
 Dr Young's philosophical character approached in (473.) 
 many important particulars to that of Newton, With Philosophi 
 much of the inventive fire of Davy, and of the rea- j^^, 
 soning sagacity of Wollaston, he combined an amount 
 of acquired learning, and a versatility in its applica- 
 tion, far superior to both. We do not ascribe to him 
 an intuitive insight so rapid and almost divine as 
 that which distinguished the author of the Prinoipia 
 above all other men, nor had Young the same strictly 
 mathematical ability ; but like Newton, whatever he 
 did was practical and sound ; nothing was done for 
 show, nothing omitted through haste. " The power 
 of patient thought" was the lever with which he 
 moved the world. His self-confidence was great but 
 unobtrusive. He attained, as he himself said, all the 
 main objects to which he had looked forward in life, 
 " such fame as he valued, and such acquirements as 
 he might think to deserve it." 
 
 § 2. Malus. — Discovery of the Polarization of Light by Reflection.^— Early History of Double 
 
 Refraction and Polarization. 
 
 (474.) 
 
 Uafas — the 
 polariza- 
 tion of 
 light. 
 
 (475.) 
 Early his- 
 tory of 
 double re- 
 fraction — 
 Huygena' 
 law. 
 
 Etienne Loxtis Malus was born at Paris on the 
 23d July 1775, and died on the 24th February 1812, 
 after a too brief but brilliant career. His principal 
 discovery, that of the polarization of light by reflec- 
 tion, is so intimately connected, both historically and 
 by the nature of the case, with double refraction, that 
 1. shall briefly sum up the scanty progress of that 
 singular subject previous to his time. 
 
 It was known to Bartholin of Copenhagen, about 
 1669, that Iceland or calcareous-spar has the pro- 
 perty of dividing a ray of light, which falls upon it 
 in almost any direction, into two ; one of which is 
 refracted according to the usual law, but the other 
 in an extraordinary manner, which was first analyzed 
 by Huygens — a problem of great difficulty, in which 
 Newton not only failed, but he also erred in con- 
 tinuing to pronounce Huygens' solution false. The 
 solution was this, that there is one direction in the 
 crystal parallel to which both the rays (called the 
 ordinary and the extraordinary^ move in a similar 
 and uniform manner. In other directions their pro- 
 pagation may be expressed by considering the ordi- 
 nary ray within the crystal to be due to a spherical 
 wave (the centre of which coincides with the point 
 of incidence), whilst the extraordinary ray corre- 
 sponds to a flattened spheroidal wave concentric with 
 the former, and having its axis coincident with a 
 diameter of the sphere, and parallel to the minera- 
 logical axis of the crystal. Both rays, on the Huy- 
 genian hypothesis, move slower than in air, but the 
 extraordinary ray everywhere faster than the ordi- 
 nary ray, excepting only in the axial direction. A 
 perfectly plain though necessarily complex construc- 
 tion was given by Huygens for the purpose of tracing 
 both rays in the course of their refraction, founded 
 on this idea. 
 
 Newton's opposition to Huygens' law as a state- (476.) 
 ment of fact left it for more than a century under ^° w'^^ . 
 partial doubt. Haiiy is stated to have verified it, or ton ; 
 at least to have shown that it approached nearer to 
 the truth than Newton's ; but Dr Wollaston first re- 
 established it in 1802 by conclusive experiments, 
 which, however, he found it impossible to connect by 
 a law until the previous generalization of Huygens 
 had been pointed out to him, — most probably by Dr 
 Young. 
 
 It was several years later that Malus directed his (477-) 
 attention to the subject, unaware of what had been ^^. ^^° ^^ 
 accomplished by Wollaston. He had returned in 
 1801 from the unfortunate French expedition to 
 Egypt, where he was engaged as an officer of en- 
 gineers, and had ruined his health through fatigue 
 and the insalubrity of the climate. He was an ac- 
 complished mathematician, having acted as professor 
 both at the Polytechnic School and that of Metz, 
 and was of course a member of the Institute of Cairo. 
 On his return to France, during the intervals of his 
 military duties, he occupied himself in the composi- 
 tion of an elaborate analytical treatise on optics, which 
 had already occupied his attention in Egypt. This 
 led him to the subject of double refraction, and he 
 verified by numerous experiments the accuracy of 
 Huygens' law. La Place wrote a paper on the mathe- 
 matical law of the velocity of the extraordinary ray, 
 in which he introduced the idea of a repulsive force 
 emanating from the axis of the crystal ; but it may 
 be truly affirmed that the notion of a spheroidal un- 
 dulation so happily introduced by Huygens is the 
 only one which really fits the case ; and by the very 
 impossibility of expressing the facts intelligibly with- 
 out it, gives an undisputed advantage to that theory. 
 
 A prize having been proposed by the Academy of (478.) 
 
104 
 
 MATHEMATICAL AND PHYSIC^^ SCIENCE. 
 
 [Diss. VI. 
 
 Essay on 
 double re- 
 fraction. 
 
 (479.) 
 Huygena' 
 discovery 
 of polariza- 
 tion by calc 
 spar. 
 
 (480.) 
 Malus dis- 
 covers po- 
 larization 
 by reflec- 
 tion. 
 
 Sciences for the theory of double refraction, Malus 
 wrote a second paper, which was crowned, but which, 
 however admirable as a specimen of mathematical 
 address, added little to what was previously known. 
 
 Malus had already, in the end of 1808, announced 
 a property of light which, if not absolutely new, was 
 entirely so with reference to the circumstances in 
 which it was produced. The polarization of light 
 was in reality discovered hy Huygens previous to 
 1 680. He had observed that the two rays into which 
 common light is divided in passing through Iceland 
 spar have a singular diversity of character, which 
 Newton afterwards described as an opposite polarity. 
 Huygens showed that if two rhombs of doubly re- 
 fracting spar are laid symmetrically one upon the 
 other, the " extraordinary" ray yielded by the first is 
 extraordinarily refracted by the second, and the "ordi- 
 nary" ray from the first is ordinarily refracted by the 
 second. But when we revolve the upper rhomb 
 as it lies upon the lower one through a right angle, 
 a remarkable change appears. The extraordinary 
 ray escaping from the first is now ordinarily re- 
 fracted by the second, and vice versa, so that the 
 qualities of the two rays difier but only so far as this, 
 that either may be assimilated to the other by making 
 it (or the crystal from which it derives its properties) 
 revolve round ninety degrees. A definite notion of 
 such a distinction may be formed by imagining a 
 musical string vibrating at one time in a vertical, at 
 another in a horizontal, plane. If we could possibly 
 imagine light to consist of vibrations of this descrip- 
 tion, the two rays of Iceland spar might be conceived 
 the one to vibrate in a plane passing through the 
 axis of the crystal, the other in a plane perpendicular 
 to that. Suchlight might truly be said to have ac- 
 quired the property of having sides. In the language 
 of Newton, it is polarized. 
 
 The discovery of Malus consisted in showing that 
 light may acquire properties identical with those of 
 either ray yielded by refraction through Iceland spar, 
 by the very simple process of simple reflection at a par- 
 ticular angle from any transparent body. Thus for a 
 surface of water he found this angle to be 52° 45' with 
 the perpendicular, and for glass 54° 35'. The reflected 
 light in either case has exactly the property of the or- 
 dinary ray transmitted by a crystal whose principal sec- 
 tion (that is, a section passing through the axis of the 
 crystal) is parallel to the plane of reflection. Con- 
 sequently this light will be acted on by a doubly re- 
 fracting crystal placed in its way precisely as if it 
 had emerged from a similar crystal; and, on the 
 other hand, if the two rays emerging from a crystal 
 be incident on water or glass as above mentioned, the 
 one will be copiously reflected from the surface, whilst 
 the other will not be reflected at all, but pass entirely 
 into the transparent substance. Farther, as might 
 be expected, light thus polarized by reflection, when 
 
 it falls on a second similar reflecting surface at the 
 same angle as before, will be copiously reflected if the 
 planes of reflection coincide, but will refuse to be 
 reflected in an appreciable degree when the planes of, 
 reflection are perpendicular. 
 
 This phenomenon was detected by Malus by casually (481.) 
 observing that a ray from the setting sun reflectedO'=f»sion 
 from a distant window, and viewed through a piece" ^ " 
 of Iceland spar, aiforded but a single image in two 
 positions of the latter. The experiment attracted uni- 
 "versal attention, and became the germ of a series of 
 optical discoveries almost imprecedented for their 
 beauty and variety ; yet most of the experiments may 
 be made quite as well when light is polarized by the 
 method of Huygens as by that of Malus. Neverthe- 
 less the former had remained a sterile fact for 130 
 years. Upon such trifling circumstances does the 
 progress of knowledge often depend. 
 
 Malus survived his discovery only four years, and (482.) 
 saw but the borders of that land of promise which he Law of the 
 had pointed out to others. A few results he however ''°*"'™" 
 obtained, which are worthy of notice. Thus he found 
 that in every instance where light is polarized in any 
 plane there is also produced a certain proportional 
 amount of light polarized in the perpendicular plane. 
 Arago afterwards proved the very important fact, that 
 these two portions are universally equal. Huygens 
 had shown in the experiment of the two rhombs, that 
 when their positions are neither symmetrical nor 
 perpendicular, each ray emerging from the first is 
 duplicated by the second. When the principal sec- 
 tions of the rhombs are inclined 45°, the duplicated 
 rays are equally bright ; as they approach parallelism 
 or perpendicularity, one pair of the rays brighten and 
 the other pair is enfeebled. Malus ascertained the 
 law of change of brightness, which is the same for 
 rhombs of spar or for plates of glass whose planes 
 of reflection vary whilst the angle of reflection re- 
 mains constant. In either case the intensity of the 
 light varies as the sqiiare of the cosine, of the angle 
 formed by tlie principal sections of the crystals or 
 the planes of reflection of the plates. This impor- 
 tant law, the best established in photometry, has been 
 applied by Arago to the measurement of light in 
 many instances, but the details were unfortunately 
 not made public before his decease. 
 
 To Malus is also due the discovery of the polariza- (483.) 
 tion of light by common refraction. When light is in- Ot'^^r^is- 
 cident on glass or water, the refracted beam contains*^"^*"**' 
 precisely as much polarizedlight as the reflected beam, 
 but oppositely polarized. The metals were at first 
 believed by Malus to polarize no appreciable quan- 
 tity of light. He afterwards found that at great in- 
 cidences the reflected light is partly polarized.' He 
 likewise ascertained the fact of the "depolarization" (as 
 it was termed) of light by many crystals, and also by 
 organized substances, such as hair, horn, and whale- 
 
 ^ See an interesting letter from Malus to Dr Young In Thomson's Anjuils, vol. iii. 
 
Chap. V., § 3.] 
 
 OPTICS. — FRESNEL. 
 
 105 
 
 bone. He does not appear to have noticed the phe- 
 nomena of colour accompanying such depolarization, 
 though he arrived at it so nearly that Arago,in all pro- 
 bability, anticipated him by presenting a memoir on 
 the subject to the Institute just one week previous to 
 Malus's announcement of what he had observed 
 (19th August 1811). In less than six months later 
 Malus was no more. 
 (484.) The writings and discoveries of Malus present evi- 
 
 dence of great talent, but of far less fertility of com- Character 
 bination than those of Fresnel, presently to be no- °^ Mains, 
 ticed. He maintained the Newtonian theory of light. 
 His reputation amongst his intimates was extremely 
 high, and it was generally believed, that had he sur- 
 vived, his discoveries would have extended much far- 
 ther. To him was applied Newton's saying on the 
 death of Cotes, — " If Cotes had lived we should have 
 learned something." 
 
 3. Fresnel. — The Undulatory Theoi-y of Light continued. — Diffraction. — Transverse Vibra- 
 tions ; Young. — Polarization and Double Refraction explained. — Lighthouse Illumination. 
 
 (485.) Atjgustin Fresnel was born at Broglie, in France, 
 loth May 1788, of a feeble constitution, and he con- 
 tinued throughout his too short life a prey to attacks 
 of bad health. As a boy, his slow apprehension and 
 uncertain memory gave no indication of the maturity 
 of his judgment. He entered first the Polytechnic 
 School, then that of Fonts et Chaussees. His fidelity 
 to the Bourbon cause occasioned his being harshly 
 treated by Napoleon, and he retired to Normandy in 
 the beginning of 1815, to pursue the scientific studies 
 which he had always loved, 
 n-ff ^^"2 Diffraction. — The theory of light in particular at- 
 
 of light, tracted his attention, and he had a steady belief that 
 the Newtonian doctrine was erroneous, though in 
 ignorance, as it appears, of the undulatory doctrines 
 of Hooke, Huygens, and Young. The phenomena 
 of diflfraction, or the coloured fringes which are seen 
 in the interior of the shadows of opake bodies when 
 illuminated by a minute source of light, attracted 
 his attention as most proper for deciding the deli- 
 cate question of the molecular or undulatory cha- 
 Presnel's racter of light. The results of his experiments were 
 detailed in a memoir confided in the first place to 
 his friend Arago, and by him communicated to the 
 Institute of France (October 1815). This remark- 
 able paper contained much which Dr Young had al- 
 ready discovered, and the explanations of the experi- 
 ments which it described, both new and old, by the 
 theory of undulations, were common to both. Dr 
 Young having anticipated the publication by at least 
 a dozen years, there could be no question of pri- 
 ority ; but it is equally certain that Fresnel was un- 
 aware of what Young had done until it was pointed 
 out to him by Arago. His memoir, which was pub- 
 lished in great part in the Annates de Chimie for 
 1816, contains much which is interesting. The mode 
 of observing the difii:action bands directly by means 
 of a lens, without the intervention of a screen, was 
 equally new and important. The observation that 
 the interior fringes of the shadow of a narrow body, 
 such as a wire, disappear when the light is intercepted 
 on either side of the wire, leading to the conclusion 
 that the union of the light from both sides is neces- 
 
 first me- 
 moir. 
 
 sary for their occurrence, was (as we have seen) 
 one of Young's capital experiments. The explana- 
 tion of Newton's rings, by the interference of the light 
 reflected from two adjacent surfaces, though partly 
 anticipated by Hooke, was equally important. Nu- 
 merous measures of the distances of the exterior 
 diflfraction bands from the geometrical shadow, as 
 formed by homogeneous red light, are then given and 
 compared with theory. Here Fresnel was on original 
 ground. These accurate numerical comparisons, af- 
 terwards pursued to a greater extent, constituted one 
 of the most important bases of the new theory. In 
 obtaining them he was materially aided by Arago, 
 who, though considerably his senior, generously as- 
 sisted him in every respect, and gave him the full ad- 
 vantage of his station as a member of the Institute, 
 and of his experience. 
 
 Fresnel's first memoir on difiraction justly excited (487.) 
 so much notice that the subject was proposed by the Second 
 Academy of Sciences in 1817 for one of their prizes, p^o^gg 
 The new essay which Fresnel then wrote was, as pro- upon 
 bably had been anticipated, the successful one. In Young's 
 this memoir he made an important step, by showing ^°''^' 
 that the exterior fringes in diEraction shadows do not 
 depend (as Young had supposed) upon the interfer- 
 ence of the direct light with that reflected at a great 
 obliquity from the edge of the difiracting body, but 
 from the interference of the difierent elementary un- 
 dulations which proceed from the disturbed surface 
 forming the front of the grand wave. Decomposing 
 the front of the wave into small portions after the 
 manner of Huygens, he computed the disturbance 
 produced by the integral efiect of the whole at a given 
 point of the screen where the picture of the shadow 
 fell and was submitted to examination, and he fouud 
 that such integral efiects have a periodic character, 
 presenting points of maximum and minimum distur- 
 bance, or of greatest and least illumination as we re- 
 cede from the geometrical shadow. These distances 
 being measured in homogeneous red light were found 
 to agTee with the results of an arduous computation, 
 requiring, as will easily be seen, an intimate acquain- 
 tance with the integral calculus and much skill in 
 
 me* 
 Im- 
 
106 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 using it. Such Fresnel possessed, though he always 
 refers with great modesty to his limited facility of em- 
 ploying the higher mathematics. 
 (488.) Transverse Vibrations — Young and Fresnel. — 
 
 Transverse Considerable obscurity hangs over the first publi- 
 vibratious cation of this important discovery. A clear and 
 and Fref- impartial abstract of the facts will be found in 
 nel. the second volume of Dr Whewell's History of the 
 
 Inductive Sciences, and some further documentary 
 evidence, including interesting letters which passed 
 between Young and Fresnel, have more recently 
 been published in the Life and Works of the for- 
 mer, edited by Dr Peacock. The difficulty of appor- 
 tioning the credit between Young and Fresnel partly 
 arises from the unfortunate system of imperfect pub- 
 lication, or non-publication, adopted on professional 
 grounds by the former, and partly from the grievous 
 delays imposed upon the latter by the opposition with 
 which his opinions and experiments were received at 
 the French Academy of Sciences. This continued to 
 the very close of Fresnel' s career. His greatest work 
 was not published in the Memoirs of the Institute 
 until six years after date ; another was mislaid for 
 above twenty years, and even the hardy friendship of 
 Arago sometimes almost recoiled before the storm of 
 opposition which the novelties of his associate were 
 sure to excite in the minds of the dominant mathe- 
 matical section. It is quite impossible to say pre- 
 cisely at what period Young first imagined that the 
 differences of oppositely polarized rays of light might 
 be explained by perpendicularity in the directions of 
 vibration of the ethereal molecules, which he compared 
 to the vibrations of a cord in which the elementary 
 movements are at right angles to the direction of wave- 
 propagation. It seems evident that Young was not 
 possessed of this idea in 1 8 1 4, when he partly explained 
 depolarization in a few pages of an article in the 
 Quarterly Review. It is equally certain that he an- 
 nounced it to Arago (with whom he became person- 
 ally acquainted in 1816) in January, 1817; and that 
 he then speaks of it as an idea which apparently had 
 recently occurred to him, most probably since their 
 interview.^ Arago and Fresnel had already, in 1816, 
 made experiments demonstrating that rays oppositely 
 polarized do not produce dark hands hy their inter- 
 ference, a memorable discovery, requiring very great 
 nicety for its satisfactory proof, which, however, 
 was completely attained. It was this observa- 
 tion which (naturally) gave Fresnel the first idea 
 of transverse vibrations, and it is much more than 
 probable that Young worked out a similar solution 
 of the great problem, in consequence of the account 
 of these experiments which he received from Arago 
 in the summer of 1816.^ Be this as it may. Young 
 
 and Fresnel unquestionably imagined the theory se- 
 parately, but Young first announced it, Fresnel being 
 discouraged by the doubts of Arago, and by his 
 awe of the Institute. As clearly, the experiment of 
 non-interference was the first which gave a colour to 
 so bold an assumption, and in the details of its ap- 
 plication to double refraction Fresnel had the undi- 
 vided merit. What is not least worthy of notice in 
 the affair, is that neither of the amiable rivals (Young ! 
 
 and Fresnel) ever published a word in disparagement 
 of the other, nor a single unfriendly reclamation of 
 priority. 
 
 The doctrine of transverse vibrations being allowed, (489.) 
 its applications and severest tests were twofold, 1st, ^PP^"^ *" 
 To the phenomena of ordinary reflection and refrac- „£ \\gTBt_ 
 tion including the polarization produced by these ope- 
 rations; and 2dly,to double refraction and the univer- 
 sally concomitant polarization. In these bold specu- 
 lations and laborious inductions, Fresnel was nearly 
 alone. Young did not appear as a competitor ; even 
 his friend Arago, though sympathizing with and 
 proud of his success, was not associated with him. 
 
 Laws of Reflection and Refraction. — With re- (490.) 
 gard to the reflection and refraction of light, its in- ™^° 
 tensity has to be defined, and also its condition as to and refrac- 
 polarization. The fundamental laws of the direction tion— 
 of the rays are not affected by this theory. Eigorous ^"^^^nel. 
 mathematicians who then doubted the possibility 
 of transverse vibrations having more than a transi- 
 tory existence, if they existed at all, could not be ex- 
 pected to supply the theory of their reflection and re- 
 fraction at the bounding surfaces of different media. 
 Fresnel, however, guided by probable mechanical 
 analogies, with an intuitive insight worthy of Newton 
 himself, gave a formula for the intensity of reflected 
 transverse vibrations, both when the plane of vibration 
 of the molecules is in the plane of reflection, and when 
 it is perpendicular to it; and he conceived common 
 light to act as if equally composed of both sets of 
 vibrations. His formula embrace the non-reflection 
 of polarized light at the critical angle, under the 
 circumstances explained in the last section. It is a 
 most remarkable fact that these inferences by Fresnel 
 as to the numerical relations of the intensity of there- 
 fleeted to the incident light through all angles of inci- 
 dence, anticipated almost every trustworthy photo- 
 metrical measure; and from their singular though 
 indirect accordance with many phenomena, they have 
 been generally accepted as an expression of a natural 
 law of great complexity, even by those who were not 
 favourable to the theoretical views on which they are 
 based. 
 
 The modifications of the state of polarization of ^*^^^ 
 light which takes place by reflection, was equally 
 
 1 " I have also been reflecting on the possibility of giving an imperfect explanation of the affection of light which constitutes 
 polarization, without departing from the genuine doctrine of undulation." He then refers to " a transverse vibration propagated 
 in the direction of the radius, the motion of the particles being in a certain constant direction with respect to that radius ; and 
 this," he adds, " is a, polarization.'" — Young's Miscell. Works, vol. i., p. 383. 
 
 2 Peacock's Life of Young, p. 390. 
 
Chap, v., § 3.] 
 
 OPTICS. — FRESNEL. 
 
 107 
 
 Circular embraced in Fresnel's theory, and equally (though 
 poiariza- unknowingly) confirmed by Sir D. Brewster's labo- ■ 
 rious observations. But on one point Fresnel him- 
 self obtained a signal triumph. Having deduced ex- 
 pressions for the intensity of refracted light, on push- 
 ing them to the limit where refraction out of a denser 
 into a rarer medium becomes impracticable because 
 the light undergoes total internal reflection, the for- 
 mulae became affected by the multiplier ^^TT, and 
 were unsusceptible of arithmetical evaluation. In 
 endeavouring to attach a meaning to these expres- 
 sions, it occurred to him that as the intensity of the 
 totally reflected ray undergoes no change with the 
 angle of incidence, the expression in question might 
 in some way determine the alteration of the phase of 
 the wave (the position and direction of motion of the 
 molecules under consideration) which took place at the 
 instant of reflection. Now, admitting this as likely, 
 it appeared that the phase would vary not only with 
 the angle of internal reflection, but with the plane of 
 pblarization of the ray. It had previously been 
 shown by Arago and by himself, that when two oppo- 
 sitely polarized rays meet or interfere, though there 
 is then no destruction of the light, there is usually 
 a remarkable change in its character. There is 
 one position of the interfering wave relative to the 
 primary one in which the combination produces light 
 polarized in a plane exactly intermediate between the 
 planes of previous polarization. If either ray be now 
 accelerated by half a wave-length on the other, the 
 new plane of polarization becomes perpendicular to 
 the former ; but if the shift of either of the primary 
 rays amounts to only one quarter of a wave-length, 
 the motion of the molecules takes place in a circle, 
 and the undulation has a helical form. Now, Fresnel 
 tested his hypothesis concerning totally reflected light 
 by calculating the circumstances of incidence which 
 should produce an effect equivalent to this ; and the 
 result completely verified his bold conjecture. The 
 apparatus employed is called FresneVs Rhomb, which 
 transforms plane-polarized light into light equally 
 reflexible in all azimuths, yet not common light, be- 
 cause it possesses properties which common light does 
 not (such as displaying the rings in crystals) ; this 
 is termed circularly polarized light. 
 (492.) Theory of Double Refraction. — The difficulty of 
 
 Double re- accounting for double refraction did not consist 
 in showing how a spheroidal wave might be pro- 
 pagated. Young had already shown, in 1809, that 
 it would result from supposing a lamellar arrange- 
 ment of the crystalline molecules so that the ether 
 was differently elastic in a direction parallel to the 
 axis than in a plane or planes perpendicular to 
 that line.^ Huygens had shown something similar 
 in accounting for terrestrial atmospheric refraction. 
 The difficulty was, to account for two waves travel- 
 
 fraction ex- 
 plained. 
 
 ling at the same tinie through the same portion of 
 matter with unequal velocities. The moment that 
 the idea of molecular movement transverse to the line 
 of propagation was admitted, it was easy to see that 
 no contradiction was involved in the idea. Two 
 waves might simultaneously travel in the same direc- 
 tion, and through the same medium, provided the 
 molecular displacements were in different planes. So 
 happy a solution could hardly fail to strike such minds 
 as those of Young and Fresnel with the impress of 
 conviction. A closer analysis confirmed the proba- 
 bility. Iceland spar (or rather the ether imprisoned 
 within it) is conceived of as a medium of uniform elas- 
 ticity in all planes perpendicular to the axis, but of a 
 different and greater elasticityin any direction parallel 
 to the axis. It is shown to result from this, that in 
 the direction of the axis alone is the motion of light 
 independent of the plane of the vibrations of which it 
 is composed, and consequently no separation of rays 
 occurs. When a ray moves parallel to what may hj 
 an analogy be called the equatoreal plane of the 
 crystal, its undulation will, generally speaking, be 
 resolved into two whose vibrations are parallel and 
 perpendicular to that plane, and which travel with 
 different velocities though in the same direction. If 
 the ray take any other direction through the crystal, 
 both the direction and velocity of the divided rays 
 differ. The form of the extraordinary wave is exactly 
 the spheroid of Huygens. 
 
 But what are we to conclude concerning those crys- (493.) 
 tals (of the discovery of which we shall speak in § 5)'^'^^'"'y "^ 
 presenting two axes of double refraction ? Fresnel at*''^^!*!' 
 once assumed that the elasticities must in that case axes, 
 vary in three rectangular directions, and he proceeded 
 to calculate the manner of propagation of a wave 
 through a medium thus constituted. I had proposed 
 to attempt some explanation of the steps of his most 
 ingenious and profound argument, but I find it incom- 
 patible with the space at my disposal, and at any 
 rate hardly to be apprehended without the use of 
 symbols or figures. For these reasons I shall merely 
 state the results. When the medium presents un- 
 equal elasticities in three rectangular directions, the 
 surface of the wave consists of two sheets each tra- 
 velling with its peculiar velocity. But neither of 
 these being spherical, the result cannot be expressed 
 by the ordinary law of refraction. In two directions 
 within the crystal, the wave surfaces coincide, or the 
 two rays coalesce. These directions are evidentlv 
 the optic axes, and the wave surface in their neigh- 
 bourhood has very interesting geometrical and 
 physical properties which have been elucidated 
 by British philosophers, as wUl be noticed in 
 another section. The true optical axes cannot 
 exceed two, and when two of the three elasticities 
 become equal, they merge into one. This is the 
 
 ' Voung's reasoning {Qaarttrly Review 1809, and Worhi, vol. i. p. 228) is based on an experiment by Chladni on the differing 
 velocity with which sound is propagated in wood, depending on the direction of the fibres. 
 
108 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (494.) 
 confirmed 
 by experi- 
 ment. 
 
 (495.) 
 Reception 
 of Fresnel's 
 theory ; 
 
 in Prance, 
 
 in Eng- 
 land. 
 
 case in Iceland spar and similar crystals. At 
 the same time tKe wave surface degenerates into 
 the united sphere and spheroid. The equation to 
 the wave surface was deduced by Fresnel in an in- 
 direct and somewhat tentative manner. It was 
 demonstrated by Ampere directly, but inelegantly. 
 M. Cauchy, Mr Archibald Smith, and Professors 
 Sir W. R. Hamilton and MaccuUagh gave more 
 complete and elegant solutions. 
 
 Fresnel submitted his theory (as usual) to experi- 
 ment. He found that in topaz, which is a biaxial 
 crystal, neither ray follows the law of common re- 
 fraction. The plane of polarization (which is always 
 perpendicular in the two rays) follows very nearly 
 indeed, by theory, the law which M. Biot had as- 
 signed by experiment. Fresnel thus stated the 
 ground of his conviction of the truth of his theory, 
 and it would be difficult to express more appropri- 
 ately the characteristics of a just hypothesis : — 
 " The theory which we have adopted, and the simple 
 construction which we have deduced from it, present 
 this remarkable character, that all the unknown 
 quantities are at once determined by the solution of 
 the problem ; — the velocity of the ordinary and ex- 
 traordinary rays, and their respective planes of polar- 
 ization. Physicists who have studied with attention 
 the laws of nature, will admit that this simplicity 
 and these intimate relations between different parts 
 of the same phenomenon present a great probability in 
 favour of the theory by which they are established." 
 
 The memoir on double refraction was received 
 with much incredulity and partial applause. It was 
 not to be supposed that a theory in opposition to 
 that imagined by Newton, and received with almost 
 general assent for more than a century and a half, 
 would not meet with many opponents ; but in the 
 case of double refraction and polarization it was also 
 essentially coupled with the idea of transverse vibra- 
 tions, whose exact mechanism was admitted on all 
 hands to be extremely obscure. Laplace, now more 
 than seventy years of age, opposed the new opinion 
 to the last. His reason for doing so was eminently 
 characteristic of the great geometer — " it was one to 
 which analysis could not be applied without much 
 difficulty;" to which Fresnel replied, " that it was 
 still harder to believe that the laws of nature were 
 arrested by such obstacles." Poisson, as might have 
 been expected, was equally opposed to the undula- 
 tory doctrine, for he was still less of a physicist than 
 Laplace. His standing argument against it was its 
 inability to explain dispersion. M. Biot, also a keen 
 supporter of Laplace, was still more strongly com- 
 promised to the theory of emission. The inertia of 
 such authorities at the Institute retarded of course 
 the growth of Fresnel's reputation at home, notwith- 
 standing the great weight of his friend Arago's opi- 
 nion. It was in fact in England that the merits of 
 
 Fresnel were first most generally and liberally ac- 
 knowledged; as, singularly enough, Young had re- 
 ceived almost the first expression of sympathy in his 
 optical discoveries from France. In 1825 Fresnel 
 received the distinguished honour of being elected 
 a foreign member of the Boyal Society of London, only 
 two years subsequent to his election into the Insti- 
 tute, and whilst his greatest paper was as yet known 
 only by an abstract. In 1827 he received the Eum- 
 ford medal from the same body. This recognition of 
 his merits was due, as we learn on the authority of 
 Dr Young (who was then Foreign Secretary of the 
 Royal Society) to the influence of Sir John Herschel, 
 at that time and afterwards a zealous supporter of 
 the undulatory theory of light, and by whom it be- 
 came first generally known in England through the 
 medium of his admirable Essay on Light. Dr 
 Young, though present, was silent ; " from being," 
 as he himself tells us, " too much interested in the 
 subject " on account of his personal share in the 
 matter. In announcing this distinction officially to 
 Fresnel (then in the last stage of consumption). 
 Young characteristically observed, " I too should 
 claim some right to participate in the compliment 
 which is tacitly paid to myself in common with you 
 by this adjudication ; but considering that more 
 than a quarter of a century is past since my prin- 
 cipal experiments were made, I can only feel it a 
 sort of anticipation of posthumous fame which I have 
 never particularly coveted."^ 
 
 I have stated in the opening of the section that (496.) 
 Fresnel, who was attached to the Bourbon cause, had I'resnei'a 
 retired to Normandy near the close of Napoleon's jfgj,j"j,°jg 
 career. On the re-establishment of the monarchy in iHumina- 
 1815 he was recalled from his retreat and appointed t'O"- 
 to an office in the departments connected with his pro- 
 fession as an engineer ; but in 1817 he was brought 
 to Paris with the express view of giving him more 
 facility in his researches. In 1819 he was placed 
 on the Commission for the Management of the 
 Lighthouses of France (of which he afterwards be- 
 came Secretary), and he entered with ardour on the 
 application of his favourite science of optics to the 
 duties of his profession and the benefit of man- 
 kind. 
 
 The use of lenses in place of reflectors for prevent- (*97.) 
 ing the indefinite dispersion of the light employed, 
 and the efiectual concentration of it in the direction 
 where it will be most useful, was not altogether new. 
 The construction of immense lenses of glass of no 
 great thickness, formed by grinding out a series of 
 concentric refracting surfaces having a common focus, 
 had also been proposed by Buftbn, and the idea of 
 constructing these rings or Sahdlons separately and 
 then uniting them had been suggested by Condorcet 
 in his Moge of Buffbn, as well as at a later period 
 
 2 Peacock's Life of Young, p. 401. 
 
Chap. V., § 4.] 
 
 OPTICS. — ARAGO. 
 
 109 
 
 by Sir D. Brewster. These proposals were all alike 
 unknown to Fresnel, who had the grand merit, in a 
 case of this kind, first, of carrying his happy idea 
 into effectual execution, and secondly, of giving it a 
 wonderful extension by the invention of a multitude 
 of other forms of refracting and totally reflecting 
 apparatus, till then unimagined as well as unexe- 
 cuted. ^ In 1823 the lighthouse of Corduan, at the 
 mouth of the Garonne, was furnished with the new 
 lenticular system, which was very skilfully executed 
 by Soleil of Paris. The illumination was provided 
 by means of a beautiful and powerful lamp with se- 
 veral concentric wicks, the joint invention of Fresnel 
 and Arago, which gave twenty-five times the light 
 of the best Argand then in u^e. The system was 
 found to work so well that it was speedily extended 
 in France, then to Holland, and in the third place to 
 Scotland, principally through the energy of the late 
 Robert Stevenson and the present Mr Alan Steven- 
 son, his son, to the latter of whom we owe the best 
 and most compendious treatise on the subject of 
 lighthouses,^ as well as the noblest exemplification 
 of it in the Skerryvore Lighthouse, erected by him 
 in 1843. The same small work contains the details 
 of Fresnel's admirably ingenious applications of the 
 principle of refraction to the distribution of light 
 under almost every circumstance, which were not, 
 however, published by their inventor. 
 (498.) In 1824, consequent upon his exertions as exa- 
 
 His prema- j^^^^j. a,t the Polytechnic School, Fresnel had the 
 ■ first seizure of the malady which brought him to the 
 grave at the premature age of 39, on the 14th July 
 1827. Eight days previously to his death he had 
 received at the hands of Arago the Rumford medal 
 before referred to, which his distinguished friend 
 
 Malus had obtained under like melancholy circum- 
 stances 16 years before. 
 
 From what has been stated it will appear that C*^^-) 
 Fresnel eminently possessed the qualities requisite ^^ p^^^^^ 
 for original investigation. So finely balanced a com- 
 bination of mathematical skill and attainment with 
 profound inductive sagacity has rarely been wit- 
 nessed. Had Young not happened to precede him 
 there can be no question but that he would have made 
 the undulatory theory entirely his own. Fresnel was 
 superior to Young in the talent for devising and 
 executing critical experiments, in which indeed he 
 showed a degree of skill equally rare and admirable. 
 It is hoped that his surviving brother, M. Leonor Fres- 
 nel, who is well qualified for the task, will collect his 
 scattered papers and edit them, with a suitable bio- 
 graphy. The Sloge of Fresnel, written bythe man most 
 competent to render him justice — Arago — remained 
 more than twenty years among the unedited papers 
 of that philosopher, and has only appeared since his 
 death in 1853. The cause of this suppression was 
 one of those partly political and partly personal dis- 
 putes which seem almost inseparable from the pro- 
 ceedings of the Institute. The Sloge was announced 
 to be read just two days before the Revolution of 
 1830 burst forth ; Arago could not persuade him- 
 self at such a moment to discuss the merits of the 
 Theory of Double Refraction without committing 
 himself also on the politics of the day. Disputes arose, 
 friendships cooled, and the unlucky work was re- 
 turned to the author's desk. Hence no biography of 
 Fresnel appears in the publications of the Institute, 
 but his reputation will be treasured in France and 
 elsewhere, when the more conspicuous laurels of many 
 of his compeers are withered and half-forgotten. 
 
 § 4. Arago. ^ — Short Account of Ms Scientific Career — He discovers the Colours of Polarized 
 Light — Laws and Theory of Depolarization ; M. Biot ; Young ; Fresnel. — Non-interference 
 of oppositely Polarized Rays — Rotatory Action of Quartz. — M. Foucault's Experiment on 
 the Velocity of Light. 
 
 (500.) 
 Arago : — 
 
 (501.) 
 his early 
 Ufe; 
 
 Dominique Feanjois Jean Akago, one of the most 
 generally known of the philosophers of the half cen- 
 tury just elapsed, though the author of a large num- 
 ber of miscellaneous writings which since his death 
 have been edited in a collected form, has not left an 
 amount of positive contribution to any one of the 
 sciences at all in proportion to the reputation for 
 ability which he very justly enjoyed. 
 
 He was born at Estagel near Perpignan, on the 
 26th February 178P, and the ardent temperament of 
 a native of the south was one of his chief character- 
 
 istics. From a fragment of his early history which 
 he left behind him, it appears that he educated him- 
 self almost without assistance, and that when he 
 was admitted to the Polytechnic School in 1803 (con- 
 sequently at the age of 17), he was intimately 
 acquainted with the chief writings of Lagrange, 
 had studied the MSoanique CMeste, and had conse- 
 quently in his possession far more mathematical 
 knowledge than would have been required of him on 
 leaving that celebrated institution. From the Poly- 
 technic School he passed into the position of Secre- 
 
 1 One of Fresnel's lenses was used in 1821 for the geodetic operations connecting France and England, and the light was ob- 
 served at a distance of fifteen marine leagues one hour after sunset. 
 
 2 Eudimentary Treatise on J/ighthouses, by Alan Stevenson. Weale, 1850. See also the Account of the Skerryvore Lighthouie, 
 with numerous plates, in 4to, 1848. 
 
 2 I may perhaps be thought to give Arago too prominent a place in the history of Optics. If so, it has arisen in part from 
 
110 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 tary to the Paris Observatory. He pursued with M. 
 Biot experiments on the refraction of the gases, and 
 in 1806 the two young philosophers were despatched 
 to the south of France and to Spain to continue the 
 triangulation interrupted by the death of Mechain.^ 
 Geodetical The next three years were spent by Arago in a series 
 obserya- pf voluntary and involuntary journeys, perils by land 
 ^"""^ ' and sea, from robbers, and from the Spanish govern- 
 ment and populace, such as have been rarely equalled, 
 — perhaps neverin the pursuit of science. The decla- 
 ration of war against France rendered his stay either 
 in Valentia or in the Balearic Isles impossible, and 
 he was conveyed in disguise from Majorca to Algiers, 
 whence he twice essayed to reach Marseilles, but 
 was once driven back to Africa by a storm, once 
 made prisoner by a Spanish corsair. After great 
 suffering, he at length reached France in July 1809, 
 carrying with him the precious record of his geodeti- 
 cal operations. From this time his promotion was 
 assured, and his life became tranquil and inactive, al- 
 though the deep attachment which he formed with 
 Baron Humboldt immediately on his return to France 
 would probably have induced him to accompany that 
 enterprising traveller to Central Asia, had that jour- 
 ney ever been accomplished. At the early age of 23 
 Arago attained the position of Member of the Insti- 
 tute, and was again attached to the Paris Observa- 
 tory, of which at a later period he became director. 
 He took a very active share in the proceedings of the 
 Academy of Sciences, and became one of its secre- 
 taries in 1830. 
 (502.) From the period of his election to the Institute, 
 
 Arago'8 Arago's career was destitute of stirring incidents, but 
 career "^°* was, from first to last, devoted chiefly to science. It is 
 ' certain, however, that he was deficient in that power 
 of continuous application, to which alone great dis- 
 coveries are commonly due. Full of ingenious, origi- 
 nal, and even profound conceptions, he shunned the 
 labour of realizing them. His appointment to the 
 charge of the Observatory of Paris was perhaps unfor- 
 tunate. Well versed in the theory of astronomy, the 
 minute drudgery of observation and the control of 
 numerous assistants, was altogether uncongenial to 
 him. It was a duty imperfectly fulfilled, to say the 
 least, for 40 years : and it is needless to add how much 
 the consciousness of habitual neglect of a duty deadens 
 the faculty of useful application to anything else. 
 /g03 ■) If the science of astronomy then owes little to 
 
 Arago, beyond the part which he took in geodetical 
 
 observation, what are we to consider his chief claims His optical 
 to a place in this history ? I have no hesitation in la*>oui'8 of 
 saying that they are to be found m connection with j^^j" ^g^J^™^ 
 the discoveries and labours of his attached friends, 
 Malus and Fresnel, and therefore we group them to- 
 gether in this chapter. Arago not only himself made 
 some important optical discoveries in 1811 and the 
 following years, but he was instrumental, as we have 
 seen, in a very important degree, in calling forth the 
 genius of Fresnel, and in obtaining a public recogni- 
 tion of the labours of Young ; a service not the less 
 worthy of note because of its eminently disinterested 
 character. The undulatory theory of light, one of 
 the greatest triumphs, if not the greatest, of our age, 
 stands where it does in no slight degree through 
 the instrumentality of Arago. 
 
 One of his most considerable discoveries was that (504.) 
 of the colours which crystallized bodies develop in Colours of 
 white light polarized before incidence on the crystal, ^J^^^^^^^ 
 and afterwards transmitted through a rhomb of calc- polarized 
 spar. These colours, by their order, the singular man- light, 
 ner of their occurrence and disappearance, and in cer- 
 tain cases by their extraordinary and beautiful forms, 
 offered a problem at once the most attractive, the 
 most definitely marked, and the most seemingly in- 
 explicable which had been met with in optics for much 
 more than a century. They exemplified a new mode 
 of analyzing light, evidently connected with the mole- 
 cular forces concerned in crystallization; and for their 
 display it was necessary that light should be in that 
 peculiar and yet mysterious state called polarized. 
 
 The substances he employed were principally sele- (505.) 
 nite, rock-crystal, and mica. When plates of the^l'^'o™™* 
 first and last of these minerals, formed by their natu- j^ation. 
 ral cleavage, are placed in a beam of polarized light, 
 and the light transmitted by them is then analyzed, 
 by being passed through a doubly-refracting prism or 
 thrown on a screen after reflection at the critical angle 
 from glass, splendid colours are the result. These 
 coloursvarywith the thickness of the plate, with its in- 
 clination to theincidentlight, and, whatis most remark- 
 able, they vary in intensity by merely turning the plate 
 ofselenite round in its own plane. When only this last 
 motion is made, there are two positions of the plate 
 where no colour results, the light passing through un- 
 changed; and these positions are at right angles to one 
 another. At all intermediate angles colours appear, the 
 light is said to be depolarized, and this depolarization 
 is most complete when the plate is moved 45" from 
 
 the difficulties inseparable from the biographical system which I have adopted. My intention was to have thrown together the 
 labours of Malus, Fresnel, and Arago into one section. But having written the different portions separately, there seemed so 
 much precision and facility of explanation to be derived from treating of them, consecutively, that I sacrificed, in some degree, 
 the biographical principle to that of systematic classification ; placing under the name of Malus what referred to the empirical 
 laws of double refraction; under thai, of Fremel the doctrine of transverse vibration (though mainly due to Young); and under 
 Arago the discoveries of Young, Fresnel, Biot, and others, relative to the great subject of chromatic polarization, to which ho 
 gave the first impulse. The establishment of the undulatory theory, principally due to Young, Fresnel, and Arago, I have con- 
 sidered as deserving of a more detailed and systematic treatment than almost any other of the numerous discoveries of which I 
 have to speak in this Dissertation. I may add, that the biography of Arago not appearing in its alphabetical place in the En- 
 cyclopaedia, M. Arago being still alive at the date of the publication of that part of the work, it has been incumbent upon me to 
 enter into more details than I should otherwise have done. I See Chapter III., Art. (166) of this Dissertation. 
 
Chap. V., § 4.] 
 
 OPTICS. — AEAGO. 
 
 Ill 
 
 (506.) 
 Observa- 
 tion of 
 Malus, 
 Arago, Sir 
 D. Brew- 
 ster, and 
 M. Biot, 
 
 attributed 
 to inter- 
 ference by 
 Young. 
 
 Case of 
 rays oppo- 
 sitely po- 
 larized — 
 Arago and 
 Fresnel. 
 
 (507.) 
 Depolari- 
 zation ex- 
 plained on 
 the undu- 
 latory 
 theory. 
 
 the positions in which the light passed through un- 
 changed. 
 
 The theory of this simple yet admirable experi- 
 ment is one of the happiest examples of Fresnel's 
 mechanical explanation of double refraction. But 
 it was not attained by a single step, nor effected 
 by a single hand. Malus had observed the fact of 
 depolarization, and the existence of perpendicular 
 neutral axes in the crystalline plate. Arago added 
 to this the knowledge of the phenomena of colour, 
 which Sir David Brewster also observed indepen- 
 dently somewhat later. He also invented a par- 
 ticular theory to explain them by what he termed 
 moveable 'polarization. But it was not a success- 
 ful effort. M. Biot assiduously studied the empi- 
 rical laws of these periodic colours, and traced 
 their dependence on the thickness of the interposed 
 plate, according to a law similar to that of Newton's 
 rings. Young made an important step farther. He 
 attributed the colour to the interference of the ordi- 
 nary and extraordinary rays into which the incident 
 light was divided on entering the crystalline plate ; 
 and he showed by accurate calculation that the retar- 
 dation of the slower-moving of the two rays during 
 their passage through the plate, did in fact produce 
 the difference of phase necessary for developing the 
 tints observed by their reunion on leaving the plate, 
 according to the usual laws of interference ; and he 
 showed that this theory coincided with M. Biot's 
 rules.^ But even this was not enough to explain the 
 facts. It was not clear why the colours due to doubly- 
 refracting plates should not be seen without reaching 
 the eye through an analyzer, or calc-spar prism. To 
 Arago and Fresnel jointly we owe the important 
 reply to this difficulty, which in fact forced upon the 
 latter the idea of transversal vibrations. Their joint 
 experiments (mentioned in the last section, art. 488), 
 had shown that oppositely polarized rays cannot in- 
 terfere unless they have, first, a common origin and a 
 common plane of polarization ; and, secondly, unless 
 they be reduced to a common plane of polarization 
 (that is, analyzed) before falling on the eye or the 
 screen : so that the theory of the colours of crystal- 
 lized plates is, briefly, as follows : — 
 
 Polarized light is represented by transverse vibra- 
 tions of ether, the particles moving all in one plane. 
 The crystallized plate has, we will suppose (in order 
 to take the simplest case) one axis of double refrac- 
 tion, and the direction of that axis is in the plane of 
 the lamina. When the vibrations of the light falling 
 on the crystallized plate are either wholly parallel or 
 wholly perpendicular to this axis, the light is trans- 
 mitted without alteration, either as an extraordinary 
 or as an ordinary ray, and it is then reflected or not 
 by the analyser, as would have been the case had it 
 not been transmitted at all through the crystal of 
 
 selenite. But if the axis of the crystal be inclined, 
 suppose 45°, to the plane of vibration of the incident 
 polarized ray, the vibration is mechanically resolved 
 into two, which are oppositely polarized. After tra- 
 versing the thickness of the crystallized plate with 
 the different velocities due to the motion of the ordi- 
 nary and extraordinary rays, they are reunited at 
 emergence, hut in altered relative phases, so that by 
 their union they form a beam no longer polarized 
 (unless by an exception) in the same plane as at first, 
 nor indeed plane-polarized at all, but most likely per- 
 forming elliptical or circular vibrations, which, again, 
 falling on the analyzer, are reflected or transmitted, 
 or partly both, in a manner quite different fi-om what 
 would have happened to the light unchanged by crys- 
 talline transmission. 
 
 White light becomes coloured because the state of 
 polarization of the emergent ray depends on the differ- 
 ence of length of path for the two rays which under- 
 went crystalline separation within the plate, and also 
 on the length of a wave of light (for this determines the 
 phase of polarization at emergence). But the wave 
 of light varies in length for each colour, consequently 
 every colour has its maximum under different circum- 
 stances, and if the incident light be white, the light 
 falling after reflection on a screen will present mixed 
 tints similar to those of Newton's rings. 
 
 This extraordinary property of a crystallized plate 
 (which, in common light, appears equally transparent 
 and homogeneous in every direction), of modifying 
 light, or dyeing it with the most gorgeous colours, 
 when the plate is merely turned in its own plane, is 
 one of the nicest tests of the polarization of the light, 
 and has been used to detect the analogous polariza- 
 tion of radiant heat, and the concomitant phenome- 
 non of double refraction, which, except in the case 
 of the heat accompanying the solar rays, has not 
 yet been independently recognized.^ 
 
 Arago applied his discovery to the construc- 
 tion of a polariscope, for estimating the feeblest 
 amount of polarization ; and he used this instru- 
 ment for some very interesting experiments on the 
 polarization of the light of the sky (which is sun- 
 light polarized by reflection from the atmosphere), 
 and on that of different incandescent and reflecting 
 surfaces. He also found that the moon and the 
 tails of comets send light to the eye which is slightly 
 polarized, thus betraying its borrowed origin. But 
 that of the sun, being absolutely neutral, is only 
 comparable (according to Arago) to the light arising 
 from incandescent vapours, thus distinguishing the 
 sun from a solid or liquid globe. 
 
 We cannot do more than allude to Arago's other 
 optical papers and experiments. He was, probably, 
 the only Frenchman of his time who was well ac- 
 quainted with Young's discoveries. The explana- 
 
 (508.) 
 Cause of 
 the colour. 
 
 (509.) 
 Similar 
 pheno- 
 menon in 
 radiant 
 heat. 
 
 (510.) 
 Arago's po- 
 lariscope. 
 
 (511,) 
 Experi- 
 ments on 
 Newton"s 
 rings and 
 
 ^ Quarterly Review, vol. xi. ; if'scell. Works, vol. i,, p. 266. 
 2 See Researches on Heat by the present writer. Edinburgh Transactions, vols, xiii, and xiv. 
 
112 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 on the ro- tion by the doctrine of interference of the colours 
 tatory ac- of Newton's rings received an important confir- 
 ''uartz mation from an experiment of Arago's, which proved 
 them to arise from the mixture of the pencils 
 of light reflected at the two neighbouring sur- 
 faces. He pressed a lens of glass against a plate of 
 metal, in which case the central spot is white or 
 black when light polarized perpendicularly to the 
 plane of incidence is reflected at an angle greater or 
 less than the polarizing angle for glass ; and the rings 
 vanish altogether at the polarizing angle ; — results 
 ■which have been found conformable to the undulatory 
 theory.^ He also discovered the peculiarity of the 
 rays transmitted along the axis of a crystal of quartz. 
 These depolarize light, or produce colours similar to 
 those of crystallized plates, varying according to a 
 well-marked law with the thickness of the plate. 
 The most singular fact is, that by turning round the 
 analyzing plate, no position of neutrality is found, 
 but a series of colours similar to those of Newton's 
 scale succeed one another. Arago showed that this 
 effect is due to a rotatory motion of the plane of polar- 
 ization within the crystal. The rotation is greater 
 for the violet than the red ray ; this was shown by 
 M. Biot, who also discovered that in some specimens 
 the rotation takes place from right to left, in others 
 from left to right — a peculiarity connected with cer- 
 tain crystallographic modifications, as was first 
 shown by Sir John Herschel. 
 ('512.') MM. Seebeck and Biot discovered an analogous 
 
 Rotation of property in oil of turpentine, and in various saccharine 
 the plane fluids^ an observation which, in many cases, allows the 
 tion°in"^^' Substitution of an instantaneous optical, for an operose 
 fluids. chemical test. Fresnel has shown that the phenomena 
 of quartz may be represented on the supposition that 
 the rays traversing the axis consist of two rays circu- 
 larly polarized in opposite directions, and travelling 
 with different velocities ; and Mr Airy succeeded in 
 calculating, by the aid of this fundamental hypothesis,^ 
 a number of most beautiful and complicated pheno- 
 mena, such, for example, as those which occur 
 when plates of right and left handed quartz are 
 superposed. MaccuUagh has shown how the ge- 
 neration of elliptical or circular vibrations may be 
 deduced from the general equations of motion, but he 
 has not invented a mechanical theory to explain 
 them. This is a point of the very highest interest, 
 inasmuch as Dr Faraday has succeeded, for the first 
 time, in inducing artificially in a substance the power 
 of rotating the plane of polarization by the presen- 
 tation of it to the poles of a most powerful magnet.^ 
 (513 ) Arago's experiments on the non-interference of 
 
 Retarda- vays of light oppositely polarized, being undertaken 
 tionoflightjji conjunction with Fresnel, have been already re- 
 
 ferred to, arts. 488 and 506 ; but to Arago alone is in denss 
 due the ingenious idea of interposing a thin slip of ™ediB 
 mica or blown glass in the path of one of the inter- ^'"Jg,,, ^ 
 fering pencils, and observing the displacement of the 
 interference-bands, which is always towards the side 
 of the interposed slip, showing that the movement" 
 of the wave has been slower within the denser me- 
 dium. 
 
 Arago continued to attach great importance to the (514.) 
 obtaining of a still more direct proof of this fact, which Experi- 
 he considered as a crucial one between the rival hypo- ™^"* *° ^^^ 
 theses of Newton and Huygens. In his last years he ty^j^^^po". 
 had the satisfaction of witnessing the accomplishment cault. 
 of it, with the result he anticipated, and by a method 
 which he had himself indicated. In 1838, he had al- 
 ready indicated the application of Mr Wheatstone's 
 beautiful invention of the revolving mirror,* as a means 
 of measuring intervals of timeincredibly short, in order 
 to compare the velocity of light in air, and in a corre- 
 sponding length ofwater. He even caused an apparatus 
 to be partly prepared, but we have seen that Arago's 
 forte was rather in suggesting than in completing re- 
 searches. After his increasing failure of sight ren- 
 dered it physically impossible that he should ever 
 realize his own idea, it was skilfully adopted by M. 
 Foucault (the author of the admirable experiment 
 with the pendulum, demonstrating the earth's mo- 
 tion'), who, by an ingenious combination of fixed and 
 revolving mirrors, succeeded in 1 850 in demonstrating 
 the retardation of light in a tube of water only 6^ 
 feet long, and with a velocity of rotation of the move- 
 able mirror not exceeding 200 turns in a second (a ra- 
 pidity four times less than had already been obtained 
 by Mr Wheatstone). The rotation was produced 
 by means of the Sirene of M. Cagniard de la Tour, 
 acting by steam. The velocity was thus raised to 
 1000 revolutions. It was afterwards, however, carried 
 by MM. Fizeau and Breguet to 2000 revolutions. It 
 will be understood, from the account of the method, 
 as applied to the measurement of the velocity of elec- 
 tricity, in another chapter, that the retardation is 
 shown by the displacement of the image of a minute 
 object seen through the water, relatively to the image 
 of the same object seen in air. If light moves faster 
 in water (as Newton imagined), the displacement of 
 the water-image will be (let us say) to the right ; but 
 if slower (as Huygens and Young believed), it will 
 be to the left. The calculated displacement, with 
 800 revolutions in a second, was "004 inch on the 
 first supposition, and '003 in the opposite direction 
 in the second, quantities easily visible with a high 
 magnifying power. The result, as has been stated, 
 confirmed Arago's original experiment of 1815 on 
 the displacement of the interference fringes. 
 
 1 Sir W. Herschel first formed Newton's rings between glass and metal. Arago's experiment was reproduced (unknowingly) 
 by Mr Airy in 1831, who first explained it fully in the undulatory sense. Comb. Trans., vol. iii. 
 
 ^ With this addition, that rays inclined to the axis are elliptically polarized, and that with a greater ellipticity as the inclina- 
 tion increases. 
 
 ^ See )ihe chapter on Electricity, § 5. 
 
 * See Electricity, § 6. 
 
 ^ See the chapter on Astronomy, Art. (258). 
 
Chap. V., § 5.] 
 
 OPTICS. — SIR DAVID BREWSTER. 
 
 113 
 
 (515.) To complete our biographical notice, we will here 
 
 decfro- J"®* allude to M. Arago's principal researches un- 
 magnetic connected with optics. One was on the magneti- 
 observa- zation of iron filings, and the formation of a tempo- 
 tions. rary magnet, by means of a helical conductor of elec- 
 
 tricity ;' the other was the important observation of 
 the seeming magnetism of copper, and other non-mag- 
 netic metals, when put in rapid rotation near a per- 
 manent magnet. Neither of these happy experiments 
 , was carried out by their author. The former was left 
 in the hands of Ampere, Sturgeon, and Henry ; the 
 latter was only rightly understood and valued when it 
 was engrafted by Mr Faraday on his splendid series 
 of researches on Magneto-Electric Induction." 
 (516.) Arago is fairly entitled to be regarded as having 
 
 Essays proved the long-suspected connection between the 
 olcy. aurora borealis and the freely suspended magnet ; and 
 this in the face of urgent contestation.^ His contri- 
 butions to Meteorology (founded rather upon the ob- 
 servations of others than upon his own) were of con- 
 siderable importance, and several of -his popular pa- 
 pers, appended to the smaller Almanac (^Annuaire) 
 of the Board of Longitude, contain a great deal of 
 well-digested and curious information. 
 (517.) -A-S Secretary of the Academy of Sciences in the 
 
 Mathematical Department (in which office he sue- Arago as 
 ceeded Fourier, in 1830), the duty devolved on him ^^"^''^^2^ °' 
 of writing the biographies of eminent deceased mem- ^g^y ^f 
 bers of the Academy. He bestowed extraordinary Sciences, 
 pains on these compositions, and strove to render 
 them popular without sacrificing their scientific cha- 
 racter. In this difficult attempt he was not always 
 successful. Abrupt transitions, piquant anecdotes, 
 paradoxical arguments, and political allusions, appear, 
 at least to the English reader, to be unacademical 
 adjuncts to the history of contemporary discovery. 
 The special pleader is too often visible, and even the 
 occasional sacrifices of the strong spirit of nation- 
 ality by which he was commonly actuated, to some 
 chivalrous adjustment of the rights of discovery, 
 do not always carry conviction to the mind of the 
 reader. The Eloge of Watt, probably the most po- 
 pular, appears to us far from being the best of these 
 biographies. Those of Sir W. Herschel and of Dr 
 Young are ably executed, and display much research 
 and candour. 
 
 After having been for three years almost with- (518.) 
 drawn from science by lingering disease, and nearly His death, 
 complete blindness, Arago expired at the Observatory 
 of Paris, on the 2d October 1853, aged 67.* 
 
 § 5. Sir David Brewster — Progress of Experimental Optics — Laws of Polarization — Double 
 Refraction produced hy Heat and Compression — Discovery of Biaxal Crystals — Laws of Me- 
 tallic Reflection — Absorption of Light ; and Lines of the Solar Spectrum ; Fraunhofer. — 
 Seebeck ; M. BiOT. 
 
 (519.) ^6 have pleasure in ranking amongst the fore- 
 
 Sir David most promoters of the science of optics in its sur- 
 Brewster. prising revival in the earlier part of this century, 
 a philosopher who still lives amongst us and pur- 
 sues with ardour the investigations of his youth. 
 (520.) Si"^ David Brewster was born at Jedburgh, in 
 
 His early Scotland, on the 11th December 1781. Ho was 
 studies. educated for the Scottish Church, and having en- 
 tered the University of Edinburgh at a very early 
 age, pursued his studies under Robison, Playfair, 
 and Stewart, and formed the friendship of those 
 eminent men. Amongst fellow- students of no 
 common distinction who at that time frequented the 
 college lectures, and of whom not a few were destined 
 to signalize themselves in literature, science, and the 
 career of politics, he formed the particular acquaint- 
 ance of Mr, now Lord Brougham, and through him 
 was led to study the inflection of light, and to repeat 
 Newton's experiments. This was in 1799 ; nor did 
 he afterwards lose sight of a science which he was 
 so signally to improve. The distraction of other 
 occupations, the calls of his profession, and his 
 indifferent health prevented, however, any very 
 constant application to optics : and the part of 
 
 the subject he then principally studied was rather 
 connected with the use and theory of instruments than 
 with physical optics in the sense in which we have 
 explained it. This is evident from his first separate 
 publication in 1813, " on new Philosophical Instru- 
 ments," which, though containing many ingenious 
 and valuable suggestions, fell short of the importance 
 of his subsequent publications. 
 
 Sir David Brewster's genius was first called forth (521.) 
 by the announcement of Malus's great discovery Directs his 
 in 1808 of the polarization of light by reflection. *"'°*!°i" *" 
 But for the unfortunate political relations of France optics. 
 and England at the time, which prevented, to a 
 degree which now appears almost incredible, the 
 transmission of even the most interesting scientific 
 facts from one country to the other, our country- 
 men would have borne a larger share in the dis- 
 coveries which immediately followed ; and it would- 
 have been an easier task to apportion with his- 
 torical accuracy what was due to each. As the 
 French philosophers remained long in ignorance of 
 the discoveries -of Davy, and were anticipated in 
 every important step in voltaic science, so Mains and 
 Arago pursued and published researches and bril- 
 
 1 See Electricity, § 4. " Electricity, § 5. 
 
 3 No doubt the fact had been already distinctly noticed by Hjorter and Celsius at Upsala in 17il. See Hansteen, Mag. 
 netismus der Erde. ' ^ _ . 
 
 * The article Polarization of Light ia this Encydopcedia, the production of Arago, contains an excellent review of many 
 of the topics of this Section. 
 
114 
 
 MATHEMATICAL AND PHYSICAL SCIENCE, 
 
 [Diss. VI. 
 
 (522.) 
 Treatise on 
 new philo- 
 sophical 
 instru- 
 ments. 
 
 (523.) 
 His re- 
 searches on 
 optical sub- 
 jects. ' 
 
 (524.) 
 Enumera- 
 of the most 
 important. 
 
 (525.) 
 Tiaw of po- 
 larization 
 by reflec- 
 tion. 
 
 liant discoveries whicli, literally for years, remained 
 unknown in England to those most interested and 
 solicitous to learn them. Thus Sir D. Brewster 
 learned first in February 1814 that Malus had in 
 March 1811 published the discovery of the polar- 
 ization of light hy refraction, which he also had made ; 
 whilst Arago's experiments on coloured polarization 
 were likewise unknown to him through the same 
 want of international communication. 
 
 The work on Philosophical Instruments, men- 
 tioned above, contains, besides what its name more 
 particularly imports, numerous observations on re- 
 fractive and dispersive powers, including the disco- 
 very of substances more refractive than diamond, 
 and less so than water. It also describes the pro- 
 perty of some agates to transmit light polarized in 
 only one plane. The imperfect polarization of light 
 by metals and by a serene sky had been anticipated 
 by Malus and A.rago. 
 
 From this time (1813) Sir David Brewster became 
 a regular contributor to the London Philosophical 
 Transactions, which, as well as those of Edinburgh, 
 contain a series of elaborate experimental investi- 
 gations due to him, which have hardly been sur- 
 passed. It is difficult to overrate the importance of 
 these researches, whether for the intrinsic interest 
 of the phenomena they reveal, or for the significance 
 of the empirical laws by which their author, vyith 
 a rare sagacity, succeeded in classifying facts, and 
 afforded a sure basis for farther generalization. The 
 number and variety of these researches is so ex- 
 ceedingly great, and in many cases so impossible 
 to explain without entering into minute detail, that 
 I shall, in accordance with the plan of this essay, 
 merely indicate some of the most generally impor- 
 tant by arranging them in groups. Such are — 
 
 I. The laws of polarization by reflection and re- 
 fraction, and other quantitative laws of phenomena. 
 
 II. The discovery of the polarizing structure in- 
 duced by heat and pressure. 
 
 III. The discovery of crystals with two axes of 
 double refraction, and many of the laws of their phe- 
 nomena, including the connection of optical structure 
 and crystalline forms. 
 
 IV. The laws of metallic reflection. 
 
 V. Experiments on the absorption of light. 
 
 I. Malus had failed to discover a connection be- 
 tween the angle at which light is completely po- 
 larized by reflection, and the other known optical 
 properties of bodies.' In 1814, Sir D. Brewster 
 discovered the beautiful and simple law, " that the 
 index of refraction is equal to the tangent of the 
 angle of polarization." He had suspected it much 
 
 sooner, but he had been baffled by the irregular re- 
 sults obtained by reflection from glass, whose sur- 
 face he found to undergo an almost imperceptible 
 chemical change. He further observed that it is 
 only in bodies of low refractive power that the po- 
 larization is sensibly complete, a result of great im- 
 portance, which has been too much overlooked until 
 the recent and valuable paper of Jamin on the same 
 subject. He deduced as a corollary, that at the 
 maximum polarizing angle the incident and refracted 
 rays are at right angles to one another, and also 
 Malus's experimental result that the rays reflected 
 from the first and second surfaces of plates are 
 simultaneously polarized. He further discovered the 
 fact that light may be completely polarized (as to 
 sense) by a sufficient number of reflections at any 
 angle, and drew the conclusion that the whole light 
 undergoes some change at each reflection, in opposi- 
 tion to the view of Malus, who maintained that, 
 except at the polarizing angle, a portion of the light 
 is polarized, and the rest is unchanged. 
 
 Sir David Brewster independently observed the po- (526.) 
 larization of light transmitted obliquely throughglass, Imperfect 
 and he calculated the number of plates necessary to ygn"^*" 
 polarize it with sensible completeness. All these 
 researches he resumed some years after (PAiZ. Trans. 
 1830), endeavouring to give a photometric estimate 
 of the efiects of reflection and refraction under all 
 circumstances. The results as regards partially po- 
 larized light may still be considered as subject to 
 doubt. His skill in obtaining a mathematical repre- 
 sentation of the phenomena was again displayed in a 
 number of laws connecting the experimental results. ^ 
 
 II. Malus had observed that a vast number of (527.) 
 sul;)stances depolarized light more or less completely ; Polarizing 
 and Arago found feeble traces of chromatic polar- ?'''1J'''"''^^ 
 ization in some specimens of glass. But the more alasa ; 
 definite characters of the beautiful phenomena of 
 glass not perfectly annealed (which proved to be of 
 unexpected importance) were noticed, independently, 
 by Sir D. Brewster and Dr Seebeck of Nurnberg. 
 The latter had priority in publication,* but the former 
 correctly ref^red them to their immediate cause — 
 the constraint produced by rapid cooling. Sir D. 
 Brewster noticed that the unannealed glass which 
 forms what are called Prince Rupert's Drops, had a 
 remarkable power of depolarization; and he also 
 observed subsequently that the plates of glass be- 
 tween which he was in the habit of squeezing heated 
 wax and resins, for the purpose of optical examina- 
 tion, transiently communicated tints to polarized 
 light. These observations, duly developed, proved 
 on the one hand that glass (and generally refracting 
 
 1 Thus he found that the eflfect of refraction on the plane of polarization of the incident light may be expressed by this 
 simple formula, — cotan a'= cotan a cos (i — i'), where a and o/are the azimuths of the planes of polarization of the incident 
 and refracted rays measured from the plane of reflection, and i and i' the angles of incidence and refraction. This result, ad- 
 mirably verified by experiment, is also conformable to Fresnel's theory. 
 
 " In Schweigger's Journal for 1813, vol. vii. I have not been able to find in this paper (which contains the first account of 
 the beautiful symmetric coloured figures displayed in cubes and cylinders of glass) the smallest trace of the true cause af the 
 phenomenon, viz., the sudden or partial cooling of the glass. 
 
Chap. V., § 5.] 
 
 OPTICS. — SIR DAVID BREWSTER. 
 
 115 
 
 (528.) 
 and in 
 bodies sah 
 jected to 
 pressure. 
 
 (529.) 
 Discovery 
 of biaxal 
 crystals. 
 
 solids not usually possessed of any polarizing action) 
 acquired such properties by being suddenly and un- 
 equally cooled; and on the other, that such sub- 
 stances undergoing partial changes of temperature, 
 possess the same property. These phenomena are 
 exceedingly beautiful, and easily displayed. It is 
 sufficient to place a rectangular piece of glass, some- 
 what thick, with one of its longer edges in contact 
 with a hot iron, and placing it between a polarizing 
 and analyzing plate, to incline the heated edge 45° 
 to the plane of polarization. Bands of light and 
 shade are seen to traverse the glass parallel to the 
 same edge, and simultaneously appear also on the 
 side farthest from the heated metal. They pass gra- 
 dually into rich coloured tints diffused with geometric 
 regularity. In the case of cubes or cylinders of glass, 
 suddenly, and therefore unequally cooled, the pheno- 
 mena are permanent, and the colours splendid, being 
 arranged in patterns which may be made to resemble 
 those of natural crystals. 
 
 Sir David Brewster at first ascribed these effects 
 to the direct effect of the heat in the glass upon 
 light, and compared its simultaneous influence over 
 a whole plate to a polar influence. Another curious 
 discovery, also due to him, leads to the simpler con- 
 clusion, that in every case the development of a 
 polarizing structure is due to the varying tension 
 (transient or permanent) into which the particles of 
 the glass are thrown by local expansion or by irre- 
 gular cooling. This discovery was, that similar 
 effects may be produced in jellies and soft transparent 
 substances by the effect of pressure, and that even 
 glass itself, when strained in any way by mechanical 
 force, shows depolarizing bands ; and crystals may 
 have their peculiar optical phenomena altered by 
 pressure. Fresnel, not satisfied with inferring that 
 the chromatic display is due to a doubly-refracting 
 structure communicated to the glass, contrived, by 
 an ingenious arrangement of prisms, actually to 
 exhibit the separation of the images under the action 
 of powerful pressure. 
 
 III. Possibly the most remarkable of Sir David 
 Brewster's discoveries, — at all events, that which 
 probably cost him most labour to develope, — was that 
 there are crystals possessing two axes of double re- 
 fraction, and showing many remarkable phenomena, 
 which indicate a connection between optical structure 
 and crystalline form. No one before him suspected 
 the existence of a doubly-refracting structure differ- 
 ing from that so ably investigated by Huygens and 
 Malus in Iceland spar. In 1813 Sir David Brew- 
 ster had discovered coloured rings in topaz when 
 viewed by polarized light. Though intimately con- 
 nected with M. Arago's observation of colours in 
 crystallized plates, these interesting phenomena had 
 
 a still more extraordinary and geometrical character. 
 When a plate of topaz, split by natural cleavage, was 
 presented between the polarizing and analyzing plate 
 (or rhomb of calc-spar), and at the same time 
 inclined in a certain manner, the colours were no 
 longer in broad sheets, but, if viewed closely, they 
 arranged themselves in oval rings of great beauty, 
 presenting orders of mixed colour analogous to those 
 described by Newton when formed between convex 
 glasses, and they were traversed by dark or white 
 brushes as the analyzing plate was held in the 
 dark or bright position. A second such system was 
 observed inclined at an (apparent) angle of 65° in the 
 same plate. 
 
 Dr WoUaston afterwards (1814) discovered a phe- (530.) 
 nomenon equally beautiful in calcareous spar, of P''^""™.""* 
 which Sir D. Brewster had already perceived traces °]^^°^^g^^ 
 in some other crystals. Concentric with the posi- by uniaxal 
 tion of the axis of double refraction (or optic axis), crystals. 
 in a crystal of that mineral cut with two parallel 
 faces perpendicular thereto, a series of perfectly sym- 
 metric and exquisitely coloured rings are seen in po- 
 larized light, having a white or black cross travers- 
 ing them, according to the position of the analyzing 
 plate. This magnificent phenomenon, which (except- 
 ing, of course, the rings of biaxal crystals mentioned 
 above) has perhaps no parallel in optical science, is 
 seen in the most perfect manner possible in an appa- 
 ratus constructed solely of Iceland spar, cemented by 
 Canada balsam. A Nicol's single- image prism -"^ is 
 used to polarize, another to analyze the light, and 
 between them is a plate of calcareous spar properly 
 cut. It is a truly astonishing paradox to see the 
 union of three perfectly transparent and colourless 
 crystals display by their union such an exquisite 
 combination of form and colour. The pole or centre of 
 the rings in calc-spar coinciding with the axis of double 
 refraction, of necessity suggested the idea that topaz, 
 which shows two systems of rings arranged round two 
 poles, must possess two axes of double refraction ; 
 in other words, that there must exist within the 
 crystal two directions (not mere lines), parallel to 
 which a transmitted ray emerges without subdivision 
 into two pencils. 
 
 This probable conjecture was verified by careful (53i.) 
 observation, not only in topaz, but also in a vast Double sys- 
 variety of other crystals which were found by Sir*®™' °S *°" 
 David Brewster much more commonly to possess two ^' °' ^^' 
 than one system of rings. Amongst the earliest ex- 
 amples which he observed were nitre, mica, acetate of 
 lead, and Rochelle salt. Of these the first is exceed- 
 ingly remarkable for the small inclination of the axes 
 (about 5°) which permits both systems of rings to be 
 readily observed at once. It was not, however, for 
 some years (1817) that he reduced these most 
 
 ^ The invention of a most ingenious person, the late Mr William Nicol of Edinburgh. One of the doubly-refracted rays is 
 throvfn completely out of the field by undergoing total reflection at the surface of a film of Canada balsam in contact vrith the 
 
 spar, whilst the other less refrangible ray proceeds quite isolated, and with scarcely any loss of brilliancy, 
 universal application in this branch of Optics. 
 
 It is of almost 
 
116 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 curious phenomena to anything like a law. It was 
 evident almost from the first, that the axes in ques- 
 tion (which he termed axes of no polarization) are 
 only the resuHtants of remoter fundamental actions of 
 the crystalline constitution. For example, these 
 axes vary in position according to the colour of the 
 light used to display them ; their position within the 
 crystal varies (as was shown by Mitscherlich) with 
 the temperature of the body, nor is it obviously 
 related to any of the geometrical lines of crystalliza- 
 Law of the tion. Sir David Brewster succeeded in finding the 
 tints. jg^^ of ^jjg tjjjtg expressed upon the surface of a 
 
 sphere of which the directions of the two axes form 
 diameters. M. Biot expressed the law more ele- 
 gantly by saying, that the tint developed by a biaxal 
 crystal in any ray, is proportional to the product of 
 the sines of the angles which the ray in question 
 makes with the two optic axes. The tints are con- 
 sequently arranged round the two poles of the axes, 
 in a series of curves resembling the figure 8, having 
 each this property, that the pr'oduct of the sines of 
 the angular distances of each point of one curve from 
 the two poles is equal to a constant quantity. Such 
 curves are called lemniscates, and are beautifully 
 seen in nitre, especially when viewed by homoge- 
 neous light. 
 
 (532.) 
 
 A series of researches of the most elaborate 
 
 Eelation of description led Sir David Brewster to this addi- 
 optical cha- ^ional and admirable discovery, viz., that the optical 
 
 TElCtGrS to • •/ ' ' X ^ 
 
 crystalline characters of single refraction, double refraction 
 forms. with one axis, and double refraction with two axes, 
 have reference invariably to the primitive crystalline 
 form of the mineral, and that the complexity of the 
 optical character is as invariably related in degree to 
 the complexity of the crystalline figure. Cubical and 
 regularly octahedral crystals (as rock salt and fluor 
 spar) being possessed of perfect symmetryin three prin- 
 cipal directions, possess also Simple refraction. Crys- 
 tals with one predominant line or axis of symmetry 
 — as rhombohedrons, octahedrons with square bases, 
 right prisms with square or hexagonal bases— have a 
 single axis of double refraction. Such, for instance, are 
 Iceland spar, zircon, ice, heryl. Finally, all crystals 
 unsymmetrical in the three principal directions, in- 
 cluding prisms and octahedrons whose bases are 
 not square, and those which are oblique, have two 
 axes of double refraction. The rarity and minute- 
 ness of many crystals, the difficulty of cutting them, 
 and when cut, of detecting their optic axes, evi- 
 dently made the research one of extreme labour, yet 
 highly remunerative, not only through the discovery 
 of the general principle, but by tlie vast amount of 
 beautiful and varied optic displays witnessed in the 
 course of it. Sir David Brewster was nearly, if not 
 quite, alone in this research, and after a short resis- 
 tance on the part of some mineralogists, his principle 
 of discrimination of primitive forms of crystallization 
 by optical characters has been perfectly established. 
 (633.) ^^- '^^® action of metals on the light which they 
 
 reflect is very peculiar. Malus, who at first believed Laws of 
 that they were incapable of polarizing it in any "^e-™^*^'};" 
 gree, afterwards changed his opinion, and inge- 
 niously suggested that whilst transparent bodies 
 reflect, at the polarizing angle, light polarized only in 
 one plane, metals reflect rays oppositely polarized 
 and then mixed. Sir David Brewster has the merit 
 of having, after several unsuccessful attempts, de- 
 duced the leading empirical laws of metallic polari- 
 zation, having been partly guided (as he states in his 
 paper in the Philosophical Transactions for 1830) 
 by Fresnel's remarkable experiments on circular 
 polarization produced by total reflection in glass 
 (see Art. 491). Having found qualities somewhat 
 analogous in light reflected one or several times from 
 metallic plates at various angles depending on the 
 nature of the substance, he gave to the light so re- 
 flected the name of elliptically polarized light. It 
 was afterwards satisfactorily proved by Mr Airy that 
 the light so named by Sir D.. Brewster is in fact 
 identical in its qualities with the elliptically polar- 
 ized light of Fresnel. 
 
 The subject of metallic polarization is rather too (534.) 
 abstruse to be explained in a popular way ; and the**^'*'}-"' 
 phenomena produced with depolarizing plates of dif-^° ""*" 
 ferent metals are not so well known as, according to 
 their discoverer, they deserve to be. My limits only 
 permit me at present to state that the care and accu- 
 racy of Sir D. Brewster's results are unquestionable; 
 that they have formed almost the sole data upon 
 which M. Cauchy and other mathematicians have 
 based their theories of metallic reflection ; and that, 
 by generalizing the more limited views entertained by 
 Fresnel as to the constitution of media and the nature 
 of reflected light, they have been mainly instrumental 
 in fixing the later views of optical writers as to the 
 precise phenomena of polarization as produced, not 
 only by metals, but by other substances. To these 
 views I shall briefly advert in the next section. 
 
 The laws of the reflection of light at crystallized (535.) 
 surfaces have also been studied by Sir D. Brewster. 
 In this case-observation is still in advance of theory. 
 
 V. Of Sir David Brewster's experiments on the ^ggg.) 
 absorption of light we must speak much more Absorption 
 briefly. White light is coloured or analyzed by°*^^'SM. 
 refraction (as in a prism) ; by simple interference, as 
 in Newton's rings ; by double refraction combined 
 with polarization. But it is also decomposed in a 
 way which, primarily at least, seems diflferent from 
 all these, — by passing through coloured, or ratner, 
 colouring media, whether solids, liquids, or gases, 
 as red glass, ink, chlorine. This, the most familiar 
 mode of coloration, is the most difficult to account 
 for, and has been (on account of its obscurity) less 
 studied than the others. In some instances, the 
 complementary colour (that which, added to the 
 transmitted tint, makes up white light) is entirely 
 absorbed or lost ; in other cases it is reflected at or 
 near the first surface of the medium. Sometimes 
 
Chap, v., § 5.] 
 
 OPTICS.— SIR D. BREWSTER— FRAUNHOPER. 
 
 117 
 
 the transmitted light is made tip of different portions 
 of the spectrum curiously blended, whilst rays 
 intermediate in the order of refrangibility are wholly 
 stifled. Many crystals have the curious property of 
 dichroism, that is, of transmitting light of different 
 colours in different directions. All these facts have, 
 been very carefully studied by Sir David Brewster. 
 (537.) But the most remarkable phenomenon to be noticed 
 aotmn of ui^^"^ this head is the wonderful action of nitrous acid 
 nitroaa gas upon light.' When abeam, either of sunlight, or 
 acid gas the light of a lamp, is passed through a bottle contain- 
 00 light, jjjg ^ small quantity of fuming nitrous acid, the light 
 emerges of a tawny orange colout, which may be 
 deepened indefinitely by heating the acid. If this light 
 be then analyzed by a common prism, a wonderful 
 spectacle is seen. The spectrum appears traversed 
 by countless bands or dark spaces, whilst the blue 
 and violet colours are nearly absorbed. The effect 
 of the gas, then, is this, — to stifle or absorb countless 
 minute portions of light seemingly selected at ran- 
 dom from every part of every colour in the whole 
 spectrum. Some of these deficient rays are broad 
 and palpable, but most of them are so fine as to be 
 visible only vrith the telescope. To understand the 
 full import of this discovery, it is necessary to 
 describe first the lines of Fraunhofer. 
 (538.) Joseph Fraunhofer, born in Bavaria, of humble 
 
 Fraunhofer parents, in 1787, raised himself by his unassisted 
 — limes gg-Qj.^g ^Q ijg ^}je £].gt practical optician of the day. 
 trum. He had also the merit of devoting his leisure and 
 
 the fine apparatus at his command to the observa- 
 tion and discovery of many optical phenomena, par- 
 ticularly those diffractive colours produced by fine 
 gratings, which are known under the name of Fraun- 
 hofer' s spectra.^ His principal discovery, however, 
 was (in 1814) that of countless deficient or dark 
 lines in the solar spectrum, resembling those which, 
 as we have mentioned, were afterwards observed by 
 Sir D. Brewster, to be produced in any kind of 
 light by the action of nitrous gas. The deficient rays 
 of solar light had, indeed, been observed still earlier 
 (in 1802) by Dr WoUaSton, but he counted only a 
 very few of the more conspicuous ones ; he described 
 them merely incidentally, and (unusually with him) 
 seems not to have perceived the great value of the dis- 
 covery both in a theoretical and practical pointof view. 
 (539.) Fraunhofer's beautiful map of the spectrum, tra- 
 
 Their num- ygj-gg,} ijy lines of every grade of darkness, and clus- 
 portance. tered with every conceivable variety of distribution, 
 was published in the Munich Transactions. He 
 counted 590 lines, but Sir D. Brewster states that he 
 has carried the number to 2000. Like the stars, they 
 are probably countless. These lines characterize solar 
 light. The light of the fixed stars and that of the 
 
 electric spark have their peculiar deficiencies diffe- 
 rent from those of our sun. These were disco- 
 vered by Fraunhofer, as well as their occurrence in 
 certain coloured flames. The order and number 
 of the lines is, in each case, independent of the 
 kind of prism used ; but the angular distribution 
 of the deficient rays varies with the material. 
 Thus an oil of cassia prism expands most in pro- 
 portion the less refrangible end of the spectrum ; 
 while water and sulphuric acid act with dispropor- 
 tionate dispersive energy on blue and violet light. 
 This property of substances had been already studied 
 by Sir D. Brewster with his usual diligence ; but the 
 importance of Fraunhofer's discovery was this, that 
 the lines (the larger of which he distinguished by 
 letters of the alphabet) furnish landmarks which de- 
 fine special rays of light invariably recognisable under 
 all circumstances, which the vague description of 
 their tints is quite incompetent to do. This enabled, 
 on the one hand, the practical optician to discover 
 the kinds of glass most fit for achromatic combina- 
 tion ; and, on the other, it afforded precise numerical 
 measures of the quality of dispersiveness in bodies 
 which have been partly already, and will yet much 
 more become, tests of some of the more obscure and 
 diflicultportionsof the theory of light, — those, namely, 
 which are connected with dispersion and absorption. 
 Fraunhofer was, after Dollond, the most eminent and 
 scientific manufacturer of achromatic telescopes, of 
 which he vastly increased the aperture. He died at 
 Munich in 1826. 
 
 Returning to Sir David Brewster's discovery of the 
 artificial production of analogous lines or deficient 
 rays in light from any source, its importance is easily 
 perceived : — ^for, in the first place, it so far accounts 
 for the strange phenomenon of the deficient rays 
 of the sun's light, by showing that it may be caused 
 by a gas resembling nitrous acid gas in its proper- 
 ties existing in the solar atmosphere ; and, farther, 
 if so astonishing a result of absorption is ever to be 
 explained by theory, the first step is to be able to 
 produce the phenomenon at pleasure, and to examine 
 the qualities of the bodies producing it. The phe- 
 nomena of coloured flames which possess standard 
 deficient rays, present perhaps a closer analogy to 
 the sidereal spectra. Sir David Brewster has far- 
 ther found that the absorptive action of the earth's 
 atmosphere (detected by the varying character of the 
 spectrum for different angular altitudes of the sun) in- 
 creases the number and also the breadth of these lines. 
 
 Intimately connected with, and nearly of the same 
 date as these experiments, was an observation of Sir 
 D. Brewster's, which has received less general assent 
 tha-n any other of the numerous and important ones 
 
 (540.) 
 Action of 
 nitrous gas 
 and of the 
 earth's at- 
 mosphere 
 on the 
 spectrum. 
 
 (541.) 
 Sir David 
 Brewster's 
 analysis of 
 the spec- 
 trum. 
 
 ^ Edinburgh Transactions, vol. xii. (1833). 
 
 ^ The peculiarity of these spectra is this, that they consist of pure colours, whilst almost all interference-colours are, like those 
 of Newton's rings, mixed and impure. One result is very remarkable. Fraunhofer obtained his spectra of such brilliancy as to 
 be able to measure the position oif the dark lines (an evidence of their exceeding purity), thus obtaining a standwrd spectrum in 
 which the material of the prism has no influence whatever in varying the ratio of the dispersion of the various colours. 
 
118 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 which we owe to his genius. It is an analysis of the 
 coloured light of the (so-called) homogeneous rays of 
 the pure spectrum hy the specific action of absorbing 
 substances. Sir D. Brewster believes that he has 
 separated the homogeneous orange of Newton into 
 red and yellow, the green into yellow and blue ; and 
 that, in fact, each of the three primary colours exists 
 at every point of the spectrum. But as grave doubts 
 have been thrown on the results, especially by the 
 recent careful experiments of Helmholz, I shall not 
 further insist upon them here. ^ Still less can I take 
 notice of a multitude of microscopic researches on a 
 variety of objects in the animal, vegetable, and mineral 
 kingdom, and on the physiology of vision, with which 
 Sir D. Brewster has filled a multitude of memoirs, 
 each bearing testimony to the zeal and aeuteness by 
 which his researches are directed. 
 (542.) Sir David Brewster received, in 1816, jointly with 
 
 His othei Seebeck, one of the g^eat prizes of the Institute ; he 
 scientific a,lso received, in succession, all the medals in the gift 
 of the Eoyal Societies of London and Edinburgh, and 
 he is an honorary member of the principal academies 
 of Europe. In particular, he is one of the eight asso- 
 ciate-members of the French Academy of Sciences. 
 To meteorology he has been a valuable contributor, 
 having discussed in an able paper the law of the 
 distribution of temperature over the globe, and 
 pointed out the near coincidence of two regions 
 or centres of greatest cold in the northern hemi- 
 ephere, with the magnetic poles. His papers are 
 so numerous, and their variety is so great, as to 
 render an enumeration, even of those containing what 
 may reasonably be termed discoveries, impossible 
 within our limits. Few persons have made with 
 their own eyes so vast a number of independent 
 observations ; few have ever observed better, or re- 
 corded their observations more faithfully. He has 
 discovered (as we have partly seen) a multitude of 
 laws of phenomena of the greatest importance in the 
 construction of a theory, but he has not been forward 
 in proposing such a theory. Neither the moveable 
 polarization of Biot, nor the transverse undulations 
 of Young and Fresnel, received his cordial assent. 
 Generally speaking, he has been favourable to a cor- 
 puscular theory of light, without, however, attempting 
 to render the Newtonian view mechanically consistent 
 with the astonishing variety of complex phenomena 
 which he aided in discovering, and which would evi- 
 dently require it (to say the least) to he completely 
 remodelled. His scientific glory is different in kind 
 from that of Young and Fresnel ; but the discoverer 
 of the law of polarization, of biaxal crystals, of op- 
 tical mineralogy, and of double refraction by com- 
 pression, will always occupy a foremost rank in the 
 intellectual history of the age. 
 (543.) Before closing this section I shall add a few words 
 respecting the discoveries of MM. Seebeck and Biot, 
 
 which have a very close relation to those of Sir David 
 Brewster. 
 
 Thomas Seebeck was born in 1770. We have (544.) 
 seen that he was one of the discoverers cf the depola- Seebeck. 
 rizing structure of heated and compressed glass (527). 
 In 1816 he observed, independently of M. Biot, the 
 property of oil of turpentine and other fluids to rotate 
 the plane of polarization of light transmitted through 
 them, thus acting similarly to a crystal of quartz on a 
 ray passiijg along its axis (512). Previously to these 
 discoveries he had repeated Sir William Herschel's 
 experiment on the position of maximum heat in the 
 spectrum, and found it to vary with the material of 
 the prism. When the science of electro-magnetism 
 was created by Oersted in 1819, his attention became 
 chiefly directed to that class of phenomena, and in 
 1823 he was fortunate enough to discover thermo- 
 electricity. He also wrote many papers on allied 
 subjects. He was a skilful observer, but deficient in 
 the power of physical analysis. He died in 1831. 
 
 M. Biot, at the time I write, the oldest member ("54.5.) 
 (I believe) of the Academy of Sciences, and one of Jjl- ^'o'— 
 the veterans of European science,^ was bom at Paris „„g ^g. 
 in 1774, and has lived to the age of 80, a life of searches, 
 almost unintermitted intellectual labour. It is im- 
 possible not to be touched by the evidence of such 
 unconquerable love of knowledge. He was, if I 
 mistake not, one of the original pupils of the Poly- 
 technic School ; and his talents being first developed 
 in an almost purely mathematical direction, he at- 
 tracted the notipe of Laplace, who introduced him to 
 the Institute, and by whom he was always befriended. 
 In 1802 he published a work on curves and surfaces 
 of the second degree, and was the first after Lambert 
 who thought of applying mathematics to the theory 
 of conducted heat. From this time his attention 
 was almost exclusively directed to the applied sciences, 
 and the number and variety of his experiments and 
 writings almost baffles enumeration. Descriptive and 
 practical astronomy, the theories of sound, of light, 
 of the voltaic pile, of terrestrial magnetism, of electro- 
 magnetism, of heat, radiant and combined, have been 
 the subjects of his studies and writings. We find him 
 in the earlier part of his career associated with Gay 
 Lussac in his first aeronautic expedition, and with 
 Arago in the geodetical and astronomical operations 
 of the great arc of the meridian. He afterwards 
 carried the penduluni to the Island of Unst, the 
 northmost land in Shetland ; and he made original 
 experiments on the propagation of heat and of sound. 
 He wrote a voluminous treatise on descriptive and 
 practical astronomy, one still more elaborate on 
 general physics, and a vast number of miscellaneous 
 papers in the Journal des Savans and the Biographie 
 Universelle. His original memoirs in the Trans- 
 actions of the Academy are usually very long and 
 elaborate, his calculations and empirical formulaa 
 
 .See Sir D. Brewster's statement and defence of his opinions in hia Life of Newton, vol. i., p. 117, &c. 
 
Chap. V., § 6.] 
 
 OPTICS. — M. BIOT— MR AIRY. 
 
 119 
 
 laboriously accurate. One of his papers fills an 
 entire volume of the Academy's Memoirs. Even 
 the astronomical hieroglyphics of the Egyptians, and 
 the chronology of Chinese eclipses, have drawn from 
 his pen learned treatises ; and he has expounded the 
 labours and discoveries of his countrymen and others 
 with almost as much care and effort as if they had 
 been proper to himself. But his subject by predi- 
 lection was optics, and here he made his most con- 
 siderable discovery, and that which he has followed 
 out with most minute industry, namely, the rotatory 
 action of fluids, in which he had Seebeck for a co-dis- 
 coverer. (See Art. 512.) He studied the colours of 
 crystallized plates with exemplary patience, and as 
 we have seen in the preceding section, by his accu- 
 rate observations on the law of the tints, prepared 
 the way for the theory of transverse vibrations ; but 
 his own doctrine of moveable polarization, which he 
 imagined to explain them, made no impression on 
 the progress of science. He was the first who di- 
 vided doubly-refracting crystals into positive (as 
 
 quartz), and negative (as calcareous spar). In the 
 former the extraordinary wave is a prolate spheroid, 
 and inclosed within the ordinary spherical wave ; in 
 the latter the spheroid is oblate, and exterior to the 
 sphere. He also discovered (very approximately) 
 the law regulating the plane of polarization of the 
 rays in biaxal crystals. 
 
 M. Biot has for about half a century been an active 
 professor and member of the Institute. His researches, 
 always marked by precision, are perhaps deficient in 
 bold conjecture and happy generalization. They are 
 conducted with a mathematical stiflFness which allows 
 little play to the fancy, and in hypothetical reason- 
 ing he rarely indulges. His style is formal yet diffuse, 
 and consequently somewhat repulsive to the student. 
 His works are consequently not easily read, and have 
 contributed less to the progress of knowledge than the 
 scrupulous care often evinced in their compilation 
 might seem to warrant. Yet the name of Biot will be 
 ever associated with devotion to science, and especially 
 with the progress of optics in our own day. 
 
 (546.) 
 
 § 6. Mr Airy, Sir William R. Hamilton, and Professors Lloyd and Maccullagh. — Confirma- 
 tion of Fresnel's Theory — Investigation of the Wave Surface completed ; Conical Refraction. 
 — M. Caitchy. Mechanical Theory of Elastic Media, and of Ordinary and Metallic 
 Reflection; M. Jamin. — Theory of Dispersion ; Professor F^well. 
 
 (547.) It would not be possible, in one short section, to 
 
 Progress of ^q justice to the various improvements and additions 
 J *"" ^g^'which the undulatory theory of light — the joint crea- 
 ory since tion of Huygens, Young, and Fresnel — has received 
 IVesnel. since the nearly simultaneous decease of the two last- 
 named philosophers. But while a vast amount of 
 labour and of mathematical and experimental skill 
 has been thus expended, of which it would be in vain 
 to attempt within our limits to give an account, we may 
 pause upon two or three of the more conspicuous re- 
 sults of these researches, which, in conformity with 
 the plan of this dissertation, may give a tolerable 
 idea of their general tendency. 
 (548.) Looking at the history generally, we find one cu- 
 
 Peculiari- rious peculiarity in the progress of this remarkable 
 h'T/"' ° theory. Its origin in the seventeenth century was 
 unattended with sympathy or success. It received 
 little support, and was well nigh forgotten for more 
 than an hundred years: it was then resumed (we might 
 almost say re-invented) in England, but it remained 
 unpopular and almost unknown until re-echoed from 
 a foreign land ; while in France itself the vie\ys of 
 Fresnel were (with one or two exceptions) as little 
 appreciated as those of Young had been in England. 
 From this period England became the place of its 
 chief development; and with the exception of one 
 eminent philosopher, M. Cauchy, its supporters and 
 extenders, whether by analysis or experiment, have 
 
 belonged to Great Britain,' a few of the most conspi- 
 cuous of whom are named at the head of this section. 
 
 The attention of the British public was forcibly (549.) 
 called to the theory of Young and Fresnel, by an S'"" J- ^^^'■ 
 able treatise on Light, contributed by Sir John Mr^A^" 
 Herschel in 1827 to the Encyclopcedia MetropoUtana. 
 The excellent method, lucid explanations, and intel- 
 ligent zeal which marked this essay compelled the no- 
 tice of men of science, too long deterred from the study 
 of the fragmentary and abstruse writings of Young, 
 It was followed four years later by a most able and 
 precise mathematical exposition of the theory, and its 
 application to optical problems, by Mr Airy (now As- 
 tronomer Royal), who was then Plumian Professor at 
 Cambridge, and who introduced this part of optics 
 as a branch of study in that university. Whilst the 
 excellent tract on the undulatory theory (published in 
 1831 in his Mathematical Tracts) opened up the 
 subject in a most accessible form to British mathe- 
 maticians, his original papers in the Cambridge 
 Transactions confirmed the doctrines of Fresnel by a 
 number of new and admirably contrived experiments, 
 some in connection with interference, some with po- 
 larization, and all were confronted with the rigorous 
 results of the mathematical theory. The f)aper on 
 Quartz, and that on the Rainbow, have been already 
 referred to (art. 466, 512). The writings of Mr Airy 
 and of Sir John Herschel have continued to be the 
 
 1 M. Moigno (a Frenchman), writing in 1847, laments that Prance was then perhaps the only country in which the experiment 
 of " conical refraction" (the triumph of Fresnel's theory to be presently mentioned) had never been repeated. 
 
120 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (550.) 
 Sir Wm. 
 K. Hamil 
 
 fraction in 
 
 "biaxal 
 
 crystals, 
 
 main sources of information on this subject, and on phy- 
 sical optics generally, not only in this country but on 
 the Continent. It is remarkable that in Prance, which 
 possesses so many admirable scientific books, there 
 should not exist a single good treatise on optics. 
 Had not Mr Airy's attention been necessarily with- 
 drawn from optics to astronomy, it is very evident that 
 the theory of light would have received from him 
 many farther important additions. 
 
 Whilst an impulse was thus given to the mathe- 
 matical theory of light in the University of Cam- 
 ton"and Drhridge, a similar progress was being made in the 
 Lloyd. sister University of Dublin, where three of her most 
 eminent professors, Sir William Egwast Hamilton 
 and Professors Lloyd and Maccullagh devoted 
 themselves energetically to its improvement and veri- 
 fication. 
 (551.) Tothe two former of thesewe owe the prediction and 
 
 Conical re- ocular demonstration of the most singular and critical 
 of all the results of Fresnel's theory. Sir William 
 Hamilton, a geometer of the first order, having un- 
 dertaken the more complete discussion of the wave 
 surface of Fresnel (see Section Third of this Chapter), 
 to the equation of which he gave a more elegant 
 form than heretofore,' ascertained the exact nature 
 of that surface, and consequently the exact direction 
 of refracted rays in the neighbourhood of the " optic 
 axes." It had been shown by Fresnel that, in the case 
 of crystals with two axes, a plane section in a certain 
 direction cuts the two sheets of the wave surface in 
 a circle and in an ellipse, which necessarily intersect 
 each other in four places. (See the annexed figure.) 
 In the lines joining these four points with the centre 
 of the figure the velocity of the two rays is equal. 
 Now the cusps or sharp inflections of the wave surface 
 in these particular directions, occur not only in the 
 particular plane of section which we have considered, 
 but in any section of the wave surface passing through 
 these lines of equal ray- velocity. In the figure, there- 
 fore, of the compound sheet there is not a. furrow, as 
 Fresnel had supposed, but a fit or dimple, with 
 arched sides something like the flower of a convol- 
 vulus, and the surfaces meet at the bottom of the pit 
 at a definite angle. Let the circle and ellipse, 
 in the annexed figure, represent the section of the 
 wave surface we have described ; then P is the line 
 of uniform propagation, and P is the bottom of the 
 
 Quater- 
 nions. 
 
 conoidal pit M P N. Now 
 suppose a slender ray of light 
 to move through the crystal in 
 the line P, and to- emerge 
 into air at a surface of the 
 crystal cut perpendicular or 
 nearly so to the direction of 
 single ray- velocity P. If we 
 confine our attention at first to 
 the plane of the figure only, 
 that ray having intersecting 
 tangents both proper to the wave surface, would 
 give rise, on Huygens' construction (art. 475), to two 
 emergent rays inclined at an angle. But since this 
 is the case, not only in the plane of the figure, but 
 (as has been stated) in any plane passing through 
 the ray in question, the emergent light must form a 
 conical luminous sheet, the angle of the cone being 
 determined by the refractive properties of the crystal. 
 This beautiful and unexpected result was verified with 
 great skill and address by Dr Lloyd in the case of 
 Arragonite, which is a biaxal crystal, and he found 
 the position, dimensions, and conditions of polariza- 
 tion of the emerging cone of light to be exactly such 
 as theory assigns. When all the necessary correc- 
 tions are attended to, the angle of the cone of light 
 is about 3°. There is another case of conical (or it 
 might be called cylindrical) refraction, which occurs 
 nearly in the same portion of a crystal, which was 
 predicted and discovered in like manner, but which 
 we will not stop to particularize.^ The observations 
 of Dr Lloyd have been extended by M. Haidinger to 
 the case of Diopside, a crystal also having two optic 
 axes. 
 
 Every one capable of appreciating such evidence, (552.) 
 will feel the irresistible impression which so curious Other 
 an anticipation, so accurately fulfilled, gives us of the ^'."'"^ "^ 
 positive truth of a theory admitting of such v^eri-j„;]j(,„' ^^^ 
 fications. The names of Sir W. Hamilton and Dr Dr Lloyd. 
 Lloyd will be handed down to posterity in connec- 
 tion with this admirable discovery. But they have 
 also other claims to our respect, to which we can 
 here only refer in the most general terms. The for- 
 mer has generalized the most complicated cases of 
 common geometrical optics by a peculiar analysis de- 
 veloped in his essays on " Systems of Rays" (Irish 
 Acad&my Transactions, vols, xv.-xvii.)^ To Dr Lloyd 
 
 - + 
 
 i2j,2 
 
 = 0. 
 
 1 The equation is- ^2:fpq72_„2 ■ a^^ + y^ + ^S^ZV^ ' ^2 + y2 + ^^_c 
 
 ^ It was shown by Sir W. Hamilton that the tangent plane M N touches the wave surface, not in two points merely, hut in a 
 circle of contact ; consequently, the perpendicular to this tangent plane, OM, is the direction of one of the optic axes (or the velo- 
 city is the same for both portions of the compound wave). Hence a ray incident externally so as to be refracted along this perpen- 
 dicular, will at entrance spread into a hollow, cone interior to the crystal, and on emergence at a parallel face each portion of 
 the ray recovers a direction parallel to its primitive direction, and a luminous hollow cylinder is the result. See Dr Lloyd, in 
 the Irish Academy Transactions, vol. xvii., and Sir W. R. Hamilton's third supplement to his " Systems of Rays" in the same vol. 
 
 ^ Sir W. R. Hamilton is also a discoverer in pure analysis and its connection with geometry. Following up the ideas of Mr 
 Warren on the geometrical significance of the symbol V — 1> as indicative of direction, Sir W. Hamilton has developed the theory 
 of a new class of imaginary quantities, which he terms qnatcrnions, by means of wliich he contrives to express simultaneously 
 the direction in space and magnitude of a line or form ; and this calculus he has applied to the solutions of problems of geometry 
 and physical astronomy. The quaternion appears to express something even beyond this ; and this redundancy has been consi- 
 dered as a diificulty by some mathematicians. The superfluous number is considered by 81* W. Hamilton as representing time 
 in mechanical problems. 
 
Chap. V., § 6.] 
 
 OPTICS. — MACCULLAGH — M. CADCHY, 
 
 121 
 
 we are indebted for several interesting experimental 
 papers on optics, for an able and impartial review 
 of the progress of the science,' and for an excellent 
 elementary treatise on the Wave Theory, which forms 
 by far the best popular introduction to the subject. 
 (553.) Closely associated in his pursuits, as in personal 
 
 Maocul- friendship, with Sir W. R. Hamilton and Dr Lloyd, 
 *S • was James Maccullagh, a native of Tyrone, born in 
 
 1809, and who died prematurely and unhappily Oc- 
 tober 24, 1847.' His first paper was communicated 
 to the Royal Irish Academy at the age of 21. It 
 was one of the earliest original contributions of this 
 country to the development of the theory of Fresnel. 
 The construction of the wave surface in biaxal crys- 
 tals was simplified and improved ; and in 1835 a 
 second paper appeared, in which geometrical construc- 
 tions of great elegance were employed for the farther 
 investigation of the subject. Mr Maccullagh next at- 
 tacked the theory of the undulations of ether in quartz 
 crystals, to which he gave a mathematical expression 
 (see art. 512). In 1838 he published a paper on the 
 laws of crystalline reflection, in which he adopted 
 certain hypotheses, such as that the vibrations of the 
 ethereal particles, in the case of polarized light, are 
 parallel to the plane of polarization (contrary to Fres- 
 nel's opinion),and,thatthedensity of ether is the same 
 in all media. In a subsequent memoir on the dyna- 
 mical theory of reflection and refraction, he arrived 
 at similar results with fewer physical assumptions, 
 and by a more purely mathematical treatment of the 
 subject. Subsequent researches, presently to be men- 
 tioned, have diminished the value of these theoretical 
 investigations. 
 (554.) Numerous mathematicians of eminence at home 
 
 Meohamcal ^^^ abroad entered upon the same arduous enquiry, 
 vibratory To attempt to deduce from the hypothetical constitu- 
 motion. tion of a very rare highly-elastic medium, together 
 with the known dynamic laws, the various complicated 
 facts of optics, was a problem whose difficulty was only 
 equalled by its indefinite character. For how little 
 do we know of the molecular constitution of such 
 fluids as air and water ? How much less then of a 
 fluid (if we may so term it) almost infinitely rarer, and 
 incapable of being inclosed, measured, or weighed 1 
 The bare possibility of transversal undulations was 
 long contested by very able mathematicians ; and con- 
 ceding it, the mutual influence of such an ether and 
 the particles of gross matter (as shown by reflection 
 and refraction) must, it would seem, for ever remain 
 problematical. Yet, however gratuitous or even er- 
 roneous our reasonings about such ultimate questions 
 may be, there is no doubt a real benefit in obtaining 
 
 from them at least a mathematical congruity with ob- 
 served facts. The progress of science shows that 
 there is a practical usefulness in this step. On the 
 other hand, we must not be discouraged to find 
 that there are so many handles to the matter, that 
 even the most profound thinkers may conceive that 
 they have reached the proposed end by different and 
 incongruous routes. Besides the mathematicians 
 whom I have mentioned, many others were in the 
 field ; for the result of tremors propagated through 
 elastic media of different kinds is an enquiry of ex- 
 cessive generality, and forms a part of many branches 
 of science besides optics. MM. Cauchy, Navier, 
 Poisson, Coriolis, Green, Kelland, and Neumann are 
 amongst those who attacked the problem. For a series 
 of years memoirs rose fast and thick on this favourite 
 battle-field ; and even a skilful mathematician might 
 find it no small penance to discuss the merits of the 
 various hypotheses and the solidity of the respecftve 
 deductions which were proposed. 
 
 It must be owned that a great part of this '^*st ^^^^-^ 
 mathematical toil has been without immediate result ;„„ ^^ ^ 
 in optics. It is by comparing the conclusions ar- tics. 
 rived at by authorities of seemingly equal weight, that 
 we learn the difference between a stable physical in- 
 duction and a clever mathematical hypothesis. Mac- 
 cullagh, for instance, maintains the vibrations of ether 
 to be parallel to the plane of polarization ; Fresnel 
 and M. Cauchy' that they are perpendicular. The 
 first mathematician considered that the vibrations are 
 wholly transversal, the last believes that the normal 
 vibrations have also their share in affecting the 
 phenomena, whilst Poisson denies that transversal 
 vibrations can bo propagated to a sensible distance. 
 Maccullagh finds that, to accoimt for metallic reflec- 
 tion, the indices of refraction of mercury and silver 
 are 15-0 and 35-0, whilst Cauchy makes them but 
 1'77 and 0"34. One theorist assumes that the 
 density of ether is the same in all bodies, another 
 that it is greatest in a vacuum, and others pre- 
 cisely the reverse ; one that vibration is not accpm- 
 panied by change of density, another that it is ;* 
 and so on in almost endless variety. A matured 
 opinion can only be formed after the results of the 
 various assumptions, and their congruity with facts, 
 have been more thoroughly worked out. Already 
 two of Maccullagh's essential postulates have lost 
 much of their plausibility ; that respecting the di- 
 rection of the vibrations in polarized ligJat has been 
 probably decided by Professor Stokes in favour of 
 Fresnel's opposite view, by an admirably devised ex- 
 periment on the effect of diffraction on polarized 
 
 ^ British Association Reports for 1834. 
 
 ^ It is unnecessary to suppress thie fact that Mr Maccullagli died by his own hand, under the pressure of a fit of despondency, 
 brought on (it is believed) by over-work ; a fate happily extremely rare amongst students of exact science. I say it is needless 
 to suppress the fact, because it infers no blame. Mr Maccullagh was an amiable, pious, and exemplary man. Irresponsible in- 
 sanity was, of course, the cause. 
 
 * This is M. Cauchy's last view ; for some years he adopted the opposite one, which he then surrendered with great frankness. 
 
 * If, however, the vibrations were wholly transversal, it seems to be admitted that they would not affect the densitj' of the medium. 
 
122 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VT. 
 
 rays ^; the existence of normal vibrations seems to 
 be proved by the ingenious experiments of M. Jamin, 
 showing that at no angle is light perfectly polarized 
 by reflection. The more we see of these diversities 
 arising in the progress of science, the less are we 
 disposed to found on merely mathematical conclu- 
 sions from an assumed constitution of elastic bodies ; 
 the more, on the other hand, do we admire the ad- 
 mirable sagacity of Fresnel — the real Newton of 
 modern optics — ^few of even the least of whose sug- 
 gestive anticipations have fallen to the ground. 
 (556.) M. AuGUSTiN Louis Cauchy has been long known 
 
 M. Cauohy j^g ^jjg pf ^jjg ablest and most prolific mathematical 
 mathemati- Titers of this century. Besides numerous and im- 
 cal labours, pprtant memoirs, on nearly every branch of pure 
 and applied mathematics, published in the Journal 
 de I'Ecole Polytechnique, and the Memoirs of the In- 
 stitute, he has published, in a separate form. Exer- 
 cises des Mathematiques in two series of volumes ; 
 and for many years scarcely a weekly meeting of the 
 Academy of Sciences occurred without a mathemar 
 tical memoir of this prolific author being laid on the 
 table, and subsequently printed in the Comptes Ren- 
 dus. The integral calculus and other parts of ana- 
 lysis form the subjects of a large part of these writings ; 
 but the theory of hydrodynamics in the earlier, and of 
 optics in the later part of his career, are largely re- 
 presented. So diflTuse and desultory a mode of publi- 
 cation has been little favourable to those who wish to 
 make themselves acquainted with what has been ac- 
 complished by M. Cauchy. The scientific world is in- 
 debted to Abbe Moigno in France, M. Kadicke " in 
 Germany, and Professor Powell* in England, for ana- 
 lyzing in part his optical labours. As the present 
 brief notice is evidently inadequate to include even 
 the most superficial view of the whole, I shall say a 
 few words upon two of his theoretical researches on 
 light, which have attracted most general attention. 
 The first is upon the theory of Reflection and Re- 
 fraction, framed so as to include the phenomena of 
 metallic reflection ; the second is upon the Dispersion 
 of Light. 
 (557.) I shall first mention some seemingly exceptional 
 
 facts to the ordinary laws of polarization by reflec- Theory of 
 tion. As early as 1814 [Philosophical Transactions, '^^^^f^f" 
 18 14, p. 230), Sir David Brewster had remarked that ^^^^^ ;„. 
 such highly refractive substances as Realgar, Diamond, eluding the 
 and Chromate of Lead, do not polarize, at any angle, ^^^^ 
 the whole of the reflected light. Mr Airy afterwards ""^ " °' 
 showed that light reflected from diamond near the 
 maximum polarizing angle, possesses qualities re- 
 sembling those of light reflected from metals. The 
 same view was more generally stated by Mr Dale ; " 
 and last of all, M. Jamin showed that all transparent M. Jamin. 
 substances polarize clliptically the light which they 
 reflect, — the difference of " phase " of the two compo- 
 nent vibrations increasing from 180° at a perpen- 
 dicular incidence, to 360° at an incidence of 90° ; and 
 that the laws of reflection at transparent surfaces, as 
 also in the case of metals, depend upon two con- 
 stants — the index of refraction and the coefficient of 
 ellipticity. And he has determined in numerous 
 cases the values of these constants. 
 
 Thus Fresnel's theory of reflection requires un- (■'558.) 
 
 doubted modification. It only holds true for sub- Pj^sn^l'" 
 
 . no • • 1 1 A £* ±\^ , theory mo- 
 
 stances whose mdex of refraction is nearly l-4b, that ^igg^ i,y 
 
 of the glass which he examined. The complication Green and 
 is held t,o arise from the existence of vibrations ^y **• 
 (called normal) in the direction of transmissioii of the ^^^ ^' 
 luminiferous wave, such as those which produce the 
 effects of Sound in air, and which produce certain , 
 efi^ects on Light at the bounding surfaces of two 
 media. In the theory of Fresnel, as also in those of 
 Maccullagh and Neumann, this influence is neglected. 
 To Green and to M. Cauchy belongs the merit of lay- 
 ing down a more comprehensive theory. Mr Green's 
 theory, published in 1837" (not long before his death), 
 is so far incomplete that it involves only one constant. 
 M.Cauchy's investigations, published two years later,^ 
 embrace the phenomena of metallic reflection by the 
 introduction of the two constants mentioned above, / 
 thus completing the theory of reflection and refrac- 
 tion both for transparent and metallic surfaces. 
 
 The fact of the unequal refrangibility (dispersion) (^^^-^ , 
 of light has ever been felt to be one of the most ^j^^pj^j"^ 
 real as well as prominent difficulties in admitting 
 
 ' Repertoire d'Optique Moderne. 1847-50. 
 
 * The Vndulatory Theory aa applied to the Sispereion of Light. 
 
 1841. 
 
 Green's 
 account of 
 his method. 
 
 ^ Cambridge Transactions, vol. ix. 
 
 ' Handbueh der Optik. Band i., 1839. 
 
 ' See Moigno Rep. d'Optique, p. 1385. 
 
 ^ Cambridge Transactions, vol. vii. The following extract from this able paper shows the independence of physical assump- 
 tions which characterizes these ultra-mathematical optical theories : — " . . . We are so perfectly ignorant of the mode of action 
 of the elements of the luminiferous ether on each other, that it would seem a safe method to take some general physical [?] 
 principle as the basis of our reasoning. . . . The principle selected as the basis of the reasoning contained in the follow- 
 ing paper is this : In whatever way the elements of any material system act upon each other, if all the internal forces exerted 
 be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be 
 the exact differential of some function. But this function being known, we can immediately apply the general method given in 
 the Mecanique Analytique, and which appears to be more especially applicable to problems that relate to the motions of systems 
 of an immense number of particles mutually acting on each other. One of the advantages of this method, of great importance, 
 is, that we are necessarily led by the mure process of the calculation, and, with little care on our part, to all the equations and 
 conditions which are requisite and sufficient for the complete solution of any problem to which it may be applied." 
 
 A consideration of the candid admissions of the preceding paragraphs (especially the last sentence) will lead the reader to see 
 how short a way a theory of so general a kind — the chief characteristic of which consists in eluding every troublesome physical 
 enquiry —can go towards explaining the relations of Light to Matter; yet it may be of use by indicating the kind of solutiona 
 which more restricted hypothesis may be expected to give of the laws of phenomena. 
 
 ^ Comptes Rcndus de VAcad. des Sciences. 
 
Chap. V., § ?.] 
 
 OPTICS. — M. CAUCHY — RITTEK. 
 
 123 
 
 (560.) 
 Depends 
 on the fi- 
 nite dis- 
 tances of 
 the vihrat- 
 ing par- 
 ticles. 
 
 the undulatory theory. That theory, in its simple 
 form, enables us indeed to explain clearly enough 
 the refraction of light owing to a change of velocity 
 in the wave as it passes from one medium to an- 
 other ; but it assigns no reason why that change of 
 velocity should be different for light of various co- 
 lours, in other words, of different wave-lengths. The 
 corpuscular theory, on the other hand, furnishes at 
 least a plausible explanation, by assuming a variable 
 attraction between refracting media and the mole- 
 cules composing the different rays. 
 
 When, however, undulationists were pressed on 
 the subject, it was easy to see the direction in which 
 at least a plausible explanation might be sought. In 
 the usual form of equation for vibrations in air, 
 given by Lagrange, the integration is effected by as- 
 suming the intervals between the particles evanescent 
 compared with the length of a wave. This is per- 
 fectly true in the case of sound, and all sounds ap- 
 pear in consequence to travel uniformly. But should 
 it fail in the case of light, that is, should the inter- 
 vals of the ethereal particles bear some sensible ratio 
 to that very small quantity, the length of a wave, 
 what would be the result ? M. Cauchy has made 
 out, by a very complex analysis, that in this case the 
 longer waves will travel most rapidly, and conse- 
 quently be least refracted. Several other writers, 
 especially Professor Kelland, obtained similar re- 
 sults ; and Mr Airy, by very simple, though only 
 approximate, considerations, showed the dependence 
 of refraction on the length of a wave. ^ M. Cauchy's 
 memoir appeared in 1835 at Prague, in a bulky and 
 abstruse form : the mathematical investigations are 
 very long and complex, the numerical verifications 
 
 scarcely less so.^ The indices of refraction, observed 
 by Fraunhofer, for different lines of the spectrum, in 
 different kinds of glass, together with the correspond- 
 ing wave-lengths for these rays, formed the principal 
 data for comparison. But others have since been 
 obtained by Rudberg and Professor Powell, and care- 
 fully compared with M. Cauchy's theory by the lat- 
 ter, and the coincidence appears satisfactory.^ But 
 in estimating the value of this coincidence, it is to 
 be observed that of 7 indices of refraction observed 
 for each substance, 3 must be used to ascertain the 
 constants in the formula, and only 4 remain to be 
 calculated. 
 
 One difficulty, however, remains. If the rays of (561.) 
 
 light travel through space with variable velocities, the ^o":"'^- 
 • i>i 11 -I f 1 ■ persion of 
 
 images of the stars would present tails or colour in- Hght in 
 
 consistent with observation.' M. Cauchy eludes this free space, 
 difficulty by the following hypothesis respecting ethe- 
 real media : — The existence of transversal vibrations 
 (according to him) requires that the law of force be- 
 tween particle and particle of ether must not be inter- 
 mediate between the inverse 2d and inverse 4th power 
 of their distance. In the former case the force is an 
 attractive, in the second a repulsive one. In the first, 
 the velocity of propagation depends on the length of 
 a wave, in the second it is independent of it. [The 
 first case, too, alone will be consistent with perma- 
 nent longitudinal vibrations.] Consequently if we , 
 suppose that in free space the particles of ether are 
 arranged in close order, and exert a repulsive force 
 on each other, no dispersion results ; but in refract- 
 ing media, supposing the distance of the molecules 
 increased, and the mutual action attractive, then dis- 
 persion occurs.* 
 
 § 7. HjTTER.-^Chemical Rays of the Spectrum. — Niepce ; Daguerre ; Mr Talbot. Art of Helio- 
 graphy or Photography — Daguerreotype — Calotype. — Professor Stokes. Chemical Rays ren- 
 dered visible — Fluorescence, 
 
 (562.) 
 Chemical 
 action of 
 light. 
 
 A very curious chapter of the history of Light re- 
 mains to be written, respecting the chemical ener- 
 gies which itis capable of exerting, or which at least are 
 found in those parts ofthe solar ray swhifch are dispersed 
 by a prism. These are in part luminous and partly 
 invisible under ordinary circumstances, the latter pos- 
 sessing these chemical qualities in a still higher degree 
 than the others. Though not perhaps very closely 
 associated with the optical discussions of the previous 
 sections, it seems impossible to separate this part of 
 the subject from the rest, since the rays called Che- 
 mical may, as we have reason to think, be reflected, 
 refracted, polarized, absorbed, and made to interfere 
 like visible light ; and farther, because to the extreme 
 
 limit of their sensible action they may, by certain 
 treatment, be made visible to the eye. The art of 
 photography, though belonging quite as much to che- 
 mistry as optics, being a means of inquiry into the 
 qualities of the solar radiations invaluable to the 
 natural philosopher, cannot by any means be excluded 
 from a sketch, however general, of the progress of 
 physical science. 
 
 J. W. RiTTER, Professor of Chemistry at Jena, (563.) 
 and well-known for his numerous contributions fitter, 
 to the earlier progress of voltaic electricity, has 
 the merit of having first clearly pointed out in 1801 
 the separate existence of chemical rays in the spec- 
 trum which extend beyond the most refrangible or 
 
 ^ In all these cases the expression for refrangibUity depends on the ratio of the sine of an arc to the arc itself; which are 
 again includes the ratio of Ar, the distance of the molecules to A, the length of a wave. When Ax becomes very small, the first 
 ratio becomes unity. 
 
 * A portion of these researches had, however, been printed in Paris (privately, I believe) in 1830. 
 
 ^ Powell on the Undulatory Theory. 1841. * Moigno, Eepertoire d'Optique, p. 128. 
 
124 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 violet rays (when the sun's light is decomposed by a 
 prism), in the same manner as the invisible rays of 
 heat were found by Sir Wm. Herschel to extend be- 
 yond the visible red. Scheele had indeed previously 
 noticed that the power of the sun's light to decom- 
 pose and blacken salts of silver increased rapidly 
 from the red towards the violet ray ; and there is little 
 doubt that Herschel's discovery suggested that of 
 Hitter, of the independent or non-luminous rays of 
 the spectrum. 
 (564-) Eitter attributed to these rays a deoxidizing qua- 
 
 ravsof the ^^^- ^"^ WoUaston, who also made experiments on 
 spectrum, the Subject, and discovered the specific action of the 
 diiferent rays on gum-guiacum, prudently suggested 
 the more comprehensive term of chemical rays. Va- 
 rious other denominations have been proposed, which 
 need not be here dwelt upon ; all that can be said is, 
 that deoxidation does not represent the solar action 
 completely. Whether it be really an independent 
 principle in the sun's rays which causes these effects, 
 or merely light and its modifications, is, as in the 
 corresponding case of heat, yet undecided. But it 
 is remarkable that, as shown by M. E. Becquerel, 
 the discontinuity of the luminous spectrum produc- 
 ing " Fraunhofer's Lines" exists equally for the che- 
 mical rays. 
 (565.) Soon after Hitter's first experiments, Dr Young 
 
 They in- proved the Interference of the obscure chemical 
 and may be ^^y^ {P^^l- Trans., 1803), a conclusion successively 
 polarized, claimed since by diflferent physicists. Berard in 1812 
 showed that these rays are polarized by reflection. 
 Seebeck observed that the difierent rays impressed 
 different colours upon salts of silver : and M. Edmond 
 Becquerel long afterwards showed that the red and 
 yellow rays, though incapable of commencing chemical 
 action, in some instances have the power of continu- 
 ing it when once excited by the more refrangible 
 rays. 
 (566.) In 1835 Mrs Somerville made some interesting 
 
 Mrs So- ^ experiments on the permeability of different bodies 
 " ° to the chemical rays, similar to those of Melloni on 
 the heating rays (see chap. VI., § 8), and she found 
 great and seemingly capricious variations in this re- 
 spect.' The account of them was addressed to Arago, 
 and published in the proceedings of the French Aca- 
 demy. She found that green glass, coloured by cop- 
 per, intercepted entirely the chemical rays, yet this was 
 not due so much to its colour as to its other qualities 
 (which are also peculiar as regards radiant heat), for 
 
 nierville's 
 experi- 
 ments. 
 
 the emerald transmits the same rays. Red glass 
 stops most of the chemical rays, whilst the garnet 
 transmits them. Though white glass has generally 
 been considered very transparent for these rays, Mr 
 Stokes has shown that it entirely stops those of the 
 very highest refrangibility, which are readily trans- 
 mitted by quartz. Sir John Herschel and Mr Hunt 
 have made manyinteresting experiments with coloured 
 media on the particular parts of the chemical spec- 
 trum absorbed, but a great deal remains to be done, 
 especially as regards the nature of the substances 
 employed. 
 
 But the great impulse given to this subject was (567.) 
 derived from the invention or discovery of the beau- ^^^^^^ 
 tiful art of Photography. phy. 
 
 In 1802 Mr Thomas Wedgewood and Sir Hum- (568.) 
 phrey Davy succeeded in forming pictures of objects " ^°g^" 
 laid on paper prepared with nitrate of silver, and in Daw. 
 taking profiles (silhouettes') by means of shadows. 
 They proposed to obtain similar effects by means of 
 the camera obscura, but their paper was not suffi- 
 ciently sensitive. The effectual bar to their proceed- 
 ings was, however, this : that they could discover no 
 means of fixing the shadows which they had ob- 
 tained, or preventing the whole surface of the paper 
 from being gradually blackened by exposure to light. 
 
 In 1814 J. NiCEPHORE NiEPCE, a retired proprie- (569.) 
 tor at Chalons sur Saone,'' entered into a similar en- Nieephore 
 quiry, but by methods quite different. He employed ^ '^^"''' 
 the solar effect upon resinous bodies, and some 
 at least of his pictures were executed on plates of 
 pewter or of rolled silver. They were mostly copies 
 of engravings, and the light parts corresponded to the 
 lights of the originals. He, however, at length suc- 
 ceeded in fixing impressions of views in the camera 
 obscura, though in an imperfect manner, and after very 
 long exposure. The pictures thus obtained had this 
 in common with more perfect processes, that the lu- 
 minous impression was first brought into view by 
 a chemical process subsequent to exposure in the 
 camera. In 1 825 Nicephore Niepce became associated 
 with Daguerre, who had previously been engaged in '^^S"^''''®' 
 the same research ; they agreed to communicate the 
 results of their several experiments. The result, as 
 is well known, was the invention of the Daguerreo- 
 type, not improperly called after Daguerre, who 
 seems really to have worked it out almost entirely 
 for himself, after the death of Niepce in 1833; 
 whilst so patient and determined was Daguerre in 
 
 Mrs Mary ^ The maiden name of this accomplished lady was Mary Somerville ; she was born, I believe, at Jedburgh, and married first Mr 
 Somerville Greig, afterwards her relative Dr Somerville. She is known in British science not only as the able commentator of Laplace's Meca- 
 — magne- nique Celeste, but as the author of some ingenious and apparently convincing experiments on the magnetizing power of the violet 
 tic action ray. Some anomaly, however, remains to be explained on this subject, as the result cannot always be obtained. Several years 
 of light [?]. before Dr Faraday made his discovery of what he terms the "magnetization of light" (see chapter vii., § 5), the writer of 
 these pages supposed that the reaction of light and magnetism, observed by Moriohini and Mrs Somerville, might be due to a la- 
 tent and casual polarization of the light which was not present in all the experiments ; and, in particular, he suspected that circu- 
 larly polarized light might have a magnetic influence ; but his experiments to this effect, in May 1836, were not successful, 
 though he thinks them worth repeating. 
 
 2 Probably one of the MM. Niepce who, in the early part of the century, are said to have propelled a boat on the Sa6ne by a 
 peculiar kind of air-engine, called pyreolophore, Delambre, Rapport Hiatorique, 1810, p. 242. 
 
Chap. V., § 7.] OPTICS (PHOTOGRAPHY).— DAGUERRE— MR TALBOT. 
 
 125 
 
 keeping his secret until brought to perfectidn, that 
 he did not even show his results until early in 1839, 
 when the numerous specimens he had to exhibit ri- 
 valled in delicacy anything that the art has since 
 produced .1 
 Th ^d**^ The daguerreotype is depicted in the camera on a 
 
 guerreo- V^^^^ of silver, coated with an evanescent film of 
 type. iodide, by exposure for a short time to the vapour of 
 
 iodine. After the light has acted, and the plate has 
 been withdrawn from the camera, no trace of a pic- 
 ture is visible until it has been exposed to the vapour 
 of mercury, which, by its peculiar action on the places 
 where light has acted, produces a correct picture of 
 the object (or positive image, as it is called, light an- 
 swering to light) . It is then fxed, as it is called, by a 
 bath of dissolved hypo-sulphite of soda, which has 
 the property of removing the iodide of silver wherever 
 the light has not acted. This singular and elaborate 
 process has since been but slightly modified by vari- 
 ous plans for rendering the iodide more exquisitely 
 sensitive. To M. Niepce belongs the credit (1) of 
 having fixed an impression of light, (2) of using 
 metal plates, (3) of forming a picture by means of a 
 camera obscura ; to Daguerre, on the -other hand, 
 the novel -and ingenious use of vapours instead of 
 washes, and the whole succession of operations in 
 the daguerreotype. When the French government 
 acquired for the public (the French public, however, 
 only) a right of property in the invention, they 
 marked their sense of the share of merit of the in- 
 ventors, by awarding to Daguerre 6000, to M. I. 
 Niepce 4000 francs per annum. 
 (571.) Mr "W. H. Fox Talbot, a Wiltshire gentleman 
 
 Mr Pox of great ingenuity and perseverance, and well ac- 
 the calo-^ quainted with mathematics and physics, applied him- 
 type. self in 1834 to the problem of fixing shadows, in 
 
 entire ignorance of what Wedgewood and Davy had 
 attempted. He used paper washed with the nitrate 
 of silver, and soon succeeded in obtaining impressions 
 of lace and leaves of plants, but yrithout Jixing the 
 shadows. This great step he, however, made a 
 year or two later : a wash of iodide of potassium, 
 or of common brine, was found to effect it. The 
 announcement of his success and of his methods 
 was called forth early in 1839'' by the first reports of 
 Daguerre's discovery. His method then consisted in 
 dipping writing paper alternately in nitrate of silver 
 and common salt, drying between the operations, 
 and afterwards fixing the image. An unnatural or 
 negative picture was thus obtained, the lights of na- 
 
 ture being darkened on the paper, and vice versa ; 
 but the truth was restored by pressing the drawing 
 thus obtained against a second prepared sheet of 
 paper, and exposing it to light, when the natural 
 lights and shades were of course obtained. This 
 derived impression is called & positive. This process 
 has evidently several advantages over Daguerre's ; — 
 such as, that paper is used instead of metal plates ; 
 and that from a single impression (negative from 
 nature) copies may be at leisure indefinitely multi- 
 plied. Pictures were thus obtained by Mr Talbot 
 with the camera obscura. 
 
 Mr Talbot's chief improvement on his first me- (572.) 
 thod he called the Calotype (1841), and consisted in Progress, 
 washing the paper successively with nitrate of silver, 
 iodide of potassium,^ and gallo-nitrate of silver. It 
 is then exposed in the camera, hut no impression 
 appears until again washed with the gallo-nitrate of 
 silver. It is then fixed with bromide of potassium, or 
 with hypo-sulphite of soda, as in Daguerre's process. 
 
 By a subsequent invention, Mr Talbot has obtained (573.) 
 what he justly calls an instantaneous process} An Instanta- 
 image was formed in a camera of a revolving wheel, "f?."' ^^°' 
 to which was afiixed a printed bill ; the room being 
 darkened, and the wheel made to revolve with the 
 speed of 200 revolutions in a second, and being then 
 illuminated by an electric spark, a legible impression 
 of the printing was obtained. We doubt if, in the 
 whole history of physics, a more astonishing result 
 is recorded. Thus Mr Fox Talbot, by his rare energy, 
 brought his inventions almost to perfection. Nume- 
 rous competitors, of course, appeared on the field, and 
 obtained many interesting results. The only one of 
 much importance to the art of photography is the 
 substitution of a film of iodized collodion on a glass 
 plate, for the prepared paper in the first or negative 
 process. 
 
 The daguerreotype and calotype processes, though (574.) 
 
 seemingly so different, have much in common : — (1) Analogy 
 
 a sensitive surface has to be prepared (iodide of silver" * ® '^^ 
 ... , , ,„, . f '^ \ ■ 1 processes. 
 
 IS the basis m both) ; (2) it is exposed in the camera ; 
 
 (3) the picture (still invisible) is developed ; (4) it is 
 jiased. In the calotype the printing process for ob- 
 taining positives must be added to these. 
 
 The chemical theory is very far behind the art of (575.) 
 photography. The most important steps of these Cl^^^ioal 
 curious and complicated processes have been at- ^"■'y^'"- 
 tained by a kind of divination after a multitude of 
 failures. The salts of silver are of a highly de- 
 composable nature, the iodides and bromides pecu- 
 
 ^ The present writer had the henefit of seeing Daguerre's marvellous productions, and making his acquaintance at Paris, 
 through the courtesy of M. Arago, while the secret was still preserved, and the public interest was excited to the highest pitch. 
 About the same time he saw M. Isidore Niepce, son of the first photographer, and the specimens in his hands, as well as those in 
 the possession of Mr Bauer of Kew, with whom they had been left by M. Nioephore Niepce, when he visited England in 1827 
 and exhibited them at the Royal Society. One of the latter was engraved on a plate resembling pewter. 
 
 ' Communicated to the Royal Society of London, 31st January, and printed in the Philoophical Magazine for March. 
 
 3 Mr Talbot says (Phil. Mag., March 1839, p. 203) that Sir H. Davy had recommended iodide of silver as a sensitive substance ; 
 but in his earlier experiments he had found it the contrary. But now, like Daguerre, be requires no immediate visible action 
 of light, but devehpes it by a subsequent reaction. 
 
 * The process is described in Hunt's Researched on Light, 2d edit., p. 140. 
 
126 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (576.) 
 
 Importance 
 of the pho- 
 tographic 
 art. 
 
 (577.) 
 Chemical 
 rays ren- 
 dered vi- 
 sible. 
 
 (578.) 
 Professor 
 
 ytokes. 
 
 (579.) 
 Shows that 
 the refran- 
 gibility of 
 light may 
 becbanged. 
 
 liarly so. The action of light appears to be to reduce 
 the metallic silver, at least partially, an operation 
 which is completed in the daguerreotype process ap- 
 parently by the affinity of the mercurial vapour for 
 iodine and for oxygen.^ 
 
 If anything were wanting to show the impossibility 
 of separating the scientific arts from the history of 
 science itself, it would be the case before us. The 
 art of photography is far in advance of the theory, 
 yet it constitutes in itself the greater part of what 
 we know in a highly interesting branch of Natural 
 Philosophy — the chemical agency of the spectrum. 
 The surfaces of Talbot and Daguerre are the philo- 
 sophical tools by which farther discoveries can alone 
 be made. 
 
 So intimately connected with the discovery of the 
 Chemical Rays of the spectrum, is that of revealing 
 their existence (at least the existence of rays of the 
 spectrum equally refrangible with those possessing 
 chemical properties) to the sense of sight, that we may 
 conveniently include in this section a very brief no- 
 tice of Professor Stokes' remarkable experiments. 
 
 Mr GrEORGE Gabriel Stokes, a fellow of Pembroke 
 College, Cambridge, and senior wrangler in 1841, 
 at present holds the distinguished position of Luca- 
 sian Professor of Mathematics. It is almost need- 
 less, therefore, to state that his mathematical talents 
 are generally acknowledged, and that he has dis- 
 played them by a ready application to many difficult 
 problems in optics and mechanics which had not pre- 
 viously been accomplished. I may refer, however, to 
 the integration of complex differential equations oc- 
 curring in the theory of the flexure of solids (see art. 
 364), and in that of the rainbow (466), and in his 
 elaborate investigation of certain cases of the friction 
 of fluids (416). But it is more to our present pur- 
 pose to observe that he combines this profound and 
 technical command of analysis with singular skill in 
 the experimental department of optics ; — not merely 
 in investigations closely connected with the wave 
 theory, and expressible by mathematical formulee,^ 
 but in those which depend on the judicious question- 
 ing of nature by critical experiments not necessarily 
 quantitative ; — such, in short, as Newton discusses 
 in his Optics ; and indeed since Newton himself occu- 
 pied the Lucasian chair, there have been perhaps 
 few philosophers who have shown so remarkable an 
 aptitude for both kinds of research. 
 
 In 1852 Professor Stokes announced that the re- 
 frangibility of light, which has hitherto been consi- 
 dered its most inherent and invariable quality, may 
 in some circumstances be altered. The fundamental 
 experiment is this : — A beam of solar light is caused 
 
 to form a pure and highly dispersed spectrum by Fluorea- 
 passing through two or three prisms in succession, ''^°''^- 
 associated with a lens. The spectrum is made to 
 fall on a glass vessel containing a solution of sul- 
 phate of quinine (a colourless fluid). Whilst the red, 
 orange, and indeed the greater part of the luminous 
 spectrum, pass through as if the fluid had been merely 
 water, from about the middle of the violet " the 
 path of the rays is marked within the fluid by a sky- 
 blue light, which emanates in all directions from the 
 fluid, as if it (the medium) had been self-luminous." 
 This appearance extends far beyond the visible violet, 
 the presence of the invisible rays (called chemical) 
 becoming disclosed by the reaction of the quinine ; 
 and the dark bands, both of the visible and the 
 (usually) invisible spectrum, are marked by obscure 
 planes traversing the mass of difiiise light. When 
 the light thus emanating from the interior of the 
 quinine is examined by a prism, it is found to con- 
 sist of rays of various colours and refrangibiUties 
 corresponding to those of the ordinary spectrum ; 
 from which Mr Stokes concludes that, since only vio- 
 let rays and the invisible rays beyond them could have 
 furnished or excited this emanation, the rays of light 
 themselves have been transformed into others, with a 
 lower degree of refrangibility, and possessing the cor- 
 responding optical properties. In conformity with 
 this explanation,. Professor Stokes has considered and 
 accounted for a number of curious phenomena de- 
 scribed by Sir David Brewster and by Sir John Her- 
 schel ; called by the former " internal dispersion," 
 by the latter " epipolic dispersion," all of which, so 
 far as they involve anything peculiar, may be reduced 
 to the general principle that certain bodies by their 
 action on light have the power of lowering the refran- 
 gibility of the rays incident upon them, whether be- 
 longing to the visible or invisible spectrum — that is, 
 of emitting rays of a lower, while under the excite- 
 ment of rays of a higher refrangibility. Hence 
 the phenomenon has been termed the " degradation" 
 of light. Mr Stokes has also called it " fluores- 
 cence " a word involving no hypothesis, being derived , 
 from the characteristic action of a certain kind of 
 fluor-spar described by Sir David Brewster. 
 
 Many substances, solid and fluid, are found to pos- (580.) 
 sess these qualities.^ Amongst others, and in the ^"^''^*^^'^®' 
 highest degree, glass coloured yellow by oxide of^^?g ^^^"^ 
 uranium, called in commerce canary glass, and solu- perty. 
 tions of horse-chestnut bark. 
 
 By using sources of light richer than sunlight in (581.) 
 the highly refrangible rays ; by also using quartz for ^™*'^''- . 
 the prisms instead of glass (which has the power mgnt^^j^th' 
 of absorbing these to a considerable extent) — Pro- electric 
 
 light. 
 
 1 I may refer to a short but clear paper on the theory and practice of photography by the Rev. W. T. Kingsley, in the Journal 
 of the Photographic Society, vol. i., August 1853. Mr Kingsley is one of the most scientific and practical improvers of the art. 
 
 2 This he has also done in a beautiful paper on the effect of polarization in modifying the phenomena of diffraction. Camb. 
 Trans., vol. ix. 
 
 3 The gieater part of these had been detected by Sir D. Brewster, with his usual acuteness and perseverance, in the course of 
 his researches on " internal dispersion." The colouring matter of green leaves is one of the most remarkable. 
 
Chap. VI., § 1.] 
 
 HEAT. — BLACK. 
 
 127 
 
 fessor Stokes has obtained a result truly astonishing. 
 In the case of the light derived from a voltaic arc, 
 produced by the battery of the Royal Institution 
 with metallic poles, the visible spectrum formed upon 
 uranium-glass extended no less than six or eight times 
 the length of the ordinary spectrum. If, by way of 
 contrast, a porcelain tablet be used as a screen, the 
 spectrum terminates at the usual point.' 
 
 C581.) [I have already (art. 471) expressed my regret 
 
 Mr Wheat- ^jj^^ ^jjg ijmitg of this Essay prevent me from devot- 
 sion— the " ™S ^ section to the physiological part of Optics ; 
 Stereo- but I cannot close the chapter without at least 
 scope. 
 
 naming Mr Wheatstone's beautiful invention of the 
 Stereoscope, as by far the most interesting contribu- 
 tion recently made to the theory of, vision, regarded 
 in a point of view not strictly anatomical. Although 
 Mr Wheatstone's paper was published in the Philo- 
 sophical Transactions for 1838, and the Stereoscope 
 became at that time known to men of science, it by 
 no means attracted, for a good many years, the at- 
 tention which it deserves. It is only since it received 
 a convenient alteration of form (due, I believe, to Sir 
 David Brewster), by the substitution of lenses for 
 mirrors, that it has become the popular instrument 
 which we now see it, but it is not more suggestive 
 than it always was of the wonderful adaptations of 
 the sense of sight.] 
 
 CHAPTER VI. 
 
 HEAT, INCLUDING SOME TOPICS OF CHEMICAL PHILOSOPHY. 
 
 § 1. Black. — Latent and Specific Heat. — Irvine. — Hutton. — Doctrines of Heat applied to some 
 
 Natural Phenomena. 
 
 (582.) Down to the close of the 18th century, the science 
 
 dered in ^^ Heat was studied and advanced mainly by che- 
 the 18th mists, and it was in all respects treated as a branch 
 century as of Chemistry ; a position of which we still find traces 
 of chemie- ^^ ^^^ introduction of the doctrines of heat (even of 
 try. radiant heat) into most of our approved treatises on 
 
 Chemistry. This circumstance brings us, in this 
 chapter, into close contact with the most illustrious 
 chemical names of the second half of the last century 
 and of the first years of the present. Such were 
 Black, Cavendish, Lavoisier, and Dalton. Of the last 
 and two first it may be doubted whether they were not 
 as prominent discoverers in Physics as in Chemistry. 
 Davy occupies a similar position. It was not, in- 
 deed, until the 19th century had made some pro- 
 gress that Chemistry assumed a strongly distinctive 
 position of its own, and began to attain that large 
 development and complex character of detail which 
 render it a science now hardly accessible to those 
 who do not devote to it their almost undivided at- 
 tention. In the days df Black and Cavendish it was 
 otherwise ; and in the first section of the present 
 chapter I shall attempt to give an outline of the 
 characters of the very remarkable men who then 
 advanced simultaneously the doctrines of Physics 
 and Chemistry ; referring, of course, chiefly to the 
 former, but not entirely to the exclusion of the lat- 
 ter portion of their researches, particularly with 
 respect to the atomic and gaseous theories of Dal- 
 ton, which have a strongly physical aspect. I have 
 
 elsewhere noticed the barrenness of the greater part 
 of the 18th century in contributions to the experi- 
 mental sciences ; the temptation is therefore the 
 greater to dwell a little even on the personal history 
 of men so celebrated and influential as Black, Caven- 
 dish, and Dalton. 
 
 Joseph Black was bom at or near Bordeaux in (583.) 
 France, in 1728. His biography, little eventful and f^^J^"^ * 
 almost exclusively academic, has been recorded in as a che- 
 some detail by his companions and friends Adam mist. 
 Ferguson and John Robison (the former of whom 
 was a relation), in the preface to the posthumous 
 publication of his Lectures on Chemistry. It is suffi- 
 cient for me to state that he entered the University 
 of Glasgow as a student in 1746. Being destined 
 for the medical profession, he removed in 1750 or 
 1751 to Edinburgh, where he benefited especially 
 by the lectures of CuUen, a most eminent physician, 
 and the author of a beautiful experiment on the cold 
 produced during evaporation. Before Black gradu- 
 ated (in 1754) he had entered upon a course of chemi- 
 cal expei-iments connected with the causticity of many 
 earthy bodies, which ended in his first (and perhaps 
 most famous) discovery of the existence ot fixed air or 
 carbonic acid gas as an essential constituent of marble 
 and other solids, together with a train of important 
 consequences. Fewinaugural dissertations have been 
 so interesting to science as that on Magnesia, printed at 
 Edinburgh in 1754, which contained these results. But 
 on this purely chemical question we will not enlarge. 
 
 ^ On Mr Stokes's experiments, see Phil. Trans., 1852-53; and Proceedings of the Boyal Institution. 
 
128 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (584.) 
 His disco- 
 veries of 
 latent and 
 specific 
 heat. 
 
 Latent 
 heat ab- 
 sorbed in 
 melting 
 
 Itsamoant. 
 
 (585.) 
 Conse- 
 quences. 
 
 The discoveries of Black with which we are chiefly 
 concerned are those of latent and specific heat. 
 The former, at least, is Black's sole and exclusive 
 property. When we look back to the state of the 
 science of heat in the\ first half of the 18th century, 
 we are surprised at the exceeding slowness of its pro- 
 gress. The thermometer had been improved by the 
 use of the freezing and boiling temperatures of water 
 for its fixed points, and the adoption of mercury in 
 its construction by Fahrenheit ; the correspondence 
 of its scale with true increments of heat had been 
 tested, though imperfectly, by Brooke Taylor ; and 
 Dr Martine of St Andrews had published an ingen- 
 ious work (the best of its period) on the expansion of 
 different liquids, and on some kindred subjects; but in 
 general no great step was made until Black, in 1757, 
 or previously,'^ concluded that during the melting of 
 snow or ice, a great quantity of heat enters into the 
 body without afiecting the thermometer in an appre- 
 ciable degree. The heat therefore spends itself or is 
 absorbed in effecting liquefaction. Black called it 
 latent (as opposed to sensible) heat. He was led to 
 this discovery by the very simple observation of the 
 extreme slowness with which ice is melted by the 
 application of an amount of heat which would have 
 raised the temperature of water to an enormous ex- 
 tent ; the thermometer plunged in the thawing ice 
 remaining stationary until it is entirely reduced to 
 water. When that occurs, heating immediately com- 
 mences according to the usual laws. One of Black's 
 original experiments clearly illustrates his mode of 
 procedure. He suspended equal weights of ice at 
 32°, and of water as near as might be at the same 
 temperature, in two thin glass vessels 18 inches 
 apart, in a spacious room having a temperature of 
 47°. The vessel containing water rose 7" in tem- 
 perature in half an hour, but the equal weight of ice 
 had not wholly melted, nor had its temperature even 
 slightly increased until 21 half hours had elapsed. 
 Whence Black concluded (approximately) that as 
 much heat is requisite merely to thaw ice as would 
 raise an equal weight of water through 7 x 21 or 
 147°; a result almost corrrect, although the experi- 
 ment in this form is manifestly not unexceptionable. 
 The converse process of freezing shows how prolonged 
 must be the application of cold to discharge water at 
 32° of its latent heat, or heat of liquefaction, and to 
 convert it into ice. 
 
 Nothing is more admirable in these results than 
 the light they throw tipon certain natural processes. 
 Were instant liquefaction the result of the smallest 
 application of heat to snow at 32°, we should many 
 times a year be the victims of uncontrollable floods ; 
 and did water instantly become ice on its tempera- 
 ture reaching the freezing point, our lakes and rivers 
 would be rapidly consolidated to the very bottom on 
 
 occasion of every frost, and animal life would be im- 
 possible. 
 
 The analogy of the gradual formation of steam in (586.) 
 boiling, to the gradual liquefaction of ice, was so Latent 
 evident as to lead Black to conclude, without any '^*** °^ 
 special experiment, that a great deal of heat' becomes 
 latent during the conversion of liquids into vapour. 
 It appears to have been in 1762 that he attempted 
 to determine roughly the amount, by a method simi- 
 lar to that just described for the heat of liquefaction. 
 He compared the time required under the action of a 
 uniform source of heat to raise the temperature of a 
 certain quantity of water from 50° to the boiling 
 point, with that required to boil it away ; and in- 
 ferring that heat was continually combining with the 
 water at the same rate, he estimated the latent heat, 
 or heat of vapour, to be as great as would have raised 
 the temperature of the water had that been possible 
 by 810°. This was in October 1762;* about two 
 years later his pupil, Irvine, made experiments under Experi- 
 his direction with a still and refrigeratory, by which ments of 
 he estimated the heat given out by steam during its Irvine and 
 reconversion into water. Mr Watt prosecuted the "***• 
 same inquiry soon after.^ How happily Mr Watt 
 applied the doctrine of latent heat thus brought ex- 
 perimentally under his notice, to the improvement 
 of the steam-engine, has been already recorded. 
 
 One thing strikes us very much on a review of ,537 \ 
 these discoveries of Black ; it is the great interval Theae laws 
 which separates the clear perception of a fact from singularly 
 the explanation of it ; or, in other words, from the ?^^ 
 clear expression of the more general fact which em- Black 
 braces it, although when once given, the explanation 
 may seem to be almost expressed in the very enun- 
 ciation of the fact. Nearly a century before Black, 
 the lynx-eyed Hooke had noticed that water during 
 the process of congelation remained unaltered in tem- 
 perature, and that the same takes place when it boils, 
 and this observation had been numberless times veri- 
 fied in ascertaining the fixe<l points of thermometers ; 
 yet no one before Dr Black had even guessed that 
 the heat which enters jnto ice during liquefaction, and 
 into water during vaporization, remained as it were 
 a constituent of the water and the steam thus formed, 
 and could at any time be recovered by a converse 
 process. Numberless instances occur in the history 
 of science in which it requires the utmost attention 
 to appreciate the importance and difficulty of draw- 
 ing such seemingly obvious conclusions. 
 
 The other great discovery of Black, Specific (sgg.) 
 Heat, was in like manner a correct interpretation of Specific 
 a fact already known. Boerhaave and Fahrenheit •'®**- 
 had found that when quicksilver and water were 
 mixed together, their temperatures being different, the 
 heat of the mixture was not, as might have been ex- 
 pected, the average of that of its ingredients, whether 
 
 1 On the authority of a letter from Black to Watt ; see Black's Lectures. ^ Black's Lectures, i., 158. 
 
 ^ Ibid., 171-173. In these early experiments the latent heat of steam was a good deal underrated. 
 
Chap. VI., § 1.] 
 
 HEAT. — BLACK — IRVINE. 
 
 129 
 
 the volumes or the weights of those ingredients were 
 equal. " Quicksilver, whether it were applied hot 
 to cold water or cold to hot water, never produced 
 more effect in heating or cooling an equal measure of 
 the water than would have been produced by water 
 equally hot or cold with the quicksilver, and only 
 two-thirds of its bulk." Of course, when equal 
 weights were used, the inequality of effect was still 
 more striking, for, from the great density of quick- 
 silver, it required no less than 30 times the weight of 
 the water mixed with it in order that it should con- 
 tribute in an equal degree to the production of a 
 mean temperature. Strange to say, the interpreta- 
 tion of this important experiment remained to be 
 made by Dr Black after half a century. He taught 
 that temperature is an effect of heat, which is neither 
 the same in all bodies nor in the same body under 
 differing circumstances; that the superior effect of 
 the water to the mercury in determining the tempe- 
 rature of the mixture was caused by the fact, that it 
 is the nature of quicksilver to require a smaller 
 amount of heat to raise its temperature through 
 -one degree than an equal volume or weight of 
 water would require under like conditions. Black 
 made many experiments to satisfy himself of the 
 constancy of this property in bodies ; and with the 
 assistance of Irvine,^ probably ascertained its nume- 
 rical value (the amount of heat necessary to raise an 
 unit of mass of water through one degree of tempe- 
 rature being the standard) in different cases ; but he 
 left the subject chiefly in the hands of that observer 
 and of Watt. The former gave the name of ca- 
 pacity for heat to this property, which was after- 
 wards more happily termed specific heat by Gadolin, 
 who made many experiments on the subject, as did 
 also Cavendish and Adair Crawford whose theory 
 of animal heat, published in 1778, turns entirely on 
 this property of bodies. 
 (589.) Irvine had the merit, such as it was, of proposing 
 
 Irvine s ^ theory on which his term capacity for heat was 
 capacity of Principally founded, which occasioned for many years 
 bodies for after, although now comparatively forgotten, much 
 heat. discussion. He assumed that the changes in the 
 
 temperature of bodies, whether by alteration of 
 their mechanical condition or by chemical combina- 
 tion, were due to a change in the capacity for heat of 
 the substance or the mixture. He also assumed that 
 the total amount of heat contained in a body is pro- 
 portional to the amount of heat necessary to raise its 
 temperature through one degree (for example, a 
 pound of mercury contains altogether one-thirtieth 
 part of the entire heat contained in a pound of water). 
 From these principles he deduced the temperature of 
 absolute zero or privation of heat as follows : — When 
 sulphuric acid and water are mixed together, the tem- 
 perature rises. This rise, according to him, is caused 
 by the capacity for heat of the mixture being less 
 
 than the average due to its ingredients. He has, there- 
 fore, got the ratio of the whole heat in the bodies 
 before mixture and after mixture. He has also got 
 the number of degrees of temperature corresponding 
 to this difference. Having the ratio of these quan- 
 tities, and also their difference, the quantities them- 
 selves, or the whole amount of heat expressed in de- 
 grees of temperature before and after mixture, become 
 known, and the temperature of absolute privation of 
 heat is also known. He applied the same reasoning, 
 with great ingenuity, to explain the latent heat of li- 
 quids and vapours, which he ascribed to their increasing 
 capacities. He thence deduced other values for the 
 absolute zero ; but whereas all these determinations 
 ought to have agreed, at least approximately, they 
 were found by later experimenters, especially by La^ 
 voisier and Dalton, to differ so widely — even by se- 
 veral thousand degrees — that, since the time of the 
 latter, this ingenious theory has been nearly aban- 
 doned, at least as far as the search after the zero is 
 concerned ; although undoubtedly change in the spe- 
 cific heat of bodies is often an important element in 
 determining their temperature. 
 
 To return to Dr Black. From 1756 to 1766 he (590.) 
 filled the chair of Chemistry and Medicine at Glas- fj^'^.^'^^g^j.'^ 
 gow, where he also practised as a physician. In i,jg diarac- 
 1766 he left Glasgow for Edinburgh, to succeed Dr ter. 
 Cullen as Professor of Chemistry — a position which 
 he held, with great credit to himself and with benefit 
 to the University, till his death in 1799. His health, 
 during the greater part of that time, was feeble, owing 
 to a pulmonary affection, which often interrupted his 
 lectures, and, it is stated, prevented him from engag- 
 ing in severe study without immediate injury. Though 
 he published one or two papers during these thirty 
 years, they were of comparatively trifling importance. 
 His influence on science was chiefly exerted through 
 the medium of his pupils and of his intercourse with 
 general society. His lectures are described by those 
 who had the good fortune to hear them as inimitable 
 of their kind — grave, dignified, and so interesting as 
 to rivet the attention. " Perfect elegance as well as 
 repose was the phrase by which every hearer and 
 spectator naturally, and as if by common consent, de- 
 scribed the whole delivery."^ It is probable, also, 
 that in his private intercourse with his pupils, he in- 
 spired them with that love of research which distin- 
 guished his own early days, and his taste for neat and 
 accurate experiment could hardlyfail of being imparted 
 to a certain extent. Yet we may be permitted to regret 
 that his constitutional indolence, almost apathy, had 
 perhaps as great a share as bad health in the inter- 
 ruption of his career of discovery. Even when quite 
 a young man, his most interesting conclusions were 
 so gradually evolved, that he himself had difficulty 
 afterwards in fixing their date ; and some of them 
 were delayed even for years, imtil he found time to 
 
 ^ Sir J. Leslie has, I think inadvertently, given the credit of the discovert/ of specific heat to Dr Irvine. ^ Lord Brougham. 
 
130 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (591.) 
 Dr Hutton 
 — Black's 
 intimate 
 friend — 
 liis theory 
 of rain and 
 vapour. 
 
 make tlie requisite experiments. So cool a tempera- 
 ment was not likely to grow warmer as age advanced. 
 Almost as indifferent to the honours of discovery as 
 his stoical contemporary Cavendish, unlike him he 
 enjoyed in a high degree intercourse with the conge- 
 nial society which Edinburgh at that time afforded. 
 He loved to converse infinitely better than to write ; 
 especially when he could converse intimately with 
 such men as Adam Smith, David Hume, Adam Fer- 
 guson, Principal Robertson, Dr John Robison, John 
 Home, Clerk of Eldin, and Dr James Hutton. 
 
 Hutton was perhaps Black's dearest friend, and 
 may be mentioned here (episodically) as no ordinary 
 thinker in Natural Philosophy, as well as in Geology 
 and Metaphysics. Besides the " theory of the Earth," 
 which will ever bear his ' name, and which, after va- 
 rious transmutations in name and form, is now by 
 far the most widely prevalent, his theory of Rain 
 was an ingenious and important speculation. Other 
 branches of Meteorology also claimed his attention, 
 particularly, as might have been expected, those 
 which are connected with the temperature of the 
 earth. He was one of the first who drew conclu- 
 sions from the temperature of springs, with regard to 
 change of climate due either to increased latitude or 
 to increased height above the sea. His hygrometer, 
 in which the dampness of the air was estimated 
 by the coolness due to evaporation, was unquestion- 
 ably the first suggestion of a method now in general 
 use. His ideas on the constitution of matter were 
 bold and ingenious, though not on all points tenable. 
 They resembled those of Boscovich, though inde- 
 pendent of them. He published a voluminous trea- 
 tise on several subjects in Natural Philosophy, and 
 a still more formidable one on the Principles of 
 Knowledge, neither of which attracted much at- 
 tention at the time, and have been long forgotten ; 
 yet it is not unlikely that some of his speculations 
 in metaphysics might be worth the labour of re- 
 
 examination. His friend and commentator, Playfair, 
 (whose style was as remarkable for perspicuity as Dr 
 Hutton's was the contrary) has drawn the following 
 lively contrast between the characters of Hutton and 
 Black, which may properly conclude this notice : — 
 " Ardour and even enthusiasm in the pursuit of Contrast 
 science, great rapidity of thought, and much anima- °^ ^^"^ 
 tion distinguished Dr Hutton on all occasions, j^^ 
 Great caution in his reasonings, and a coolness of 
 head which even approached to indifference, were 
 characteristic of Dr Black. On attending to their 
 conversation, and the way in which they treated any 
 question of science and philosophy, one would say 
 that Dr Black dreaded nothing so much as error, 
 and that Dr Hutton dreaded nothing so much as ig- 
 norance ; that the one was always afraid of going 
 beyond the truth, and the other of not reaching it. 
 The curiosity of the latter was by much the more easily 
 awakened, and its impulse most powerful and imperi- 
 ous. With the former, it was a desire which he could 
 suspend and lay asleep for a time; with the other, it was 
 an appetite that might be satisfied for a moment, but 
 
 was soon to be quickly renewed Each 
 
 had something to give which the other was in want 
 of. Dr Black derived great amusement from the vi- 
 vacity of his friend, the sallies of his wit, the glow 
 and original turn of his expression ; and that calm- 
 ness and serenity of mind which, even in a man of 
 genius, may border on languor and monotony, re- 
 ceived a pleasing impulse by sympathy with more 
 powerful emotions."^ 
 
 Black died on the 6th December 1799.^ His death, (592.) 
 as recorded by his kinsman, Adam Ferguson,^ was Black's 
 one of the most touching on record. It succeeded his '^^''*''' 
 customary state of health by an interval inappre- 
 ciably short, and, as appeared by the accompanying 
 circumstances, without the slightest physical emotion. ^ 
 The philosophic composure of his whole life was mir- 
 rored in the serenity of its close. 
 
 § 2. Cavendish.* — His Singular Character and Attainments — Eminent Chemical Discoveries- 
 Observations on Heat and on other Branches of Physics — Lavoisier — The Calorimeter- 
 
 Theory of Combustion and of Oondation. 
 
 Cuvier has justly remarked, in his biography of 
 (593.) Cavendish, that he had to struggle in his scientific 
 Cavendish, g^reer against obstacles much more rarely encoun- 
 tered, and perhaps less easily overcome, than those 
 
 which beset the progress of genius cramped by poverty 
 and neglect. Cavendish was the descendant of one 
 of England's noblest families, and he was likewise 
 the possessor of enormous wealth ; yet neither of 
 
 ^ Playfalr's Biographical Account of Dr James Hutton, Works, vol. iv. 
 
 ^ Muirhead's Correipondmce of James Watt. Introd., p. xxii. _ 3 Preface to Black's Lectures, by Robison, p. Ixxi v. 
 
 * I find an apology almost necessary for introducing at some length the biography of Cavendish into a chapter professedly on 
 Heat, his positive discoveries connected with which were less notable than in some other departments. But besides that his posi- 
 tion in the first rank of chemists naturally indicates his place to he between Black and DaltOD, I felt a wish to bring out the 
 relief of the striking intellectual characteristics of those three remarkable men, by placing them in juxtaposition. I may add 
 that these three sections were the earliest written of this Dissertation, at a time when I had hoped to interweave into its compo- 
 sition more of the purely biographical character of each period of scientific history than I found it afterwards practicable in all 
 instances to carry out. I trust, however, that it may be found a not unwelcome variety amidst the abstruser details of science. 
 In the case of Cavendish, too, so various are his claims on our notice, that it was inevitable to recur to them in different chap- 
 ters, especially in those on Astronomy and Electricity. It was not, therefore, really material under which head the more strictly 
 personal detaUs were given to which I have alluded. 
 
Chap. VI., § 2.] 
 
 HEAT. — CAVENDISH. 
 
 131 
 
 (594.) 
 His per- 
 sonal his- 
 tory. 
 
 (595.) 
 His won- 
 derful 
 range of 
 scientific 
 knowledge. 
 
 these powerful temptations could withdraw him even 
 for an hour from the course of study which he had 
 marked out ; and which constituted for him at once 
 labour and relaxation, the end of living, and almost 
 life itself. 
 
 The Honourable Henry Cavendish, son of Lord 
 Charles and Lady Anne Cavendish, was born at Nice, 
 October 10, 1731.1 He entered St Peter's College, 
 Cambridge, 24th Noveinber 1749, where he resided 
 during the usual terms for above three years, when 
 he ought naturally to have graduated, which, how- 
 ever, he never did. That he had pursued at least 
 his mathematical studies with ability and success is, 
 however, nearly certain from the firm hold which he 
 ever after retained of them. He joined the Koyal 
 Society of London in 1760, and published his first 
 paper in their Transactions in 1766. From the time 
 of his leaving Cambridge for some years his personal 
 history is not known, though he probably resided in 
 London. 
 
 The subsequent history of Cavendish is the history 
 of his studies and his discoveries. The latter were 
 published in concise memoirs, written with scrupulous 
 precision, and all printed in the Philosophical Trans- 
 actions. ' If collected (which they have not been) they 
 would fill but an insignificant volume, yet include all 
 the requisites to establish a first-rate reputation. His 
 studies no doubt were enormous, for they occupied 
 every disposable moment of a life prolonged almost 
 to fourscore. They may be guessed at (in addition 
 to the published results) from his manuscript remains, 
 a few of which have been edited recently, but the 
 larger part remains in manuscript in the possession of 
 his heirs. Few if any branches of exact science were 
 unfamiliar to him ; and his published papers include 
 astronomy, mechanics, electricity, heat, chemistry, 
 and meteorology, besides which he cultivated mathe- 
 matics and geology. His reputation is one of those 
 which may be called in a peculiar sense European or 
 universal, because it marked a great epoch in science 
 to which the publication of his writings materially 
 contributed. That epoch was when chemistry be- 
 came a science of weight and measure. Cavendish 
 was a weigher and measurer almost by nature, and 
 entirely so by habit. It appears from his note-books 
 that he took the most scrupulous pains to ascertain 
 and record the quantities of the ingredients employed 
 in every experiment, even though they might be im- 
 material to the result ; and his whole life was metho- 
 dical in the same proportion. The immense impor- 
 tance of Cavendish's labours to the progress of science 
 in his day is found in the unanimous testimony of 
 his contemporaries ; and notwithstanding the extreme 
 retirement in which he lived, and the rarity of his 
 appearances as an author, he was generally regarded 
 as perhaps the leading man of science in England of 
 
 his day ; and his good opinion was considered by con- 
 temporary philosophers as their highest praise. Sir 
 Humphry Davy's opinion of him (recovered and 
 published by Dr Davy from a manuscript lecture) 
 represents that of such of his countrymen as were 
 qualified to form one, and the writer of it was 
 usually fastidious in his judgments of others : — " It 
 may be said of Mr Cavendish, what can perhaps hardly 
 be said of any other person, that whatever he has 
 done has been perfect at the moment of its produc- 
 tion. His processes were all of a finished nature. 
 Executed by the hand of a master, they required no 
 correction ; and though many of them were per- 
 formed in the very infancy of chemical philosophy, 
 yet their accuracy and their beauty liave remained 
 amidst the progress of discovery, and their merits have 
 been illustrated by discussion, and exalted by time." 
 
 After this eulogium of so competent a judge, I (596.) 
 shall be satisfied by a simple enumeration of those Chemical 
 
 chemical discoveries which were the most splendid <''8^''^^"*8 
 f 1 ' 1 I'll 11 ^.,.01 Caven- 
 
 results or ms career, but which hardly come withm jUsj,. 
 
 the immediate scope of this dissertation. To him we 
 are mainly or entirely indebted for the knowledge of 
 hydrogen as a distinct elastic fluid or gas ; of the 
 exact constitution of the atmosphere, and the won- 
 derful constancy of its ingredients ; of the composi- 
 tion of nitric acid ; and finally, according to the 
 opinion of most persons (at least till lately), of 
 the non-elementary nature of water, and of its 
 precise constituents. This last and crowning dis- 
 covery has indeed been contested, and made the sub- 
 ject of a prolonged and bitter scientific controversy, 
 which hardly could be said to exist until the con- 
 temporary generation who witnessed the facts, and 
 also the succeeding one, had passed away. For Caven- 
 dish received until his death, and for nearly thirty 
 years after, the unquestioned tribute of at least the 
 primary merit in so great a step in science. The ' 
 
 topics more peculiar to the present essay (sufficiently 
 extensive besides) enable us to dispense with the un- 
 welcome task of once more analyzing a controversy 
 purely personal, and which has almost filled volumes. 
 I shall content myself with stating two considera- 
 tions, which must have great weight in turning the 
 balance of the evidence (supposing it balanced) in 
 Cavendish's favour. The first is founded on the 
 behaviour of Watt himself; the second on the known 
 character of Cavendish. 
 
 As to the former consideration, I would remark that /gg^ \ 
 Watt withdrew the letter to Priestley which he had Contro- 
 submitted to the Royal Society and which contained '^J^^J o" 
 his views respecting the composition of water, before I.'?'^™''^ 
 it had been read at the meetings of that body.^ The position of 
 causes of this suppression are candidly stated by water. 
 Watt in a letter to Sir Joseph Banks, published by 
 Mr Muirhead,* in which he states that he " thought 
 
 ^ Life of Cavendish, by Dr George Wilson ; a valuable biography, which has been printed in the series of publications of the 
 " Cavendish Society," and thus unfortunately has had but a limited circulation. 
 
 ^ Correspondence on the Composition of Water, p. 30. ^ Ibid. p. 52. 
 
132 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Argument it prudent to delay the publication until he should 
 from^ have considered it [the theory of the composition 
 haviour ^" °^ water] more maturely, and have made some ex- 
 periments to determine the proof or falsehood of it.' ' 
 This, it must be owned, was not the language of a man 
 who had acquired that amount of conviction which 
 is needful, — not to broach a theory, — but to hold fast 
 by it against all opposition. With the caution which 
 formed part of his character, Watt was unwilling 
 to hazard his reputation by adhering to a doctrine 
 which appears at the time to have received no sup- 
 port from his scientific friends, especially Dr Black.. 
 Having read the correspondence published by Mr 
 Muirhead, I cannot doubt that Watt, whatever his 
 private opinions might continue to be, would never 
 have urged his views on an unwilling public, but 
 would have finally suppressed the letter to Priestley, 
 had not the experiments and claims of Cavendish at 
 home, and of Lavoisier in France, reanimated all 
 his zeal for the assertion of his opinion. This in- 
 deed Watt ingenuously admits in the letter to Sir 
 Joseph Banks just cited, where he states that the 
 fact of similar theories having since been supported 
 by philosophers of first-rate abilities, removed his 
 second objection to publication. As the suppression 
 of his paper would have relieved Watt of all the re- 
 sponsibility of error, it seems impossible to allow him 
 the advantage — of which that suppression deprived 
 him — of anticipating the date of his matured convic- 
 tion; and to this conviction we have his own evidence 
 that Cavendish's publication as well as certain addi- 
 tional experiments of his own influentially contri- 
 buted. Watt, in after life, may be said to have tacitly 
 relinquished to Cavendish the honour which, in the 
 first irritation of the conflict of their claims, he showed 
 nodisposition to do; it is, therefore, reasonable to infer 
 that, on reflection, he saw good reasons for doing so. 
 By this I mean that he suffered judgment to be passed 
 in favour of Cavendish's claim in the writings of many 
 of his eminent contemporaries, without attempting 
 publicly to correct the all but universal impression 
 which they made. In one instance, he almost ho- 
 mologated this adverse judgment : — In the article on 
 Steam, written by Robison, and revised by Watt in his 
 last years and after Cavendish's death, this passage 
 appears, — '^ This is fully evinced by the great disco- 
 very of Mr Cavendish of the composition of water ;" * 
 from which it must be concluded, first, that Robison, 
 the intimate friend of Watt, and the almost chival- 
 rous defender of his fame, believed Cavendish to 
 be the true discoverer 5^ secondly, that Watt, in 
 commenting on this article in 1814, permitted the 
 fact to be thus transmitted to posterity. For, in 
 
 his numerous animadversions on other parts of the 
 same papers, he gives (as I have pointed out in the 
 note to art. 318) free expression to the sensitive-' 
 ness which he felt lest Dr Black should derive any 
 credit to which he was not entitled in connection with 
 the steam-engine, but he suffers the passage just 
 quoted to pass without remark. Such being the 
 case, and waiving all purely chemical discussion, 
 I am of opinion that Watt's friends should have 
 left the matter as he was content to leave it. 
 
 With reference to the argument from Cavendish's (598.) 
 character, I would remark that whilst the claim of Arguroent 
 Watt cannot be maintained without impeaching the ^r"" ^^^ 
 honour and integrity of his rival, and showing that he „£ t-aven- 
 stooped to subterfuge in order to appropriate to him- dish. 
 self a discovery due to another- — it would yet be diffi- 
 cult to find in the whole range of scientific history 
 (without excepting the venerable name of Newton), an 
 individual so devoted to knowledge for its own sake, 
 so indifferent to the rewards of discovery, so averse to 
 the publication of what he felt to be important, and 
 knew to be original, so insensible to the voice of 
 praise when applied to himself, so ardent in acquaint- 
 ing himself with the labours of others, and so liberal 
 in assisting them. Such a man was Cavendish ; and 
 that he should stoop even to the common artifices of 
 little minds for exalting his own reputation at the ex- 
 pense of others, would itself be incredible ; how much 
 more the insinuation (grounded solely on alleged cir- 
 cumstantial evidence) that in doing so he disregarded 
 the plainest dictates of honour and justice. 
 
 Black and Cavendish were nearly contemporaries, (6?9-) 
 the former having been born only three years earlier. ?.*y™" 
 But I doubt whether these two men, so congenial in periments 
 their studies, so different in almost every circum- on latent 
 stance, whether of fortune or temperament, ever met. ^^ specific 
 They had this, however, in common, that they pub- 
 lished their discoveries and observations with reluc- 
 tance, and were fastidious in the manner of doing so. 
 Black's experiments, both in chemistry and on heat, 
 preceded those of Cavendish, and with regard to the 
 latter subject (heat) it is probable that Cavendish 
 pursued investigations and made original experi- 
 ments, in which he had been unknowingly anticipated 
 by the Scotch professor. His researches on latent 
 and specific heat (though he did not employ these 
 terms) appear to have been subsequent to Black's, 
 but to have preceded those of Crawford and Wilcke ; 
 and it is not impossible that his was the earliest, or 
 one of the earliest, determinations of the amount of 
 heat absorbed in the conversion of water into steam, 
 for which he obtained various results between 923° 
 and 982°, a mean of which would be very near the 
 
 ^ Robison's Mechanical Philosophy, ii., 21. 
 
 2 The article Water in the early editions of the l!ncyclo]!>mdia Britannica has been quoted as the produetion of Robison, 
 of which there does not appear to exist any proof, whilst the probability, as shown in the text, lies all the other way, I learn 
 upon the best authority that the proprietors of this Uncyclopcedia have no clue to the authorship of that article, and that it is 
 not included in the lists of Robison's known contributions. The part relating to the present question was expunged in the Fourth 
 Edition, and a reference made to the article Chemistry where Cavendish received the credit of the discovery. 
 
Chap. VI., § 2.] 
 
 HEAT.^— CAVENDISH. 
 
 133 
 
 (600.) 
 Papers on 
 the earth's 
 attraction, 
 and theory 
 of electri- 
 city. 
 
 (601.) 
 Singular 
 personal 
 character- 
 istics of Ca. 
 vendish. 
 
 truth. But it is needless to dwell upon these obser- 
 vations, however original, because they were volun- 
 tarily suppressed by the author, and have only re- 
 cently been brought to light from his manuscripts. "^ 
 What he did publish in connection with this subject 
 was a paper on the construction and graduation of 
 meteorological instruments, especially thermometers, 
 and others on the temperature at which mercury 
 freezes, and on freezing mixtures. The former of 
 these papers was, as might be expected, far in ad- 
 vance of its age in the degree of exactness which was 
 shown to be attainable in the construction of ther- 
 mometers, and scarcely even now can it be considered 
 as obsolete. The papers on freezing mercury finally 
 corrected the exaggerated notion at first entertained 
 of the extreme cold at which that metal becomes 
 solid, and also contain valuable views on the sub- 
 ject of congelation, and fixed the latent heat of water 
 at 150°. He calls this, " generation of heat" during 
 liquefaction, objecting to Black's term as relating 
 " to an hypothesis, depending on the supposition that 
 the heat of bodies is owing to their containing more 
 or less of a substance, called the matter of heat ; and 
 as I think Sir Isaac Newton's opinion that heat con- 
 sists in the internal motion of the particles of bodies 
 much the most probable, I chose to use the expres- 
 sion, heat is generated,"^ 
 
 Two of Cavendish's most important researches re- 
 fer to the attraction and density of the earth, and to the 
 mathematical theory of electricity. The former (which, 
 in principle, was derived from the Be v. John Michel!) 
 has been already analyzed in the chapter on Astro- 
 nomy (art. 156). The latter will be more conve- 
 niently referred to in our chapter on Electricity. 
 
 Cavendish's publications extended over the greater 
 part of his active life, but those on chemistry and 
 electricity, on which his fame principally depends, 
 do not extend beyond the year 1775 ; the date of his 
 paper on the density of the earth is 1798. He died 
 24th February 1810, at the age of 79- He appears 
 to have.exercised scarcely less influence by his general 
 devotion to science, than by his specific discoveries, 
 great and original as they were. In 1782, when 
 Playfair met him incidentally in London, he de- 
 scribed him as being generally looked up to as one 
 possessed of talents confessedly superior, and as the 
 only member of the Boyal Society who then united 
 the knowledge of mathematics, chemistry, and ex- 
 perimental philosophy. The absolute devotion of 
 his life to inquiries the most abstractly scientific, 
 whilst he showed an entire indifference to the luxuries 
 which his wealth might have commanded, and the 
 social station to which his birth entitled him, could 
 not fail to inspire respect for his character, as well 
 as to obtain the homage of mankind for pursuits 
 so dignified and so generally disregarded. Many 
 
 (602.) 
 
 curious anecdotes are related of the annoyance which 
 the inevitable accumulation of his unspent income 
 occasioned. He no doubt would have distributed more 
 liberally what he so little valued, but for the amount 
 of time and inquiry which such a course must have 
 compelled him to withdraw from his beloved pursuits. 
 Some instances of his generosity are on record, and 
 others, no doubt, will never come to light. M. Biot's 
 epigrammatic description of him will probably long 
 remain applicable, — " II etait le plus riche de tous 
 les savans, et probablement aussi le plus savant de 
 tous les riches." 
 
 This isolation of interest was doubtless due, quite 
 as much to a constitutionally morbid temperament, 
 as to a real misanthropy. He avoided even the most 
 casual intercourse with his fellow men, excepting only 
 when it was likely to bear the immediate fruit of 
 scientific information. He almost never visited his 
 relatives, and his heir paid him a visit of a few minufes 
 once a year ; but he frequented regularly the social 
 meetings of the Boyal Society Club, and the evening 
 reunions of Sir Joseph Banks. But he came, not to 
 participate, but to increase his stores ; if he spoke, it 
 seemed to be by inadvertence, and he was silenced 
 by a question, or even by a look. " A sense of iso- 
 lation from his brethren made him shrink from their 
 society, and avoid their presence ; but he did so as 
 one conscious of an infirmity, not boasting of an ex- 
 cellence. He was like a deaf-mute sitting apart from 
 a circle, whose looks and gestures show that they are 
 uttering and listening to music and eloquence in pro- 
 ducing or welcoming which he can be no sharer. . . . 
 He was one of the unthanked benefactors of his race 
 who was patiently teaching and serving mankind, 
 whilst they were shrinking from his coldness, or 
 mocking his peculiarities. . . . Such was he in life, 
 a wonderful piece of intellectual clock-work, and as he 
 lived by rule he died by it, predicting his death as if it 
 had been the eclipse of some great luminary, . . . and 
 counting the very moment when the shadow of the 
 unseen world should enshroud him in its darkness."^ 
 
 I shall only add, that Cavendish was elected one 
 of the eight Associates of the French Institute in 
 1803. This is a distinction perhaps the highest, of 
 a formal kind, to which a scientific man can aspire, 
 and was given at a time when, as an Englishman, he 
 must have felt it to be peculiarly honourable. 
 
 The philosophical character of Cavendish resembled 
 in many respects that of Newton; and with but a slight His"philo- 
 modification of its secondary ingredients, he might sophical 
 have been, perhaps, another Newton in experimental character, 
 physics. His singular ineommunicativeness, and the 
 absence of a laudable ambition to perpetuate his name 
 by the establishment of great theories, are perhaps 
 the main reasons why his reputation, except in che- 
 mistry, did not stand yet higher than we find it. 
 
 (603.) 
 
 (604.) 
 
 1 By the Kev. W. Vernon Harcourt in British Association Report for 1839. Compare Wilson's Id/e of Cavendish, p. 446. 
 
 2 Phil. Trans. 1783. 
 
 ^ Wilson's Life of Cavendish. 
 
134 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (605.) 
 Lavoisier. 
 
 (606.) 
 His contri' 
 butions to 
 heat and 
 cliemistry. 
 
 A man indifferent to external relations pursues even 
 his studies at a disadvantage ; and the patient la- 
 bours of so long a life devoted to a single object, 
 vrould perhaps have told to greater effect had he 
 published the results more frequently, and had he 
 communicated more freely with those qualified to in- 
 terchange their views with his. His excellent mathe- 
 matical education, and his unusual skill in experi- 
 ment, combined with a habit independent of either, 
 but not less valuable, of patiently drawing inferences, 
 might have placed him in the first rank as a discoverer 
 in Heat, in Electricity, or in Optics,^ each of which 
 sciences was so soon to take a surprising step in ad- 
 vance. In several of his important researches, he 
 was more or less anticipated ; a circumstance which 
 his cold nature would perhaps scarcely have allowed 
 him to make an effort to prevent. Black preceded 
 him in most of his excellent experiments on heat; 
 .Slpinus in his theory of Electricity ; Watt was at least 
 close on his traces in suspecting that water consists 
 of oxygen and hydrogen ; and the admirable experi- 
 ment on gravitation had been devised by his friend 
 Michell, and was not improbably recalled to his re- 
 collection, by the happy use of the torsion balance 
 by Coulomb. It is given but "to a few to achieve great 
 discoveries, nor is the longest life always the most 
 productive. Cavendish had his share, and some of 
 the most considerable of these were even made later 
 in life than is usual amongst experimentalists.^ It 
 is no mean eulogy of him to say, that the purity and 
 ardour of his pursuit of truth were never exceeded, 
 and that had he been more ambitious of praise, he 
 might have stood as pre-emiuent in mathematical 
 physics as he did in chemistry. 
 
 Antoine Laukbnt Lavoisiek stands in intimate 
 connection with Cavendish, as well by the nature of 
 his pursuits generally, as by the brilliancy and im- 
 portance of his chemical discoveries, which were 
 nearly contemporaneous with those of Cavendish. 
 He was born in 1745, and suffered by the guillotine 
 on the 8th May 1794, without even the shadow of 
 a misdemeanour. He was attached to the sciences 
 of Heat and Chemistry, which he prosecuted with 
 admirable success. He happily availed himself of 
 the discoveries of Black, Priestley, and Cavendish, as 
 well as his own, to establish the important chemical 
 theory which has immortalized him. It is to be re- 
 gretted that he was not always just in citing the 
 English vmters from whom he so freely borrowed. 
 Such looseness was, however, common at that period, 
 and (unfortunately) has continued to be so in France 
 even to our own time. 
 
 Lavoisier's more important papers may be classed 
 under two heads ; those referring more immediately 
 to the subject of Heat as a branch of physics ; and 
 those of a more strictly chemical character, princi- 
 pally in support of the " Oxygen-Theory," and con- 
 
 sequently also intiiAately connected with the doctrine 
 of heat considered in reference to its most ordinary 
 source. Combustion. 
 
 He published in 1772 a paper on the Latent Heat (607.) 
 of Water, and some years afterwards one on the Latent Papers on 
 Heat of Steam, which, in general, merely reproduce ^^^^^^*- 
 the views of Black. In the memoirs of the Aca-gpgg;flg 
 demy of Sciences for 1780 (published 1784), we heat, 
 find an important paper on Heat written in conjunc- 
 tion with Laplace, in which the calorimeter is de- 
 scribed, though not under that appellation, together 
 with its applications and their results. The prin- 
 ciple of the calorimeter is too well known to require 
 to be detailed here; but the authors of the joint 
 memoir refer, with commendable precision, to the pre- 
 vious labours of Wilcke of Sweden, who first employed 
 the melting of snow to measure the quantities of heat 
 given off by bodies in cooling. To Laplace and La- 
 voisier, is, however, due an important addition which 
 could alone impart any value to the results, — that of 
 the external chamber of ice which prevents fusion 
 taking place by the contact of the external air and 
 by radiation. The French philosophers were not so 
 successful in eliminating the other source of inac- 
 curacy specified by Wilcke, which arises from the 
 difficulty of drawing off the whole of the melted 
 water. Sir John Herschel has of late years proposed 
 what seems to be an important improvement on the 
 calorimeter, by filling the interstices of the snow or 
 ice with water, and estimating the quantity of the 
 former melted by the contraction of volume" of the 
 compound mass. I am not aware that it has been 
 as yet practised. I have stated in Art. (88) one ground 
 on which the idea of the calorimeter (so far as not 
 anticipated by Wilcke), may be probably ascribed to 
 Laplace. Another is to be found in the fact that, 
 in the opening of the description of the method in 
 the paper which we are considering, Laplace writes 
 of himself in the first person. 
 
 Of the memorable revolution which Lavoisier in- (608.) 
 troduced into chemistry, more immediately in con- Chemical 
 nection with the subject of combustion, I cannot be ^v^°. 
 expected to speak here at length. It is well known tion and 
 that the early chemists entertained more correct oxidation, 
 views as to the calcination of metals than those pre- 
 valent during the greater part of the eighteenth cen- 
 tury under the influence of Stahl's theory of Phlo- 
 giston ; and that Lavoisier, in the first instance, only 
 led chemists back into the right road by insisting 
 that the increase of weight observed when metals are 
 calcined in air, must be due to some ponderable sub- 
 stance associated with the metal and derived from the 
 air, and not to the escape of an imaginary spirituous 
 substance, endued with positive levity, and termed 
 Phlogiston. But it required the progress which had 
 already been made in pneuinatic chemistry by Black 
 and Priestley, and especially the discovery of oxygen 
 
 ^ This last subject seems to have been comparatively indifferent to him. 
 
 2 His discovery of tho composition of water was made when he was about fifty years of age. 
 
Chap. VI., § 3.] 
 
 HEAT. — LAVOISIER— DALTON. 
 
 185 
 
 by the latter (a fact sparingly alluded to by Lavoi- 
 sier), to give to the true theory a stable foundation. 
 That metals' calcine, and that flames burn by the aid 
 of the vivifying principle of the atmosphere abstracted 
 from it, and which adds its weight to the compounds 
 produced, was the primarystep made by Lavoisier ; 
 to which, by cautious, yet rapid inductions, he added 
 the knowledge of oxygen as the usual (he believed 
 the sole) acidifying principle, and demonstrated the 
 true nature of carbonic acid. To these various phe- 
 nomena thus happily reconciled, he added the theory 
 of respiration, confirming it by the eifects observed 
 in air which has undergone that process. These, and 
 many other consequences of the " oxygen theory," 
 were developed in a numerous series of admirable 
 memoirs. The reception of it was anything but in- 
 
 stantaneous ; and the hesitation and delay which oc- 
 curred, enable us, as Dr Whewell has well remarked, 
 to estimate the force of mind which was required to 
 promulgate the theory, — as the subsequent course of 
 discovery, and its infinite applications in practice, best 
 attest its importance. 
 
 Lavoisier was still occupied in extending the (609.) 
 conclusions of his chemical doctrines, when he was ^^^ °''' 
 overtaken by the unprovoked sentence to a violent death, 
 death. Like Archimedes, he begged a short respite 
 for the completion of experiments in Which he was 
 immediately engaged, but he was silenced by the brutal 
 reply that " the Eepublic had no need of philoso- 
 phers." He left a name equal to any in the science 
 of his time,' and adorned by the memory of public 
 and private virtues. 
 
 § 3. Dalton. — Theoinf of Gases and Vapours. — Law of Expansion hy Heat. — Atomic Theory of 
 
 Chemistry. — GuT-LusSAC. 
 
 (610.) 
 Dalton — 
 his early 
 circum- 
 stances ; 
 
 contrasted 
 with those 
 of Caven- 
 dish and 
 Black. 
 
 John Dalton, the chief author of the theory of che- 
 mical equivalents or the Atomic Theory (as he preferred 
 to call it), and of many important researches on the 
 constitution of elastic fluids, was born at Eaglesfield, 
 near Cockermouth in Cumberland, on the 5th of 
 September 1766.^ His parentage was humble, and 
 his family belonged to the sect of Quakers, whose 
 tenets he, to the close of his life, professed. Had 
 we wished to invent a striking antithesis in the per- 
 sonal histories of the cultivators of science, or to 
 illustrate merely the various soils on which rich 
 crops of discovery may be reared, we could scarcely 
 have imagined more striking contrasts than in the 
 social positions and advantages of Black, Cavendish, 
 and Dalton — three of the nameswhich we have selected 
 in illustration of the history of physics of their age. 
 Cavendish we have seen connected with one of the 
 noblest families in England, and wealthy almost be- 
 yond the dreams of the covetous ; spending his life 
 in or near London, and enjoying every facility of di- 
 rect communication with the first scientific celebrities 
 at home and abroad ; — Black, almost the heau ideal 
 of an Academic, not wealthy indeed, but surrounded 
 by all the opportunities of study, of information, and 
 of social intercourse which he desired; passionless 
 almost to a fault ; admired by his pupils and friends ; 
 enjoying, in short, all the advantages which educa- 
 tion and a literary position can afibrd for the prose- 
 cution of a favourite study ; — Dalton, on the other 
 hand, poor and hardly winning a well-earned sub- 
 sistence by private tuition, from the time he was 
 himself a child until near the close of his long ca- 
 reer, — with few friends, a scanty education, and a 
 scantier library, — attaining, through his unaided and 
 long almost unheeded efforts, and by means of an 
 
 apparatus constructed entirely by himself, a position 
 in the world of science unquestionably not second to 
 that of either of his more highly-favoured contem- 
 poraries. 
 
 At the age of thirteen he had commenced the ardu- (611.) 
 ous office of an instructor; and from 1781 to 1792 
 pursued the same occupation in a humble sphere- 
 at Kendal, where he fortunately became acquainted 
 with Mr Gough, a blind gentleman of some fortune, 
 who devoted his time to the prosecution of science 
 in nearly all its branches, and particularly of mathe- 
 matical subjects, of which he has left an enduring 
 record in many ingenious papers, published chiefly 
 in the Manchester Transactions and in Nicholson's 
 Journal. He patronized young Dalton, giving him 
 free access to his library and apparatus, and receiv- 
 ing from him in return the benefit of his assistance in 
 prosecuting his experiments. Dalton always recog- 
 nised (as he had unquestionably good reason to do) 
 the merits of his patron, and the importance of the 
 advantages which he had derived from his advice 
 and example. Indeed, without some such fortunate 
 concurrence of circumstances (and something simi- 
 lar may be noted in the history of nearly all self- 
 educated men), it could hardly have been hoped that 
 Dalton would have been so well grounded in the ma- 
 thematical principles of at least some branches of 
 Natural Philosophy as he probably was. For, though 
 his discoveries bear mainly on the science of chemis- 
 try in the wide sense in which it was then under- 
 stood, yet geometrical precision is after all their fun- 
 damental characteristic ; and whether in treating of 
 the constitution of a gas, or of the scale of a thermo- 
 meter, or of the composition of a salt, it is evident that 
 numbers and ratios were the ideas predominating in 
 
 1 Life of Dalton, hy Dr Henry, in the publications of the Cavendish Society. 
 before the appearance of this biography. 
 
 The present section was originally vfritten 
 
136 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI 
 
 his mind. In ttis lie resembled Cavendish ; but he 
 did not resemble him, and in one sense may be said 
 to have surpassed him, in the boldness, we might call 
 it audacity, with which on a frequently too slender 
 foundation of facts Dalton established, to his own 
 satisfaction, by reasoning almost as much ct priori as 
 that of the mathematician, comprehensive physical 
 theorems expressing the laws of phenomena. 
 (612.) The more important of these refer to the consti- 
 
 Dalton's tution of gases and vapours, together with their rela- 
 writings. tioQg tQ iieat, and to the combinations of bodies by 
 chemical aflSnity. We shall endeavour to give some 
 account of these researches separately. They are to 
 be found detailed in the Memoirs of the lAterary and 
 Philosophical Society of Manchester (particularly the 
 fifth volume), and in Dalton's New System of Che- 
 mical Philosophy, of which three successive parts ap- 
 peared in 1808, 1810, and 1827, of which the first 
 is the most original and important. 
 (613.) I. We shall first speak of his researches connected 
 
 Researches ^^.jj gases and vapours. It had been noticed by 
 and va-^ Priestley and others that when gases exercising ap- 
 pours. parently no chemical action upon one another, are 
 mixed in a confined space, they become, after the 
 lapse of a longer or shorter time, completely inter- 
 mingled, and that without any regard to even great 
 differences in their density, the particles of the lighter 
 gas diffusing themselves contrary to gravity through 
 those of the denser, and causing them in their turn to 
 ascend. The uniform composition of our atmo- 
 sphere, in all circumstances and at all heights, is a 
 striking example of this property. In explanation of 
 it, Dalton had in 1801 arrived at the conclusion, 
 " that the particles of one gas are not elastic or re- 
 pulsive in regard to the particles of another gas, but 
 only to the particles of their own kind." The fun- 
 damental experiment on which this singular con- 
 clusion was based was the following: — ^That the 
 quantity of vapour of water (which, when purely 
 elastic, may be considered as a gas) which can exist 
 uncondensed in a given space, depends solely upon 
 the temperature, and is independent of the presence of 
 air and of its own density. Thus water, or any other 
 evaporable liquid, being introduced into a space con- 
 taining air, or any other gas, of any density, but 
 subject to a constant external pressure, the space in 
 question becomes damp by the evaporation of the 
 liquid ; now the amount of the latter converted into 
 vapour depends, according to Dalton, upon the single 
 circumstance that the vapour yielded by it must 
 have the precise elasticity due to its temperature. 
 
 Its elastic force being added to that of the dry air, 
 the whole will expand until equilibrium is restored 
 with the constant pressure without, and this will oc- 
 cur as soon as the elasticity of the dry air alone 
 (proper to its increased volume), added to the elasticity 
 of the vapour alone (depending solely on its tempera- 
 ture), are together equal to the pressure which they 
 have to support. In short, to use the precise enun- 
 ciation of Dalton himself, " in all cases the vapour 
 rises to a certain force, according to temperature, 
 and the air adjusts the equilibrium by expanding or 
 contracting as may be required."^ 
 
 The importance of this law (easily verified in the (614.) 
 particular case) is readily perceived. Not only did Theory of 
 it affect the results of almost every experiment in^ys^"™'" 
 pneumatic chemistry, but it rendered a new theory of '^' 
 hygrometry indispensable. The older theory of Hal- 
 ley, Leroy, and Franklin was, that the direct affinity 
 between air and water drew up a portion of the lat« 
 ter into the former with the aid of heat, whilst De 
 Saussure (JEssai sur VHygromStrie, 1783) believed 
 that the conversion of water into vapour took place 
 first and independently by the action of heat, and that 
 it was then drawn up into the atmosphere by the at- 
 traction of the gases which compose it. Dalton's 
 experiments show that the air and the vapour mix 
 without the slightest mutual interference or reac- 
 tion. He founded thereupon an excellent prac- 
 tical method of determining the amount of vapour 
 in the atmosphere. He first formed a table of the 
 elasticities of watery vapour or steam for all tem- 
 peratures between 32° and 212°; and so simple and 
 accurate were his methods, at least for the lower de- 
 grees of the thermometer, that his numbers are still 
 received as amongst the best we have. He operated 
 merely with a carefully constructed barometer, into 
 the vacuum of which he introduced a few drops of 
 water, and raising the temperature by means of a 
 tube embracing it, and which could be filled with 
 water at pleasure, he observed carefully the depres- 
 sion of the mercurial column. The elasticities thus 
 determined commenced with 0'2 inches of mercury at 
 32° up to 30 inches at 212°. These numbers, con- 
 sequently, represent the utmost elasticities of vapour 
 which can exist either in air or without air at the cor- 
 responding temperature. If we attempt to add more 
 vapour, or to lower the temperature, in either case 
 moisture will be deposited. Hence to find the quan- Dew-point 
 tity of vapour in the atmosphere when not absolutely ^g^^"' 
 damp, it is sufficient to ascertain the temperature at 
 which it becomes so. This Dalton did by filling a 
 
 ^ The exact expression of the effect is this, v=S- where p represents the pressure expressed in inches of mercury upon a 
 
 given volume (equal to unity) of dry air ; / the force of the vapour in vacuo at the temperature of experiment, also in inches of 
 mercury ; and « the volume which the mixture of air and vapour occupies under the given pressure p after saturation. It is evident 
 that/) — / being the pressure due to the elasticity of the dry air apart fromthe vapour, when we affirm that the volume (1) becomes 
 
 ■£— , we in effect affirm that Mariotte's (or Boyle's) law connecting volume and pressure holds true for air which is mixed with 
 P-f 
 
 vapour, just as though vapour were absent or its space void. 
 
Chap. VI., § 3.] 
 
 HEAT (ATOMIC CHEMISTRY).— DALTON. 
 
 137 
 
 thin glass with cold spring water, or by adding, if 
 necessary, the solid nitrate of ammonia, until the 
 temperature fell so far that dew began to be deposited 
 on the surface. This excellent method constitutes 
 in fact the dew-point hygrometer. It has received 
 various forms from Mr Daniell and others, but the 
 ■ original one is probably the best. 
 (615.) These important laws and deductions being fully 
 
 mixed" Understood, the theory of the mixed dry gases follows 
 gasea. as a simple corollary. For it merely asserts of them 
 what has been admitted in the case of steam, that 
 they may diffuse themselves, and exert their elastic 
 forces quite independently of one another; so that, for 
 example, in our atmosphere the total pressure is made 
 up of the partial elasticities of the oxygen, nitrogen, 
 and carbonic acid which compose it, each acting to 
 the same amount as if it alone had existed in the 
 space which it occupies. In his essay of 1801,' Dal- 
 ton stated his view of these facts thus : — " The par- 
 ticles of one elastic fluid may possess no repulsion or 
 attractive power, pr be perfectly inelastic with regard 
 to the particles of another." 
 (616.) Discoveries so practical could not fail to excite 
 
 Dalton's immediate attention, especially at a time when the 
 mechanical researches of chemists were earnestly directed towards 
 the subject. *^'® gases. "The facts and experiments," Dal ton 
 tells us in his Chemical Philosophy, "were highly 
 valued ; some of the latter were repeated and found 
 correct, and none of the results controverted ; but 
 the theory was almost universally misunderstood." 
 Its opponents were BerthoUet, Thomson, Henry, and 
 others, and the replies of the author are contained in 
 the work just cited. But he appears to have felt the 
 force of the objection, " Can it be conceived that an 
 elastic substance exists which adds its volume to that 
 of another, and which, nevertheless, does not act on 
 it by its expansive force V — for in his chemical phi- 
 losophy he abandons the comparison of gaseous par- 
 ticles to similar magnetic poles which repel each 
 other, but are inert towards non-magnetic matter, and 
 allowing that heat is the primary cause of repulsion 
 in all gases, ascribes their diffusion contrary to gravity 
 to the dissimilar size of their spherical molecules. 
 " The particles of one kind being from their size un- 
 able to apply properly to the other, no equilibrium 
 can ever take place amongst the heterogeneous mole- 
 cules. The intestine motion," he adds, " must there- 
 fore continue till the particles arrive at the opposite 
 surface of the vessel against any point of which they 
 can rest with stability, and the equlibrium at length 
 is acquired, when each gas is uniformly diffused 
 through the other." It may be seriously doubted 
 whether this theory of the facts will bear examina- 
 tion, at least no attempt has been made to demon- 
 strate it on mechanical principles. The subject has 
 been allowed to remain during more than forty years of 
 unequalled activity in such speculations without ma- 
 terial light being thrown upon the proximate causes 
 
 of these wonderfully general and simple truths. Yet 
 it can hardly be doubted that the mechanical theory 
 of the gases and vapours is capable of a great exten- 
 sion, and even of being illustrated by simple experi- 
 ments. But the attention of chemists has been with- 
 drawn from the physical bearings of their science by 
 the prodigious increase in the number of compounds 
 which they have had to analyze and classify. The 
 most important sequel to Dalton's discoveries has 
 probably been that of Professor Graham, whose ex- Mr Gra- 
 periments prove that gases when separated by a ham's law- 
 porous partition permeate it in both directions, until °.^^' "' 
 they have mixed in proportions which are inversely 
 as the square root of their density. This law clearly 
 shows the purely mechanical causes by which the 
 diffusion is effected. 
 
 A discovery of Dalton, which has scarcely been (617.) 
 considered second in importance to those we ha,ve J^alton on 
 mentioned, is that the rate of expansion of all gases gjon gf the 
 by heat is the same. Thus thermometers of air, hydro- gases by 
 gen, and carbonic acid would all mark the same degree ^^^*'- 
 when plunged in the same medium ; whilst the mer- 
 curial thermometer shows a more rapid expansion, at 
 higher temperatures, if the air thermometer be taken 
 as the standard. This important fact was soon 
 after but independently announced by Gay-Lussac of 
 Paris. Dalton's publication dates from 1801. In 
 his Chemical Philosophy, he gives his view of the 
 difficult subject of a true thermometric scale ; which 
 he does not suppose to be correctly represented by 
 the simple expansion of any known substance ; but 
 that the gases expand with true increments of heat 
 in a very slow geometrical progression, whilst li- 
 quids expand as the squares of the true temperatures 
 from their freezing points. These and other laws 
 equally arbitrary have not received support from 
 later and more precise experiments ; and in the se- 
 cond volume of his work (1827) he freely acknow- 
 ledges the correction of his hypothesis by the more 
 recent French experiments. 
 
 II. I now proceed to the other part of Dalton's (618.) 
 labours on which his reputation is principally based ; atomic 
 namely, the clear assertion and experimental esta- Theory, 
 blishment of the Atomic Theory or doctrine of chemi- 
 cal equivalents. I introduce it here on account of 
 its important bearing on all physical questions in 
 which the constitution of matter and the forces act- 
 ing at minute distances are involved. 
 
 Early opinions on the constitution of matter and (619.i 
 chemical combination. — Two opinions have prevailed Early opl- 
 from the very earliest times respecting the constitu- °'°°^ °° . 
 tion of body : — that which supposes its entire homo- tution of 
 geneousness, and that which allows that it consists matter. 
 of material parts or atoms separated by void spaces ; 
 these parts or atoms being indivisible. This last is 
 the doctrine of Democritus and Epicurus, and in 
 modem times of Bacon, Newton, and Dalton.^ The 
 former opinion has been held by Leibnitz, and many 
 
 1 The reader will find ample details on the opinions of the older philosophers in Daubeny's Introduction to the Atomic Theory, 
 
138 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 writers of the recent German school. Abstracting 
 as far as possible from the more purely metaphysical 
 difficulties (such as those which the consideration of 
 Leibnitz's law of continuity introduces), we may 
 perhaps be justified in stating that, whilst ihe objec- 
 tions urged against the existence of atoms fall upon 
 our inability to conceive and describe the properties 
 of these individual ultimate parts in a consistent 
 mannerj — the objections to the other notion meet us 
 at an earlier stage, and seem to defy any clear con- 
 ception of the nature or possible existence of com- 
 pound bodies, or of bodies in two states of consis- 
 tence. Admitting atoms — ^whilst acknowledging our 
 inabilityto describe them individually — we can clearly 
 enough conceive the phenomena of condensation, ra- 
 refaction, evaporation, &c., and also of the combina- 
 tion of elements in compounds possessing distinct 
 properties ; but excluding them, or allowing that 
 matter is penetrable by matter throughout, is it pos- 
 sible to conceive clearly of such a compound, — as for 
 example, of the perfect diffusion of two gases in the 
 same space, yet each gas retaining its individuality 
 so completely as to admit of easy and complete se- 
 Boscovich. paration from the other ? The theory of Boscovich, 
 which has been sufficiently touched upon by Sir John 
 Leslie in the previous Dissertation, was intended, no 
 doubt, to reconcile, the two opposing theories, and it 
 cannot be doubted that it is in many respects an in- 
 genious solution. Yet it is essentially (as Professor 
 Robison maintains) a corpuscular or atomic doctrine, 
 and it farther appears to be difficultly reconcilable to 
 the doctrine of inertia ; for how can a finite number of 
 unextended physical points, though they may be the 
 centres of intense forces, constitute a finite aggregate 
 mass ? Nevertheless this speculation has been on 
 the whole favourably received, and in our own time 
 seems to have been adopted by so eminently practical 
 a philosopher as Dr Faraday. 
 (620.) About Dalton's idea of atoms, however, there can 
 
 Dalton's ^g no doubt. They are, according to his view, pon- 
 thelubiect ^^rable, indivisible masses, having length, breadth, 
 and thickness, consequently form. He had distinct 
 conceptions of their relative weights, distances, and 
 specific heats. He was particularly fond of depicting 
 them in diagrams, to which he often refers for a clearer 
 exposition of his views than he chose to give in words. 
 A mechanical mixture of gases like the atmosphere is 
 for him a uniform diffusion of the atoms of each gas 
 throughout the space occupied by the whole, and 
 
 without reference to t}ie position of the atoms of any 
 of the others. But a chemical compound consists 
 of molecules or complex atoms, each composed of 
 two or more ultimate particles of the constituents 
 firmly united by a chemical force, and these complex 
 molecules act towards one another exactly as simple 
 ones might do. The general notion of chemical forces 
 or afinities (as they were perhaps first called by Geoff- 
 rey, a French chemist) appears to have been appre- 
 hended in two different senses corresponding to the 
 atomic or non-atomic theory of body. For the former 
 proceeds on the assumption of direct attractions or 
 repulsions (push-and-pull forces, as they have been 
 called) uniting some and tending to separate others, 
 thus assimilating completely chemical with mechani- 
 cal forces. The other school adopts the word affinity 
 as expressing a mode of action of matter upon matter 
 totally distinct from that of force producing motion 
 in its particles, to which it is difficult to give an in- 
 telligible form, much more to prove that the assump- 
 tion is warranted by the facts.^ In this state of 
 matters the choice between an opinion perhaps erro- 
 neous, and one which assumes no definite shape, can 
 hardly, to the practical philosopher, remain long 
 doubtful ; when new facts shall have enabled him 
 to express intelligibly a new hypothesis, it will be 
 time enough to adopt it. 
 
 Dalton's Atomic Theory. — I shall first briefly state (621.) 
 the general facts or laws to which Dalton gave an uni- i^^g™ gji^. 
 versal application, and then briefly refer to the un- mical com- 
 doubted anticipation of part of them by earlier chemists, bination. 
 For the sake of distinctness ihe facts of the atomic theory 
 may be thus enumerated : — 1. That when two bodies 
 unite, not merely by mechanical mixture but through 
 a chemical affinity of the elements, — two or more in- 
 gredients forming a wholewith new properties, — these 
 ingredients are invariably found to exist in constant 
 proportions. For instance, the carbonate of lime in- 
 variably consists of 44 parts by weight of carbonic 
 acid and 56 of lime, the slightest addition of either 
 element remaining uncombined, or only mechanically 
 mixed with the chemical product. 2. In many 
 instances, however, more than one chemical combi- 
 nation can be formed between two or more elements, 
 and in the simplest cases, where the elements are 
 two in number and one remains constant in quantity 
 whilst the other increases in amount, a fresh che- 
 mical union of the particles does not occur until one 
 of the ingredients reaches precisely double the amount 
 
 and in Whewell's Philos. of Inductive Sciences, vol. i. Newton's conjecture is expressed in these words : — " All things considered, 
 it seems probable that God, in the beginning, formed matter in solid, massy, hard, impenetrable, moveable particles, of such 
 sizes, figures, and with such other properties, and in such proportion to space, as most conduced to the end for which he formed 
 them. And that these primitive particles being solids, are incomparably harder than any bodies compounded of them; even 
 so very hard as never to wear or break to pieces; no ordinary power being able to divide what God himself made one in the 
 first creation." Horsley's Newton, vol. iv., i!60, quoted by Daubeny. 
 
 1 A profound and subtle thinker of our own time (Mr Leslie EUis, of Trinity College, Cambridge) has made a definite suggestion 
 as to a possible form of chemical forces, viz., that they may not be such as are directly exerted between a particle A and a particle 
 B, but only by their presence enable A to act on B, or bear the same relation to force (common force) as force in mechanics does 
 to the motion which it causes. Thus, the science of mechanics would include — 1st, Kinematics, or pure motion depending on 
 equations of the first order ; 2d, Dynamics, depending on equations of the second order ; 3d, Chemical, Vital, &c., forces, depend- 
 ing on equations of higher orders. Camb. Tram., viii., 604, &c, 
 
Chap. VI., § 3.] 
 
 HEAT (ATOMIC CHEMISTRY). — DALTOIf. 
 
 139 
 
 wHcli had chemically combined -withthe other ; and 
 if it happen that fresh compounds are formed pos- 
 sessing new qualities, then the varying ingredient 
 reaches 3, 4, or 5 times the amount which it had in 
 the first combination ; or more generally the propor- 
 tions by weight of the combining elements may be 
 exactly represented by whole numbers. 3. " If two 
 bodies combine in certain proportions with a third, 
 they combine in the very same proportions with 
 each other." This is called the law of reciprocal pro- 
 portion. Thus, suppose that one ounce of a body A, 
 saturates or forms a chemical combination with two 
 ounces of B, 5 of C, and 11 of D ; then if B, C, and D 
 are capable of combining, it will be in the exact pro- 
 portions of the numbers 2, 5, and 11. Hence a single 
 number being determined for each body, determines 
 all its possible combinations with other known bo- 
 dies. 4. It may perhaps be added as an indepen- 
 dent fact, that when complex bodies combine with 
 other bodies, no matter whether simple or compound, 
 the combining number of the complex body is the 
 sum of the numbers representing the constituents. 
 Thus the combining number of lime is 28 ; but lime 
 consists of calcium 20 and oxygen 8. So also the 
 combining number of water is 9 ; but water consists 
 of hydrogen 1 and oxygen 8 : and the combining 
 number of hydrate of lime is 37, the sum of the 28 
 parts of lime and 9 of water of which it is composed. 
 (622.) The discovery of these laws has been termed by 
 
 Partial an- gir John Herschel the most impqrtant, after the laws 
 of aoml°of °^ mechanics, which the study of nature has yet dis- 
 these laws, closed. No slight or transient reputation is due 
 to him who first clearly apprehended and taught them. 
 Nor must we be surprised to find several claimants to 
 a share of the honour. It is the invariable history of 
 all great generalizations, that, they have been partly 
 anticipated ; and it may serve to moderate the self- 
 esteem of even the greatest discoverers, that however 
 high may be their individual merits, they are in some 
 sense the mere exponents of the aggregate know- 
 ledge of their contemporaries. The laws of motion 
 were partially anticipated before the time of Galileo, 
 and could not have remained much longer undefined ; 
 and even the unparalleled discoveries of Newton 
 must, in all probability, have ere long been made 
 piecemeal by the united energy of his contemporaries 
 and immediate successors. The steam-engine was 
 not the sole creation of Watt, nor was Davy the first 
 to apply the voltaic battery to chemistry. In like 
 manner, Dalton's laws of chemical combination were 
 published at a happy moment, which gave them 
 speedy acceptance with the active chemists of his 
 day; whilst those who had seen with sufiicient clear- 
 
 ness portions of these laws twenty. or thirty years 
 before, addressed a scientific public by no means pre- 
 pared to appreciate their value, or to feel a conviction 
 of their generality. Had Wenzel,^ Higgins,* and Wenzel, 
 Eichter^ individually apprehended the great impor- ^'SP^^' 
 tance of the definite and multiple combining pro- ^^j, 
 portions which they announced, — ^had they felt the 
 theory of them to constitute the very foundations of 
 chemistry, — they would not have rested until they 
 had verified it in numerous details, and applied it to 
 the various purposes of speculation and practice, as 
 Dalton did. But whether from want of energy, or 
 from ill fortune, their ideas sunk into entire oblivion ; 
 and the ingenuity and social position of BerthoUet 
 were giving a currency to opinions respecting chemi- 
 cal forces which tended to undo even the far more 
 elementary notions of the constancy of elective aflS- 
 nities, at the time when Dalton's researches were 
 unostentatiously brought before the world. His first 
 insight into the theory of chemical combinations 
 dates from the year 1803. It was expounded by 
 him both in conversation and by lectures in 1804, 
 at which date Dr Thomas Thomson recorded the 
 results of a conversation held with him at Manches- 
 ter, which, three years later (evidently with Dalton's 
 approbation), he published in his work on Chemistry, 
 Finally, Dalton himself, in 1808, announced the prin- 
 ciples of his theory at no greater length than five 
 pages " on Chemical Synthesis" in his Chemical 
 Philosophy. 
 
 Now, it is to be observed, that Dalton's views were (623.) 
 all along expressed in the language of a strictly Ato- Importance 
 
 ■ iX. n A 1 1, • 11 of tlie Ato- 
 
 mic theory. Compounds are only chemically com- ^j^ ijjjgQj._ 
 
 plete, when one or several atoms of an element com- to the pro- 
 bine with one, two, or more atoms of another. Any gress of 
 superfluity of either element remains uncombined, or " ^""'^'T' 
 mechanically mixed. All the other parts of the laws 
 of combination readily lead to the same idea, and, in 
 fact, find in it their simplest expression. There is 
 no wonder, then, that Dalton firpily believed in the 
 physical existence of his atoms, and that the new 
 properties of compounds are due to the peculiar mo- 
 dification of the most elementary parts into which 
 bodies can be divided without a loss of those proper- 
 ties, that is, without decomposition. He figured 
 these elementary molecules by uniting the symbols 
 of their constituents, and by so doing, may be said 
 to have laid the foundation of those algebraic sys- 
 tems of technical notation, which speak to the eye 
 only in another way from Dalton's diagrams, and 
 which have been of such eminent service to the 
 chemist. Nor must we think too lightly^ of a hypo- 
 thesis which served so materially to aid in realizing 
 
 . ^ Lehre von der Verwandschaft der Korper, 1777. He shows that in a double decomposition the new compounds are chemi- 
 cally perfect. 
 
 ^ A Comparative View of the PMogistio and Antiphlogistic Theories, 1789, hy Mr William Higgins, points out the multiple com- 
 bining proportions of sulphur and oxygen, and of nitrogen and oxygen, but only incidentally. Dr Bryan Higgins, a relative of 
 Mr W. H., had published, in 1786, a work said to contain the idea of definite atomic combinations. 
 
 3 Anfangsgriinde der Stochyometrie, 1792. He gave a series of jumbers representing the combining proportions of different 
 elements. 
 
140 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 a discovery of such magnitude. Dalton's earlier re- 
 searches were far more physical than chemical ; and 
 it is evident that the eifort of representing to his 
 mind, geometrically and atomically, the condition of 
 mixed gases and vapours, led him to form clear 
 ideas on the definiteness of chemical combinations. 
 The delay in publishing his views, no doubt de- 
 pended on his desire to present them to the public 
 in the form of a somewhat wide induction, although 
 it is certain that his own opinion was fully formed 
 from a knowledge of only one or two cases of multi- 
 ple proportions, and especially the combinations of 
 hydrogen and carbon. It cannot be fairly urged as 
 conclusive against the theory of atoms, that cases 
 .■«cur difficult to reconcile with the author's formal 
 statement of it. There is no great theory — not even 
 that of gravitation itself — which has not met with 
 similar apparent contradictions. 
 (624.) ijijie reception of the views of Dalton was some- 
 
 tira in^^' ''^^^* gradual, yet might be called rapid, considering 
 England, the obscurity of the author, and his provincial resi- 
 dence. The energy of Dr Thomson of Glasgow con- 
 tributed more than any other circumstance to com- 
 pel the attention of chemists. He personally brought 
 it under the notice of WoUaston and Davy ; and the 
 former, who, by his habits of precise thought and ac- 
 curate experiment, as well as from his extensive che- 
 mical knowledge, would of all others have been the 
 most likely to see its importance and probability, 
 was doubly predisposed in its favour by having been 
 himself for some time in possession of facts illus- 
 trating the numerical laws of combination similar to 
 those which Dalton possessed. Wollaston published 
 these in the Philosophical Transactions for 1808, in 
 which he expressly states, that Dalton had antici- 
 pated him in the results of his enquiry into multiple 
 combinations of elements. Davy, as might have been 
 expected, was less prepared to accept a doctrine 
 having the form of a mathematical law ; he did so, 
 however, after a short resistance. In his Chemical 
 Philosophy he ascribes most if not all the merit of 
 it to Higgins, and is supposed to have looked coldly 
 upon Dalton's growing fame; but it is gratifying to 
 add, that in almost his last appearance in public as 
 president of the Royal Society, when presenting Dal- 
 ton with the first royal medal, he should have ex- 
 pressed himself in terms of cordial praise. 
 (625.) ju Prance the new doctrine soon spread, notwith- 
 
 ^v-Lus-*^* standing its violent contradiction to the theories of 
 sac's law of Berthollet. Gay-Lussac was amongst its earliest 
 volumes, and most enlightened advocates; and he had the 
 good fortune to add, in 1809, a new law to the 
 principles of chemical combination, which is, that 
 the gases, in uniting chemically, combine in equal or 
 multiple volumes, and when any condensation occurs 
 after they have united, it amounts to an exact frac- 
 tion (^ or ■^) of their joint bulk. This was the only 
 addition made for a very long period to Dalton's 
 laws, even if we consider the theory of Isomorphism 
 
 and of Substitutions to take the same rank ; and as 
 it evidently includes the idea that the atomic weights 
 of the gases have a simple numerical relation to their 
 densities, it confirms Dalton's views of the great sim- 
 plicity and uniformity of constitution of those bodies. 
 In Sweden the doctrine of definite proportions found 
 one of its earliest advocates in Berzelius, and his 
 analyses contributed perhaps more than those of 
 any other chemist to its perfect establishment. 
 
 It is not to be concluded, however, that the atomic (626.) 
 or theoretical part of Dalton's laws obtained the same " Chemical 
 currency with the conditions of chemical combina- lenj^'*" 
 tion which they serve to define. Wollaston and 
 Prout were perhaps the most favourably disposed 
 to the doctrine of atoms, though the former invented 
 the term " chemical equivalents" to escape from the 
 theoretic inference, and the latter believed that Dal- 
 ton's law was only a portion of a more complicated 
 one regulating chemical combinations. Wollaston 
 even sought evidence in favour of ultimate atoms, 
 from considerations of a purely mechanical kind, 
 such as the existence of a limit to the atmosphere 
 (Phil. Trans. 1822). We may however admit, with 
 those who have taken an opposite view, that the 
 finite extent of the atmosphere is consistent with a 
 continuous mathematical law suitably assumed, and 
 without reference to atoms at all ; if, indeed, we can 
 imagine a medium varying enormously in density, 
 yet possessing perfect continuity of body. But we 
 will not enlarge farther on these almost metaphysi- 
 cal considerations. 
 
 During the period from his settlement in Man- (627.) 
 Chester in 1793, to the publication of his Chemical^'^^^^ 
 Philosophy/ in 1808, Dalton was occupied in tuition, history 
 first in the Mosley Street Institution, where he lee- continued. 
 tured on mathematics and natural philosophy for six 
 years, and afterwards, privately, in a very humble 
 and unpretending manner. His speculations and ex- 
 periments gradually became more and more strictly 
 chemical ; and, aware that his atomic theory was to 
 be the great foundation of his fame, he spared no 
 pains in illustrating it by numerous analyses. Con- 
 temporary chemists have testified to the ingenuity 
 and fidelity of these. Yet, isolated as he was, and 
 unacquainted perhaps with those niceties of manipu- 
 lation which are suggested by the experience of pro- 
 fessional chemists, and rapidly communicated in great 
 cities, his numerical conclusions were often inexact. 
 Probably he felt some discouragement from this, at 
 well as from the indifferent reception of the later parts 
 of his Chemical Philosophy, in which he had to admit 
 the inaccuracy of his theoretical scales of heat and 
 expansion. At all events, his publications became 
 more scanty and less original, though he was still near 
 the meridian of life. The reality of his discoveries 
 had been somewhat coldly acknowledged, and he felt 
 little temptation to adventure himself in a more bust- 
 ling arena, for which his habits and circumstances 
 seemed to unfit him. Nevertheless, he had been, as 
 
Chap, VI., § 3.] HEA,T (ATOMIC CHEMISTRY). — DALTON — GAY-LUSSAC. 
 
 141 
 
 (628.) 
 His charac- 
 ter 
 
 early as 1816, elected a corresponding member of the 
 Institute of France — WoUaston being then probably 
 the only other English name on the list.^ Dalton 
 found- his way to Paris in 1822, and was agreeably 
 surprised by the distinction with which he was re- 
 ceived by the most eminent members of the Academy 
 of Sciences. Perhaps this first 'personal recognition 
 of his exalted station, as a man of science, had some- 
 thing to do with the tardy adjudication to him four 
 years later of one of the medals of the Royal Society 
 of London. In 1830 he was elected one of the eight 
 associates of the Academy of Sciences in the room of 
 Sir Humphry Davy. 
 
 In 1833, at the age of sixty-seven, he received a 
 pension from government, up to which time he had 
 maintained himself in the way already mentioned, 
 with the utmost simplicity and contentment. Even 
 in his lifetime it was impossible for his eulogists 
 to forbear from some reference to this essential part 
 of his really philosophic character. " Mr Dalton 
 has been labouring," says Sir Humphry Davy, " for 
 more than a quarter of a century with the most dis- 
 interested views. With the greatest modesty and 
 simplicity of cljaracter, he has remained in the ob- 
 scurity of the country, neither asking for approba- 
 tion, nor offering himself as an object of applause." 
 "There is little doubt," says Dr Thomson, "that 
 Mr Dalton, had he so chosen it, might, in point of 
 pecuniary circumstances, have exhibited a much more 
 brilliant figure. But he has displayed a much more 
 noble mind by the career which he has chosen ; 
 equally regardless of riches as the most celebrated 
 sages of antiquity, and as much respected and be- 
 loved by his friends, even in the rich commercial 
 town of Manchester, as if he were one of the greatest 
 and most influential men in the country." All who 
 had the good fortune to know him personally — to see 
 him, as the writer of these pages has done, in his 
 modest school-room, and surrounded by his unpre- 
 tending apparatus — will own that these eulogies are 
 and death, not overdrawn. His latter days were spent in cheer- 
 fulness and comfort ; he expired on 27th July 1844, 
 having nearly completed his seventy-eighth year. 
 (629.) The philosophical character of Dalton may be 
 
 Dalton's briefly summed up. He had immense vigour of con- 
 caUharac- ception, and an ardent love of truth. He was tho- 
 roughly devoted to the pursuit of science during his 
 long career, and he evidently sought and expected 
 no higher reward than the insight which he obtained 
 into the laws of nature. His mind, like his frame, 
 was of a strongly masculine character, and happily 
 exempt from nervous sensibility and other like in- 
 firmities of genius. Whilst he held his own opinions 
 with tenacity, and criticised freely those of his op- 
 ponents, there is not a trace of acrimony in any 
 
 cal charaC' 
 ter. 
 
 of his writings ; and he always spoke in terms of 
 high respect both of those who pursued science in a 
 similar direction with himself, and (what was more 
 difiicult) likewise of those who, having the good for- 
 tune to hold more conspicuous positions, showed him 
 the smallest degree of kindness, which he always 
 gratefully acknowledged. He was unlike Black and 
 Cavendish, in the rapidity with which he seized on a 
 few isolated facts, and made them the basis of an 
 inference of great generality ; this, indeed, was his 
 leading characteristic; and he differed from them 
 equally in the boldness with which he claimed from 
 the public a general acceptance of his conclusions. 
 Some of his inferences were unguarded enough, and 
 have not been confirmed ; and the reception of what 
 were correct was naturally delayed by the evident 
 facility with which his theories were shaped in his 
 own mind. Most of his papers appeared in rapid 
 succession ; only the Atomic Theory was brought 
 with some evident hesitation before the world. In 
 all this we see the results of a vigorous imagination, 
 united with great perseverance, in working out an 
 idea. The imaginative element would have been 
 more under control had his education been of a less 
 irregular kind. We see the effect of an opposite 
 turn in his eminent predecessors just named. They 
 would have done more, had they trusted more. Dal- 
 ton's discoveries may be said to have terminated at 
 the age of forty. Though he laboured for thirty 
 years after, the conceptive faculty seems to have 
 spent itself in its earlier efforts. 
 
 Joseph Louis Gay-Lussac, an eminent French 
 chemist and physicist, contemporary with Dalton, Gay-Las- 
 has been mentioned in the course of the present sec- sac— che. 
 tion, as having discovered independently the equal "JJ' 5;^;^'^ 
 dilatation of the gases, and also a law of their com- 
 binations in connection with their volumes, which 
 was peculiar to himself. Besides these researches, 
 science owes many useful observations in physics to 
 his energy and talent, which, in the origin of his 
 career, promised more of originality than his ma- 
 turer life perfectly fulfilled. He was born in the old 
 province of Limousin in 1778, and became the pupil 
 of BerthoUet in chemical researches, and was one of 
 the earliest and most active members of the Societe 
 d'Arceuil. In physics, he was the collaborator of 
 MM. Biot, Humboldt, and Laplace. With the first Remark- 
 of these philosophers he made his earliest experi- able bal- 
 ment in aerostation, which he repeated alone on the 1°"° *s'=«°'- 
 16th September 1804, when he attained the amaz- 
 ing height of 701 6 metres (23,019 English feet), an 
 elevation previously unattained, and which in the 
 course of the succeeding half century has only twice 
 been touched, or exceeded by a small quantity.^ Con- 
 
 (630.) 
 
 * So stated by Dalton himself {Life by Dr Henry, p. 163) ; but I suspect some misapprehension. Considering the importance 
 attached to these nominations, it is to be regretted that it is at all times difficult to ascertain who are, or have been, associates 
 and correspondents of the Academy of Sciences. 
 
 " Once by MM. Bixio and Barral in 1860, and once by Mr John Welsh in 1852. Since this passage was written I find it 
 stated, that, on the 10th September 1838, Mr Green and Mr Rush reached a height of 27,148 feet. See The Times of \5th Sept. 
 1838. 
 
142 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 sidering the novelty of the experiment in 1804 (only 
 twenty-one years after Montgolfier's first successful 
 experiment), this fact speaks strongly for his courage 
 and zeal. These ascents were also the first undertaken 
 with strictly scientific aims, and the observations made 
 were highly interesting in connection with the decre- 
 ment of temperature in the atmosphere, with the uni- 
 formity of composition of air at all heights, and with 
 the question of whether the magnetic force of the 
 earth diminishes at such elevations. This last en- 
 quiry was not conclusively answered. 
 (631.) "VVith M. de Humboldt he made observations on 
 
 terrestrial magnetism in Italy, and on other subjects. Miscella- 
 By desire of Laplace he studied the facts of capillary neons ex- 
 attraction. In more immediate connection with the P^""'^"'^ 
 subject of the present chapter, he made some valu- Lussac." 
 able experiments on hygrometry, on the mechanical 
 properties of vapour of difierent kinds, and on the 
 specific heat of the gases. His fame, however, mainly 
 rests on the two investigations to which we previously 
 referred, and on the results of his balloon journey. 
 His later years were devoted to practical enquiries 
 connected with chemistry, and to his official duties at 
 the Mint. He died at Paris on the 9th May 1850. His death. 
 
 4. EuMFORD. — Economical applications of Heat. — Point of Maadmum Density of Water; Hope. 
 — Friction as a source of Heat. Theory that Heat is convertible into Mechanical Energy ; 
 Mr Joule. 
 
 (632.) 
 Thomson, 
 Count of 
 Rnmford. 
 
 (633.) 
 His early 
 history 
 andstudies. 
 
 (634.) 
 Enquiries 
 into the 
 economical 
 applica- 
 tions of 
 heat. 
 
 The name of Thomson, Count of Rumford, de- 
 serves a passing notice in the history of the physi- 
 cal sciences, if not for the absolute importance of 
 his discoveries, at least as an instance of a class of 
 benefactors to manki:tid at once in a physical and in- 
 tellectual point of view. He was altogether in ad- 
 vance of his age in the application of correct theory 
 to the improvement of the social condition of the 
 lowest classes ; and many of his experiments, and, 
 indeed, discoveries, seem now at once so simple and 
 so familiar, that we are apt to forget how entirely 
 original they were sixty years since. 
 
 Sir Benjamin Thomson, an American by birth, a 
 British knight, and a Bavarian or rather Austrian 
 count, was born in the United States in 1753, and 
 passed his earher years almost entirely at military 
 stations during the American war, being engaged 
 on the British side. After the establishment of in- 
 dependence, he quitted his country for ever ; came 
 first to England, where he was well received, and 
 proposing to enter the Austrian service, he proceeded 
 as far as Munich, where, having become known to 
 the elector of Bavaria, he was induced to settle ; 
 and having received diiferent civil and military ap- 
 pointments, he devoted himself for a series of years 
 to the improvement of the social condition of that 
 capital. He introduced great improvements into the 
 management of the army; the mechanical and chemi- 
 cal departments of the artillery had a peculiar charm 
 for him ; they were conducted on strictly scientific 
 principles, and, in return, were made to contribute 
 important results to science. His experiments on the 
 heat of friction, deduced from the boring of cannon, 
 are amongst the best we possess ; and they led him 
 to results of considerable theoretical importance to 
 which I shall presently refer. 
 
 But his most serviceable efibrtson behalf of man- 
 kind were in the treatment of the mendicant classes 
 
 with which Munich then swarmed. Salutary views 
 of the importance of industry, order, morality, and 
 public economy, were most happily united to a 
 happy versatility of talent in physical research, to 
 unwearied patience and great liberality, in efiecting 
 one of the greatest social reforms on record. The 
 strict statistics of a great house of industry were 
 ascertained with reference to the most seemingly in- 
 significant details, and, in particular, all the appli- 
 cations of Heat to the physical wants of mankind 
 were s>tudied with equal assiduity and success. The 
 warmth of clothing was traced to the amount of still 
 air entangled amongst its fibres, — the dissipation of 
 heat, whether from a thermometer or a kitchen boiler, 
 was classified under radiation, conduction, and con- 
 vection, the last and often most important of which 
 (signifying the influence of currents in liquids and 
 gases in conveying heat by the changing density of 
 their parts) had hardly before been recognised, or at 
 least made the subject of formal experiment, — the 
 effective heat due to the combustion of difierent kinds 
 of fuel, tested by a calorimeter of his own invention, 
 — the economy of light based on an investigation of 
 the properties of flame ; — these were but a few of 
 the trains of enquiry, of which his Mendicity House 
 was the primary object. Charity and science went Practical 
 hand in hand ; and when we award to "Wa.tt the benefits re- 
 highest honours for an invention which enabled him ^''™°S- 
 to create mechanical force at an economy of two- 
 thirds of the coal previously consumed, shall we 
 deny Eumford a civic crown for having so improved 
 the methods of heating apartments and of cooking 
 food, as to produce a saving in the precious element 
 of heat, varying from one-half to seven-eighths of the 
 fuel previously consumed ?^ When we consider the 
 enormous price of wood in nearly every part of the 
 Continent, the destruction of forests which has oc- 
 curred, and the consequent injury to the climate, as 
 
 ^ In the hospital of Verona he reduced the consumption of wood to one-6'i 
 would not rest until he had cooked his dinner with his neighbour's smoke 
 
 Some one wittily said of Rumford, that he 
 
Chap. VI., § 4.] 
 
 HEAT. — KUMFORD — HOPE. 
 
 143 
 
 (635.) 
 Different 
 experi- 
 ments. 
 
 (636.) 
 
 well as to the material wealth of many districts, we 
 are disposed to give Eumford a higher place than has 
 generally been accorded to him. Had his excellent 
 principles been universally carried out, some millions 
 sterling would have been saved to every large state 
 in Europe. Fontenelle characteristically says of a 
 certain savant, who made experiments on nutrition, 
 with a view to carry fasting to the utmost practicable 
 extent, that his researches had the double aim of 
 a place in heaven and in the academy. Cuvier, who 
 tells the anecdote in his Eloge of Rumford, adds, 
 that the latter had a truer claim to the questionable 
 compliment. That science is surely not despicable 
 by which a pound of wool, of fuel, or of food, can be 
 made to go one-half farther than before in warming 
 the naked and in feeding the hungry. 
 
 All Rumford's experiments were made with admir- 
 able precision, and recorded with elaborate fidelity, 
 and in the plainest language. Everything with him 
 was reduced to weight and measure, and no paing 
 were spared to attain the best results. His experi- 
 ments on heat, and the properties of bodies in con- 
 nection with it, are the most important. He first 
 applied steam generally in warming fluids and to the 
 culinary art. He maintained the paradox of the 
 non-conducting power of liquids, which, though prac- 
 tically true, appears not to be rigorously so. He 
 contrived many ingenious instruments ; but his ther- 
 moscope, identical with Leslie's differential thermo- 
 meter, was probably of later invention, if not in 
 some measure borrowed from it. In like manner his 
 proofs of the maximum density point of water were 
 unquestionably suggested by Dr Hope's beautiful ex- 
 periment, although this derives its meaning fi'om the 
 laws of convection, which Rumford first established. 
 
 That water expands in bulk below the temperature 
 
 Dr Hope on of 39° or 40° Fahr. until it freezes, is a fact which 
 
 the maxi- 
 mum den- 
 sity point 
 of water. 
 
 had been asserted since the middle of the seventeenth 
 century. But for 150 years its great improbability, 
 and the unquestionable uncertainty introduced into 
 the resxdt by the irregular expansion of the contain- 
 ing vessel or glass of the thermometer, enabled scep- 
 tics in every generation to withhold their assent. Per- 
 haps the last who doubted was the illustrious Dalton. 
 He allowed himself however to be convinced by Dr 
 Hope's experiment, in which the temperature of the 
 denser and rarer water is measured by two thermo- 
 meters placed at the bottom and top of a cylindrical 
 jar, and nothing interferes with the natural tendency 
 of a fluid to arrange its particles according to their 
 specific gravity, the lighter resting on the heavier 
 ones. It is to be regretted that Hope did not pro- 
 secute original enquiry, for which the conception of 
 this experiment, and the mode in which he conducted 
 
 it,i show that he had excellent qualifications. Hope 
 was first the colleague, then the successor of Black 
 in the chair of chemistry in Edinburgh ; and in his 
 time probably the most popular teacher in Europe 
 of that science. He died on the 13th June 1844, 
 in the seventy-eighth year of his age. 
 
 Rumford's name will be ever connected with the (637.) 
 progress of science in England by two circumstances ; R""»f<"'d 
 first, by the foundation of a perpetual medal and Rgyai in. 
 prize, in the gift of the Council of the Royal Society stltution. 
 of London, for the reward of discoveries connected 
 with Heat and Light ; and secondly, by the estab- 
 lishment, in 1800, of the Royal Institution in Lon- 
 don, destined, primarily, for the promotion of original 
 discovery, and, secondarily, for the diffusion of a taste 
 for science amongst the educated classes. The plan 
 was conceived with the sagacity which characterized 
 Rumford,' and its success has been greater than could 
 have been anticipated. Davy was there brought into 
 notice by Rumford himself, and furnished with the 
 means of prosecuting his admirable experiments. 
 He and Mr Faraday have given to that institution 
 its just celebrity with little intermission for half a 
 century. 
 
 Rumford spent his later years in Paris, where he (638.) 
 died in 1814. The estimation in which he was then Rumford's 
 held may be judged of from the fact, that he was '^^'* ^^^^^ 
 one of the eight foreign associates of the Academy 
 of Sciences. He was very capable of having done 
 more for science : the versatility of his talents, the 
 accidents of his early life, and the strong hold which 
 principles of philanthropy and public utility always 
 exerted over him, account for the absence of more 
 sustained and erudite researches. But in those very 
 particulars he deserves to be cited as a practical phi- 
 losopher, as to many things in advance of his age, 
 and a benefactor both to science and to mankind.^ 
 
 In the history of pure science Rumford will be 
 chiefly remembered by his espousing the (not new) 
 theory that heat consists in a motion of some kind 
 amongst the particles of matter, in opposition to the 
 opinions then so prevalent amongst chemists, which 
 almost tended to regard it as an element capable of 
 forming combinations. Rumford's view was mainly 
 based on the facts of friction, which he showed to be 
 irreconcilable with the notion of a change in the spe- 
 cific heat of the abraded matter, and to be seemingly 
 inexhaustible so long as the force producing friction 
 is continued. His conclusion was, that the heat 
 then generated cannot be a substance, but an affec- 
 tion of body of the nature of vibratory motion. The 
 amount of heat evolved in boring cannon is very 
 
 (639.) 
 His opi- 
 nions on 
 the nature 
 of heat im- 
 portant. 
 
 Derived 
 from expe- 
 riments on 
 friction. 
 
 ^ Edinburgh Transactions, vol. v. 
 
 2 Kumford married (for the second time) Lavoisier's widow ; his daughter (by his first marriage) became Madame Cuvier. 
 Hence Cuvier's Eloge of Rumford contains the most authentic particulars of his life. Madame Rumford survived until a few 
 years since, residing at Paris, where she formed a link between the savans of the age of Lavoisier, and those of the middle 
 of the nineteenth century. 
 
144 
 
 MATHEMATICAL AND PHYSICAL SCIENCE, 
 
 [Diss. VI. 
 
 great, an operation with which, as we have seen, he 
 was professionally connected. In one experiment, a 
 steel-borer pressed with a force of 10,000 lbs. against 
 gun metal, and revolving 32 times in a minute, gene- 
 rated in 2 J hours the heat necessary to boil 18J lbs. 
 of water. It is probable that Eumford carried his 
 views so far as to infer a necessary and constant 
 relation between the quantity of heat generated and 
 mechanical action expended ; and if we take an esti- 
 mate of horse-power more conformable to reality 
 than the nominal horse-power of Watt (33,000 lbs, 
 raised 1 foot in the minute, which is too great), we 
 shall find a tolerable approximation between his re- 
 sults and those now generally admitted. Davy fa- 
 voured Eumford' s theory, but the mechanical ques- 
 tion remained for 40 years almost unconsidered. 
 (640.) At length, about 1845, Mr Joule of Manchester en- 
 
 ^"^J®*^' ^^' deavoured to establish a rigorous connection between 
 Mr Joule. ^^ mechanical effort expended and the heat gene- 
 Mechanical rated by friction ; and he appears to have satisfac- 
 effect of toriiy established {Phil. Trans., 1850) that in the 
 case of water agitated by beaters, the work expended 
 by the fall of 772 pounds through 1 foot is capable 
 of raising the temperature of a pound of water by 1° of 
 
 Fahrenheit. ^ Mr Joule's experiments and inferences, 
 however, go much farther than this, namely, that in 
 all circumstances where heat is generated, it is at 
 the expense of a precisely similar equivalent of me- 
 chanical effect ; and conversely, that mechanical effect 
 is never used up, without a corresponding evolution 
 of heat, and that this is the case whatever be the 
 fluids or other substances employed. Thus in the 
 steam-engine the possible eflBciency of the engine is 
 only limited by the mechanical effort due to the heat 
 given out by the condensed steam. So the heat given 
 out by compressed air represents the force expended 
 in compression; and even the heat produced by voltaic 
 or magnetic electricity is that which corresponds to 
 the work it might do. A step farther leads to the 
 equivalence of heating effects by chemical combina- 
 tion to the amount of energy which, differently di- 
 rected, might have been realized in the shape of 
 work ; and though a larger induction is still required 
 to justify all the conclusions which the zealous pro- 
 mulgators of this comparatively new "mechanical 
 theory of heat" have advanced, it cannot be doubted 
 that there is a basis of important truth in the matter 
 which well deserves farther enquiry. 
 
 § 5. Sir John Leslie. — Establishment of certain Laws of Radiant Heat. — Pictefc— Prevost. 
 
 heat. 
 
 (641.) The fact that heat is radiant, or passes through 
 
 Sir John space in the manner of light, apparently disengaged 
 proffrassof ^^°^ ^^7 material vehicle, became known at an early 
 the science period. Porta in the sixteenth century, and the Flo- 
 of radiant rentine academicians in the seventeenth, had reflected 
 heat by mirrors. Marriotte and Newton respectively 
 assigned some of the laws which characterize it. 
 Lambert, in the middle of the last century, made 
 some real advances, but it was not until the very 
 close of that period that heat in the radiant form was 
 carefully and systematically studied. The group of 
 philosophers simultaneously engaged on it consisted 
 of Leslie, Kumford, Herschel, Pictet, and Prevost. 
 The two last named were earliest in point of date ; 
 but as we owe to Leslie by far the ablest series of 
 experiments, and which for many years,' and even to 
 the present time, have formed part of the body of 
 science, we shall connect his name principally with 
 this section. 
 
 Sir John Leslie, born in 1766, completed his 
 studies at a very early age in the University of St 
 Andrews. From boyhoid he was remarked for a 
 decided and independent turn of character ; and as 
 his favourite studies were mathematical, he for some 
 time pursued them to the exclusion of the classics. 
 Ultimately, however, he attained also to a respect- 
 able knowledge of these, and by his strong natural 
 
 (642.) 
 His early 
 Btudies ; 
 
 talents, and his love of reading, he acquired an im- 
 mense stock of information on all sorts of subjects. 
 This he displayed not only in his conversation, but 
 also in his writings on technical and purely scienti- 
 fic matters, in which he frequently introduced with- 
 out much apology illustrations from his miscella- 
 neous reading, and even metaphysical disquisitions. 
 
 As is frequently the case in persons addicted to (643.) 
 natural philosophy, his first original researches were »id essays 
 
 connected with mathematics. Playfair, who was""." j 
 .,, ,. . TTT , matiCB and 
 
 eighteen years his senior, encouraged and directed electricity, 
 him ; Ivory, who was almost his contemporary, and 
 also his fellow-student at St Andrews, was per- 
 haps no less influential in confirming his geometrical 
 tastes. The former communicated Leslie's first ori- 
 ginal paper to the Royal Society of Edinburgh in 
 1788. It was on Indeterminate Equations, and was 
 printed in their Transactions, Down to this period 
 we have no record of his being engaged in original 
 experiments ; but it is probable that such was the 
 case, for in 1790, and the following years, we have 
 evidence not only of his having speculated on subjects 
 of natural philosophy, but also that he had made 
 experiments intended to confirm or refute prevailing 
 theories. A paper on Electrical Theories was read 
 to the Royal Society of Edinburgh, which, finding 
 them reluctant to print, he withdrew, and he only 
 
 1 To Rumford, I believe, is due the attempt (in conformity with this view) to ascertain the heat developed by the friction of 
 fluids, for instance in churning (which, I think, was one experiment proposed by him), but I have not been able to find a 
 reference to it amongst his scattered writings. 
 
Chap. VI., § 5.] 
 
 HEAT. — SIR JOHN LESLIE — PICTET. 
 
 145 
 
 published it more than thirty years after, when cer- 
 tainly it was not calculated to advance science in a 
 perceptible degree. An essay on Heat and Climate, 
 read at the meetings of the Royal Society of London 
 in 1793, had not a more favourable reception ; and 
 though published twenty-six years later in Thomson's 
 Annals, it was refused a place in the Philosophical 
 Transactions. The author, no doubt, attributed these 
 rejections to the boldness with which he criticised 
 opinions currently received, and to the novelty of 
 the views which were shadowed forth ; but something 
 is, no doubt, to be allowed for the real immaturity of 
 these works, the involved and even inflated style in 
 which they were written, and the questionable evi- 
 dence for some of the conclusions. In these, and in 
 some subsequent scattered papers in Nicholson's 
 Journal, we observe, with all the faults, yet many of 
 the merits of those researches which afterwards made 
 him justly famous. We find acute observation, in- 
 genious, if not close reasoning, considerable inven- 
 tiveness in imagining experiments and in constructing 
 apparatus, and a general tendency to express physi- 
 cal laws in a mathematical form. It must be con- 
 fessed, that these merits were united to a good deal 
 of dogmatism, and a somewhat supercilious judgment 
 of persons eminent in science whose years and at- 
 tainments should have commanded respect. This, 
 however, is a fault which many ardent students not 
 very conversant with the world have had abundant 
 occasions to regret at leisure. Whether or not he 
 believed Sir William Herschel to have had some 
 share in the refusal of his paper by the Royal So- 
 ciety I do not know, but it is difficult, on other 
 grounds, to understand the bitterness with which he 
 expressed himself as to that eminent person, in con- 
 nection with his experiments on heat. 
 (644.) One of the circumstances which most contributed 
 
 Travels. ^^ encourage Mr Leslie's taste for experiment, was 
 , his engagement for above two years as tutor and 
 companion in the family of the ingenious Mr Wedg- 
 wood. Another was the opportunities which he 
 found or made for himself of foreign travel. With 
 or without companions he visited, in the early period 
 of his career, America, and most of the northern 
 countries of Europe, particularly Holland, Germany, 
 Switzerland, Sweden, and Norway. He also medi- 
 tated a journey to Egypt and the East, a project 
 reluctantly abandoned, and to which he reverted even 
 in the last years of his life ; but it was never carried 
 into effect. Nothing, perhaps, fosters so surely, a 
 taste for science as such extended tours ; and the 
 acquaintance made under the mo&t agreeable cir- 
 cumstances with foreign philosophCTs, and the fami- 
 liarity gained with their language and experiments, 
 contributes to it in no small degree. 
 (645.) We have now come to the period of Mr Leslie's 
 
 Publishes ijfg -when his character and position became esta- 
 o« ^a«? Wished, the first by the publication of his Experi- 
 mental Inquiry into the Nature and Propagation of 
 
 I ings. 
 
 Heat, in 1804; the latter by his appointment to the 
 chair of mathematics in the University of Edinburgh 
 in 1805. I shall first say a few words on his cha- 
 racter as a mathematician. 
 
 Mathematics were, as has been stated, his earliest (646.) 
 pursuit, and he cultivated them with great industry Mathemati- 
 and success. His adviser, Playfair, was attached ?^„7" ' 
 to the methods of the foreign mathematicians ; and 
 Leslie no doubt acquired from him, as well as from 
 his continental friends, a taste for the notation of 
 Leibnitz, then hardly employed in this country, but 
 which he uses in his work on Heat, and elsewhere. 
 Nevertheless, his real preference appears to have 
 been decidedly geometric. He almost always pre- 
 fers demonstrations, whether in mathematics or na- 
 tural philosophy, in the manner of Huygens and 
 Newton. He could hardly be called a discoverer in 
 mathematics ; but his work on Geometrical Analysis 
 and the Higher Curves shows much taste and know- 
 ledge, and is justly commended by Chasles and other 
 foreign writers. His attempt to replace Euclid's Ele- 
 ments by a new work on Elementary Geometry was 
 not more successful than such attempts have usually 
 been. 
 
 Unquestionably, the bent of Leslie's mind was (6*7-) 
 to physical research, in which he showed a peculiar impOTtance 
 talent ; and his selection of Heat was, as we have of the sub- 
 hinted, well - timed ; since there appeared a con- jeo* of ra- 
 vergence of attention to the subject, such as usually '*°' ^^'' 
 heralds some eminent discovery. The doctrines of 
 heat in combination, of which we have already spoken, 
 had engaged the attention of Black, Cavendish, and 
 Lavoisier; the subject of meteorology, in which Leslie 
 took the greatest interest, was becoming a science in 
 the hands of De Saussure and Deluc ; whilst Pictet 
 repeated (without being aware of the anticipation) 
 the curious observation of Porta on the apparent con- 
 centration of cold by a concave mirror. As this ex- 
 periment really opened anew the subject of radiant 
 heat, we shall dwell for a moment on Pictet's labours 
 and their results. 
 
 Geneva was at this time nearly in the zenith of its (648.) 
 reputation as a nursery of the sciences. The most p'^"'* °^ 
 eminent and independent of its citizens were proud 
 of being also amongst its instructors, and the office 
 of professor was then, as it still is, considered one of 
 the most honourable in the state. About 1790 De 
 Saussure, the most eminent physical geographer of 
 his time, was in the vigour of his intellect, and amongst 
 his friends and coadjutors Maro-Atjguste Pictet 
 held a conspicuous place. The latter was professor 
 in the Academy, and being a person of popular man- 
 ners and great information, was known and esteemed 
 by the learned throughout Europe. He was the 
 author of numberless papers in a scientific jour- 
 nal which he edited ; but his work on fire — Essai sur 
 le Feu — published in 1791, was his principal pub- 
 lication. It contains some good observations on latent 
 and specific heat ; and on the power of difierent kinds 
 
 Geneva, 
 
146 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 (649.) 
 Prevost — 
 moveable 
 equili- 
 brium of 
 heat. 
 
 (650.) 
 Leslie's 
 Essay on 
 Heat—Vii- 
 ferential 
 thermome- 
 ter. 
 
 of surfaces to reflect and absorb it. He noticed the 
 different heights at which a blackened and a bright 
 thermometer stand even when exposed to common 
 daylight ; but so far as I have observed, he did not 
 distinguish the effect of colour in absorbing heat when 
 that heat is accompanied by light or the reverse; and, 
 indeed, this portion of his work stops short on the 
 threshold of most interesting enquiries. He showed 
 that radiant heat travels with great velocity, and ob- 
 served the heating and cooling of thermometers in 
 exhausted receivers. His work also contains obser- 
 vations on hygrometry, on some points of meteoro- 
 logy, and on the heat of friction. Indeed, its chief 
 fault is embracing so many topics in so short a com- 
 pass, thus preventing him from thoroughly examin- 
 ing any one of them. To Pictet is due the establish- 
 ment of meteorological observations at the convent 
 of the Great St Bernard, which are amongst the 
 most interesting which have ever been made, and 
 which are still continued. He died in 1825, at the 
 age of seventy-three. 
 
 The interesting experiment of the reflection of cold 
 led PiEERE Prevost, one of Pictet's colleagues, to 
 devise the theory of " the Moveable Equilibrium of 
 Heat. " His idea is, that heat is a substance associated 
 with bodies, of a highly elastic nature, and continu- 
 ally given ofiF from them in proportion to their tem- 
 perature, which may represent the tension of the 
 imaginary elastic fluid. When the temperature of a 
 body is stationary, it is (according to this view) be- 
 cause it receive^ by radiation from surrounding bodies 
 exactly as nluch' heat as it parts with in the same 
 way. The general structure of this theory was sus- 
 tained by the experiments of Leslie, and by some 
 later ones on the law of cooling by Dulong and Petit, 
 which, indeed, realize it in a remarkable manner. 
 Prevost first published his ideas in 1791, in the 
 Journal de Physique, and afterwards in a special 
 work. Prevost was a man of an active and vigorous, 
 rather than profound intellect. He was a foreign 
 member of the Royal Society, and died in 1839, at 
 the advanced age of eighty-eight. 
 
 We now come to speak of Leslie's important Essay 
 on Heat which received from the Royal Society the 
 distinction of the Rumford medals, and which pro- 
 cured for him a European reputation. It is a work 
 difficult to analyze, from the very fact, that its con- 
 struction is fragmentary, and its arrangement desul- 
 tory and obscure. Our limits will only allow us to 
 mention the methods of research and their chief re- 
 sults. As a thermoscopic instrument, he used a 
 modification of the common air thermometer (which 
 last had been employed by Pictet), which, havii^g two 
 balls at a certain distance, connected by a bent tube 
 containing a coloured liquid, showed the difference of 
 temperature of the balls; and being hermetically 
 closed, was free from the disturbing variation of at- 
 
 mospheric pressure. This he called the differential 
 thermometer. A similar instrument had been de- 
 scribed by Sturmius in the seventeenth century. 
 Whether Leslie had any previous knowledge of this 
 does not appear ; but, as Dr Young very correctly 
 observes in one of his anonymous critical articles,— 
 " The principle of the differential thermometer is too 
 simple to be called an invention, and it is only by 
 its ingenious application that Professor Leslie has 
 made it an object of attention." He usually em- 
 ployed as a source of heat a canister of block tin, 
 filled with boiling water, and having sides with dif- 
 ferent surfaces. The radiating or emissive efiect ofEmissive 
 these surfaces was measured by the rise of the ther-^^°^^^^ 
 mometer exposed to their successive influence in thegm.fa5gg_ 
 focus of a metallic reflector. The result showed a 
 great variety of effect, varying from 100 when the 
 surface was blackened, to 12 when it was of polished 
 metal. The absorptive power of surfaces to non- 
 luminous heat is also in exact proportion to their 
 emissive power — a property which seems essential 
 for preserving the equilibrium of like temperatures. 
 
 Another and not less important law clearly esta- (651.) 
 blished by Leslie was this, that the radiation of ^eat^^^^"^.^^ 
 from a plane surface takes place with unequal force ^f radiant 
 in different directions.^ When the specific heatingheat. 
 power or density of the calorific rays is estimated in 
 a direction perpendicular to the surface from which 
 it emanates, it is found to be a maximum. At any 
 other angle with the surface, it varies as the sine of 
 the angle. This law (which Fourier showed later to 
 be necessary for the equilibrium of temperature) 
 obtains also in the case of light. Hence the appa- 
 rent specific brightness or warmth of a surface is 
 the same under whatever angle it is viewed with re- 
 ference to the plane of the surface, which, when 
 placed obliquely, contributes rays from a larger ex- 
 tent of surface, owing to the foreshortening, but being 
 weaker in the same proportion from every point, the 
 aggregate efiect is the same. Some interesting ex- 
 periments were made on the number of coats of 
 isinglass necessary to efifect a complete transformation 
 of the metallic into the gelatinous surface, which was 
 found to be considerable ; and, in like manner, the 
 reflective character of metals was only very gradu- 
 ally destroyed by varnishing. This observation, 
 rightly interpreted, showed that some solids are per- 
 meated by radiant heat, a conclusion which Mr Leslie 
 utterly rejected. 
 
 Another fundamental experiment less decisively (652.) 
 proved was, that the law of radiation varies inversely ^j^gj^^g^jB 
 as the square of the distance. Perhaps the most square of 
 convincing, as well as the simplest proof of this has the die- 
 been given more recently by Melloni. If a delicate *'""''• 
 thermometer or other apparatus for measuring radi- 
 ant heat be confined in a case, so as only to admit 
 rays coming within a definite angular space — and if 
 
 This result had already been anticipated by Lambert ; Pyrometrie, p. 197. 
 
Chap, VI., § 5.] 
 
 HEAT. — SIR JOHN LESLIE. 
 
 147 
 
 the instrument be placed in front of an indefinite 
 plane (such as a wall) hotter than itself — the rise of 
 temperature will be precisely the same, whatever be 
 the distance at which it is presented to the heated 
 surface. 
 (653.) The influence of colour on the heating of bodies 
 
 Influence ^a,s considered by Leslie in an original manner. It 
 on radiant ^^^ found to be effectual only when the radiations are 
 heat. luminous. A thermometer painted black or white 
 
 (provided the texture of the surface be the same) 
 parts with its heat, and also absorbs the heat de- 
 rived from such a source as boiling water, in an al- 
 most equal degree. The effect depends chiefly on the 
 degree of polish or condensation of the surface. But 
 with luminous sources of heat the case is widely dif- 
 ferent. This subject had been carefully considered 
 previously to the date of Leslie's work by Sir W. 
 Herschel, who had studied the absorbing power of 
 different colours on the sun's rays. Black and white 
 form the two extremes, and Leslie availed himself of 
 this principle to construct his photometer, which cer- 
 tainly (whatever may be its defects) is an elegant mo- 
 dification of the differential thermometer. It is an 
 instrument having one ball of black, the other of 
 pellucid glass, and united by a tube of the form of 
 the letter U, containing sulphuric acid tinged red as 
 an indicator. As the texture of the surfaces of both 
 balls is the same, dark heat is equally absorbed by 
 both, and the indicating liquid remains stationary. 
 But in the sun's rays, or even in common daylight, 
 the dark ball becomes most heated ; and it is not 
 unreasonable to conclude, that when the source of 
 heat remains the same, its variations of intensity are 
 correctly shown. Leslie, however, erred in consider- 
 ing that it was applicable to measuring light differing 
 in origin and quality on a comparative scale ; and 
 this error he unfortunately persevered in, after un- 
 questionable experiments had Shown its fallacy. 
 (654.) The Essay on Heat contains an elaborate and 
 
 Thelawsof jjjggjjjjjyg research into the law of cooling of bodies, 
 der Tarioas including the effects of mass, surface, contact of air, 
 circam- currents of air, and likewise of inclosure of the cool- 
 stances, jjjg body in successive envelopes or thin cases ; and 
 the author ingeniously compared the results of actual 
 experiment with formula based on principles more 
 or less theoretical. But a fundamental error unfor- 
 tunately runs through all this research, and shows 
 in a striking manner the fatal influence of theo- 
 retical preconception steadily maintained through a 
 Leslie's course of experimental enquiry. He starts with the 
 peculiar notion, that the presence of air is essential to the 
 Ihe^r™ propagation of Heat,.generally called "radiant." In 
 gation o^T fact, for radiation he usually substitutes the word 
 heat. « pulsation," and ascribes the effect of surface in mo- 
 
 difying the cooling of bodies to its faculty of trans- 
 mitting pulsations or tremors, more or less readily, 
 to the vehicle of the air. He was indeed compelled 
 to admit that air had a double agency ; one " abduc- 
 tive," as it draws off heat by contact and by what is 
 
 generally called " convection," that is by currents 
 which the communication of heat itself produces ; the 
 other, " pulsatory," which corresponds to what is 
 usually termed radiation, but which Leslie persisted 
 in believing to be due to tremors propagated in air, 
 after the manner of sound, and with the same velocity. 
 In the concluding chapter of the work before us he 
 considers the cooling effect of different gases, and of air 
 of different degrees of rarefaction ; and this last ex- 
 periment might, one would have thought, have satis- 
 fied him of the fallacy of his opinion ; since, taking 
 his own numbers, when air is rarefied 1024 times, the 
 " pulsatory energy" is only diminished one-third part. 
 In fact, it appears as if his work broke off abruptly, 
 when the course of observation became irreconcilable 
 with the opinions advanced in the early part of it. 
 
 After this analysis of Leslie's greatest contribution (656.) 
 to science, I cannot afford space to dwell upon his His minor 
 minor inventions. I pass over them, however, with YllezmB~ 
 the less regret because they have been fully dwelt experi- 
 upon in his " Dissertation," of which the present is a ment. 
 continuation, and in his articles on Cold and Meteo- 
 rology in the Eiicycloptedia. The most original and 
 important of these was his very beautiful process of 
 producing ice in quantity by the cold of evaporation, 
 in the receiver of an air-pump ; rendered effectual by 
 his ingenious use of absorbent surfaces for "with- 
 drawing the vapour. This experiment was completed 
 in 1811, and attracted much attention. It was con- 
 nected with his researches on hygrometry, to which 
 he also adapted his differential thermometer. But 
 in the development of this diflScult theory, he was 
 less successful, nor indeed could he well be so, whilst 
 he adhered to the old opinions respecting the affinity 
 of air for moisture. 
 
 Having filled the Mathematical Chair from 1805 to (656.) 
 1819, Leslie was in the latter year translated to that Close of his 
 of Natural Philosophy, vacant by the death of Play- 
 fair. He had a good collection of apparatus, and de- 
 vised many ingenious experiments. In 1820, he was 
 elected corresponding member of the Institute of 
 France, and died on the 3d November 1832, at the' 
 age of 66, having received the honour of knighthood, 
 on the recommendation of Lord Brougham, but a few 
 months before. 
 
 In closing this brief sketch of Sir John Leslie's (657.) 
 career, we cannot fail to observe the combination of His philo- 
 unusual powers with unusual drawbacks to their ^°P * 
 complete and vigorous exertion. Whilst he had the in some 
 chief merits, he had also the most serious defects, of points de- 
 the self-formed student. He was ardent and ambi- ^^^^tive 
 tious in the pursuit of knowledge. He must have 
 been for many years a hard, if not a methodical stu- 
 dent ; he united good mathematical knowledge with a 
 real love of experiment ; he was gifted with a strong 
 memory, and confident in the exercise of all his 
 powers. Why, with so many advantages he did not 
 achieve more, nor put forth even what he did to 
 
148 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 greater advantage, was mainly because he yielded to 
 the guidance of an imagination which often carried 
 him into fanciful speculation, yet which was strangely 
 united with dogmatism in maintaining what he had 
 once maintained, and a disposition to accuse others of 
 misinterpreting nature, whenever they arrived at con- 
 clusions inconsistent with his own. 
 (658.) Ii such sciences as those which he chiefly culti- 
 
 vated, — sciences eminently progressive, imperfect, 
 and dependent on experimental proof, — a just appre- 
 ciation of the labours of others is one of the most 
 essential parts of the philosophic character, whilst 
 an absence of it infallibly condemns the dogmatic 
 theorist to be gradually left behind, even in the paths 
 which he had at first trod with the greatest distinc- 
 tion. With few exceptions, Sir J. Leslie carried his 
 scientific views of 1804 with him to the grave. The 
 possibility of the passing of heat, except solar and 
 highly luminous heat, through any solid body, such 
 as glass, though proved by Haycock, De la Roche, 
 and Powell, — the existence of dark heating rays in the 
 sunbeam, less refrangible than the red, demonstrated 
 by Herschel, and afterwards confirmed by many 
 others, — the doctrine of gases and vapours as laid 
 down by Dalton, — ^the maximum density point of 
 water shown so .ably by Hope and Rumford, — the 
 
 existence of climates in the arctic regions of which 
 the mean annual temperature does not exceed 0° of 
 Fahrenheit, proved by Party and his successors, — 
 all these, and many other demonstrated truths in his 
 own peculiar walk of science, were, we fear, practi- 
 cally ignored by him throughout life. (659.) 
 
 But we willingly leave the ungrateful task of indi- Merit of Ms 
 eating defects. Let us recollect rather with pleasure t^/'re™™' 
 how much we owe to his beautiful discoveries. It is searchfeB. 
 perhaps not an insignificant test of their originality, 
 that though they were generally adopted (at least to 
 the extent which his own experiments justified), Les- 
 lie's observations were but rarely repeated, and that 
 only in the way of general confirmation and iUustra^ 
 tion. I mean that for a great many years the path 
 which he had opened, and the methods which he de- 
 scribed, were not seized upon by others, as leading to 
 a sure course of discovery. Until the time of Dulong, 
 his experiments on cooling were perhaps never care- 
 fully resumed, and a very great number of his sub- 
 jects of enquiry were only taken up thirty years after 
 their publication, as we shall see in a future section. 
 
 The observations of Herschel on the Refrangibility (660.) 
 of Solar Heat, I shall include in the notice of the 
 experiments of Berard and De la Roche, to which 
 -we shall presently turn. 
 
 § 6. Fourier. — Mathematical Theory of the Conduction of Heat. 
 Temperature of the Earth and of Space. 
 
 Lambert; Poisson.- 
 
 (661.) It is stated by Arago, that when the Academy of 
 Theory of Sciences, above a century ago, proposed as a prize sub- 
 ttenofheatJ'^''*' " La Nature et la Propagation du Feu ;" adding, 
 —Lam- " la question ne donne presque aucun prise 3, la geo- 
 bert. metric," — a majority of the candidates treated of the 
 
 methods of preventing the burning down of houses ! 
 It is true, however, that on that occasion, Euler sent 
 a memoir which, though crowned, was unworthy of 
 his genius. Lambert in his " Pyrometrie," in 1779/ 
 had the rare merit of laying the foundations of the 
 science of conduction. He solved correctly this ques- 
 tion : — " If a thin conducting bar of indefinite length 
 be kept with one extremity heated to a constant degree 
 above the surrounding space, required the tempera- 
 ture of any point in the axis of the bar'?" The solu- 
 tion is, that the temperatures, or rather excesses of 
 temperature, diminish in a geometric ratio, at dis- 
 tances reckoned in arithmetical progression, from the 
 origin of the heat.^ In this solution it is assumed, 
 (1.) That the flow of heat along the bar, is at any point 
 proportional to the rapidity with which the tempera- 
 ture at that part of the bar is lessening as we recede 
 from the source ; in other words, that the flow of heat 
 from the hot part to the cold part, is more rapid in 
 
 proportion as the difference of temperature of two 
 sections of the bar at a given short interval is greater. 
 (2.) That the bar parts with its heat to the surround- 
 ing space, exactly in proportion to its excess of tem- 
 perature at every part. 
 
 This beginning, which perhaps like many of Lam- (662.) 
 bert's other writings was not very generally known, Biot. 
 had no sequel until 1804, when M. Biot attempted to 
 find the differential equation of the general movement 
 of heat on the same principles. But the form which 
 he obtained, including a mathematical solecism, be- 
 trayed some error in stating the conditions. Three 
 years later Fourier had more success. But, conform- 
 ably to the plan of this discourse, I shall premise 
 some facts regarding his early career, which was far 
 from commonplace. 
 
 Joseph Fotjeibe was born in 1768, at Auxerre in (663.) 
 France. He was of humble parentage, and being Fourier— . 
 early left an orphan, was educated by the Benedic- Jj^ ^^"^^ 
 tine monks who, singularly enough, conducted with '" 
 success in that town a military school. It seemed 
 his fate to become either a priest or a soldier ; yet he 
 was neither, though ere long familiar with camps. 
 He became first a pupil of the old normal school of 
 
 * Pyrometrie, oder, von Maasse des Feuers und der Wdrme. Berlin, 4to, 1779. This work was posthumous, and contains many 
 riginal observations on Thermometry, Conduction, Solar Radiation, and Climate, ' Pyrometrie, p. 184. 
 
Ghap. VI., § 6.] 
 
 HEAT — FOUEIER. 
 
 149 
 
 The Egyp- 
 tian Insti- 
 tute. 
 
 (664.) 
 Fourier 
 first states 
 correctly 
 the analy- 
 tical form 
 of the pro- 
 blem of 
 conduction' 
 
 Tardy pub- 
 lication — 
 rivalry in 
 the 'Insti- 
 tute. 
 
 Paris, when Lagrange, Laplace, and BerthoUet were 
 amongst the professors. He had already presented 
 to the Academy, at the age of 21, a paj er*n the nu- 
 merical solution of equations, a subject of predilec- 
 tion with him, and to which we shall presently return. 
 After leaving the Normal School, he was named one 
 of the original professors of the Polytechnic School, 
 a station of which he was justly proud, but from 
 which he was withdrawn by the requisition to join, 
 along with Monge and other savans, the Expedition 
 to Egypt under Napoleon. It was the singular fancy 
 of that extraordinary man, to create an Egyptian 
 Institute, of a constitution similar to that of France. 
 Fourier was perpetual secretary. But it proved little 
 better than a waste of talent. The arts of Egypt were 
 not regenerated, and France was despoiled of some 
 of her ablest philosophers. Fourier had quite as much 
 to do with battles and treaties as with equations and 
 experiments. Yet he often referred afterwards with 
 partial recollection to those stirring times, and re- 
 counted, with the ardour of a somewhat garrulous 
 temper, the valiant feats of arms which he had wit- 
 nessed. Fourier edited the account of the Expedition 
 to Egypt, and wrote the historical preface, the com- 
 position of which ultimately procured for him a seat 
 in the AcadSmie Frangaisc. 
 
 On his return to Europe, he was appointed Prefect 
 of the Isere in 1802, and Grenoble became his 
 home for some years. Whilst he devoted a just 
 share of his attention to his public duties, he found 
 time to produce his greatest work. The Analytical 
 Theory of Heat. His first paper on this subject 
 dates from 1807. It was communicated to the Aca- 
 demy of Sciences, but not printed. The subject was 
 however proposed for a prize, to be decided in 1812, 
 when Fourier's essay was crowned, but, strange to 
 say, not published. The cause, it is to be feared, lay 
 in the jealousy of the greatest mathematicians of the 
 age. Laplace, Lagrange, and Legendre, the committee 
 of the Academy, whilst applauding the work, and ad- 
 mitting the accuracy of the equations of the move- 
 ment of heat thus for the first time discovered, insi- 
 nuated doubts as to the methods of obtaining them, 
 and likewise as to the correctness of the integrations, 
 which were of a bold and highly original kind. 
 These disparaging hints were not supported by any 
 precise allegations ; and we can scarcely blame Fou- 
 rier for feeling indignant at the tyranny of the mathe- 
 matical section, and little disposed to regard with 
 favour the few and comparatively insignificant efibrts 
 of several of its members subsequently to ratify and 
 extend the discoveries which he had unquestionably 
 made. The manuscript, after lying for twelve years in 
 the archives of the Institute, where it was consulted 
 by difFerentpersons, was finally printed, u)ord/or word, 
 as it stood in 1812.^ Fourier's long absence from 
 Paris in a remote provincial town, rendered this in- 
 
 dignity possible at first ; and afterwards, it was his 
 misfortune to be unable to hold a political station 
 without offence, amidst the violent intestine conflicts 
 with which Prance was afilicted. He alternately dis- 
 pleased his old master Napoleon and the Bourbons, 
 and the consequence was, that after the Restoration 
 he found himself dispossessed of every employment, 
 master of not one thousand pounds, and refused by 
 the government even a seat at the Institute. This 
 indigence, so honourable to himself, and this neglect, 
 so disgraceful to others, tended, no doubt, to increase 
 an irritability, such as intense mental exertion often 
 produces, and which the injustice of his scientific 
 countrymen had already aggravated. Finally, how- 
 ever, be received a modest post connected with the 
 civil administration of the department of the Seine ; 
 he was also elected a member of the physical section 
 of the Academy of Sciences, and he finally became 
 perpetual secretary of that body. 
 
 Fourier's papers on Heat show a remarkable com- (665-) 
 
 bination of mathematical skill with a strict and pre- ^f^,]^,' 
 1 ' 1 '3 • X 1 • 1 *'*^ preci- 
 
 cise attention to physical considerations. In thishegion — ex- 
 excels almost every writer of his time, and especially periments. 
 his colleague and younger rival, Poisson. His expe- 
 rimental skill is not to be so highly praised, although 
 he illustrated several of his solutions by actual trials, 
 which he submitted to calculation, and showed to 
 agree with theory. Their degree of precision, how- 
 ever, hardly allows them to be considered as tests 
 of theory. 
 
 Fourier assumes the correctness of Newton's law, /gae.) 
 as well for communication of heat from point to point Assnmp- 
 of a solid, as for the external radiation by which ittionsof the 
 parts with its heat into the surrounding space. In ij, w™"' 
 the former case, the flow of heat is proportional to 
 the rapidity of the depression of temperature, in the 
 direction in which the motion of the heat is considered; 
 in the latter, it varies as the excess of temperature 
 of the surface of the hot body above the surrounding 
 space, affected, of course, by a constant depending on 
 the radiating power of the surface. These, as I have 
 said, were also the Postulates of Lambert's solution. 
 Fourier's researches, fortunately perhaps, preceded 
 for the most part Dulong and Petit's enquiry into the 
 true law of cooling. I say fortunately, since other- 
 wise Fourier might have been discouraged from at- 
 tempting the solution of problems which are highly 
 important even in an approximate form. 
 
 With regard to the law of radiation, Fourier had (667.) 
 the merit of showing, for the first time, the necessity of ^*jv ^^}*^ 
 Leslie's experimental law of the intensity of emanated of emana- 
 heat being proportional to the sine of the angle which tion. 
 the direction of emanation makes with the surface. 
 This he considered both mathematically and physi- 
 cally. Mathematically, he showed that were this law 
 not true, a body might be maintained for an indefinite 
 time within an envelope of constant temperature, and 
 
 ^ See Fourier's note at the commencement of his paper, in Memoirs of the Institute for 1819 (printed 1824). 
 
150 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 yet never acquire that temperature, even approxi- 
 mately ; and physically, considering that radiation 
 proceeds not from a mathematical surface, but from 
 a material physical stratum of an imaginable thick- 
 ness, but which rapidly absorbs the emanations pro- 
 ceeding from the inferior particles, he proved that 
 the attenuation due to oblique emanation will fol- 
 low Leslie's law, independent of the precise rate of 
 absorption in traversing the physical surface. 
 (668.) Fourier takes extraordinary pains to define and 
 
 Definition justify every step of his demonstrations. He has the 
 ing power gi'eat merit of having first given a clear definition of 
 conducting power, or conductivity proper, which is 
 this : — " The number of units of heat (measured by 
 the weight of ice which it can melt) passing in unit 
 of time across a square unit of surface of an infinitely 
 extended plate bounded by two parallel surfaces at 
 unit of distance which are respectively maintained 
 at the freezing and boiling temperatures (unit of dif- 
 ference of temperature)."'- In like manner, the " ex- 
 and of terior conductivity" expresses the number of units 
 " exterior of heat parted with by unit of surface to the air and 
 conducti- surrounding space, when the difference of their tem- 
 perature amounts to unity. 
 (669.) Account of the Theorie Analytique de la Chaleur. 
 
 y°""f "^"j — ^The problems considered by Fourier in his Theorie 
 alpiqm de -Analytique, refer principally to the propagation of 
 laChaUur. heat in homogeneous conducting solids of definite 
 forms, and in some cases maintained in certain parts 
 at fixed temperatures. 
 (670.) The number of examples fully worked out is very 
 
 orloWms^'"^^^' ^^^ ^^^^ °^*y ^® referred to the following 
 solved by classes : — (1.) When some part of a solid has an inde- 
 him. finite source of heat applied to it, the remaining sur- 
 
 face being exposed to the air, or having determinate 
 temperatures maintained at certain parts. In this 
 case, the state of the solid in regard to heat is per- 
 manent, or independent of time ; and the problem is to 
 assign the temperature of each part, -and the flow of 
 heat through that part in a given direction. (2.) To 
 assign the temperature of every point of a solid pri- 
 mitively heated, either uniformly or after any assigned 
 law, and at any given moment. (3.) To solve the 
 last question only in the case where the cooling at the 
 surface has been going on for an exceedingly long 
 time. 
 (671.) Of the first class of problems, the slender bar heated 
 condition^ by a constant source of heat at one end, and exposed 
 of heat in a to the cooling influence of radiation and of the air, 
 slender which had been treated of by Lambert, is the simplest 
 ''"''• and most important. The temperature of any thin 
 
 slice perpendicular to the axis of the bar, is the 
 result on the one hand of the heat which it acquires 
 from the hotter slice nearest to it on the side of the 
 source of heat ; and on the other, of the heat with 
 which it parts to the slice next beyond and also to 
 the air in contact with the exterior surface of the 
 slice and by radiation from the same surface. The 
 solution of this problem is that of a simple difierential 
 equation of the second order, and the result is the 
 diminishing geometrical progression of temperature 
 already mentioned. This has been approximately con- 
 firmed by some careful experiments of M. Biot, which 
 indeed are nearly the best which we yet possess on the 
 subject. But instead of drawing from them, as he 
 does, an argument for the accuracy of the Newtonian 
 law of cooling, the diminution of temperature along 
 the bar is far more rapid at first, and less afterwards 
 than that law indicates. In fact, the apparent agree- 
 ment of the formula is owing to the use, in a case to 
 which it does not correctly apply, of that often mis- 
 applied rule of the doctrine of chances — the method 
 of least squares. 
 
 The solution of another case of stationary temper- (672.) 
 ature, — an indefinite solid bounded by three infinite 1° an infi- 
 planes (two of which, B, G, are parallel, and the third, "'** *" ' ' 
 A, perpendicular to both) having determinate tem- 
 peratures, — requires the introduction of a species of 
 analysis, in which Fourier acquired great dexterity, 
 but which is of so subtle a kind as to have created 
 doubts in the minds of the committee of the Institute 
 to which the Memoir was referred, and to have been 
 a sourpe of some controversy and much discussion 
 since. Fourier contrives to express, by an infinite 
 trigonometrical series, the law of temperature in such 
 a solid, which shall not only satisfy the differential 
 equation of the equilibrium of heat, but also the 
 conditions of temperature at the bounding planes, B 
 and C, which being zero by the problem, the value 
 of the temperature which, up to that point was finite, 
 suddenly comes to nothing, and has no value beyond. 
 This problem leads to a long digression on the pos- 
 sibility of expressing by trigonometrical series, quan- 
 tities which, vary according to any conceivable law 
 and of determining the co-efficients of the successive 
 powers of the sines and cosines employed. The 
 theorem to which Fourier is led, in which any function 
 of « is expressed by a series of definite integrals, in- 
 cluding sin X and cos x, is known by his name. 
 
 The problem, however, which Fourier most elabo- (673.) 
 rately treated, belongs to the 2d and 3d class, — Movement 
 namely, the cooling of a sphere primitively heated °^^®*' " * 
 
 ^ Let P be the flux of heat measured as above, K the constant of interior conductivity, z an ordinate measured across the 
 
 thickness of the plate, and v he temperature of the stratum of which z is the ordinate ; then P= — K — ; in the permanent 
 
 state the temperature varies uniformly /ro<n stratum to stratum. When the thickness and difference of temperature both are 
 
 dv 
 equal to unity, K=F. The expression F=: — ^ J- manifestly expresses the Newtonian Law, interpreted by Fourier as 
 
 stated above. 
 
Chap. VI., § 6.] 
 
 HEAT. — FOURIEE. 
 
 151 
 
 in a given way, but so that points equi-distant from 
 the centre have a common temperature.^ It might 
 be expected that the symipetry of the conditions would 
 admit of a simple solution ; and such indeed was 
 sought by Professor Playfair long before, in a paper 
 in the Edinburgh Transactions, with reference to Geo- 
 logical Speculations. It was, however, by no means 
 sufficiently general. It is shown by Fourier, that 
 even in the simplest supposable case — that where the 
 teihperature of the sphere was originally uniform — 
 the resulting expression for the temperature of any 
 stratum at any time, though capable of algebraic ex- 
 pression, cannot be assigned in finite terms, and no* 
 attempt has been made to evaluate it generally. The 
 special cases which have been considered, are when 
 the sphere is extremely small, or has been cooling 
 for a very long time. 
 (674.) The extreme complication of even such apparently 
 com^ Uca°^ simple cases when solved in all their generality con- 
 tion in the ^ists in this, that the flow of heat across each part is 
 Problem of in fact dependent at each instant on the state of heat 
 the Sphere, in each other part, and this distribution of the whole 
 is equally unknown with the local distribution on 
 which the movement of heat in each part depends. 
 To this must be added the peculiarity of conditions 
 at the surface, where the temperature undergoes an 
 abrupt change. The law according to which the su- 
 perficial particles radiate heat, is also different from 
 that according to which they receive it from the in- 
 terior. When a body uniformly heated to a consider- 
 able temperature cools in air, the subtraction of heat 
 from the surface commences with great rapidity, the 
 excess of temperature of the superficial particles being 
 very much greater than it ever can be afterwards. 
 The drain of heat from the interior of the sphere is 
 at first nearly imperceptible. The exterior cooling 
 will by and by become slower; and the degree in 
 which it takes place, will depend upon the rapidity 
 with which the conducting mass of the sphere is able 
 to supply fresh heat to the surface ; then the rate of 
 superficial cooling will become relatively somewhat 
 accelerated, and a fresh drain will take place from 
 the interior towards the surface. It is only in the 
 case of exceedingly small bodies, or those of an in- 
 finite degree of conductivity, that the body will cool 
 according to a simple law. In all other cases, there 
 will be characteristic periodical inflections in the 
 course of cooling. These, no doubt, are represented 
 in Fourier's series, if it could be numerically calcu- 
 lated ; and it is to be desired that some attempt were 
 nade to represent it approximately. When the cool- 
 ing has endured for a very long time, these gashes 
 of heat cease altogether; the surface has attained 
 nearly to the temperature of the surrounding space, 
 and the drain of heat from the interior is so slow, 
 
 that the progression of temperature is very gradually 
 and slowly disturbed. 
 
 Application to the Thermal condition of the Earth. (676.) 
 — ^This last case has been discussed by Fourier with Applica- 
 great address, relatively to the present condition of tJ,°°g°prin- 
 the Earth, considered as a mass which has been once cipies to 
 at a high temperature, of which we have evidence the ther- 
 in the general increase of heat as we descend in mines, ""■^ """^ 
 or when we penetrate its crust by Artesian wells, jjanh. 
 The surface of our planet receives a large amount of 
 heat annually by absorbing the sun's rays, but parts 
 with it by radiation into free space, to an extent which 
 preserves a sensible uniformity of temperature from 
 age to age. The considerations connected with the 
 subject are these : — (1.) The proper heat of the earth, 
 and how much heat reaches the surface from the 
 (perhaps) still incandescent interior ; (2.) How much 
 heat do we receive from the sun, what share of it 
 enters the surface, and how far, and according to 
 what periods does the influence of the seasons extend 
 below the surface ? (3.) What is the amount of refri- 
 geration of the earth's surface ? — how does the atmo- 
 sphere affect it ? and, if the cooling be due entirely 
 to radiation, what are we to set down for the temper- 
 ature of space! so as to account for the heat lost ? 
 
 First, As to the proper heat of the globe. Not to (676.) 
 go further back than the last century, the incandes- ?*'*j^J°JE^' 
 cence of the earth's nucleus was assumed as very pro- gjo^g . 
 bable by Bufi'on and other popular writers, and their 
 opinions were, on the whole, confirmed by the pro- 
 gress of observation. The existence ofvolcanoes was, 
 of course, an obvious argument ; another was, that 
 if the earth were once hot it must be stiU cooling ; con- 
 sequently, climates are continually becoming colder, 
 especially in the Arctic regions, which it was supposed 
 depended most on the supply of heat from within. In 
 evidence of this change were quoted, not only the 
 remains of elephants found interred with flesh and 
 skin in the midst of Siberian ice, but also the un- 
 equivocal proofs, so well known to geologists, that 
 at a period indefinitely more remote, tropical plants 
 of gigantic growth, and animals of a class which now 
 frequent only southern seas, appear to have lived 
 and flourished in high northern latitudes. But even 
 in the time of Buffon, attention was directed to a fact 
 yet more important for the theory of heat, namely, 
 the increase of temperature observed in deep mines. 
 Notwithstanding many sources of doubt and confu- manifested 
 
 sion, such as the heat from candles, and from men at ^^ *''® '°' 
 , . ■ n 1 • 1 1 • crease of 
 
 work m mines, from chemical changes in some cases, hgat i^ 
 and from the increased density of the air, the fact of mines, 
 the increase is now well established, and also its 
 rate of progression with more certainty than in the 
 time of Fourier. On an average (including the best 
 data of all, those yielded by Artesian springs), the 
 
 ^ The problem of the Armil or ring, heated at one or several points, is one which offers considerable facilities for its solution, 
 but the results are of little utility, thf form being so peculiar ; and even as a test of theory, the variations of temperature from 
 point to point are insufficient under the limited conditions in which the numerical solution is practicable. 
 
152 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 increase appears to be 1° Fahr., for 50 or 60 English 
 feet of descent. Fourier first undertook to enquire, 
 Whether, supposing the earth to have no primitive 
 internal heat, the continual action of the sun might 
 not produce the increasing temperature observed. 
 But he found, on the contrary, that there is no such 
 tendency, and that after a long time, the temperature 
 at any moderate depth below the surface (but be- 
 yond the varying influence of the seasons) will be 
 constant. Now, observations on the temperature of 
 mines and Artesian springs extend to the depth of 
 1700 English feet, and the influence of the seasons 
 is usually quite extinct (in this latitude) at 50 or 60 
 feet. The nearly uniform increase beyond is there- 
 fore due to a source of heat within, or, what amounts 
 to the same thing, to the relatively warmer state of 
 the nuc|eus. The analysis of Fourier shows, that 
 the variation of temperature in the successive strata 
 of a spherq, cooling with excessive slowness, is very 
 closely allied to the flux of heat which passes through 
 it, and which is spent by radiation or otherwise at the 
 Its insigni- surface. The result is exceedingly striking, and may 
 ficant effect |jg considered as remarkably well established; the 
 ■ flow of heat from the interior contributes to raise 
 the temperature of the surface by only one seven- 
 teenth of a degree of Fahrenheit ; or would melt an- 
 nually a stratum of ice ^^jth inch in thickness. This 
 is all the refrigeration which the earth's surface can 
 ever sufier on this account, and in its present state 
 of cooling, it would take millions of years even to 
 reduce it by one half. So little ground is there for 
 the belief of Buffon and his friends, who imagined 
 that the destruction of animal and vegetable life must 
 rapidly ensue by reason of the diminishing central 
 heat. 
 (^^7.) Again, the depth to which we must descend in 
 
 thTfluid order to reach a temperature sufficient for the supply 
 nucleus, of molten lava, is not excessive : for this depends 
 entirely on the conductivity of the earth's crust, 
 which we know to be very small. A familiar in- 
 stance occurs in streams of recent lava, where a crust 
 soon forms, on which a man may walk safely, yet 
 only be separated by a foot or less from the fiery 
 liquid. ' Fourier calculated that the temperature of 
 incandescence may prevail at a depth within the 
 earth of only about 15 English miles, without affect- 
 ing the superficial temperature by more than a small 
 fraction of a degree. 
 C678.) As it seems scarcely possible to ascribe some, at 
 Cause of iga,st, of the geological efiects already mentioned to a 
 change of cause of which the variations are imperceptible in 
 climate. • such vast periods, other writers have suggested dif- 
 ferent possible explanations. One which appears to 
 have considerable probability, is that of Arago, that 
 the heat emitted by the sun has a secular rate of 
 change ; in other words, that our sun is a variable star. 
 
 Secondly, As to the efiects of the sun's heat on (679.) 
 the earth. It has been already stated that Fourier ^*^'=* °f 
 showed that below a moderate depth, the heat of the heat on the 
 earth would be uniform and invariable, so far as solar earth, 
 radiation is concerned. At smaller depths, it will 
 vary according to the season of the year, and these 
 variations will at all depths be gone through in the 
 same period with the variation at the surface, which, 
 is of course annual, but the inflections follow a pe- 
 culiar law in each latitude and climate, and even in 
 one year compared with another. Within the depth 
 to which the influence of the seasons extends, the 
 amount of the range of temperature continually di- 
 minishes, nearly in a geometrical progression, and at 
 length it becomes insensible. At increasing depths, 
 the periods of maxima and minima are continually 
 retarded, so that at a certain depth, the earth is hot- 
 test in winter and coldest in summer. A smaller 
 fluctuation of the same kind, and penetrating to a 
 smaller depth, follows the diurnal range of tempe- 
 rature. The manner in which these interesting phe- 
 nomena are connected with the conducting power and 
 specific heat of the earth's crust, was clearly pointed 
 out by Fourier. 
 
 Before as well as after these theoretical investi- ,ggQ , 
 gations, observations on thermometers sunk to dif- Theory 
 ferent depths in the ground had been made, and the compared 
 results confirm these conclusions of theory in every ^'^ ^^^ 
 respect. Such observations were made by De Saus- 
 sure, Leslie, Arago, Quetelet, and other experimen- 
 ters, including the writer of these pages, who caused 
 careful experiments to be made for five years, on 
 three sets of thermometers, placed in difierent kinds 
 of SOU and rock, extending to a depth of above 25 
 feet. By means of these, the conductivity of those 
 various soils was determined' with accuracy, and data 
 aflbrded for subsequent enquiry. "^ 
 
 Amongst the most interesting enquiries connected (681.) 
 with this subject, is the total quantity of heat re- Totalquan- 
 ceived in a year from the sun by the absorptive ''*y .°^ ^\'* 
 
 • 1 F6CG1V6Q DV 
 
 action of the earth's surface ; but this does not ap- tj,g g^yt], 
 pear as yet to have been successfully answered, from the 
 Nevertheless, M. Pouillet, from merely experimen- ^""• 
 tal data, considers that he has proved that the 
 amount of solar radiation which reaches the earth 
 would melt in a year an average thickness of 31 
 metres of ice, all over its surface, provided that it 
 were entirely absorbed. Poisson has obtained a re- 
 sult four times less, and estimates the effect of the 
 sun in raising the temperature of the climate of Paris 
 at 24 centigrade degrees, a result incredibly small. 
 
 Thirdly, On the temperature of space. Fourier ,„„^. 
 was probably the first who introduced this idea into The tem- 
 science. The term perhaps is a doubtful one andperatureof 
 liable to misconception, but the object of the enquiry °P°''^*~ 
 admits of being precisely stated. The researches of 
 
 ^ See Jkamantions of the Royal Society of Edmbmgh, vol. xvi., where a history is given of the observations previously 
 made. 
 
Chap. VI., § 6.] 
 
 HEAT. — FOURIEE — P0IS80N. 
 
 153 
 
 Fourier. 
 
 Dulong and Petit^ upon the cooling of a body by 
 radiation only within an envelope having a tem- 
 perature lower than itself, include, as a particular 
 case, that in which the body receives nothing from 
 the envelope, — when the radiation is entirely that 
 of loss without any gain ; and yet the cooling pro- 
 ceeds with a finite velocity. It could not with any 
 propriety be said in such a case, that the tempera- 
 ture of the space in which the body cools is in- 
 finitely low ; it cannot be said to have any tempera- 
 ture at all. 
 (683.) Now, in the case of our globe and its atmosphere, 
 defined by we have a heated mass, suspended as it were, in space. 
 If there were no other bodies in the universe, the earth 
 must by degrees lose its heat. We know indeed that 
 it is cooling. The proportion of its native heat an- 
 nually emitted, would melt a crust of ice i^^ inch 
 thick. This heat is dissipated in space. It may 
 therefore be enquired, whether a sphere of known 
 conducting power and of known temperature at the 
 surface, is parting with its heat to space at a rate 
 which supposes it to radiate without any requital, or 
 whether it receives from space (or the bodies which 
 space contains, independently of the sun) any portion 
 of the heat which it thus dissipates. To solve this 
 question, we must evidently know with great accu- 
 racy the radiating power of the surface of the earth, 
 than which, unfortunately, no datum is more com- 
 pletely uncertain: and the influence of the atmo- 
 sphere (which is truly a part of the earth) renders the 
 solution still more indeterminate. It is not known 
 what method Fourier took to arrive at a numerical 
 result, but it is well known that he obtained it in a 
 way which appeared satisfactory to himself, and that 
 he often referred to it. He supposed the " temper- 
 ature of space" to be 50° or 60° below zero on the 
 centigrade scale, and believed he did not err in fixing 
 it by more than 8° or 10°. By this we understand, 
 that after infinite ages, the earth, or any other body 
 placed in the same situation and previously heated, 
 would attain this temperature and no lower. 
 
 (684.) 
 
 This slight sketch gives an imperfect idea of the 
 extent and originality of Fourier's labours. But 
 enough has been said to show, that he must rank 
 amongst the most considerable philosophers of his 
 day. That he' excited the jealousy of the great ma- 
 thematical geniuses of the previous generation, and 
 that his new train of research, though fully accepted 
 by those who succeeded him, has as yet received but 
 slight extension at their hands, are facts which con- 
 cur to prove his originality and merit. That he 
 did not solve more cases of the propagation of heat, 
 and that some of his solutions are so complicated 
 as hardly to be such in a practical sense, show only 
 the extreme difficulties of a subject which touches 
 every where the boundaries of existing mathematical 
 
 knowledge. In the opinion of many persons, it is to 
 be desired that some at least of the problems of con- 
 duction were treated in a somewhat different way, 
 and approximations obtained by the application of a 
 less abstruse calculus. But towards this desirable 
 result, little has yet been done. 
 
 As a pure mathematician, Fourier occupies a (685.) 
 distinguished rank. His conversion of functions of ^"**°S8 
 every kind into series of periodical quantities — his on p„re 
 treatment of problems, involving discontinuous laws mathema- 
 — ^his solution of higher difierential equations — are *"'^- 
 all important additions to analysis, to the improvement 
 of which, as he has himself very justly observed, 
 physical problems are ever the most important ave- 
 nues. Such considerations as Fourier treated of 
 could hardly have entered into the mind of a mathe- 
 matician not guided by a specific physical enquiry. 
 His favourite subject of the solution of Numerical 
 Equations, which brought forth his first essay — which 
 occupied him even on the banks of the Nile— and an 
 elaborate work on which was almost his last addition 
 to science, — is of course one of less general interest. 
 
 His experimental abilities, as we have said, were (686.) 
 not equal to his mathematical; and it is to be re-^^P^"" 
 gretted that his schemes for several practical appli- ^lyil~ 
 cations of theory seem to have been left imperfect. 
 He invented a Thermometer of Contact, an instrument 
 for determining the conductivity of bodies, which is 
 but little known or used, and of which the theory 
 was left incomplete. He also joined Oersted in ex- 
 periments on Thermo-Electricity. He studied with 
 great care the principles on which his theories were 
 based, and seems throughout to have desired to leave 
 no doubtful step in his reasonings, nor to make any 
 tacit or unproved assumptions. His compositions 
 are minutely clear. To them we might apply the re- 
 mark attributed to Voltaire—^" Whatever is obscui-e 
 is not French." If there be obscurity, it is only due 
 to the abstruseness of the subject, not to the manner 
 of conveying it. 
 
 Fourier succeeded Delambre as Secretary of the Ma- (687.) 
 thematical Class of the French Academy of Sciences, ^i^ death. 
 and wrote several Eloges. He died no the 16th May 
 1830, generally respected. 
 
 We will here, in a few words, comment on the (688.) 
 
 subsequent progress of the subiect of the Conduction ^°°"«' ^ 
 » TT J. successors. 
 
 of Heat. 
 
 Whilst Fourier's papers were still in the archives (689.) 
 of the Institute, they were consulted by Poisson, who Poisson. 
 published solutions of several problems based on 
 Fourier's principles, and coinciding in result with his. 
 As the analysis used was somewhat different, the 
 coincidence in so new a subject was not without im- 
 portance. In 1835, the Theory of Heat of the same 
 author appeared, based on the law of cooling, dis- 
 covered by Dulong and Petit, which Poisson, with 
 
 1 See the next Section. 
 
154 
 
 MATHEMATICAL AND PHYSICAL SCIENCE, 
 
 [Diss. VI. 
 
 (690.) 
 Professor 
 Kelland's 
 Theory of 
 Meat. 
 
 unaccountable yet charg,cteristic rashness, chose to 
 consider as applicable to the communication of heat 
 from particle to particle, as well as to its dissipa- 
 tion from the surfaces of bodies. But the result was 
 worthy of the looseness of the assumptions; the terms 
 arising from the peculiarity of Dulong's law are 
 mostly dispensed with as the investigation proceeds ; 
 and the whole work is to be regarded rather as a 
 mathematical exercitation, than as a serious step in 
 physics. Having elsewhere recorded a criticism on 
 that part of Poisson's work which treats of the Heat 
 of the Globe, I shall not dwell farther on its defects. ^ 
 Professor Kelland has published a work^ — the only 
 one intended for students — on this subject, and he has 
 likewise made a valuable report to the British Asso- 
 ciation, on the best means of comparing the Mathe- 
 matical Theory of Heat with Observation.* He has 
 
 suggested, that the results of the Newtonian law of 
 cooling may be used in combination with such an 
 hypothesis as to the relation between quantities of 
 heat and the temperature shown by an air thermo- 
 meter, as will reconcile it with Dulong's law. But 
 there is reason to think, that internal conductivity 
 varies with temperature in the j-everse manner of ex- 
 ternal cooling ; in other words, that it diminishes as 
 the absolute temperature increases.* 
 
 MM. Duhamel and Stokes have considered the (691.) 
 propagation of heat in bodies which do not conduct it Case of 
 uniformly in all directions ; and their investigations jf.'^j^ , 
 are very interesting in connexion with the beautiful notconduct 
 observation of M. de Senarmont, that such is the case heat uni- 
 in crystallized bodies. It is easily shown in a plate ^^f^f^ "" 
 of gypsum coated with a thin layer of wax, to a small ^ig^^g_ 
 part of which heat is applied. 
 
 § 7. DuLONG. — The Law of Cooling. — Progress of the Science of Radiant Heat between Leslie's 
 and Melloni's Discoveries ; transmission of Radiant Heat through Glass. Herschel ; De la 
 Roche ; Professor Powell. — Theory of Dew ; Wells. 
 
 radiant 
 heat re- 
 sumed. 
 
 (692.) The researches of Leslie on Badiant Heat, though 
 
 Subject of very generally appreciated both at home and abroad, 
 were not, on their publication, immediately repeated 
 or extended. On some points they were seriously 
 controverted. But the labours of most of his imme- 
 diate contemporaries, of whose names we have given 
 a few at the head of this section, were rather prepa- 
 ratory to the fuller developments of a later time^-to 
 be made with improved apparatus — than demon- 
 strated discoveries. I make an exception, however, 
 with regard to the experiments of Dulong and Petit 
 on the laws of simple radiation and of the cooling 
 of bodies by the contact of gases, not only because 
 they established propositions quite new in an incon- 
 trovertible manner, but also because they introduced 
 into this branch of science a mode of investigation so 
 delicate and precise, and methods of reduction and 
 of physical analysis so beautiful and convincing, as 
 placed the whole science of Heat on a new footing. 
 The main credit is due, we believe, to Dulong, who 
 was one of the most estimable and accomplished phi- 
 losophers of his time. 
 (693.) Pierre Louis Dulong was born in 1785, and 
 
 "?" showed precocious talents. He was admitted to the 
 chemist. Polytechnic School at the age of 16, and rose through 
 every grade of that celebrated institution until he 
 became " Directeur des Etudes." It is superfluous 
 to say that he was a good mathematician. He was 
 
 also a most excellent chemist ; and the honour of 
 being discoverer of the most terrific of fulminating 
 compounds (chloruret of azote) was purchased by the 
 loss of one of his eyes. But his experiments on 
 Heat are those by which he will be longest remem- 
 bered. The most important series of these was de- 
 voted to a rigid examination of the amount of heat 
 radiated under different circumstances, and of that 
 dissipated by the contact of air. 
 
 Thelawof Cooling. — Ithad beensuggested by New- (694.) 
 ton, and tacitly admitted by nearly all writers on heat, Dulong 
 
 including the most eminent, that simple radiation (or *°^ ^**'' 
 
 7 • • ,1 1 o-r T s , 1 1 ■ \- correct the 
 
 pulsation, in the language or Leslie) takes place in di- ifewtonian 
 
 rect proportion to the excess of temperature of the hot law of 
 body above the surrounding space. Martine, and par- '"'°l"'g- 
 ticularly De la Roche, had indeed thrown doubt on 
 the subject, and had rendered it probable that at high 
 temperatures the velocity of cooling (which is propor- 
 tional to the radiant energy) is considerably greater 
 than Newton's law supposes. Dulong and Petit, 
 however, first demonstrated this. They disengaged 
 the experiment as far as possible from the influence 
 of the contact of air, by using the most perfect ex- 
 haustion which the best air-pumps could produce ; 
 and it appeared very plainly from the result of ob- 
 servations made under successive degrees of rarefac- 
 tion, that instead of there being the slightest appear- 
 ance of radiation ceasing to take place when the vehicle 
 
 ^ See Second Keport on Meteorology, Brit. Aiaoo. Reports, 1840. 
 
 " Theory of Heat. Camb., 1837. ^ Brit. Assoc. Reports, 1841. 
 
 * This at least is the result of an experimental investigation by myself x>n the conductivity of iron, executed on a principle 
 which I believe to be new, but which I have not yet been able to publish. Mr Airy and Professor Kelland are each in possession 
 of the outline of my method ; and the result noted in the text was briefly announced by me in the Reports of the British Aitooiation 
 for 1852. If my health permits, I shall resume and publish these experiments. I may here add, that I pointed out in 1833, 
 from some experiments which I made at that time (Proceedings of the Royal Society of Edinburgh, vol. i. p. 6), that the metals 
 range in the same order as conductors of Heat and of Electricity ; and this law appears to be confirmed by more recent obser- 
 vations. 
 
Chap. VI., § 7.] 
 
 HEAT. — DULONG AND PETIT. 
 
 155 
 
 of air was absent, tlie influence of the latter became 
 less and less perceptible. 
 (696.) The principal apparatus of Dulong consisted of a 
 
 Their ap- balloon of thin copper about a foot in diameter, coated 
 para s. internally with lamp black, and placed in connection 
 with an air-pump, so that any portion of atmospheric 
 air could be extracted up to about f f ^ of the whole, 
 and any other gas could be introduced into it. The 
 temperature of the balloon could be nicely regulated by 
 introducing it entirely into a water trough. Into the 
 centre of the balloon, thermometers of different sizes, 
 or having different kinds of surface, could be intro- 
 duced. The temperature of the balloon having been 
 first regulated, the thermometer under experiment 
 (being itself the radiating and cooling body) was 
 heated nearly to the boiling point of mercury, and 
 inserted in the balloon so as to occupy the centre of 
 it. The exhaustion and other arrangements being 
 made, the observations on the rate of cooling of the 
 thermometer commenced when its temperature was 
 as high as 250° or 300° centigrade, equivalent to 482° 
 and 572° Fahrenheit. 
 (696.) With respect to simple radiation, or when the 
 
 cooline^not**'^®''* °^ ^''^ ^^ *^^ balloon is estimated as nothing, 
 simply as the inaccuracy of the Newtonian law was soon ap- 
 the excess parent. Whilst the excess of temperature of the 
 of heat. cooling body above the envelope or balloon remained 
 constant, and the absolute temperature of both was 
 made to vary, the velocity of cooling, instead of 
 being constant, increased rapidly with the tempera- 
 ture. Thus the excess of temperature being in every 
 case 200° centigrade, and the temperature of the 
 balloon being ... 0°, 20°, 40°, 60°, 80°, 
 
 the rate of cooling was 7-4, 8-6, 10-0, 11-6, 13-4. 
 The whole of an elaborate series of observations was 
 beautifully and satisfactorily represented by a for- 
 mula admitting of this simple physical interpre- 
 tation, viz., that the cooling of the thermometer is 
 the difference between the heat which it parts with to 
 the envelope and the heat which it receives from the 
 envelope; and that the heat thus parted with, either 
 by the thermometer or the envelope, varies in a geo- 
 metric ratio with its temperature.^ 
 (697.) The effect of contact of a gas in cooling the ther- 
 
 Effect of mometer is more complex. It is independent of the 
 air on the *«**^''^ ofthe surface, as Leslie had already supposed. 
 rate of The cooling power of a gas is proportional to a cer^ 
 cooling. fi-fin power of its elasticity, which varies for each ; it 
 takes place more rapidly in hydrogen than in any 
 other known gas, which was likewise discovered by 
 Leslie. It also comes out rigorously, that the ratio 
 of the radiating power ofUifferent surfaces is the same 
 at all temperatures. This ratio for glass and silver 
 
 is 5-707 : 1. Assuming this last principle, and also 
 that the cooling due to the contact of air is indepen- 
 dent of the surface, the law of cooling in vacuo may 
 be deduced from the observed cooling of two thermo- 
 meters suspended in air, and having glass and sil- 
 vered surfaces respectively. Dulong and Petit found 
 that, when they analyzed their experiments in this 
 way, they obtained values for the radiation in vacuo 
 almost absolutely coinciding with what direct experi- 
 ment had already given. No more perfect criterion 
 could be desired of the soundness of every link of the 
 chain of experiment and induction. 
 
 We shall not analyze Dulong's other memoirs. (698.) 
 They regarded matters in the science of Heat requir- ^"?®'' ™^' 
 ing the same skill m devismg appai'atus and in mam- Dulong on 
 pulation, the same caution in eluding errors, and the the laws 
 same just principles of calculation as in the investi- °^ ^^^*" 
 gations already specified. They did not, however, 
 lead to the discovery of laws so striking and so ge- 
 neral. They included the very delicate and diificult 
 subject of the laws of the thermal expansion of 
 bodies, particularly that of air and of mercury, which 
 were applied to the theory of the thermometer, the 
 very basis of all exact knowledge in the doctrine of 
 heat. Another referred to the specific heat of the Specific 
 gases, an enquiry of the very greatest difficulty, in ''**' °^ 
 which we still find physicists disagreed. Dulong 
 bethought himself of using Laplace's celebrated cor- 
 rection for the velocity of sound due to the heat de- 
 veloped during the compression of an elastic medium 
 (art. 433), and proposed to deduce the heat thus 
 developed, by a comparison of the observed and theo- 
 retical (Newtonian) velocity of sound, and thence to 
 obtain the specific heat. The theoretical velocity is 
 easily obtained from the density of a gas under a 
 given pressure : the observed velocity was ingeni- 
 ously found by sounding one and the same organ 
 pipe with the different gases in succession, and ascer- 
 taining the pitch by the aid of Cagniard de Latour's 
 Sirene. (441.) 
 
 One of Dulong's latest, most elaborate, and most (699.) 
 useful labours, was ascertaining the elasticity of high- ?°.?* ®i*°" 
 pressure steam in terms of its temperature. These steam. 
 experiments were carried as far as 24 atmospheres 
 of pressure. In the course of them the law of Ma- 
 riotte and Boyle was verified up to the same limit. 
 The condensatiop of air was found to be exactly pro- 
 portional to the pressure. We shall return to the 
 subject of these later experiments of Dulong in men- 
 tioning the still more recent ones of M. Eegnault. 
 
 Dulong was unfortunately lost to the world at the (700.) 
 comparatively early age of 54. His was the peculiar Character 
 merit of a well-balanced scientific mind. He felt° °°^' 
 
 F= »(«« + "-«"); 
 
 1 Thus symbolically expressed : — 
 
 where V is the " velocity of cooling," or depression of the thermometer in centigrade degrees in one minute, supposing it to con- 
 tinue constant for so long; i is the temperature of the envelope ; t + P, that of the thermometer ; a is a constant independent of 
 the size and surface of the cooling body, and which is ^ 1'0077 ; m is a constant depending on the dimensions and surface of 
 the body. 
 
 X 
 
156 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (701.) 
 
 (702.) 
 Observa- 
 tions of Sir 
 "W. Her- 
 echel on 
 the heat of 
 the solar 
 Epectrum. 
 
 (703.) 
 Other ex- 
 periments. 
 
 the necessity of introducing into physics a degree of 
 precision then almost unthought of. Coulomb had 
 done something of the kind in other branches ; but 
 in Heat it was really new. It was speedily succeeded 
 by a rapid advance of precision in almost every kind 
 of delicate experimental research. Nowhere can 
 the student of physics find a better model than in 
 the celebrated memoir on the Law of Cooling, which, 
 we may add, received, as a matter of course, from 
 the Academy of Sciences, the prize in competition 
 for which it had been composed.^ It is only justice 
 to the countrymen of Dulong to say that they retain 
 the superiority in the deduction of numerical laws 
 from observation, which Coulomb and he conspicu- 
 ously exemplified. The industry of the Germans and 
 of the English have indeed been great ; but in this 
 particular enquiry they have not equalled in address 
 the members of the French Academy. 
 
 In order to complete our sketch of the more im- 
 portant steps connecting the discoveries of Leslie with 
 those of Melloni, we will now, going back a little in 
 point of date, trace the origin of correct experiments 
 on the immediate transmission and refraction of heat 
 by solid substances. 
 
 Sir William Hersehel having found it requisite in 
 the course of his arduous observations on the sun to 
 devisemeans for preventing the intense heat of its rays 
 from reaching the eye, was naturally led to observe the 
 effectof different coloured glasses, and even of coloured 
 liquids in this respect. He also placed thermometers 
 in different parts of the spectrum formed by a prism, 
 in order to discover which of the rays it W^as most 
 important to exclude. The singular result at which 
 he arrived was this, that the intensity of heat accom- 
 panying the light of the sun not only increases from 
 the violet to the red end of the spectrum (as was 
 already known), but is more intense quite beyond 
 the red, and gradually diminishes in force for a long 
 way farther. This result was keenly contested by Les- 
 lie, butwas confirmed by Englefield and Davy. Berard 
 admitted the existence of invisible heating rays from 
 the sun, but yet found the maximum effect within 
 the red. Seebeck, by numerous experiments, proved 
 that the position of the maximum depended on the 
 natui-e of the prism, being found even in the yellow 
 ray when a prism of water is employed, whilst with 
 flint glass it always occurs in the space beyond the 
 red. The rationale of this curious result was first 
 discovered by Melloni, whose labours will be detailed 
 in another section ; and it was shown to depend on 
 the different degree of absorption exercised on the heat 
 of the several rays of the spectrum by the differing 
 material of the prisms. 
 
 Hersehel made a very great number of experiments 
 
 on the transmission both of solar and fire-heat through 
 different kinds of glass and other bodies. But they 
 were rough trials, giving a sort of practical test of 
 this quality, rather than admitting of accurate esti- 
 mations of the quantities of transmitted heat. It 
 was impossible, for instance, to infer from them the 
 degree in which the warmth induced in the glass or 
 other medium by the heat which it absorbed, tended 
 to raise the indications of the thermometer beyond ; 
 although such an efTect was manifest from the re- 
 sults of the experiments themselves. Hence it was 
 open to an objector to deny the direct transmission 
 of radiant heat through such bodies as glass, except 
 in the cases of the sun and of brilliant combustion, 
 when it cannot be doubted. 
 
 Prevost had proved to his own satisfaction the (704.) 
 immediate transmission of heat derived from bodies Important 
 even when below the temperature of visible redness, ^^*j"' , 
 by using thin screens of glass, and renewing them De la 
 frequently before they could have absorbed muchEocheon 
 heat. Maycpck obtained a similar result; but to*?*""*"^" 
 De la Koche is due nod only the establishment oiTSLdiant 
 this fact beyond any reasonable doubt, but also the heat 
 discovery of certain laws of its operation which are through 
 inexplicable on any other supposition but that of ^ *^^' 
 immediate transmission. One of these laws, for in- 
 stance, was this, that when a series of thin glasses 
 are interposed between a source of heat and a ther- 
 mometer, each successive glass transmits a larger pro- 
 portion than the previous ones of the heat which falls 
 upon it. De la Koche rightly accounted for this sig- 
 nificant fact by assuming that heat is not homoge- 
 neous, and that the heat which has once passed 
 through glass has lost the rays which glass most 
 easily intercepts. He farther found that the sus- 
 ceptibility of heat to pass through glass increases 
 rapidly with the temperature of its source. The 
 experiments of De la Roche date from 1812. 
 
 The next step was made by Professor Powell of (705.) 
 Oxford (1825). He showed that the quality/ of the Professor 
 heat transmitted by glass is not the same as that P"''^"- 
 of the incident heat. This he proved by ascertaining 
 the proportion of heat absorbed by a black relatively 
 to a luhite surface. This proportion was invariably 
 increased by the interposition of glass. Mr Powell 
 concludes that heat consists of two kinds intimately 
 mixed. That of which the absorption depends on the 
 colour of the surface on which it falls, is usually 
 luminous, and is most easily transmitted by glass. 
 That kind of heat which is equally absorbed by black 
 and white surfaces is totally devoid of light, and is 
 sometimes considered as pure radiant heat. 
 
 It will be sufficient here to refer to an interesting (706.) 
 Bssai/ on Dew, published by Dr "Wells in 1815, in Wells' 
 which he applies Leslie's experiments on the radiating ^^°^^ ° 
 
 1 As the original paper of Dulong and Petit, in the Memoirs of the Institute, or the Annales de Chimie, is not always acces- 
 sible, I may mention tliat it is translated almost or quite in extenso in Thomson's Annals of Philosophy, vol. ziii., and in 
 Mr Lunn's excellent treatise on Heat in the Mncydopmdia Metropolitana, 
 
Chap. VI., § 8.] 
 
 HEAT. — MELLONI. 
 
 157 
 
 power of different surfaces to account for tlie appa- below the " dew-point," by tHeir unrequited radiation 
 rently capricious formation of dew in diiferent situ- of heat towards a clear sky. A slight wind, by con- 
 ations, — establishing that it is moisture deposited tinually restoring the equilibrium of temperature to 
 from the lowest stratum of air upon surfaces cooled the surface, prevents the deposition. 
 
 § 8. Melloni. — Recent History of Radiant Heat — Transmission and Refraction of Heat ; Pro- 
 perties of Heat analogous to Colour. — Experiments in Great Britain on the Polarization 
 and Double Refraction of Heat. 
 
 (707.) 
 Eecent ob- 
 servations 
 on radiant 
 heat. 
 
 (708.) 
 Melloni — 
 the asso- 
 ciate of No- 
 bUi. 
 
 (709.) 
 The ther- 
 mo-multi- 
 plier, an 
 instrument 
 of research. 
 
 (710.) 
 
 The length to which this chapter has already ex- 
 tended, must be my apology for bringing concisely to a 
 conclusion what remains to be stated regarding the 
 progress of the subject of radiant heat. With the ex- 
 ception of the excellent researches of De la Roche on 
 the immediate transmission of radiant heat through 
 glass (mentioned in the preceding Section), but which 
 that ingenious philosopher did not live to extend 
 and complete, little of importance was done between 
 the researches of Leslie and those of Melloni, of 
 which we are now to speak. 
 
 Macedonio Melloni, a native of Parma in Italy, 
 became associated as an experimenter, probably about 
 the year 1828 or 1829, with Nobili, a skilful and 
 ingenious physicist of Eeggio (Modena). Nobili 
 was well known by his experiments on galvanic Elec- 
 tricity and on Electro-Magnetism. He was also the 
 great improver of Schweigger's Multiplier, rendering 
 it an instrument of precision ; and to him we owe the 
 happy and ingenious application of Thermo-Electri- 
 city to the measurement of minute effects of heat. 
 
 The Thermo-Mitltiplier, a thermometer of extreme 
 delicacy, though improved by Melloni, was (as has just 
 been stated) the invention of Nobili. It consists of 
 two portions, a sentient part and an indicating part. 
 The first is composed of a number of short thin bars of 
 antimony and bismuth, arranged like a square faggot, 
 pairs of bars being soldered together in consecutive 
 order at the opposite ends of the faggot, so as to form 
 a single bent metallic conductor. If the junctions 
 exposed at one end of the faggot are subjected to 
 heat, and those at the other end kept cool, the effect 
 will be a thermo-electric current of considerable in- 
 tensity generated by the pile. This current is con- 
 veyed by means of two wires from the opposite ends 
 of the system, which are connected with a delicate 
 galvanometer which forms the indicating part of the 
 apparatus. In practice, one end of the pile, armed 
 with a conical reflector for concentrating the rays of 
 beat, is exposed to a calorific source whose radiant 
 effect is to be measured, whilst the other end is care- 
 fully screened from external influences. The devia- 
 tions of the galvanometer needle indicate the heating 
 effect as on the scale of a thermometer. The pre- 
 cautions required in the construction and use of the 
 instrument, and in the interpretation of its results, 
 are too numerous to be mentioned here. 
 
 Nobili, in conjunction with Melloni, applied the 
 thermo-multiplier (amongst other experiments) to 
 
 the proof of the instantaneous transmission of heat 
 through glass and other solid and liquid bodies. 
 
 From 1831, this enquiry was conducted nearly (711.) 
 exclusively by Melloni, who about that time settled Melloni 
 first in Geneva and then in Paris, having been com- the™ on-' 
 pelled, on political grounds, to quit Italy. His first derful 
 and most important original memoir was presented trans- 
 to the Academy of Sciences early in 1833, and was P^^^^^^^ °^ 
 received with marked coldness, if not incredulity, by f^p ^eat. 
 that body. A few months later, the writer of these 
 pages had an opportunity of seeing Melloni's ex- 
 periments in P-aris, and he made known their im- 
 portance at the immediately succeeding meeting of 
 the British Association at Cambridge. The Royal 
 Society of London in no long time awarded their 
 Rumford medal to Melloni, after which mark of 
 foreign approbation, he first obtained a hearing 
 from the Institute of France. The most consider- 
 able result at which he had then arrived was this : 
 that rock-salt possesses a power unapproached by 
 any other substance of transmitting heat of any 
 temperature and from whatever source, with ex- 
 tremely little loss ; and as a natural consequence of 
 this, that heat wholly devoid of luminosity, such as 
 that from boiling water, or even the heat of lie hand, 
 may be refracted by prisms and lenses of rock-salt 
 exactly in the same manner as light is refracted by 
 glass. The reality of these effects (which had excited 
 the persevering scepticism of the Parisian savans) 
 was demonstrated by a great number of most inge- 
 nious experiments, in which every possible source of 
 error and confusion was avoided or allowed for. 
 
 Melloni even believed that the loss observed in 
 passing heat of any temperature, high or low, through 
 polished screens of rock-salt, was precisely the same ; 
 and, moreover, that it occurred entirely at the two 
 surfaces by partial reflection, so that the solid me- 
 dium was absolutely transparent for every kind of 
 heat. It is certain that the loss is in every case 
 small; but this almost paradoxical conclusion has 
 not been completely confirmed by those who have 
 repeated his experiments. The important and un- 
 expected discovery of the nearly complete trans- 
 parency of rock-salt for heat, enables us to construct 
 pomplex thermotic apparatus for refracting and con- 
 centrating it, analogous to those of glass which are 
 used in optics. 
 
 The next point clearly made out by Melloni, was 
 the specific action of different bodies in sifting the 
 
 (712.) 
 
 (713.) 
 
158 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 The specific rays of heat they transmit, stopping altogether certain 
 aouon of j^injs ^y. qualities of heat and transmitting others, 
 substances Substances, in general, transmit most readily the heat 
 on the rays radiated by surfaces having a high temperature; this 
 of heat.— jjj^^ already been shown to be true in the case of glass 
 of heat ""^ ^7 ^^ ^^ Roche. That experimenter had also demon- 
 strated Cas we have seen in Art. 704) that successive 
 plates of glass intercept a constantly decreasing per- 
 centage of the heat incident upon them. This may 
 he explained by supposing radiant heat to be, like 
 the light of the sun or of a flame, heterogeneous, 
 containing rays of different qualities, some of which 
 are easily transmitted and others are wholly stopped 
 by glass. And if we pursue the analogy with re- 
 spect to other substances, we may imagine (for the 
 sake of illustration) heat to be coloured, and that 
 diiferent media, though equally transparent and co- 
 lourless as regards light — such as glass, rock-crystal, 
 and ice — exercise a specific action on the rays of heat, 
 each transmitting certain portions of the heat and 
 stopping others. Rock-salt alone (according to Mel- 
 loni)is absolutely cotourZesswithrespect to heat, trans- 
 mitting all its varieties with uniform facility. Thus 
 equally thick and equally clear plates of salt, glass, 
 and alum, transmit, out of 100 rays of heat from 
 diiferent sources the following proportions : — . 
 
 Rock-salt .. 
 
 Heat from 
 
 a bright 
 
 flamo. 
 
 92 
 
 Heat from 
 incandes- 
 cent Pla- 
 tinum. 
 92 
 
 Heat from 
 a snrface 
 
 at 700° 
 
 Fahi;. 
 92 
 
 Heat at 
 212° 
 
 92 
 
 Plate-glass 
 
 39 
 
 24 
 
 6 
 
 
 
 Alum 
 
 9 
 
 2 
 
 
 
 
 
 (714.) Let, however, heat which has been sifted by a plate 
 
 Refrangi- ofalum fall ou another similar plate, then instead of 
 Heat. ^ P^"^ cent., 90 per cent, will be transmitted. On the 
 
 other hand, if we unite two plates of opposite trans- 
 missive qualities, as alum and green glass, the com- 
 bination is almost absolutely opake, just as a combi- 
 nation of two coloured glasses giving different pure 
 tints (say red and green) would be opake for light. 
 The working out of this beautiful enquii-y is entirely 
 due to Melloni ; and he has published a separate work 
 on the " Coloration of Heat."^ He also rendered it 
 probable that the rays most easily absorbed by glass 
 and bodies generally are the least refrangible ; and this 
 has been made certain by direct experiments by the 
 author of this Dissertation, who, by a peculiar me- 
 thod, founded on the Total Reflection of heat within 
 a prism of rock-salt, has obtained the following In- 
 dices of Refraction : — 
 
 Heat from a lamp, mean refractive index 1-531 
 
 Do. passed through glass 1'547 
 
 Do. do. alum 1'558 
 
 Mean luminous ray 1562 
 
 Explana- Melloni ingeniously apphed the facts previously 
 tion of mentioned to explain the variable position of the 
 point of hottest part of the spectrum, as observed by Sir 
 
 maximum 
 
 heat in the '. 
 
 spectrum. i ^^ Tliermochroie, ou la Coloration Oalorijique. Naples, 1850. 
 
 William Herschel and others. It depends on the 
 nature of the prism employed. In a prism of rock- 
 salt, the hottest part of the spectrum is as far beyond 
 the extreme visible red, as the interval between that 
 red and the yellow ray in an opposite direction. 
 
 Through the intervention of Arago and of Baron (^^^O 
 Humboldt, Melloni ultimately obtained permission to jjelioni 
 return to Italy and to reside at Naples, where he spent 
 his latter years. He ceased, however, to prosecute 
 his researches on radiant heat with the same energy, 
 undercircumstances of ease and comparative affluence, 
 that he had done in the period of distress and obscu- 
 rity. Nevertheless, several original papers were writ- 
 ten by him at this period, as well as the condensed 
 account of his earlier researches on the Coloration of 
 Heat, of which only the first volume appeared. Mel- 
 loni died of cholera at Portici, in August 1854, 
 aged.53. 
 
 The analogy of Radiant Heat to light, strikingly (717.) 
 established by Melloni, with respect to the diversified f"^? ^'" 
 refrangibility and other qualities of the various radi- polarize ra- 
 ations emitted by one or different sources, suggests diant heat 
 an enquiry as to the intimate nature of these two i'eJ'T'i- 
 agencies. No answer is likely to be so conclusive 
 as an appeal to the test of Polarization, which, in 
 the case of light, has been so remarkably explained 
 by the theory of the transverse undulations of a me- 
 dium. Some years before any of Melloni's papers 
 appeared, — indeed, before he had entered on the in- 
 vestigation just noticed, — the writer of the present 
 Dissertation had attempted, by means of common 
 thermometers, to test the polarizability of heat. The 
 trial was not a new one ; but, except in the case of 
 the heat of the solar rays, the results seemed to be 
 inconclusive, or were even wholly negative. Berard 
 had, indeed, not long after the discovery by Malus of 
 luminous polarization by reflection, repeated (in 18 12) 
 that experiment with sun-heat, and also with the 
 heat emanating from terrestrial sources ; and as he 
 believed with success.^ I have ventured to call his 
 experiments inconclusive, because others besides my- 
 self vainly endeavoured to repeat them. Professor 
 Powell failed with ordinary thermometers, and at a 
 later period Nobili announced a decidedly negative 
 result, obtained with the thermo-multiplier. Simple 
 radiant heat, he affirmed, is not polarizable by re- 
 flection.* 
 
 I have just referred to my own early experiments (718.) 
 on the subject (which were likewise inconclusive), ^^P^"- 
 in order to explain that it was natural, on hear- ^^^ppg-^n* 
 ing of the application of the thermo-multiplier writer, 
 to measure radiant heat, that I should wish to 
 repeat them with the new instrument. This I 
 did in 1834. I first succeeded in proving the 
 polarization of heat by tourmaline (which Mel- 
 
 ^ La Thermochrose, ou la Coloration Oalorijique. 
 2 Memoires d^Arceuil, vol. iii., p. 5. 
 
 ' Bibliothegue Universelle, Sept, 1834. 
 
Chap. VI., § 9.] 
 
 HEAT. — M. REGNAULT. 
 
 159 
 
 Depolari- 
 zatioD of 
 beat. 
 
 loni had announced did not take place) ;^ next, by 
 transmission through a bundle of very thin mica 
 plates, inclined to the transmitted ray ; and after- 
 wards by reflection from the multiplied surfaces of a 
 pile of thin mica plates placed at the polarizing angle. ^ 
 I next succeeded in showing that polarized heat is 
 subject to the same modifications which doubly re- 
 fracting crystallized bodies impress upon light, by 
 suffering a beam of heat (even when quite obscure), 
 after being polarized by transmission, to pass through 
 a depolarizing plate of mica, the heat traversing a 
 second mica bundle before it was received on the 
 pile. As the plate of mica used for depolarization 
 was made to rotate in its own plane, the amount of 
 heat shown by the galvanometer was found to fluc- 
 
 tuate just as the amount of light received by the eye 
 under similar circumstances would have done. This 
 experiment which, with the others just mentipned, 
 was soon repeated and confirmed by other observers, 
 still remains the only one proving the double refrac- 
 tion of heat unaccompanied by light ; and though 
 somewhat indirect, it will hardly be regarded by 
 competent judges as otherwise than conclusive. Ice- 
 land spar and other doubly-refracting substances, 
 absorb invisible heat too rapidly to be used for effect- 
 ing directly the separation of the rays, which requires 
 a very considerable thickness of the crystal. I also 
 succeeded in repeating Fresnel's experiment of pro- Circular, 
 ducing circular polarization by two internal reflec- pol*"^*- 
 tions. The substance used was of course rock-salt.* 
 
 (719.) 
 M. Reg- 
 nault. 
 
 (720.) 
 Skill of 
 French ex 
 perinien- 
 ters. 
 
 (721.) 
 
 Co-ef- 
 ficients of 
 expansion 
 of gases. 
 
 § 9. M. Regnault. — Numerical Laws of Expansion by Heat ; Rudberg. — Vaporization; 
 
 Dulong. — Latent Heat ; Hygrometry. 
 
 The limits of this Essay will not permit me to do thrown upon the accuracy of Gay-Lussac's coefficient Coefficient 
 
 more than allude in very general terms to the merito- of the expansion of the gases (0-375 of the vo-°^ *"?*"' 
 
 rious services of M. Henri- Victor Regnattlt in the lume at 32° for the expansion between 32° and 212°g^°s°and 
 
 science of heat. In the seventh section of this chapter Fahrenheit) by Rudberg a Swedish philosojiher, who mercury ; 
 
 I have mentioned his name in connection with that determined a new coefficient (0-3645). M. Reg- ^^^'^^^''g 
 
 of Dulong, whose researches he has prosecuted, and nault finds for air of the ordinary density a cb- ~ °"^' 
 
 whose position in the College de France he now fills, efficient nearly the same as that of Rudberg, but 
 
 The attention of M. Regnault has been devoted differing slightly for the same fluid under differing 
 chiefly to heat in its combinations with matter — to pressures, and also for the various gases.* The ex- 
 dilatation and vaporization. I have already said, in pansibility of all of these fluids appears to tend to 
 speaking of Dulong, that, in point of numerical pre- the same limiting value when they are sufficiently 
 cision in the results of experimental physics, the attenuated. As a preliminary to these experiments, 
 French are unrivalled. The ta,lent which they have the expansion of mercury was ascertained by its hy- 
 shown in the construction of apparatus, skill in its use, drostatic equilibrium at different temperatures, as 
 and patience in deducing results with due attention to had already been done by Dulong, and with almost 
 every numerical correction, have not been equalled coincident results. The dilatation of mercui-y was 
 either in England or Germany, much less elsewhere, used to ascertain that of the glass vessels employed. 
 
 We must, however, note that doubts were first The irregularity of the dilatation of glass is one of (722. 
 
 1 Annales de Chimie, torn. Iv. (1833). 
 
 * I was led to polarize heat by transmission through mica films from having observed the extraordinary permeability of those 
 films to radiant heat, and from the facility of adapting them to tubes applied to the pile. The idea of using bundles of mica for 
 reflecting heat did not occur to me until some time after. But 1 cannot here omit mentioning a circumstance of vrhich I only 
 became aware some years after the publication of my reseai'ches. In arranging my correspondence, I found some letters from 
 Sir David Brewster, with whom I had communicated as to the best means of polarizing heat, during my earliest and unsuccessful 
 attempts with common thermometers. In one of these letters he recommends, among other methods, the reflection of radiant 
 heat from mica bundles. This suggestion was not put in practice; for, owing to change of residence and other circumstances, 
 my attention was diverted to other subjects, and only recalled, after a lapse of some years (as stated in the text), to the polari- 
 zation of heat, by the invention of the Thermomultiplier. Nor was Sir D. Brewster's suggestion recollected by me until I ac- 
 cidentally met with it (after, another long interval), in the manner which I have just stated. I am glad to have an opportunity 
 of acknowledging the friendly assistance and encouragement in all matters of science which at an early age I received from him 
 when I was an obscure, though ardent student, and when he was my only scientific adviser. 
 
 3 1 have not thought it proper to go into farther details concerning ray own experiments on radiant heat. Those who desire 
 more information will find it in Professor Powell's Second Report on Radiant Heat, in the Brit. Assoc. Reports for 1840. But I 
 may here state, that M. Melloni's first experiments on polarization were made with mica piles, furnished to him by myself in 1835. 
 
 * M. Regnault's experiments were published in 1841. Professor Magnus of Berlin was at the same time engaged on similar 
 experiments, and with nearly coincident results. The following table contains the summary of all these experiments : — 
 
 Dalton's coefficient 0-391 
 
 Gay-Iiussac's coefiicient , 0-375 
 
 Iludberg's coefficient 0-3645 
 
 M. Regnault's coefficient (from the expansion observed under a constant pressure) 0367 
 
 M. Regnault's coefficient (from the elasticity obsei-ved under a constant volume) 03665 
 
 M. Magnus' coefficient (from the elasticity observed under a constant volume) 0-3665 
 
 Dalton's experiments were made between 55° and 212°, and after allowing for the expansion of glass, he obtains for the relative 
 volumes of air at those temperatures 1000 and 1325, giving jj, of the volume at 55° for 1° Fahr.j or ^J^ of the volume at 32°, 
 which agrees with the co-efficient given above. See Manchester Memoirs, vol. v., p. 598-9. 
 
160 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI, 
 
 Irregular 
 dilatation 
 of ?lasE. 
 
 (723.). 
 Dulong 
 and M. 
 Regnault 
 on the elas 
 ticity of 
 steam. 
 
 (724.) 
 M. Reg- 
 nault on 
 latent heat 
 
 (725.) 
 
 the great difficulties not only of these enquiries, but 
 generally, in constructing comparable thermometers. 
 It varies so much with the composition of the glass 
 as to leave a serious amount of uncertainty in the 
 measure of temperatures above that of boiling water. 
 M. Regnault has had the perseverance himself to 
 graduate the thermometers which he uses. 
 
 These enquiries were in some measure introductory 
 to the determination of the elasticities of steam at 
 different temperatures, which had been already ascer- 
 ' tained with so much care by Dulong (nominally in 
 conjunction with Arago and other academicians), as 
 to leave little need for their repetition, except on the 
 ground of the uncertainty of the indications at high 
 temperatures of the thermometers which they used. 
 All M. Regnault's results are most carefully expressed 
 in terms of temperatures measured on an air thermo- 
 meter corrected for the expansion of glass. They agree 
 well with those previously ascertained by Dulong. 
 
 In connection with this subject, the important law 
 of the latent heat of steam at different temperatures 
 has been correctly ascertained for the first time by M. 
 Regnault. Watt maintained that the sum of the 
 sensible and latent heats of steam is constant at 
 aU temperatures : Southern and others, on the con- 
 trary, believed that the latent heat has a constant 
 value, whatever be the temperature of vaporization. 
 M. Regnault shows that the true law is intermediate. 
 The latent heat diminishes as the sensible heat of steam 
 increases, but in a slower proportion. 
 
 Our author also followed the steps of his prede- 
 
 cessor Dulong in verifying the law of Mariotte and Law of 
 Boyle on the compressibility of the gases. He found ■^'"''°**^ 
 it to be indeed very approximately true, yet not ab- °'" °^ *' 
 solutely so for any gas. For atmospheric air and for 
 most other gases the compression increases rather 
 faster than the strict proportionality to the pressures 
 would assign. In hydrogen gas the contrary is the 
 case. This result, together with that on the dilatation 
 of different gases, shows (if fully confirmed hereafter) 
 that mere simplicity or uniformity of result is not by 
 any means a sure ground of induction as to a law of 
 nature. That simplicity often appears to be predi- 
 cable only of some abstract condition of matter which 
 we may assign or imagine, but which we rarely if 
 ever find realized amongst the bodies around us. 
 
 The preceding investigations, the result of an (726.) 
 amount of minute and assiduous labour almost fear- 
 ful to contemplate, are to be found collected in the 
 21st volume of the Memoirs of the French Academy 
 of Sciences, which they entirely occupy. 
 
 M. Regnault has elsewhere published analogous (727.) 
 researches on the Specific Heat of a great variety of *^- ^^S" ' 
 substances, and on the theory and practice of Hygro- gp^^jg " 
 metry, both of which are highly interesting and im- Heat and 
 portant, but which I have not here space to analyze. Hygrome- 
 He is also favourably known as the author of an ^^' 
 excellent treatise on chemistry, and in fact sits in the 
 Institute as a member of the Chemical Section. He 
 now directs the manufactory of porcelain at Sevres ; 
 and being still in the prime of life, much may yet be 
 hoped from his devotion to science. 
 
 CHAPTER VI I. 
 
 (728.) 
 Galvani. 
 
 ELECTRICITY— MAGNETISM— ELECTRO-MAGNETISM. 
 
 § 1. — Galvani. — Discovery of Galvanism ; Proper Animal Electricity. — The subject revived by 
 Nobili. — MM; Matteucci and Du Bois Eeymond. 
 
 (729.) 
 His posi- 
 tion as a 
 discoverer 
 difficult to 
 estimate. 
 
 There are few discoverers in science whose posi- 
 tion it is more diflBcult to assign with accuracy than 
 Galvani. Attaining at first, by a curious observa- 
 tion patiently reflected on and carefully repeated in 
 detail, to the rank of the founder of a new science, 
 he was so far outstripped in its applications, that his 
 merit was soon in a measure overlooked, and his un- 
 questionable discoveries ascribed to capricious acci- 
 dent. 
 
 We find that a concurrence of circumstances con- 
 tributed to this result. Galvani was advanced in 
 years, and, it would appear, somewhat exhausted in 
 constitution, when he made his famous observation 
 on muscular contractions. He was an anatomist, 
 far more than either a chemist or physicist; — no 
 blame, surely, is to be attributed to him on that 
 account ! His discovery was chiefly interesting in 
 his eyes, as illustrating the laws of sensation and 
 
 the source of nervous irritability. It was calculated 
 to throw great light on these most abstruse enquiries. 
 Groping to find the thread which should reveal to 
 him that labyrinth, is it surprising that he devoted 
 himself exclusively to those effects which gave him a 
 real promise of success ? — a promise held out still by 
 the same facts — still the envied goal of physiologists 
 — yet how little realized by the unremitting labours 
 of two subsequent generations ! 
 
 Again, the almost irresistible temptation of con- (730.) 
 verting successful philosophers into heroes, at the Contrast of 
 expense of their contemporaries, added to a less par- and™olta. 
 donable wish to relieve the tedium of scientific dis- 
 cussion, by the introduction of a lively, though ques- 
 tionable anecdote, has induced the eulogists of Volta 
 to exalt his unqestionable claims by the deprecia- 
 tion of those of his less widely known and less for- 
 tunate countryman, Galvani. Their contrasts in cha-- 
 
Chap. VII., § 1.] 
 
 ELECTRICITY. — GALVANI. 
 
 161 
 
 racter and circumstances were sufiRciently marked. 
 Galvani was a professional anatomist and physiolo- 
 gist ; Volta a physicist. Galvani was little known, 
 and had probably travelled little beyond the province 
 in which he resided ; Volta was personally and ad- 
 vantageously known in Paris and London. Galvani, 
 soon after his discovery, fell into undeserved political 
 disgrace, which undermined his health ; Volta lived 
 to an advanced age, his experiments and discoveries 
 rewarded by every honour which not only academic 
 authority could bestow, but which the almost uni- 
 versal sway of Napoleon could render to his genius. 
 Galvani died prematurely, and whilst his best obser- 
 vations were contested ; Volta survived to nearly 
 the latest term of human life, having witnessed the 
 fruits of his great invention in the splendid disco- 
 veries of Davy and Oersted. 
 (731.) The biographical particulars of Galvani's life may 
 
 be passed over in a few words. The history of his 
 discoveries has been recently materially enlarged and 
 corrected, by the researches of the Academy of Bo- 
 logna to which he belonged, and especially by those 
 of Professor Gherardi ; it forms, together with his 
 collected writings, a ponderous quarto volume.'- The 
 diifuseness of the commentary, and that of Galvani's 
 writings also, is a defect in this compilation, which 
 tends to weaken the unquestionable force of the evi- 
 dence in his favour. 
 (732.) LuiGi Galvani was bom in 1737, and was 
 
 Galvani's promoted in 1762 to the chair of anatomy at Bo- 
 m'^jjtfon'^' logna, his native place, the seat of a most cele- 
 the Ner- brated university. He studied and taught his science 
 vous Sys- yf[ii^ great success, and published several memoirs. 
 *"" Probably he would have become still more widely 
 
 known, but that he was anticipated in some of his 
 observations (particularly on the organ of hearing) 
 by the celebrated Scarpa ; in consequence of which, 
 Galvani, with his customary modesty, suppressed 
 what had already become known through that able 
 anatomist. As early at least as 1780 (as we learn 
 from the researches of Gherardi, and the MSS. of 
 Galvani himself), he made experiments on muscu- 
 lar contractions taking place by electric influence 
 from the electrical machine, the electrophorus, and 
 the Leyden phial.^ The experiments were made 
 on frogs in particular. This was ten years antece- 
 dent to the commonly alleged casual discovery of 
 galvanism. The experiments were continued in 1781 
 and 1782, when he drew up a paper (not pubhshed) 
 
 tern, 
 
 " On the Nervous Force and its relation to Electri- 
 city."^ In 1786 he pursued the enquiry, with the 
 aid of his nephew Camillo Galvani ; and the effect 
 of thunder-storms in occasioning muscular contrac- 
 tions in the frog (which he had previously noticed), 
 was farther studied. He then designated the pre- 
 pared frog as "the most delicate electrometer yet and on _ 
 
 discovered."* But this year was also the one otf^^"'^"'"-*'^ 
 1 • 7 T 11, 1 .in connec- 
 
 his real discovery, namely, that muscular contrac- yon y^jth 
 
 tions are sometimes occasioned by causes remoteit. 
 from any then known to be connected with electricity. 
 Camillo Galvani, pursuing his uncle's experiments 
 on Atmospheric Electricity, had prepared some frogs, 
 by dividing them about the middle, and detaching a 
 portion of the lumbar nerves from the integuments, 
 leaving them in contact with a portion of the verte- 
 bral column which was then suspended by an iron 
 hook. These prepared frogs were lying horizontally 
 on the top of an iron rail of a balcony on the third 
 floor of Galvani's house, where he was in the habit of 
 observing the effects of atmospheric electricity. The 
 nephew noticed that when the hook or the vertebrse 
 were pressed on the rail by the finger or otherwise, 
 muscular contractions ensued, which he pointed out to 
 his uncle, who lost no time in repeating the observa- 
 tion, which seems to have been made early in Sep- 
 tember 1786.® His experiments in this and the fol- 
 lowing month are detailed, with the exact dates still 
 preserved, with this remarkable title in Galvani's 
 hand-writing, ■ — Esperimenti circa V Eletricitd, dei 
 Metalli; and the results are formally drawn up 
 in a Latin Dissertation of 62 pages, bearing date 
 30th October 1786, forming the substance of the 
 most important section of his Commentary on the 
 Electric Forces, &c., published five years later, but 
 differing from it in some important particulars.* 
 Thus it appears distinctly, that one metal alone 
 ■ — iron — was used in producing the convulsion;^ 
 whilst in the printed Commentary, the hooks are 
 said to be of brass or of copper. The explanation is, 
 that Galvani having become aware of the superior 
 efficacy of unlike metals in contact, described the ex- 
 periment, not as it was first made, but as it might be 
 made with greater certainty. Yet, singularly enough, 
 this Dissertation is entitled, — De animali Electrici- 
 tate; showing, that in the short space of a few weeks, 
 he had abandoned his earlier notion of themetals being 
 the source of the electricity, and ascribed the effects 
 to the proper electricity of the nerves and muscles. 
 
 1 Opere edite ed ine.dite del professore Luigi Galvani, raccolte e puiblicate per cura deW Accademia delle Scienze delV InstituU di 
 Bologna. Bologna, 1841. The copy which I use belongs to the Royal Society of Edinburgh. 
 
 2 Mapporto, &c., p. 11 (in the work above cited). ^ lb- p- 18. 
 
 * lb. p. 30. The expression is remarkable, because Volta is often regarded as the first who considered the frog in the aspect 
 of a mere electroscope. 
 
 ^ Eapporto pp. 33, 36. lb. p. 35, 36. It were to be desired that this MS. were published in full. 
 
 ' The passage from the MS. is conclusive, — " Ranas itaque consueto more paratas uncino ferreo earum spinali medulla perfo- 
 rata atque appensa Septembris initio [1786] die vesperascente supra parapetto horizontaliter coUocavimus. XSncinus ferream 
 laminam (namely, the top of the iron parapet or rail) tangebat ; en motus in rana spontanei, varii, haud infrequentes ! Si digito 
 uncinulum adversus ferream superficiem premeretur, CLuiesoentes excitabautur et toties ferme quoties hujusmodi pressio adbi- 
 beretur." — Eapporto, p. 36. 
 
162 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (733.) Of these two very opposite aspects of this remark- 
 
 able experiment, it might have been reasonably enough 
 anticipated, that one should be wholly erroneous. 
 This, however, is not the case. Galvani was justified 
 in both his inferences, although he unquestionably 
 believed that only one could be true. As a physio- 
 logical anatomist, he not unnaturally adhered finally 
 to the opinion of vital or animal electricity being the 
 cause of the phenomenon which he had observed. Vol- 
 ta, on the other hand, already an experienced natural 
 philosopher, though for a short time an entire con- 
 vert to Galvani' s published opinions, maintained the 
 contact of metals, unlike either in kind or in their 
 mechanical condition, to be the source of the nervous 
 commotion ; and whilst he was enabled to support his 
 opinion by very striking experiments, its popularity 
 was not unjustly perhaps exalted to the highest pitch 
 by the happy application which he made of it, to the 
 construction of that wonderful instrument, the vol- 
 taic battery, which effectually withdrew attention for a 
 time from the comparatively feeble and obscure effects 
 of the electric power residing in the animal tissues. 
 (734.) TJie historian of science, well aware how far the in- 
 
 eiectrUrftv"^ trinsic importance of discoveries is from depending 
 of the frog, upon the mere magnitude of their effects, and how 
 often the philosopher, dazzled by the splendour of a 
 new truth, overlooks some minute concomitant phe- 
 nomenon which hereafter may rival or eclipse its 
 splendour, — readily recognises the perseverance with 
 which Galvani maintained his theory of animal elec- 
 tricity as a part of the true philosophical character, 
 and therefore as enhancing his reputation. The 
 metallic arc which, by connecting the muscular part 
 of the limb with the root of the lumbar nerve, occa- 
 sioned the convulsion, was to be regarded, on his 
 theory, as merely establishing equilibrium between 
 those parts to which the vital principle had commu- 
 nicated an electric tension similar to that which sub- 
 sists on the opposite surfaces of a charged plafe or 
 Leyden jar. Galvani gradually disembarassed his ex- 
 periments from the suspicious presence of metals alto- 
 gether. Taking the prepared hind-limb of a frog, 
 with the connected nerve entering the spine, he found 
 that when the latter was suffered simply to touch the 
 bare surface of any muscular part, and without the 
 Confirmed intervention of metal or any other conductor, a spasm 
 A^ von°" °^ *^^ ^™'' immediately occurred. "■ This important 
 Humboldt, experiment was repeated and varied in 1795, by the 
 celebrated Baron Alexander von Humboldt, who pub- 
 lished a paper on the subject in GrerCs Journal, fully 
 confirming Galvani's conclusions. Volta, on the other 
 hand, admitting the facts, strove to explain them on 
 the supposition, that they were due, like other electric 
 currents, merely to the heterogeneous nature of two 
 solid bodies, the muscle and the nerve brought into 
 opposition, and moistened by a conducting liquid.' 
 
 Experiments instituted after a lapse of 30 years, with 
 the aid of new instruments, and vastly increased know- 
 ledge of electric manifestations, have conclusively de- 
 monstrated the accuracy in this respect of Galvani's 
 reasoning in preference to Volta's. 
 
 The publication of the results already noticed did (735.) 
 not take place till 1791 in his celebrated paper in the <^"'*'J"al 
 Bolognese Transactions. The statement popularly q^"^^^^*,^'' 
 made by almost every writer (and which may be views, 
 traced to Alibert, one of the earliest historians of the 
 subject, but whose authority seems to be of little 
 weight), is that the discovery of Galvanism was made 
 in 1790, in Madame Galvaiji's kitchen, where a frog 
 soup was being prepared for that lady's repast, she 
 being at the time in delicate health. The absurdity 
 of the invention is evident from the history which 
 we have given, founded on unquestionable documents. 
 The memoir of 1791 was the resumi of elaborate ex- 
 periments continued with (apparently) little inter- 
 ruption for eleven years ; and the most interesting 
 results had been digested in a Latin tract five years 
 before. All this shows at once great patience and 
 intelligence on the part of Galvani, who, perceiving 
 the difficulty and also the probable importance of 
 the subject (in a physiological view) — oscillating per- 
 haps in some measure between the two very opposite 
 opinions regarding the source of muscular excitement 
 which we have seen that he almost simultaneously 
 held, — postponed for so long a time the publication of 
 a discovery which he must have been sure would con- 
 fer upon him a great reputation. By the time of his 
 publication his views had become fixed in favour of 
 animal electricity ; and he defended it in several suc- 
 ceeding memoirs. 
 
 The unjust deposition of Galvani from his chair on (736.) 
 political grounds affected seriously his health and Ui^ death, 
 energies. Perhaps his latest experiments were on the 
 Electricity of the Torpedo. He died 4th December 
 1798, aged only 61 — happy perhaps in not having 
 witnessed the discovery of the Pile, which, by its as- 
 tonishing results, was to throw into the shade Gal- 
 vani's more intricate and difficult studies. 
 
 To appreciate justly Galvani's place in scientific (737.) 
 history, we must recollect three circumstances which His distin- 
 have often been overlooked, — i''iVst,thathis discoveries g"'*®* 
 were the result of patient, ingenious, and protracted 
 research, not of a casual observation exciting ignorant 
 surprise. Secondly, That however deficient was Gal- 
 vani's theory of animal electricity to explain all, 
 or even the most conspicuous facts vdtnessed by him, 
 it was a real discovery which has been confirmed by 
 the latest and most scrupulous researches, and of a 
 physiological importance which can hardly be over- 
 rated. Thirdly, Galvani's Commentary was received 
 at the time with enthusiasm, not only from the im- 
 portance of the facts vyhich it contained, but from the 
 
 . 1 The earliest notice of this result is found iD one of Galvani's autograph MSS., which appears certainly to date from 1786, 
 Raxiporlo, p. 48, § 18. 
 
Chap. VII., § 2.] 
 
 ELECTRICITY.— GALVANI—NOBILI — VOLTA. 
 
 163 
 
 ability shown by tlie author in discussing them. 
 There was no part of Europe in which Galvani's ob- 
 servations were not held to bear out his theory ; and 
 the warmest eulogy of them is to be found in the 
 writings of Volta himself, who soon advocated a dif- 
 ferent explanation. Volta calls animal electricity "a 
 great and luminous discovery which forms an epoch 
 in the annals of physical and medjcal science," and as 
 " proved to demonstration {ad evidenza) by many ex- 
 periments well contrived and accurately executed." ^ 
 Had there been as little novelty as has sometimes 
 been alleged in Galvani's observations, they would 
 not have been heard of at once, and repeated in every 
 civilized country, nor have given birth to a new and 
 splendid science. Nothing then in progress, either 
 in the hands of Volta or of any one else, gave the 
 slightest clue to the invention of the Pile, which, but 
 for Galvani, might have been yet undiscovered. 
 (738.) Revival of Experiments on Animal Electricity. — 
 
 Revival The grand discovery of Oersted, which gave a fresh im- 
 of experi- p^jgg ^q gg many branches of science, revived likewise 
 animal ^^^ subject of the proper electricity of the animal tis- 
 eleotricity sues, which had been well-nigh forgotten since the 
 — -Nobili. death of its discoverer Galvani. Twenty-nine years 
 later, in 1827,Nobili of Florence demonstrated the ex- 
 istence of what has been termed " The current of the 
 frog." We have seen that a momentary spasm is 
 produced when a circuit is completed, including the 
 muscle and nerve of the recently dead animal. But 
 by the aid of that admirable instrument the Galvan- 
 ometer, Nobili succeeded in showing that a continu- 
 ous current of positive electricity constantly passes 
 from the feet to the head of the frog. This he de- 
 tected by placing the feet of the animal in connec- 
 tion with one end of the galvanometer wire, and its 
 spine with the other (the whole being properly insu- 
 lated), when the needle of the instrument was per- 
 manently deflected to the amount of 5° or more — 
 indicating the passage of a stream of electricity in the 
 
 direction already mentioned, which continued for se- 
 veral hours after death. Strange to say, Nobili mis- 
 apprehended the nature of the phenomenon, ascrib- 
 ing it to Thermo-Electricity, though he ought to 
 have been undeceived by the singular intensity of 
 the animal current, which, feeble as it is, can force 
 its way along thousands of feet, or even some miles of 
 fine wire.^ 
 
 These experiments were renewed in 1837 by M. (739.) 
 Matteucci of Pisa, who has the merit of reviving the *^*^- ?***" 
 original and correct opinion of Galvani as to the vital p^ g^j^ 
 source of this electricity. To his researches, and the Keymond. 
 still later ones of Dr Du Bois Reymond of Berlin, we 
 owe the knowledge of most of the facts as yet ascer- 
 tained in this most difficult and obscure branch of 
 enquiry, where the sources of error are so numerous 
 as only to be eluded by consummate skill on the part 
 of the experimenter. It appears to be established 
 that the vital electricity exists both in the muscles 
 and in the nerves of many, probably of all animals 
 when living or recently dead ; that therefore the frog 
 current of Nobili is only a single case of the general 
 muscular current, and that the latter arises from the 
 electro-motive action of even the minutest fibres of 
 which a muscle is composed — the general law being 
 (according to Dr Du Bois Reymond) that positive elec- 
 tricity moves from the transverse section to the longi- 
 tudinal section of a muscle or a nerve, or any portion 
 of either. Finally, the last-named writer has shown, 
 to the satisfaction of many eminent men who have 
 witnessed his experiments, that powerful muscular 
 contraction, whether induced by stimuli or the result 
 of volition, tends to diminish the force of the natural 
 muscular current. This he demonstrated first on the 
 frog poisoned by strychnine, but afterwards on the 
 muscles of his own arm, in which by voluntary con- 
 traction he could diminish at will the force of the 
 natural current, which in the state of rest is directed 
 from the shoulder to the hand. 
 
 (740.) 
 Volta. 
 
 § 2. Volta. — Progress of Discovery in Common and Atmospheric Electricity — The Electro-motive 
 Theory — Voltaic Pile — Chemical Analogies and Decomposition — Fabbroni ; Nicholson and 
 Carlisle. 
 
 Volta was the first among philosophers whose 
 career lay solely in the study of electricity. Franklin 
 and .fflpinus, Beccaria and Wilke, Cavendish and 
 Coulomb, gave it only a share of their attention ; but 
 Volta *as from boyhood exclusively an electrician. 
 Such devotion deserved success, and he achieved it. 
 He was already famous, and an honorary fellow of 
 the Royal Society, long before his principal discovery 
 of the Pile. A review of his career may therefore 
 be conveniently divided into two parts — what con- 
 
 cerns ordinary and atmospheric Electricity ; and the 
 new doctrine of Galvanism and the Electro-motive 
 force. 
 
 I. Alessandro Volta was born at Como, of a noble tt.^^*^',-' 
 family,in 1745. His first paper on Electricity was ad- experi- ^ 
 dressed to Beccaria at the age of eighteen. But it was ments — 
 not till 1775 » that he published a description of the liisElectro- 
 Electrophorus, an ingenious instrument in which a cond^' 
 conducting body becomes electrified an indefinite num- 
 ber of times in succession by being brought near to an 
 
 1 Opere del Volta, ii., p. 13, 14. 
 
 ^ The galvanometer of Du Bois Keymond contains 317 English miles of wire, in 24,160 coils. 
 * See the letter to Priestley in the First volume of Volta's Works. 
 
 T 
 
164 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 excited cake of pitch and resin. This charge is re- 
 ceived by induction merely ; and as it expends none 
 of the electricity connected with the pitch, the suc- 
 cessive charges are precisely equal, a circumstance 
 which enabled Volta very simply to give a nume- 
 rical value to the amounts of electricity used in his 
 experiments, as they were given by one, two, or 
 more contacts with the electrophorus. The Con- 
 denser, an ingenious and useful instrument for ac- 
 cumulating small charges of electricity until they 
 attain a measurable amount, or cause divergence in 
 the electrometer, was described by Volta in 1782 in 
 the Transactions of the Royal Society, its construction 
 having occurred to him in following out the idea of 
 the electrophorus. This instrument was ultimately 
 of essential service in establishing his theory of Elec- 
 tro-motion. The theory of both the electrophorus 
 and condenser had been indicated by .Slpinus some 
 time before Volta constructed them ; but he did not 
 apply theta in the practical way which Volta did to 
 the improvement of his science. Volta being, be- 
 sides, unquestionably ignorant of ^pinus's labours, 
 has been generally and justly regarded as the real 
 inventor. Though both of these instruments depend 
 on the principle of induced electricity, Volta never 
 appears to have possessed correct views on that sub- 
 ject, but throughout his writings speaks of electrical 
 atmospheres, and uses other phrases of the old school 
 of electricians, showing a certain vagueness in his 
 conception which a study of the writings of his able 
 contemporaries, .Spinus and Coulomb, would have 
 dissipated. 
 (742.) But Volta's tact was unconnected with any tinge 
 Volta 8 of mathematical reasoning: his experimental ability, 
 Electrome- his caution, and his persevering devotion to one sub- 
 ter. ject, enabled him, however, to advance science in a 
 
 different way. Even the simple Straw Electrometer 
 which he generally used, was tested by him with 
 such skill and care as to lead to correct results in 
 the measurement of small quantities of electricity. 
 M.Biot has indeed criticised his preference for so rude 
 an instrument, which depends, mathematically con- 
 sidered, upon repulsions of a very complicated cha- 
 racter ; but as Volta carefully tested its comparabi- 
 lity up to 30" of divergence, and found it proportional 
 to the force, there is no doubt that he was justi- 
 fied in relying on its use; and Arago, in opposition 
 to his colleague, maintains that Volta's essay on the 
 Straw Electrometer is one of the best examples of 
 experimental research which can be put into the stu- 
 dent's hands. This instrument is described in the 
 first of a series of letters to Lichtenberg collected in 
 the first volume of his works ; the subject of these 
 letters being the Electricity of the Atmosphere. 
 (743.) The important experiments of Dalibard and Frank- 
 
 Atmosphe- jjn^ repeated with fatal consequences by Kichmann, 
 citv* ^^ ^^' ^^^ demonstrated the perfect resemblance or rather 
 
 identity of lightning and electricity. Lemonnier dis- 
 covered the fact of electricity being manifested when 
 no thunderstorm threatened, and even when the sky 
 was cloudless, and that it was subject to diurnal va- 
 riations of intensity. Beccaria farther ascertained 
 that with a clear atmosphere the electricity of the 
 air is always , positive. De Saussure, Deluc, and 
 Volta continued the interesting enquiry. The 
 first, availing himself of the known action of points 
 to draw off electricity, connected his electrometer 
 with a pointed rod two or three feet in length. 
 Volta substituted for this the flame of a lamp pro- 
 ducing a heated current of air, which has a won- 
 derful power of drawing off electricity; and he sug- 
 gested the employment of large fires during thunder- 
 storms in preference to metallic conductors. Volta 
 hesitates not to ascribe to the worshippers of Jupiter 
 Tonans the secret intention to draw off the electricity 
 of heaven by the action of the flames on the altar.^ 
 Arago has ingeniously suggested that a statistical 
 enquiry as to the frequency of thunderstorms in the 
 neighbourhood of extensive iron-smelting furnaces 
 might test the value of this safeguard. The straw 
 electrometer which Volta connected with his appara- 
 tus was capable (by a gradation of instruments of 
 greater or less delicacy) of measuring numerically 
 the force of charges from 1000 to 2000 units. 
 
 That the chief source of atmospheric electricity is (744.) 
 evaporation appears first to have occurred to Volta, 
 
 Due to eva- 
 poration. 
 
 and to have been first demonstrated by experiments 
 made either with him or by his suggestion, at Paris 
 in 1780, by Lavoisier and Laplace. The history is 
 given by Volta himself in a paper in the Philosophical 
 Transactions ioT 1782. When water is thrown upon 
 an insulated heated body so that evaporation takes 
 place, or when hot coals are thrown into an insulated 
 vessel of water, the hot body is usually found to be 
 electrified negatively. Volta has very candidly stated 
 the inversions of effect which occasionally occur, and 
 which still throw some doubt upon the precise signi- 
 ficance of this very important experiment. Later 
 experimenters have thought that absolutely pure 
 water developes no electricity: this, however, will 
 not affect the validity of the explanation of the origin 
 of atmospheric electricity. To prevent misappre- 
 hension it may be observed that the astonishing de- 
 velopement of electricity from high-pressure steam 
 escaping through a small aperture, as lately observed 
 by Mr Armstrong, appears, from the experiments of 
 Dr Faraday, to depend on an entirely different cause. 
 Of Volta's electrical theory of Hail we cannot now 
 stop to speak. 
 
 Volta, who understood chemistry and who always (745.) 
 took a peculiar interest in the inflammable gases, p°^*.*^ 
 contrived the Eudiometer which is often erroneously meter 
 called Cavendish's, having been frequently used by 
 that philosopher. The amount of oxygen in the air 
 
 ^ Opere, vol. i., part 2., p. 205. Volta's contrivance dates from the beginning of 1787. Bennett imagined it independently. 
 
Chap. VII., § 2.] 
 
 ELECTRICITY— VOLTA. 
 
 165 
 
 (746.) 
 Practical 
 character 
 of Volta's 
 inventions, 
 
 (747.) 
 History of 
 the Pile 
 —Volta's 
 early pa- 
 pers on 
 galvanism. 
 
 His letters 
 to Cavallo. 
 
 is tested by mixing the latter in known proportions 
 with hydrogen in a close vessel through which an 
 electric spark can be passed. Detonation takes 
 place, and the quantity of gas which has vanished (by 
 conversion into water) measures the amountof ogygen 
 which has combined with hydrogen in the experi- 
 ment. It was for a long period employed as by far 
 the best means of testing the purity of air. 
 
 All the preceding labours of Volta (and I do not in- 
 tend to touch on any minor ones) have evidently an 
 intensely practical character. His aim throughout 
 was to improve the instrumental means of detecting 
 and measuring electricity, and to detect and measure 
 it as it occurred in practice, rather than to form theo- 
 ries of its nature.'- Even the discovery of galvanism, 
 which vividly excited his interest, only partially di- 
 verted him from his scientific destiny. Volta will 
 indeed be always remembered as the author of the 
 plausible theory of electro-motion, and as having 
 corrected the too exclusive doctrine of Galvani con- 
 cerning the sources of electric excitement ; but his 
 real claim to immortality is the invention of the PUe. 
 To this part of the history we therefore proceed. 
 
 II. When Galvani announce^ his discoveries in 
 the Bolognese Transactions in 1791,^ Volta was 
 Professor of Physics at Pavia, having been appointed 
 to that post in 1774. As has been mentioned in a 
 former section, the announcement of these researches 
 excited the immediate attention of electricians and 
 anatomists in every part of Europe. Of course Italy 
 was not exempted from the general impulse. In that 
 country physiological observations have always been 
 prosecuted with interest and success ; and indeed it 
 has never been deficient in persons of ability, whether 
 in physical or in purely mathematical enquiries, since 
 the very dawn of letters, at which time Italy made so 
 distinguished a figure in literary progress. Volta, 
 Aldini, Valli, and Spallanzani were all, at the time 
 of which I now speak, actively engaged in the 
 pursuit of science; and Galvani' s opinion that the 
 commotion of the frog by the connection of the 
 muscle and nerve through a " qonducting arc " of 
 metal was due solely to animal electricity, was gene- 
 rally adopted, and by none more cordially than by 
 Volta in a letter and memoirs published in Brug- 
 natelli's Journal early in 1 79 2 . These were speedily 
 followed by two letters to Cavallo, dated October of 
 the same year, and communicated to the Royal So- 
 ciety of London, in acknowledgement, as the author 
 states, of the honour recently done him of electing 
 him an Honorary Fellow. The title of this com- 
 munication deserves notice, — " Account of some 
 Discoveries made by Mr Galvani of Bologna, with 
 Experiments and Observations on them ;" * and 
 also the first sentence (the letters are in French), 
 
 — "Le sujet des decouvertes, et des recherches, 
 dont je vais vous entretenir, Monsieur, est I'elec- 
 tricitS animale." In the course of the paper, how- 
 ever, he distinctly states that whilst he agrees with 
 Galvani in considering that the convulsions of the 
 frog, obtained vidth homogeneous conductors, are 
 d|ie to a proper animal electricity (§§ 12, 16), the 
 more powerful effects occasioned by the contact of 
 unlike metals are caused by " common electricity " 
 developed at the junction, and having the nature, not 
 of a discharge, but of a continued stream. He re- 
 peats and modifies Galvani's experiments on animals, 
 cold and warm-blooded, and makes interesting ob- 
 servations on the excitement of the nerves of taste 
 and sight by the contact of unlike metals. The con- 
 clusion of his paper is in opposition to its earlier 
 portion. He expresses a grave doubt whether there 
 be any vital electricity in the matter. 
 
 The induction of Volta was imperfect in this, that (748.) 
 he did not prove that the effects which he attributed Volta re- 
 with great probability to the contact of metals pro- (fopley 
 duced any other recognised electric effect than the phy- Medal, 
 siological ones. Galvani had gone very nearly as far. 
 He had even hesitated between the terms animal 
 electricity and electricity of metals ; he had considered 
 the frog as a very sensitive electrometer, exactly as 
 Volta did ; and the manner of so using and applying 
 it is ascribed by the latter in this memoir to Galvani, 
 who having thus invented the instrument which 
 for years served alone to indicate the presence of the 
 new species of electricity — and having also described 
 accurately the influence of the heterogeneous metals 
 in aiding the results — ^left to Volta only the credit of 
 the assertion that in some instances the effect was 
 due to the metals themselves, in others to the natural 
 electricity of the animal frame. Under these cir- 
 cumstances, I think that the award of the Copley 
 Medal by the Royal Society to Volta, rather than to 
 Galvani, was a questionable decision : the great va- 
 lue of Volta's paper, at the time, was undoubtedly 
 that it directed the attention of English experimen- 
 ters to Galvani's discoveries, then quite recent and 
 probably imperfectly known. * 
 
 Many publications followed. I shall only notice (749.) 
 that by Dr Fowler of Edinburgh (afterwards of Salis- Robison's 
 bury), which is remarkable as containing a letter by ^."''"P^" 
 Professor John Robison (335), who first thought of Voita's 
 increasing the effect of heterogeneous contact by using pile. 
 " a number of pieces of zinc made of the size of a shil- 
 ling, and making them up into a rouleau with as 
 many shillings." We have here unquestionably the 
 first idea of the pile, which moreover was actually 
 constructed. This was in May 1793. It was only 
 applied, however, to excite the nerves of the senses. 
 
 In various scattered memoirs, from 1793 to 1796, (750.) 
 
 1 His arguments as to the primary law of electric attractions and repulsions, are wholly inexact. His electrometer was unfitted 
 for such enquiries. 
 
 " Vol. vii. His paper was reprinted separately at Modena In 1792. ^ Philosophical Transactiont, 1793. 
 
 * See the grounds of the award stated by Sir Joseph Banks. Weld, Hist. R. Society, ii., 202. 
 
166 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Volta'B 
 theory of 
 electro- 
 motion. 
 
 Invention 
 of the pile. 
 
 Repulsion 
 due to con' 
 tact of 
 metals. 
 
 we iind Volta gradually insisting more on the purely 
 mechanical nature of the electrical excitement. The 
 last-named year produced an important letter to 
 Gren of Halle,^ which contains the real germ of the 
 invention of the pile, though it has been little taken 
 notice of. We there find conducting bodies divided 
 into two classes, primary and secondary ; the fir* 
 including metals, metallic ores, and charcoal ; the se- 
 cond liquids, solutions, animal tissues, &c. The first 
 class he also called motors. Using the prepared 
 frog always as an indicator, he tried the effect of 
 combining three or more elements of the two kinds. 
 He found that a double combination of three ele- 
 ments, when arranged so that their order was re- 
 versed, neutralized each other, or produced no 
 spasm ; on the contrary, when the two combinations 
 conspired in direction, the convulsions were in- 
 creased (§ § xii., XV., xix.). This appears to define the 
 date of Volta's discovery of the principle of the pile 
 — ^that, namely, of superadding minute effects — to be 
 August 1796. Theformof the arrangement resembled 
 that afterwards adopted in the Couronne des Tasses. 
 The second letter to Gren, dated the same month of 
 August 1796, contains the important discovery (the 
 most important abstractly of any due to Volta), that 
 the electricity set in motion by the contact of unlike 
 metals may, by means of the condenser (due also to 
 him), be made evident by the usual effect of repul- 
 sion on the common electrometer : — thus when zinc 
 and silver are used, the former is positive, the latter 
 negative, and so of other metals. Volta used for 
 this experiment Nicholson's ingenious modification of 
 his own condenser, called a Revolving Doubler. It 
 must be owned that the experiment, in its simplest 
 form, is difficult of repetition, and that Nicholson's 
 instrument sometimes gives delusive results. But 
 Volta's great address in practical electricity, and his 
 fairness in stating his results, leave no doubt of the 
 reality of his discovery, which evidently for the first 
 time eliminated the physiological element of Gal- 
 vani's experiments, leaving the recognised mechanical 
 effects of electricity due to the contact of unlike 
 metals ; and, therefore, deserved the highest honour 
 which could be bestowed. Pfaff had already con- 
 structed a table of the electro-motive power of metals 
 by their actions on the frog, in which zinc stood at 
 one end, carbon at the other. But one of the most 
 curious parts of the paper by Volta is the evidence of 
 a strong suspicion which had crossed his mind, and 
 been for a time entertained, that in his experiments 
 with combinations of three elements — two metallic, 
 and one humid — the electricity was developed sepa- 
 rately at the contacts of the latter with the two for- 
 mer, and that the resulting current was merely the 
 difference of the two in favour of the stronger. Truly 
 in this whole history we may see how often first sug- 
 gestions have a peculiar and intuitive worth, which 
 
 reflection and controversy often only obscure ! This 
 is, of course, the case rather in the research of causes 
 than of the means of rendering discovery practical. 
 
 Whilst Volta was thus maintaining the opinion (751). 
 that the electricity excited by the contact of metals ^ab^roni 
 was entirely mechanical, and due to contact merely ;^]jg°^g^j_ 
 — and whilst Galvani, his. relative Aldini, and others, cal origin 
 maintained strenuously the vital theory, in which they of galvan- 
 were substantially confirmed by no less authorities " " 
 than WeUs and Baron von Humboldt — a third school 
 appeared, at first little popular, represented by Fab- 
 BRONi, a Tuscan chemist and natural philosopher of 
 no small merit. His papers published, I believe, 
 in 1799, though written several years previously, and 
 some as far back as 1792, of which a full abstract is 
 given in Nicolson's Journal,^ show great acuteness. 
 He attributed the effects of the contact of metals to 
 a chemical action developed at the place of contact. 
 He referred to Sulzer's experiment of the taste of 
 heterogeneous metals applied to the tongue — and to 
 manyinstancesof the rapid oxidation of heterogeneous 
 metals in contact, when exposed to heat and mois- 
 ture. Amongst others, by a remarkable anticipation 
 of one of the most curious applications of the elec- 
 tro-chemical theory, he notices the oxidation of the 
 copper sheathing of ships. Without " excluding all 
 electrical influence from the prodigious effects of gal- 
 vanism," he infers that there are chemical forces 
 " exerted with the swiftness of lightning," to which 
 the physiological effects, and perhaps some others 
 ascribed to electricity, are probably due. Thus, he 
 says, " the experiment of Sulzer is nothing more 
 than a combustion or chemical operation, as is proved 
 not only by its result but by its duration ; for elec- 
 tricity acts always instantaneously, whereas the ef- 
 fect of chemical affinities continues so long as the 
 re-agents are not saturated." The weak point of 
 Volta's theory of electro-motion is here cleverly hit. 
 That effects indefinitely prolonged, capable of pro- 
 ducing mechanical, chemical, and vital changes, 
 without any mutual action between the touching 
 bodies, save mere pressure, appears indeed a paradox 
 startling even to a first inventor, but which, when 
 maintained by successive generations of able men, 
 may rank as a delusion more memorable than the 
 phlogistic theory of the older chemists. Fabbroni 
 did not himself pursue his ingenious speculations, 
 but his papers, though now almost forgotten, acted 
 powerfully on the minds of his contemporaries, as 
 we shall see in the next se'ction. He died at the age 
 of 70, in 1822, having spent most of his life in pa- 
 triotic and useful labours in his native country.* 
 
 We have seen that already in 1796 Volta had ar- (752.) 
 rived at a knowledge of the principle that the electric .**.' '^ 
 effect of the metals might be increased by combining ^is pile, 
 two sets of triple elements similarly disposed, which, and its ef- 
 unknown to him, Robison had already done (749). ^^"='^- 
 
 * Volta, Opere, vol. ii., part 2. " In quarto, vol. iv. (1800). ^ ggg jm account of him in the third volume of Cuvier's Elcges. 
 
Chap. VII., § 2] ELECTRICITY — VOLTA — NICHOLSON AND CARLISLE. 
 
 167 
 
 But three years seem to have elapsed before he was 
 led to the invention of the pile, although it is in truth 
 nothing more than the same arrangement frequently 
 repeated. In March 1800 he wrote from Como a 
 letter to Sir Joseph Banks, which was printed in the 
 Philosophical Transactions for the same year, and in 
 which he describes the Pile and the Couronne des Tas- 
 ses. The former consisted of 20 or more copper or sil- 
 ver coins interlaid with as many disks of tin or zinc, 
 and others of paper or leather, soaked in water or 
 brine. Thesameorderofsequenceof the three elements 
 was carefully preserved throughout ; and the whole 
 formed a vertical pile or rouleau. Several such piles 
 could be used together. The effects were — 1. The ready 
 excitement of the common electrometer by the aid of 
 the condenser ; 2. The production of smart shocks 
 through the hands and arms, similar to those pro- 
 duced by the torpedo ; 3. The production of vivid 
 sensations of taste, of sound in the ears, and of flashes 
 of light. There was nothing new in these effects (it 
 may be seen) except that their intensity was much 
 exalted, and the verification of the metallic theory 
 was thereby rendered more easy. Volta attributes 
 the action to the effect of " simple contact" of the me- 
 tals, allowing to the fluid element no other share than 
 that of conducting sufiiciently, but not too rapidly, 
 the impulse thus excited. Having an eye probably to 
 Fabbroni's opinions, he insists on the superior effects 
 obtained with saline and alcaline fluids, and with hot 
 in preference to cold fluids, being explicable solely 
 by their increased conducting power. He justly de- 
 scribes the effects of the pile as similar to those of 
 an immense electric battery with a very feeble charge ; 
 only the action is continuous, instead of intermittent. 
 (753.) But the invention had scarcely become known in 
 
 London when the importance of the pile, as an in- 
 strument of discovery, was keenly appreciated in 
 consequence of one capital discovery. 
 (754.) Nicholson, a good electrician and chemist, and 
 
 ^'d^o^^"" Carlisle (afterwards Sir Anthony), a medical man, 
 lisle obtain were the first in England to construct one of Volta' s 
 chemical piles. It consisted first of 17, afterwards of 36, half- 
 effects crowns, with as many disks of zinc and of paste- 
 pU™ * * board, soaked in salt water. Experimenting upon 
 the electrical effects of the pile, they used a drop of 
 water " to make sure the contacts" upon the upper 
 plate. Carlisle first observed a disengagement of 
 gas round the wire which the water moistened. 
 Nicholson suspected it to be hydrogen, and pro- 
 posed to break the circuit by enclosing water in a 
 tube between the two wires. This was accordingly 
 done on the 2d May 1800, within a month of the 
 arrival in England of the first four pages of Volta's 
 letter to Sir J. Banks, which preceded the remainder 
 by a considerable space of time. The brass wire in 
 the water tube, which was connected with the posi- 
 tive end of the pile, became tarnished and black. 
 
 whilst minute bubbles of gas were evolved from the 
 other, to the amount of tV^'i "f * cubic inch in 2^ 
 hours. Being mixed with an equal quantity of com- 
 mon air, and a lighted waxed thread being applied, 
 it exploded. It was, therefore, concluded to be hv- 
 drogen derived from the decomposition of the water, 
 whose oxygen had combined with the brass of the 
 positive wire.^ Nicholson, it appears, was well ac- 
 quainted with Fabbroni's writings on the relation of 
 galvanism to chemical action ; and in the very paper 
 where he describes Volta's pile and his own discovery, 
 he expresses his astonishment that Volta should 
 have taken no notice of Fabbroni's results, or of the 
 rapid oxidation of zinc in contact with other metals 
 which appears in the pile, and which had been no- 
 ticed by Fabbroni in every case where two metals 
 differing in oxidability are placed in water, and 
 in contact with each other. The experiment was 
 repeated at Vienna, and then by Volta himself, who 
 called attention to an experiment by three Dutch 
 chemists. Pacts, Van Troostwyk, and Dieman, who 
 had decomposed water by common electricity in 
 1789. 
 
 Volta, himself, however, did not enter with zeal (755.) 
 upon this new career ; he even left to others the ^°l*^ "■«• 
 task of improving the form and increasing the energy *"yrff,ng^' 
 of his battery, which was first done by the useful from jya- 
 arrangement of Cruickshank. He was now ap- poleon, and 
 proaching his 60th year, and seems to have beeuj™"!*^^ , 
 
 not indisposed to pass an old age of ease, and to re- pranoe 
 
 ceive in tranquillity the marks of distinction which 
 were showered upon him. In 1801 Napoleon called 
 him to Paris, attended the meeting of the Institute 
 where Volta explained his theory of the pile, caused 
 to be voted to him on the spot a gold medal, and 
 sent him home with a valuable present in money. 
 He was then made a Senator, finally a Count : he was 
 also made an Associate of the Institute in 1802. 
 No scientific discovery ever excited the enthusiasm 
 of Napoleon to the same degree as that of the 
 Pile. He even extemporized a theory of life from 
 its phenomena, comparing the vertebral column 
 in man to the pile, the bladder being the posi- 
 tive and the liver the negative pole. An eminent 
 medical chemist, Dr Prout, has seriously main- 
 tained a somewhat similar hypothesis. The fa- 
 vours lavished on Volta excited, perhaps, some jea- 
 lousy amongst the French philosophers ; for it is 
 remarkable how little was added in France to the 
 progress of the revived science of electricity. The 
 French ruler, however, had himself in some measure 
 to blame for this ; for the rigid exclusion of foreign, 
 and especially of English publications, for a number - 
 of years, was felt to be highly injurious, and was in 
 vain remonstrated against by Berthollet and others. 
 
 Volta survived his great invention above a quar- f^gg •, 
 ter of a century. He died 5,th March 1827, aged 82. His death. 
 
 1 Nicholson's Journal (series in quarto), iv., 182. 
 
168 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (757.) 
 His scien- 
 tific clia> 
 Tacter. 
 
 His scientific character is easily summed up. He 
 was patient, intelligent, and devoted to science from 
 youth to age. He had, in an eminent degree, that 
 patience and tenacity of purpose and of interest 
 which Newton described as the chief attributes of his 
 own genius. He had the candour which is more 
 especially tp be desired in the experimentalist ; and 
 he wrote without pretension, and generally clearly, 
 though not without that diffuseness which is often 
 associated with the use of the Italian language 
 even in matters of science. On the other hand, his 
 intellect may be rather described as opening itself to 
 jonviction, than as forcing its way by a native power 
 of penetration to great results. His taste and his 
 talent lay far more in experimental than in abstract 
 reasoning. His explanations of the effects which he 
 observed were often involved and obscure ; yet he had 
 a very happy talent of combination, which led him 
 
 to effect what others only talked about. His instru- 
 mental inventions, including the pile, were his hap- 
 piest efforts. His theories, on the other hand, were 
 surrounded, even in his own mind, with a certain 
 obscurity. Even the contact theory, with its manifold 
 paradoxes, was perhaps only vigorously carried out 
 by him under the excitement of an active contro- 
 versy. The invention of the pile may, in very many 
 respects, be placed on a par with that of the steam- 
 engine. The results of the former were indeed more 
 interesting, immediately, to pure science; the latter 
 to the arts of life and the needs of civilization. Yet, 
 after half a century, this distinction can hardly be 
 drawn with severity. The rapid pace of steam is 
 insufficient for our demands. The electric wire con- 
 veys to its destination, ere the locomotive has time to 
 start on its journey, tidings of joy and sorrow — life 
 and death — of victories won, and kingdoms lost. 
 
 § 3. Sir Humphry Davy. Progress of Voltaic Electricity — Electro-Chemistry ; Berzelius. — 
 Davy's Invention of the Safety -Lamp. — ^Wollaston; his Electrical and other Observations. 
 Contrast of his Character with that of Davy. 
 
 Volta con' 
 tinued. 
 
 (758.) The pile of Volta was, in one sense, rather a 
 
 History of means of discovery than a discovery itself. Volta 
 the pile of jjg^^ neither a just theory of the source of power 
 which he invented, nor was he successful in applying 
 it to any important research. The discovery of its 
 chemical efficiency by Nicholson and Carlisle, stimu- 
 lated, as we have seen, for a short time his interest 
 and curiosity ; but he never seriously attached him- 
 self to this line of discovery. His subsequent papers 
 are chiefly controversial, in support of the Contact 
 theory. The generation, as well as the expendi- 
 ture of chemical forces by the pile, consequently re- 
 mained, as far as he was concerned, in complete 
 obscurity. 
 
 The invention of the pile having been communi- 
 cated to the world through the Royal Society, natu- 
 rally gave an impulse to English electricians and che- 
 mists. The first discoverers of its chemical energy 
 did not however themselves prosecute their experi- 
 ments to a great extent, but Cruickshanks decom- 
 posed salts and revived the metals by the voltaic 
 current, whilst he improved the form of the appa- 
 ratus in an important manner. Colonel Haldane 
 ascertained the significant fact that the action of the 
 pile cannot be continued in an atmosphere deprived 
 of its oxygen. Hisinger and Berzelius, carrying out 
 Cruickshanks' experiments, showed that, generally 
 in the decomposition of compounds, the alcaline and 
 metallic elements appear to be attracted towards the 
 negative wire of the battery, and the acids to the po- 
 sitive one. In the mean time, Davy and WoUaston 
 appeared on the arena, and the former especially filled 
 so important a part in the history of science for the 
 next twenty years, that we can hardly give his name 
 too great a prominence in a review of the character- 
 istics of the period. The constitution of Davy's miad 
 
 (759.) 
 Cruick- 
 shanks, 
 WoUa'Ston, 
 Davy. 
 
 was also more than usually interesting, and his career ' 
 
 of discovery, short, brilliant, and decisive, is at once 
 one of the most instructive and remarkable of 
 those which we have to consider. The contrast be- 
 tween him and his contemporary, WoUaston, was 
 one of those curious antitheses of really great minds 
 which occasionally occur in such close connection, 
 and with such prominent relief, as to compel rather 
 than invite a comparison between them. It is an 
 instructive lesson to observe, how natures, the most 
 unlike, cultivated in a school the most opposite, may 
 yet, when both directed by a common impulse to 
 similar objects, promote the development of truth, 
 and the cause of scientific discovery. 
 
 Sir Humphry Davy was bom at Penzance on the g; g ii- 
 17th December 1778. His was an ardent boyhood, phry Davy 
 Educated in a manner somewhat irregular, and with — Ms early 
 only the ordinary advantages of a remote country town, history and 
 his talents appeared in the earnestness with which he ablegenius.' 
 cultivated at once the most various branches of know- 
 ledge and speculation. He was fond of metaphysics ; 
 he was fond of experiment ; he was an ardent student 
 of nature ; and he possessed at an early age poetic 
 powers, which, had they been cultivated, would, in the 
 opinion of competent judges^ have made him as emi- 
 nent in literature as he became in science. All these 
 tastes endured throughout life. Business could not 
 stifle them, — even the approach of death was un- 
 able to extinguish them. The reveries of his boy- 
 hood on the sea- worn cliffs of Mount's Bay, may yet 
 be traced in many of the pages dictated during the 
 last year of his life amidst the ruins of the Coli- 
 seum. But the physical sciences — those more em- 
 phatically called at that time chemical — speedily 
 attracted and absorbed his most earnest attention. 
 The philosophy of the imponderables— of Light, Heat, 
 
Chap. VII., § 3.] 
 
 ELECTRICITY.— DAVY. 
 
 169 
 
 and Electricity — was tte subject of Ms earliest, and 
 also that of his happiest essays. He was a very able 
 chemist in the strictest sense of the word, although 
 his ardour and his rapidity of generalizing might seem 
 to unfit him, in some measure, for a pursuit which 
 requires such intense watchfulness with regard to mi- 
 nutiae, such patient weighings of fractions of a grain, 
 such frequent though easy calculations. To Caven- 
 dish and Dalton, his great contemporaries — to whom 
 We may now add Wollaston — these things were a 
 pleasure in themselves ; to Davy they must ever have 
 been irksome indispen sables to the discovery of truth. 
 But, in fact, Davy's discoveries were almost indepen- 
 dent of such quantitative details : Numerical rela- 
 tions, and harmony of proportion, did not affect his 
 mind with pleasure, which possibly was one reason 
 of his deficient appreciation of works of art, the 
 more remarkable from his poetic temperament. 
 Dalton's doctrine of atomic combinations was (as we 
 have seen) slowly and doubtfully received by him 
 whilst Wollaston perceived its truth instantaneously. 
 A keener relish for such relations might most natu- 
 rally have led Davy to an anticipation of Mr Fara- 
 day's notable discovery of the definite character of 
 electrical decomposition, and the coincidence of the 
 Electro-chemical proportions for different bodies with 
 their atomic weights. 
 Hi^^ar t '^^^ ^^^^^ papers of Davy refer chiefly to Heat, 
 
 papers, and Light, and Electricity. He was, in fact, a physicist 
 experi- more than a chemist. Whilst yet a surgeon's ap- 
 ments on prentice at Penzance, he satisfied himself of the im- 
 oxidT' materiality of heat, which he illustrated by some in- 
 genious experiments, in which, concurring unawares 
 with the conclusions of his future patron Rumford, 
 he laid one foundation of his promotion. Removed 
 to a sphere of really scientific activity at Clifton, 
 under Dr Beddoes,' he executed those striking re- 
 searches in pneumatic chemistry and the physiologi- 
 cal eflfects of breathing various gases which gave him 
 his first reputation ; researches so arduous an,d full of 
 risk as to require a chemist in the vigour of life, 
 and urged by an unextinguishable thirst for dis- 
 covery, to undertake them. Even his brilliant dis- 
 covery of the effects of inhaling nitrous oxide brought 
 no competitor into the field ; and the use of anses- 
 thetics, which might naturally have followed — the 
 greatest discovery (if we except, perhaps, that of 
 vaccination) for the relief of suffering humanity 
 made in any age— was delayed for another generation. 
 But so it was in all his triumphs. He never seemed 
 to drain the cup of discovery. He quaffed only its 
 freshest part. He felt the impulse of an unhmited 
 command of resources. He carried on rapidly, and 
 
 seemingly without order, several investigations at 
 once. As in conversation he is described as seem- 
 ing to know what one was going to say before utter- 
 ing it, — he had the art of divining things complex 
 and obscure. Seizing on results, he left to others the 
 not-inconsiderable merit, as well as labour, of pur- 
 suing the details. Keenly alive as he was to the 
 value of fame, and the applause which his talents 
 soon obtained for him, he left enough of both for his 
 friends ; his contemporaries, as well as his successors, 
 were enabled to weave a chaplet from the laurels 
 which he had not stooped to gather. 
 
 These remarks apply quite as strongly to his dis- (762.) 
 coveries in the laws and facts of electro-chemical de- Removed 
 composition — those on which his fame most securely s,oyal In- 
 rests. Promoted in 1801 to a situation in the Labo- etitution — 
 ratory of the Royal Institution in London, he attached experi- 
 himself to the study of galvanism in the interval of "gjjJJ'" 
 the other and more purely chemical pursuits which electricity, 
 the duties of his situation required. He had already, 
 at Clifton, made experiments with the pile of Volta, 
 and taken part in the discussion of its theory and 
 effects, then (as we have seen) so actively carried on 
 in Britain. In his papers of that period we find not 
 only excellent experiments, but happy and just rea- 
 soning. The chemical theory of the pile — namely, 
 that the electrical effects observed by Galvani and 
 Volta are due solely or chiefly to the chemical ac- 
 tion of the fluid element on the metals — was more 
 strongly embraced by him then than afterwards. In 
 November 1800 he concluded that "the pile of 
 Volta acts only when the conducting substance be- 
 tween the plates is capable of oxidating the zinc ; 
 and that in proportion as a greater quantity of oxy- 
 gen enters into combination with the zinc in a given 
 time, so in proportion is the power of the pile to de- 
 compose water and to give the shock greater." He 
 concludes that " the chemical changes connected 
 with" oxidation " are somehow the cause of the elec- 
 trical effect it produces."'^ His views on this sub- 
 ject underwent some modification afterwards. In 
 his Elements of Chemical PAiZosopAj/, published twelve 
 years later, we find the following statement of his 
 opinions on the subject: — " Electrical effects are exhi- 
 bited by the same bodies acting as masses, which 
 produce chemical phenomena when acting by their 
 particles ; it is, therefore, not improbable that the 
 primary cause of both may be the same." A little 
 further on he adds : — " They," speaking of electrical 
 and chemical energies, " are conceived to be dis- 
 tinct phenomena, but produced by the same power 
 acting in the one case on masses, in the other on par- 
 ticles."3 
 
 1 Davy hit off his principal's character in a single sentence, — " Beddoes had talents which would have exalted him to the pin- 
 nacle of philosophical eminence, if they had been applied with discretion." 
 
 2 Works, ii., 162. 
 
 3 Works iv. 119. In his Bakerian lecture (1806), he had said, " In the present state of our knowledge, it would he useless 
 to attempt to speculate on the remote cause of the electrical energy, or the reason why different bodies, after being brought into 
 contact, should be found differently electrified ; its relation to chemical affinity is, however, sufficiently evident. May it not 
 be identical with it, and an essential property of matter V— Works, vol. v., p. 39. 
 
170 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (763.) 
 Electro- 
 chemical 
 theory — 
 Berzelius, 
 Hisinger — 
 Davy's 
 first Bake- 
 rian lec- 
 ture. . 
 
 (764.) 
 Davy's sa- 
 gacious 
 I'ndactione 
 I'especting 
 polar 
 forces. 
 
 Electro-chemical Theory — Decomposition of the 
 Alcalies. — In 1804 Berzelius had published, in con- 
 junction with Hisinger, a paper on Electro-chemical 
 Decompositions, in which he insisted on the general 
 fact, that alcalies, earths, and combustible bodies seem 
 to be attracted to the negative pole, and oxygen and 
 acids to the positive. He also showed that the sub- 
 division of bodies thus obtained was only a relative 
 not an absolute one ; for the same body may act 
 as a base to a second, and as an acid to a third. 
 But we must observe that results almost similar 
 were contained in the early papers of Davy, and 
 that Berzelius did not carry out his own principle 
 so far as to lead to any striking discovery between 
 1803 (when his experiments were made) and 1806 
 (the date of Davy's first Bakerian lecture), during 
 which time the science of Galvanism or Voltaism 
 made little real progress. The numerous experi- 
 menters engaged with it were baffled by the anoma- 
 lous chemical results obtained, and by the appearance 
 of decompositions under circumstances wholly unex- 
 pected, such as appeared to threaten the existence of 
 some of the best established chemical truths. The 
 chemical theory of the pile, at first so plausible, pre- 
 sented new difficulties, and Berzelius having for a 
 while defended it, returned to the simple contact 
 theory of Volta. It was then that Davy seriously 
 addressed himself to the subject, resolved to trace 
 to their source every chemical anomaly ; and this 
 he effected in a masterly manner in his Bakerian lec- 
 ture read before the Royal Society in 1806. In it he 
 traces the unaccountable results of his predecessors to 
 impurities in the materials used by them, or to those of 
 the vessels in which the decompositions were made ; 
 and he brings into a far distincter light than his pre- 
 decessors had done, the power of the galvanic circuit 
 to suspend or reverse the action of even powerful 
 chemical affinity ; " different bodies naturally pos- 
 sessed of chemical affinities appearing incapable of 
 combining or of remaining in combination when placed 
 in a state of electricity different from their natural 
 order." We here see the fundamental doctrine of 
 the electro-chemical theory, that all bodies possess 
 a place in the great scale of natural electrical rela- 
 tions to one another ; that chemical reactions are 
 intimately connected with this electric state, and are 
 suspended or reversed by its alteration. 
 
 In the interpretation of those striking experi- 
 ments, in which he caused acids to pass to the posi- 
 tive pole of the battery through the midst of alcaline 
 solutions, and the converse, we find so close an ap- 
 proach to the theory of polar decomposition as enfor- 
 ced by the discoveries and reasoning of Mr Faraday, 
 that it seems impossible to deny to Davy the merit 
 of having first perceived these curious relations. 
 " It is very natural," he says, " to suppose that the 
 repellant and attractive energies are communicated 
 
 from one particle to another particle of the same kind 
 so as to establish a conducting chain in the fluid, 
 and that the locomotion takes place in consequence;" 
 and presently adds, " there may possibly be a succes- 
 sioji of decompositions and recompositions through- 
 out the fluid" (p. 29).'- He likewise shows (p. 21) 
 that the decomposing power does not reside in the 
 wire or pole, but may be extended indefinitively 
 through a fluid medium capable of conducting elec- 
 tricity. Mr Faraday's experiments, which led him to 
 discard the term pole, lead to the same conclusion, 
 and are of the same character, A few pages further 
 on in this same Bakerian lecture, Davy observes (p. 
 42), that " allowing that combination depends on a 
 balance of the natural electrical energies of bodies, 
 it is easy to conceive that a measure may be found 
 of the artificial energies as to intensity and quantity 
 capable of destroying this equilibrium ; and such a 
 measure woiild enable us to make a scale of electrical 
 powers corresponding to degrees of affinity." Here 
 we see the acute presentiment of the beautiful disco- 
 very of the definiteness of electrical decompositions; 
 as in the concluding portion of the same remarkable 
 paper we find a clear anticipation of natural elec- 
 trical currents to be discovered in mineral, and espe- 
 cially metalliferous deposits, since established by 
 Mr R. W. Fox, and of the agency of feeble electric 
 energies, long continued, in effecting geological chan- 
 ges, and in producing insoluble combinations of earths 
 and metals, so ingeniously confirmed by the beautiful 
 and direct experiments of Becquerel. 
 
 The sequel to this remarkable paper, read to the 
 Royal Society in November 1 807, contained the splen- 
 did application of the principle and methods which it 
 described, to the decomposition of the alcalies and to 
 the discovery of their singular bases, — substances po- 
 sessing the lustre and malleability of metals, yet so 
 light as to float upon water, and having the extraordi- 
 nary property of becoming inflamed in contact with 
 ice. Potassium was discovered in the Laboratory of 
 the Royal Institution on the 6th October 1807, and. 
 sodium a few days later. The battery used con- 
 tained 250 pairs of plates of 6 and 4 inches square. 
 ,Such success was fitted to charm a disposition like 
 that of Davy, and more than reward him for all his 
 toils. To have discovered two new bodies, and 
 opened an entirely new field of wide chemical re- 
 search, would itself have been enough. But the 
 extraordinary properties of the new bases were such 
 as seemed to correspond to the lively imagination 
 of the Chemist who produced them, and to transport 
 him to an Aladdin's palace more brilliant than even 
 his fertile imagination had ever conceived. Yet it is 
 pleasing to remember that these popular discoveries 
 ■ followed, at the interval of a year, the patient and 
 able resparches which led him to them, and which 
 had already been rewarded, at a period of the bitter- 
 
 (765.) 
 
 Second Ba- 
 kerian lec- 
 ture — de- 
 composi- 
 tion of the 
 alcalies. 
 
 Receives a 
 prize from 
 the Insti- 
 tute of 
 France. 
 
 1 Of the Bakerian Lecture, in his collected Works. 
 
Chap. VII., § 3.] 
 
 ELECTEICITY. — DAVY. 
 
 171 
 
 (766.) 
 Distin- 
 gaisbed 
 testimonies 
 to Ms 
 scientific 
 character. , 
 
 (767.) 
 Cliemioal 
 researches 
 on chlo- 
 rine and 
 iodine. 
 
 (768.) 
 Davy's ex- 
 tensive po- 
 pularity, 
 and its 
 results. 
 
 est international hostilities, by the scientific piize of 
 3000 francs, founded by the Emperor Napoleon.^ 
 
 The genius displayed in these, Davy's most cele- 
 brated researches, is evident on a careful perusal of 
 his papers; but still more from a consideration of the 
 state of science of the time, and of the willing tribute 
 to his merits paid by the ablest of his contempo- 
 raries. Few persons of the present day will venture 
 to controvert the assertion of his acute contem- 
 porary, Dr Thomas Young (than whom no man was 
 ever a less indiscriminate eulogist), that Davy's 
 researches were " more splendidly successful than 
 any which have ever before illustrated the physical 
 sciences, in any of their departments ;" and that the 
 contents of the Bakerian Lectures, in particular, " are 
 as much superior to those of Newton's Optics, as the 
 Principia are superior to these or any other human 
 work." ^ A not less impartial tribute to his superla- 
 tive genius has been yielded by M. Dumas, who, if I 
 mistake not, has described Davy as being the ablest 
 and most successful chemist who ever lived. A si- 
 milar homage is paid to him by the sagacious Cuvier. 
 
 It is not within our scope to consider minutely 
 Davy's purely chemical discoveries and experiments, 
 though they were numerous and important, indepen- 
 dently of those made with the aid of electricity. His 
 proofs of the elementary nature of chlorine and iodine 
 were amongst the most considerable in their results. 
 But as a mere analyst, Davy had neither the leisure 
 nor the taste for continuous plodding labour, and 
 he therefore naturally made mistakes in chemical 
 details. His Elements of Chemical Philosophy re- 
 mained, in consequence, a fragment of an exten- 
 sive work. His contemporary, Berzelius, following 
 his steps in electro-chemical discovery, attained far 
 greater address, and became an author of high and 
 merited reputation, whilst his school surpassed all 
 others in Europe in producing accomplished analysts .^ 
 
 The years immediately following the publication of 
 his Bakerian Lectures were passed by Davy in the 
 u envied possession, of the highest fame, and in the 
 tranquil furtherance of his first and greatest disco- 
 veries. His lectures at the Koyal Institution con- 
 tinued to be one of the most -fashionable resorts in 
 London, and he was freely admitted in return into 
 the most aristocratic society ; he had but to express a 
 wish, and a voltaic battery of no less than 2000 pairs, 
 containing 128,000 square inches of surface, was con- 
 structed for his use, by means of a liberal subscrip- 
 tion. His health, when seriously compromised by 
 the severity, of his labours, was a matter of public 
 concern, and its variations were announced by frequent 
 bulletins. The copyright of his lectures on agricul- 
 ture was sold for a price unexampled perhaps before 
 
 or since for such a work. In 1812 he was knighted 
 by the Prince Regent, and soon after he married a 
 lady of fortune and accomplishments. His duties at 
 the Royal Institution became thenceforth honorary. 
 He had in a space of ten years attained the pinnacle of 
 scientific reputation, and he was for the time truly 
 happy : — unenvious of others— deeply attached to 
 his relatives — generous of his resources — unwearied 
 in his philosophic labours. A certain change (it 
 must with regret be owned) came over his state of 
 mind, tarnished his serenity, and gradually though 
 imperceptibly weakened his scientific zeal. It was 
 to be ascribed solely, we believe, to the severe ordeal 
 of exuberant but heartless popularity which he un- 
 derwent- in London. The flatteries of fashionable 
 life acting on a young, ardent, and most susceptible 
 mind, mingling first with the graver applause of his 
 philosophic compeers, and at length, by their reitera- 
 tion and seductions quite overpowering it, by degrees 
 attached Davy to the fashionable world, and loosened 
 his ties to that laboratory which had once been to him 
 the sole and fit scene of his triumphs. Had he been 
 blest with a family, his course would probably have 
 been evener and happier. Let us not severely criti- 
 cise, where we still find so much to admire and to imi- 
 tate. But we record the fact, for the consolation of 
 those who, beginning the pursuit of science, as Davy 
 did, in a humble sphere, and with pure ardour, may 
 fancy that they are worthy of pity, if they do not at- 
 tain with him the honours of wealth and title, and the 
 homage, grateful to talent, of rank, wit, and beauty. 
 
 A research, second perhaps only to his electro- (769.) 
 chemical discoveries, remains to be noticed, as the Third pe- 
 chief fruit of the third period of his life, on which we [j°g ° '^ 
 now enter ; the first being his early career before 
 settling in London ; the second, that passed in the 
 Royal Institution. 
 
 Researches on Flame — The Safety-Lamp, — The (770.) 
 subject was, the laws of combustion, and the happy Researches 
 invention of the safety-lamp. Though intimately jj^ safety^ 
 connected with the doctrine of simple heat, it may, lamp, 
 most properly, from its chemical character, and 
 from its connection with Davy's history, be considered 
 briefly here. The lamentable loss of life occurring 
 in coal mines from explosions of fire-damp or inflam- 
 mable air disengaged from the workings, had for 
 many years attracted the attention and sympathy of 
 the public, and had likewise been carefully considered 
 by scientific men. The explosive gas was known to 
 be the light carburetted hydrogen. Two plans alone 
 seemed to present themselves for diminishing the 
 danger : — the one to remove, or chemically to de- 
 compose the fire-damp altogether ; the other, to pro- 
 vide a miner's lamp which, by its construction, should 
 
 Berzelius. 
 
 1 Such was the national feeling at this time in England, that worthy people were found who considered Davy as almost a 
 traitor, when he accepted the French prize. See Southey's lAfe, 
 
 2 Quarterly Review, No. 15. 
 
 3 Jons Jacoh Berzelius, the greatest analytical chemist of his day, was born in East Gothland, in the same year with Davy, 
 and died in 1848, when he had almost completed bis 69th year. He contributed, in a signal manner, to the establishment of 
 Dalton's principle of definite chemical equivalents ; but he made no single discovery of commanding importance. 
 
 Z 
 
172 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss, VI. 
 
 be incapable of causing explosion. The former of 
 these modes of protection, it was soon seen, could only 
 be palliative ; the only efficient form which it took, 
 was that of a more effectual ventilation ; but the ter- 
 rific rapidity with which a mine may be suddenly in- 
 vaded by fire-damp, from channels opened by a single 
 blow of the pickaxe, must prevent it from ever act- 
 ing as a cure. The latter plan had as yet yielded 
 nothing more effectual than the steel mill long used 
 by miners, which produced an uncertain and inter- 
 mitting light, by the rotation of a steel wheel against 
 a flint, the scintillations of which were incapable of 
 inflaming the fire-damp. The insufficiency of the 
 light prevented it from being used, except in circum- 
 stances of known danger. The celebrated Baron 
 Humboldt, Dr Clanny, and several others, had in- 
 vented safety-lamps on different principles ; but they 
 were all clumsy and more or less ineffectual.^ 
 (771.) At last, in the summer of 1815, the Eev. Dr 
 
 aef'ven- ^^^^ (afterwards Bishop of Bristol), then chair- 
 tion of the ^^^ of ^ committee appointed by a benevolent as- 
 safety sociation at Bishop Wearmouth for the prevention of 
 lamp. colliery accidents, applied to Davy, who was then on 
 
 a sporting tour in Scotland, requesting his advice and 
 assistance. Sir Humphry answered the call with 
 promptitude. On his southward journey, in the 
 latter part of August, he visited the collieries, ascer- 
 tained the circumstances of the danger which he had 
 to meet, and was provided by Mr Buddie with speci- 
 mens of the inflammable air for examination. Within 
 a fortnight after his return to London, he had ascer- 
 tained new and important qualities of the substance, 
 and had already four schemes on hand for the pre- 
 vention of accident. Before the end of October, he 
 had arrived at the following principles of operation 
 in connection with a safety-lamp. " First, A certain 
 mixture of azote and carbonic acid prevents the ex- 
 plosion of the fire-damp, and this mixture is neces- 
 sarily formed in the safe-lantern ; secondly, The fire- 
 damp will not explode in tubes or feeders of a certain 
 small diameter. The ingress to, and egress of air from 
 my lantern," he adds, " is through such tubes or feed- 
 ers ; and, therefore, when an explosion is artificially 
 made in the safe-lantern, it does not communicate to 
 the external air." The effect of narrow tubes in inter- 
 cepting the passage of flame, is due to the cooling effect 
 of their metallic sides upon the combustible gases of 
 which flame is composed ;^ and one of his first and 
 most important observations was the fortunate pecu- 
 liarity that fire-damp, even when mixed with the 
 amount of air most favourable to combustion (1 part 
 of gas to 7 or 8 of air), requires an unusually high 
 temperature to induce combination. Olefiant gas, 
 carbonic oxide, and sulphuretted hydrogen, are all in- 
 flamed by iron at a red heat, or ignited charcoal, but 
 
 carburetted hydrogen does not take fire tmder a per- 
 fect white heat. The earliest safety-lamp consisted of 
 a lantern with horn or glass sides, in which a current 
 of air to supply the flame was admitted below by 
 numerous tubes of small diameter, or by narrow in- 
 terstices between concentric tubes of some length ; or, 
 finally, by rows of parallel partitions of metal, form- 
 ing rectangular canals extremely narrow in propor- 
 tion to their length. A similar system of escape 
 apertures was applied at the top of the lantern. 
 
 With characteristic ingenuity, Davy did not stop 
 here. He continued to reduce at once the apertures 
 and length of his metallic guards, until it occurred 
 to him that wire gauze might, with equal effect, and 
 far more convenience, act upon the temperature of 
 flame, so as to reduce it below the point of ignition, 
 and thus effectually stop its communication. The ex- 
 periment was successful, and by the 9 th November 
 1815, or within about ten weeks after his first experi- 
 ments, an account of the safety-lamp defended by wire 
 gauze was presented to the Boyal Society. About two 
 months later he produced a lamp entirely enveloped 
 in metallic tissue. 
 
 There are none of Davy's researches which 
 will stand a closer scrutiny than those which ter- 
 minated thus successfully. No fortuitous obser- 
 vation led him to conceive a happy idea and to 
 apply it to practice. A great boon to humanity 
 and the arts was required at his hands ; and without 
 a moment's delay, he proceeded to seek for it under 
 the guidance of a strictly experimental and induc- 
 tive philosophy. Without, perhaps, a single false 
 turn, and scarcely a superfluous experiment, he pro- 
 ceeded straight to his goal, guided by the prompt- 
 ings of a happy genius aided by no common industry. 
 The chemical, the mechanical, and the purely physi- 
 cal parts of the problem were aU in turn dealt with, 
 and with equal sagacity. It may safely be affirmed 
 that he who was destitute of any one of these quali- 
 fications must have failed in attaining the object so 
 ardently desired, unless by the aid of some rare good 
 fortune. We have it on Davy's own authority, that 
 none of his discoveries gave him so much pleasure 
 as this one. His whole character possessed in it 
 much of a sympathizing and generous humanity; 
 his ideas of the dignity of science were from the first 
 (as his researches in Dr Beddoes' laboratory showed) 
 intimately connected with the aim of advancing the 
 welfare, and of diminishing the misfortunes of man- 
 kind : the rapidity and singular success of his inves- 
 tigation in the case of the safety- lamp, kept his ardent 
 soul all alive, and afforded him the triumph of a Eu- 
 reka at its completion. To these sources of inward 
 gratification was added the unstinted meed of praise 
 bestowed on him by his contemporaries. Playfair, 
 
 (772.) 
 The safety 
 lamp per- 
 fected. 
 
 (773.) 
 Considered 
 as a model 
 for similar 
 investiga- 
 tions. 
 
 ^ I have spoken in Art. 393 of the independent and ingenious efforts of George Stephenson tonnwds the invention of a safety- 
 lamp contemporaneously with those of Davy. 
 
 ^ This fact had been ascerta,ined some years previously, by Mr Tennant and Dr Wollaston, but it remained unpublished, and 
 was Jiot applied by them to the prevention of colliery explosions. 
 
Chap. VII., § 3.] 
 
 ELECTEICITY. — DAVY. 
 
 173 
 
 (774.) 
 Rewards. 
 
 (775.) 
 Davy mo- 
 difies La- 
 voisier's 
 theory of 
 combus- 
 tion. 
 
 (776.) 
 Davy's 
 protectors 
 for ships. 
 
 " the true and amiaWe philosopher," as Davy long 
 before described him, thus proclaimed his victory in 
 the Edinburgh, Review : — After describing the course 
 of a discovery " which is in no degree the effect of ac- 
 cident," he adds, "this is exactly such a case as we 
 should choose to place before Bacon were he to re- 
 visit the earth, in order to give him, in a small com- 
 pass, an idea of the advancement which philosophy 
 has made since the time when he had pointed out to 
 her the route which she ought to pursue. The re- 
 sult is as wonderful as it is important. An invisible 
 and impalpable barrier made effectual against a force 
 the most violent and irresistible in its operations ; 
 and a power that in its tremendous effects seemed 
 to emulate the lightning and the earthquake, con- 
 fined within a narrow space, and shut up in a net of 
 the most slender texture — are facts which must excite 
 a degree of wonder and astonishment, from which 
 neither ignorance nor wisdom can defend the be- 
 holder." 
 
 For this truly patriotic labour, the only national 
 testimony which Davy received was the inadequate 
 one of a baronetcy, which was conferred on him by 
 the Prince Regent in 1818; but his real triumph 
 and great reward were in the enthusiastic apprecia- 
 tion of his entire success by those on whom he had 
 disinterestedly conferred so great a benefit. A tes- 
 timonial, in the form of a service of plate, of great 
 value, was presented to him by the coal-owners of 
 the north of England. 
 
 Davy's researches on flame were intimately 
 connected with his electrical and chemical discove- 
 ries. He remodelled Lavoisier's theory of combus- 
 tion, and put an end to the distinction between com- 
 bustibles and supporters of combustion. Chemical 
 combination, effected with great energy, and accom- 
 panied by a high temperature, is essential to com- 
 bustion, and either element of the combination is 
 equally entitled to the denomination of combustible. 
 Guided by the electro-chemical theory, Davy appears 
 to have thought that the heat of flame has an elec- 
 trical origin. 
 
 But I must hasten to close this section. Among 
 the labours of his latter years, there was none which 
 interested Davy more, or which reasonably promised 
 more useful results, than his plan for protecting the 
 copper sheathing of ships from the corrosive action 
 of sea water, by affixing plates of zinc or iron, which 
 shouldrenderthe copper slightly electro-negative, and 
 thus indispose it for combining with acid principles. 
 It is a somewhat singular fact that Fabbroni, about 30 
 years before, had instanced the corrosion of copper 
 sheathing near the contact of heterogeneous metals, 
 as an instance of the chemical origin of galvanism.^ 
 Davy's experiments were conducted with his usual 
 skill and success, and the remedy only failed of 
 general adoption on account, it may be said, of 
 
 being too effectual, other and opposite injurious 
 effects having been found to arise. 
 
 Davy was elected President of the Eoyal Society 
 in 1820, in the room of Sir Joseph Banks, who had 
 held the office for 42 years. It was a distinguished 
 compliment, for the election was all but unanimous. 
 He continued to communicate papers for several 
 years subsequently ; but his energy, his temper, and, 
 finally, his health began to give way — showing that 
 the ardent labours of his youth and prime had in- 
 jured his constitution. Attacked with paralysis in 
 1827, he spent his last years chiefly abroad, and 
 died at Geneva (where he was buried), on the 29th 
 May 1829. 
 
 The character of Davy was a rare and admir- 
 able combination. The ardour of his researches, and 
 the deep devotion of his whole being to scientific in- 
 vestigation, have been already proved. They had the 
 effect of completely annihilating every baser passion. 
 He valued property only in so far as he could apply 
 it usefully ; and his disinterestedness with respect to 
 the fortunes which several of his practical discoveries 
 might have honourably earned, was one of the most 
 striking parts of his chara,cter. His fancy was dis- 
 cursive to a degree rarely met with in men of science. 
 He continued to write poetry nearly all his life, and 
 the tone of it was that of grave speculation, always 
 reverting to the destiny of man and the beneficence 
 of the Creator. His lectures were composed with 
 care ; and their effect, even as pieces of oratory, was 
 striking. Coleridge frequented them " to increase 
 his stock of metaphors;" — ^yet they were always to 
 the point, and never degenerated into rhetorical dis- 
 play. For a man of such extraordinary liveliness of 
 fancy and impetuosity of action, his mistakes were 
 astonishingly few. After his very first experience, 
 his publications were made with great care and judg- 
 ment. His estimates of his contemporaries appear 
 generally to have been fair and liberal, though it 
 would be incorrect to affirm that he was universally 
 popular among them. The combination of isolated 
 and intense occupation in his laboratory, with ex- 
 citement in the mixed society of an admiring London 
 public, was a trial which few, if any, could have 
 escaped better than he did ; and so far as we can 
 judge of a man from his expressed opinion of his 
 own successes, whether recorded in his works or in 
 his intimate correspondence, Davy must be accounted 
 to have acquitted himself gracefully and well. He 
 always spoke of the Pile of Volta as the first source 
 of his own success. " Nothing tends so much to the 
 advancement of knowledge as the application of a new 
 instrument," he says ; and then adds, " The native 
 intellectual powers of men in different times are not 
 so much the causes of the different success of their 
 labours, as the peculiar nature of the means and 
 artificial resources in their possession ;" a proposition 
 
 (777.) 
 Davy as 
 President 
 of the 
 Eoyal So- 
 ciety — his 
 death. 
 
 (778.) 
 Philosophi- 
 cal charac- 
 ter. 
 
 1 There appears, however, to have been something erroneous in the details of Fabbroni's observations, or at least in the account 
 of them given in NichoUon'i Journal. 
 
174 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 ■wLich he applies to Lis own discoveries. But we 
 may truly say with one of his biographers, that to 
 him " the Voltaic apparatus was the golden branch 
 by which he subdued the spirits that had opposed the 
 advance of previous philosophers ; but what would 
 its possession have availed him had not his genius,' 
 like the ancient sybil, pointed out its use and appli- 
 cation?" 
 (779.) The last, and not least, extraordinary characteris- 
 
 Numerous ^jg ^f Davy to which I shall now advert, was the 
 inventions. ^i^S^^J practical turn of a mind which seemed formed 
 in a speculative mould. Four at least of his chief 
 researches were of this kind — his experiments on 
 breathing the gases ; his lectures on agricultural 
 chemistry ; his invention of the safety-lamp ; and 
 his protectors for ships. No man, whose path so 
 clearly lay in original discovery, ever left so many 
 valuable legacies to art and to his country. 
 
 (780.) The name of Davy gave to England a distinguished 
 
 Davy's as- pre-eminence in science during the first 25 years of 
 Young^and ^^^ century. But two others, less noticed at the time, 
 WoUaston. were also among her worthiest sons. These were 
 Young and Wollaston. They were all three nearly 
 contemporaries ; all lived on good terms with one an- 
 other, and united in promoting natural knowledge in 
 their several spheres. Young was Davy's early, 
 though less successful colleague at the Eoyal Institu-^ 
 tion ; and Wollaston was joint-secretary with him 
 to the Eoyal Society. All three were originally 
 educated for the medical profession, and they all 
 abandoned it for the pursuit of science. Not the 
 least singular coincidence was in the periods of 
 their deaths, which all occurred within the spape of 
 six months. 
 (781.) Our notice of Young, the first optical philosopher 
 ^^'^'*^ of his age, belongs to another chapter. Wollaston, 
 laston— hiB*^°"S'^ an original observer in nearly every branch 
 contribu- of exact Science, considered himself as a chemist ; 
 tioDs to and his observations on Electricity were amongst his 
 ec nci y, ^^^^ ^^^ ^^^^ contributions to science. After the 
 impulse given to discovery by the invention of the 
 Pile, and the proof of the decomposition of water, 
 Wollaston' undertook to compare critically the efiects 
 of galvanic and frictional electricity — a task of some 
 nicety, and of very great importance at a time 
 when it could hardly be considered as certain that 
 these agents were bot specifically difierent. By 
 methods peculiarly his own, he produced decomposi- 
 tion, accompanied with separation of the elements at 
 the respective poles by means of common electricity. 
 He at the same time gave his powerful support to 
 the purely chemical theory of the Pile. 
 (782.) His most important inventions were rather in- 
 
 andthe struments which, in the hands of others, were to 
 other SCI- produce important discoveries, than discoveries in 
 themselves. One was the invention of the Reflect- 
 ing Goniometer for measuring the angles of crys- 
 tals, now so essential to mineralogy ; another, the 
 
 art of rendering platinum malleable, which has con- 
 ferred inexpressible benefits on chemistry, and on the 
 arts connected with it. The principle of the reflec- 
 tion of a ray of light for measuring angular spaces, 
 though it existed already in the single instance of the 
 sextant, has been, since it was applied to the gonio- 
 meter, a;dapted to a multitude of most ingenious and 
 valuable contrivances. 
 
 Wollaston was an excellent optician, and of some (783.) 
 of his observations I have already spoken (476), 
 (538). 
 
 The strong points of his character were precision .(784.) 
 
 and rare acuteness in observation, patience and cau- '' " * 
 
 Til. IT. PI. . racter con- 
 
 tion m deduction, and habitual devotion ot his time trasted ' 
 
 and energies to scientific pursuits. His foibles were with that 
 an excess of caution, and a certain microscopic turn °^ Davy, 
 of mind which, though it sometimes rewarded him 
 with valuable discoveries, consumed his time in oc- 
 cupations of mechanical ingenuity, and prevented 
 him from grappling with almost any of the great 
 theories of his day. An exception, yet one which 
 illustrates his character, may be found in the fact 
 that he had all but anticipated Dalton in his disco- 
 very of the multiple combinations of salts, whilst, with 
 his characteristic sense of justice, he disclaimed any 
 participation in the merit (624). While Davy was de- 
 lighting crowded audiences with his eloquence, his 
 discoveries, and their wonderful results, Wollaston 
 was pursuing his solitary experiments on a scale so 
 small that scarcely three persons could witness them 
 at once. While Davy was firing his potassium with 
 ice, and making mimic volcanos heave by the oxida- 
 tion , of his new metals, Wollaston was extract- 
 ing, by minute analyses, from the refractory and 
 unoxidable ores of platinum, substances previously 
 undetected, which, neither by their quantity nor 
 their characters, could ever interest any but a man 
 of science. While Davy was charging his prodi- 
 gious battery of 2000 pairs, — the largest which 
 has ever been constructed (a homage to his ge- 
 nius, provided by his numerous admirers), — Wol- 
 laston was proving, after his fashion, how similar 
 eifects could be produced by the very same agency 
 on a small scale ; and with no greater apparatus than 
 a shred of zinc, a few drops of acid, and an old thimble, 
 he would gratify his friends by exhibiting the mimic 
 glow of an almost microscopic wire of platinum. 
 Davy seemed born to believe ; Wollaston to doubt. 
 Davy was a poet ; Wollaston, a mathematician, or, 
 at least, capable of becoming a great one. Davy 
 announced his discoveries in fiery haste, and pre- 
 sented all their consequences and corollaries as a free 
 gift to mankind ; Wollaston (estimating more truly 
 the rarity of the inventive faculty) hoarded every ob- 
 servation, turned it over and over, polished it, ren- 
 dered it exact beyond the reach of criticism, and 
 then deliberately laid it before the world. He had 
 the coldness and the accuracy of Cavendish, but he 
 wanted the spur of his genius, and the wide grasp 
 
Chap. VII., § 4.] ELECTRICITY. — W0LLA8T0N — OERSTED — AMPERE. 
 
 175 
 
 of his apprehension. Among other legitimate re- 
 sults of discovery, WoUaston was not unwilling to 
 claim for his own the material profits which such 
 researches sometimes, though rarely, yield ; whilst 
 Davy, as we have seen, spurned every possible attri- 
 bution of an interested motive. Davy never made 
 a shilling in his life, save as an author or a lecturer 
 (except as paid assistant to Dr Beddoes) ; WoUaston 
 realized a fortune by his art of working platinum. 
 Davy was admired by thousands both at home and 
 abroad ; WoUaston was little known except to a small 
 
 circle who could appreciate the resources of a mind 
 rarely opened in confidence to any one, and of which 
 the world was only partially informed. 
 
 WoUaston was born in 1766, and died in December (785.) 
 1828. The composure of his end rivalled that of ^'^ '^^**''- 
 Black and Cavendish. His disorder was one of the 
 brain. When he had lost the power of speech, his 
 attendants remarked aloud that he appeared imcon- 
 scious. Making a sign for a pencil and paper, he 
 wrote down a column of figures, added them up cor- 
 rectly, and expired. 
 
 § 4. Oersted. — Ampere. — Discovery of Electro-Magnetism — Electro-Dynamic Theory — 
 Discovery of Thermo-Electricity ; Seebeck. The Galvanometer of Schweigger and Nobili. 
 
 (786.) 
 
 Oersted 
 rendered 
 famous by 
 a single 
 discoTery. 
 
 (787.) 
 
 (788.) 
 His early 
 studies. 
 
 (789.) 
 His first 
 "writings on 
 electricity. 
 
 Hans Christian Oersted was born in Langeland, 
 one of the Danish isles, on the '14th August 1777. 
 Of him it might almost be said that " on awaking 
 one morning he found himself famous." The single 
 discovery of the mutual action of magnets and elec- 
 tric conductors gave him a celebrity which a life-long 
 devotion to science has oftener than the contrary 
 failed to secure. 
 
 Yet in this, and perhaps every similar case, it will 
 be found that brilliant, and, as the world, or jealous 
 rivals esteem it, fortunate success, was not the result 
 of an isolated effort, but was connected with a long 
 career of patient though comparatively obscure la- 
 bour. 
 
 At the age of 20, Oersted, whilst yet a student at 
 the University of Copenhagen, became an author. 
 His first publication was a prize essay on an aesthe- 
 tical subject. Being intended for the medical pro- 
 fession, he soon after wrote some chemical papers, 
 and, in 1801, his first " On Galvanic Electricity." 
 But his turn of mind at this time, as well as later, 
 was of a strongly metaphysical cast, and of course 
 tinctured with the peculiarities of the German 
 school as regards the study of physics, of which 
 the title of his thesis on graduation may be given 
 as an instance : — It was On the Architectonicks of 
 Natural Metaphysics. His studies in voltaic elec- 
 tricity were made chiefly under Ritter, an obscure 
 and mystical writer, though the author of some cu- 
 rious experiments on what were called Secondary 
 Piles ; and he at length obtained, in 1806, a pro- 
 fessorship in his own university ; but his associates 
 appear to have been rather literary than scientific 
 persons, such as Steffens, Oehlenschlager, Niebuhr, 
 and Fichte ; he also engaged in controversies of a 
 theological tendency, which, to the end of his life, 
 appear to have had a great attraction for him. 
 
 In 1812 Oersted visited Berlin, and published 
 there a work on Chemical and Electrical forces, tend- 
 ing to prove their identity, which was translated into 
 French by Marcel de Serres. The author afterwards 
 looked back to the period of the publication of this 
 treatise as the dawn of his electro-magnetic discovery. 
 
 So far as I know of its contents (for I have never 
 seen a copy), it does not contain anything beyond 
 indefinite anticipations of the real identity of electri- 
 city and magnetism. In this, indeed, there was no- 
 thing new. Compass-needles had been seen to be 
 reversed by lightning ; electric shocks had been 
 passed through steel without any certain effect ; and 
 Van Swinden had published a work in three volumes 
 expressly on the subject, containing the results of a 
 mass of ingenious failures. Nor, perhaps, can we 
 give Oersted credit, at that early period, for a more 
 distinct apprehension of the relation so anxiously 
 sought for, than was possessed by several of his con- 
 temporaries. His belief is said to have been grounded 
 on the notion, that "if galvanism be only a hidden 
 form of electricity, then magnetism can only be elec- 
 tricity in a still more hidden form" — a syllogism 
 which, if it satisfied Oersted's nietaphysical friends, 
 would hardly be accepted as demonstrative in the 
 laboratory ; and, after all, it suggests no one form of 
 relation rather than another. 
 
 Professor Forchhammer, the friend and pupil (790.) 
 of Oersted, states that, in 1818 and 1819, it was ^^^ "^^^^o"" 
 well known in Copenhagen that he was engaged gfg^^j.°. 
 in a special study of the connection of magnetism magnetism, 
 and electricity. Yet we must ascribe it to a happy 
 impulse — the result, no doubt, of much anxious 
 thought — that, at a private lecture to a few advanced 
 students in the winter of 1819—20, he made the ob- 
 servation, that a wire uniting the ends of a voltaic 
 battery in a state of activity, affected a magnet in 
 its vicinity. It was in the fact of the circuit being 
 closed, that the main difference consisted between this 
 and previous attempts, in which galvanic pairs or bat- 
 teries not connected by conductors were expected to 
 show magnetical relatiohs, though, in such a case, 
 the electricity was evidently stagnant. 
 
 Some mystery hangs over Oersted's apprehension (791.) 
 of his own experiment. It seems difiicult to believe Details re- 
 that he clearly saw its significance. Unlike Davy, ^pecting it. 
 when he first saw the fiery drops of potassium flow 
 under the action of his battery, and recorded his 
 triumph in a few glowing words in his laboratory jour- 
 
176 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VL 
 
 nal, Oersted took no immediate measures either to 
 complete or to publish his discovery. Some months 
 appear to have elapsed whilst waiting for the conve- 
 nience of a larger battery before he repeated the ex- 
 periment with the aid of Professor Esmark and other 
 friends. The battery then employed contained 20 
 twelve-inch elements, charged with water and ^\fth of 
 mixed nitric and sulphuric acids. The conducting 
 wire was heated red hot, which must have rather dimi- 
 nished the effect than otherwise. The nature of the 
 wire was found to be unimportant. If positive electri- 
 city passed from north to south through a conducting 
 wire placed horizontally in the magnetic meridian, 
 then a compass needle suspended over it had its north 
 end deviated to the west ; if under it, to the east ; if 
 the needle was placed on the east side of the conduc- 
 tor, its north end was raised ; if on the west side, it 
 was depressed. Oersted further found that needles 
 of non-magnetic substances, such as brass and gum- 
 lac, were not affected, and that the electrical efficiency 
 depended on the quantity, not the intensity, of the 
 current. These experiments seem to have been made 
 in July 1820 ; and Oersted and his friends being now 
 fully alive to the novelty and importance of the dis- 
 covery,he circulated extensively copies of a Latin tract, 
 dated the 21st July, in which the effects of the "electric 
 conflict," as he terms the presumed combination of the 
 opposite electricities in the " conjunctive wire" upon 
 a magnet, were described.^ In this tract we find the 
 following expressions : — " The electric conflict acts 
 in a revolving manner." " It resembles a helix." 
 " The electric conflict is not confined to the conduct- 
 ing wire, but it has aroimd it a sphere of activity of 
 considerable extent." 
 (792.) The effect of this pamphlet, consisting of a few 
 
 Speedily pages only, was instantaneous and wonderful. The 
 bv Am^^ author probably counted on the opportunity of devel- 
 pere, oping his discovery at leisure, but it was seized on 
 
 Arago, and with Such avidity, and pursued with such signal suc- 
 ''y' cess, particularly in France, that he probably gave up 
 the race of invention iu despair. Ampere had already 
 communicated experiments to the Institute on the 
 18th and 26th September. Arago and Davy sepa- 
 rately, and but little later, discovered the magnetiz- 
 ing power which the voltaic conductor exerted on iron 
 filings, and the latter tried in vain the magnetizing 
 power of common or machine electricity, which, how- 
 ' ever, was soon after shown by Arago, who enclosed 
 steel wires in helices of copper wire, through which 
 the discharges were passed. When soft iron was 
 placed in such a helix, it was found to become a tem- 
 porary magnet of great power whilst the voltaic 
 current continued. Thus magnets' of enormously 
 greater power than any previously known were con- 
 structed ; one of the first large ones was made by Pro- 
 fessor Henry of the United States. 
 (793.) ^ut the progress of electro- magnetismas a science 
 
 was far more indebted to Ampere, a professor at 
 Paris, than to any other philosopher. I shall, 
 therefore, introduce here some account of his dis- 
 coveries before closing what I have to say of Oer- 
 sted. 
 
 Andee Marie Ampbee was born in 1775 at Lyon. (794.) 
 He was an able mathematician, and wrote several Electro- 
 memoirs on Chances, and on the Integration of Par- ?/°^'°"'|. 
 tial Differential Equations. But with this he com- Ampere, 
 bined a taste for, and a practical acquaintance with, 
 the experimental sciences. He was a very good che- 
 mist, and showed himself particularly attentive to 
 Davy on his first visit to Paris. He was also much 
 attached to metaphysical speculation. His skill in 
 devising apparatus and in performing experiments was 
 eminently shown in his electro-magnetic researches ; 
 whilst he judiciously rendered his mathematical 
 knowledge subservient to them. In this respect he 
 had greatly the advantage of Oersted, who appears to 
 have been little acquainted with mathematics, and, 
 perhaps, in common with his metaphysical friends of 
 the German school, misapprehended their utility in 
 physical discoveries. Three different hypotheses Various 
 were speedily broached to represent mechanically options 
 the singular kind of force mutually exerted between "'^ ™® 
 a conductor and a magnet. The first and most ob- of the elec- 
 vious was, that this action was not a pusk-a/id-pull tro-mag- 
 force, but a force producing rotation without direct °®'"' *°™®' 
 attraction and repulsion, or of the nature of a couple 
 exerted between any part of an electric current, and 
 a small magnet or magnetic element. The second 
 opinion was, that an electric current may be esteemed 
 equivalent to a magnetizing force at right angles to 
 it. The third, that a magnet is composed of ele- 
 ments which act as if a closed electric circuit ex- 
 isted independently within each of them ; that is, 
 each magnetic molecule may be replaced by a small 
 conducting wire bent upon itself, in which some un- 
 failing source of electricity, like a galvanic pair, keeps 
 up, in the same direction, a constant current. 
 
 This last hypothesis, arbitrary and improbable as (795.) 
 it may sound, was that defended by Ampere. Whilst Theory or 
 few will be disposed to regard it as a true and com- ^do^ted b" 
 plete physical picture of the condition of magnetized Ampere, 
 bodies, it seems impossible not to award to it the same 
 sort of credit which we do to Newton's " fits of easy 
 reflection and transmission" of light, when we find 
 that it not only serves to represent the more obvious 
 phenomena, but has suggested experiments absolutely 
 new, and which turned out in accordance with the 
 anticipation ; and that, finally, by the sagacity and 
 industry of its author it was made to include, by 
 merely mathematical deductions, and without any 
 complication of the hypothesis, certain experiments 
 of a very singular kind, which at first seemed inex- 
 plicable by it. I proceed to develope a little farther 
 this consideration. 
 
 ' The exact title was, Experimenta circa effectum Conflictus Uleetrici in Acum Magneticum. 
 
Chap. VII., § 4.] 
 
 ELECTRICITY. — OERSTED — AMPERE. 
 
 177 
 
 (796.) The theory of Ampere rejects all but push-and- 
 
 actioifof ^^^^ forces, such as are commonly recognized in me- 
 electric chanical physics. These forces are mutual, and he- 
 conductors, long to electric currents. A permanent magnet is 
 a congeries of minute parallel and circular currents, 
 all acting in the same direction, which is at right 
 angles to the magnetic axis or line of force. Grant- 
 ing this for a moment, Oersted's experiment shows 
 that the current in the conductor acts on the currents 
 in the magnet ; and as a magnet places itself trans- 
 versely to a conductor, the currents in the magnet 
 tend to place themselves parallel to that in the con- 
 ductor. Do we then find such properties in move- 
 able electric conductors alone 1 Have they any 
 mutual action 1 Does that mutual action tend to 
 produce parallelism ? And if so, may it be farther 
 analysed into direct attractions or repulsions of the 
 several parts of the electric currents upon one 
 another ? All these questions were answered by 
 Ampere afirmatively after due appeal to experiment. 
 Two copper wires connected with voltaic circuits, 
 and suspended with the requisite degree of freedom, 
 approach when the currents have a similar direction, 
 but are repelled when the direction is opposite in 
 the two. When two moveable conductors are placed 
 at right angles, or indeed at any angle, they tend to 
 parallelism. All the usual phenomena of a magnet 
 may be imitated by a long helix of copper wire 
 through which electricity is made by some artifice 
 continually to circulate. The position of the poles 
 is the same as in a real magnet, and the name of 
 pole is determined by the direction (right or left 
 handed) in which the helix is wound. Such an in- 
 strument, not containing one particle of iron, is at- 
 tracted and repelled by a steel magnet, — obeys the 
 directive influence of the earth, — gives transverse 
 motion to an electric conductor near it, — in short, 
 does whatever magnetized iron does. 
 (797.) Thus, in the mutual action of electric currents 
 
 emen- ^fQj. tj^g phenomena of static electricity are wholly 
 the inrerse unlike) we recognize the great discovery of Ampere, 
 square of A new Science was formed, which he called electro- 
 the dia- dynamics, which he proceeded to develope with great 
 skill and success. MM. Biot and Savary found that 
 the electro-magnetic force exerted by an indefinite 
 straight conductor and needle, varies inversely as the 
 simple distance from the conductor; but looking 
 to the elementary actions of each portion of the cur- 
 rent, it will be found that this corresponds to the 
 usual physical law of the inverse square of the dis- 
 tance between the magnetic and the electric ele- 
 ment. 
 (798.) Whilst Ampere was pursuing his inquiries into 
 
 ^^ ^^H^n *^® properties of electric currents, others were vary- 
 la Rive— ^ iiig> ^ ^ great variety of ways, Oersted's fundamental 
 Electro- experiment. A great number of beautiful mechani- 
 magnetie gg,! arrangements were invented, particularly by the 
 elder De la Rive and by Mr Faraday. The latter, 
 however, had the sole merit of effecting a most singu- 
 
 rotations. 
 
 lar kind of motion, that in which a magnet float- 
 ing in mercury is made to revolve continuously 
 around a central conducting wire, and in like man- 
 ner a conductor may be made to revolve round 
 a fixed magnet ; nay, stranger still, a magnet 
 acting at once as conductor and magnet, revolves 
 with great velocity on its own axis when an elec- 
 tric stream is made to traverse one half of its 
 length. These astonishing experiments, which, in 
 an earlier age, might have founded a new sect of 
 astronomers and replaced the theory of Vortices, 
 offered also considerable difiiculties in the applica- 
 tion of Ampere's theory. They were, however, ulti- Accounted 
 mately removed by Ampere himself, who analysed ^^^^.^ 
 with great skill the mechanical conditions of each 
 case, and interpreting them into the language of his 
 theory, showed how continuous rotations might be 
 produced, according to the laws which he had esta- 
 blished, by electric currents alone suitably arranged ; 
 and he efiected by most ingenious experimental combi- 
 nations purely electro-dynamic rotations. Some other 
 experiments, in which magnets seemed to produce a 
 different efiect from electro-dynamic cylinders, pre- 
 sented a more serious obstacle, which, however, was 
 removed by a rigorous demonstration of the eflTects 
 which must ensue, if we. regard the elementary mole- 
 cules of a magnet as very small, and consequently the 
 entire magnet as a collection of indefinitely small and 
 correspondingly numerous electro-dynamic cylinders. 
 By means of four critical experiments, Ampere de- 
 termined completely the elementary laws of the 
 mutual action of currents, including that previously 
 established by Biot and Savary in the case of a mag- 
 net and a conductor. This investigation was one of 
 great intricacy, and was carried out with remarkable 
 skill. Ampere had the field almost to himself, Savary 
 making some contributions ; and, what is remarkable, 
 little or nothing has been added either to the theory, 
 or to the deductions from it, since his death. The 
 progress of the science of electro-magnetism has 
 been so astonishingly rapid since the year 1820, that 
 one set of phenomena after another has for the 
 time attracted almost exclusive notice. The disco- 
 very of diamagnetism will probably lead to a recon- 
 sideration of Ampere's theory as applicable to all 
 matter in a more general form. 
 
 This rapid succession of interesting topics has pre- (799.) 
 vented attention from being perhaps sufficiently di- Great 
 rected to the importance of Ampere's labours. He™^"'°^ 
 is at least as well entitled as any other philosopher ^^^ 
 who has yet appeared, to be called " the Newton of 
 Electricity." 
 
 Ampere was of an amiable, though rather eccentric (800.) 
 character. His absence of mind was proverbial, and "ieath. 
 his style is somewhat cumbrous and obscure. But 
 he was devoted to science, the promotion of which 
 was ever his first consideration, and he evidently 
 himself possessed great clearness in his conceptions. 
 He died on the 17th May 1836. 
 
178 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 LDiss. VI. 
 
 (801.) 
 Seebeck. 
 Discovery 
 of thermo- 
 electricity. 
 
 (802.) 
 Invention 
 of the 
 galvan- 
 ometer — 
 Schweig- 
 ger and 
 Kobili. 
 
 (803.) 
 Oersted's 
 history 
 continued. 
 
 Whilst Ampere, Arago, Davy, the two De la 
 Eives, and Mr Faraday, were throwing light on 
 the causes, and developing the consequences of 
 Oersted's experiment, Seebeck of Berlin discovered 
 in 1822 a new source of electric excitement, 
 which has since become indirectly of very great im- 
 portance. This was Thermo-Electricity. He found 
 that when heterogeneous metals are united, either 
 by soldering or pressure, and the junction heated, a 
 current of electricity is established. The order of 
 metals which produces the most energetic combina- 
 tions, is wholly unlike the arrangement of the vol- 
 taic series, and has no apparent reference to any 
 other known property of those substances. Bismuth 
 and antimony stand at the opposite extremities of 
 the scale, and a pair formed of them is consequently 
 the most powerful which can be made. When heat- 
 ed at the junction, positive electricity passes from 
 bismuth to antimony. In 1823, Oersted, then on 
 a visit to Paris, united with Fourier in making 
 experiments on this subject, and was probably the 
 first who constructed thermo-electrical piles. Un.. 
 questionably, the most important application of these 
 was to the construction of an instrument for measur- 
 ing the effects of radiant heat, by Nobili and Melloni, 
 of which an account has already been given, Art. 
 (709). 
 
 An application of electro-magnetism of extreme 
 importance, was the Multiplier or Galvanometer, 
 contrived by Schweigger of Halle. In it the idea 
 was first realized of measuring the power of an 
 electric current by its effect in deviating a mag- 
 netic needle. Schweigger perceived that he could 
 multiply the action of one and the same current, by 
 causing it to traverse successive parallel coils of the 
 conducting wire carried round the needle. Its sensibi- 
 lity was still farther, and almost indefinitely increased 
 byNobili's invention of rendering the needle a«iatic, or 
 diminishing its natural directive power in anyrequired 
 degree. This he did by connecting it firmly with a 
 second needle parallel to the first, of nearly equal 
 strength, with its poles placed in an inverted posi- 
 tion relatively to the other, and moving freely in a 
 plane altogether exterior to the coil, so that whilst 
 the directive effect of the earth's polarity is almost 
 neutralized, the electro-magnetic effect of the coil 
 tends to produce a similar deviation in both needles. 
 This is one of the most precious philosophical instru- 
 ments ever invented. It has been employed for 
 thirty years in almost every electrical research or 
 application. One of its best forms for many pur- 
 poses (though hitherto little used) is the Torsion 
 Galvanometer of Ritchie. . 
 
 Oersted, of course, interested himself in this new 
 application of his own great discovery. Indeed, hav- 
 ing the good fortune to survive that discovery for 
 more than thirty years, with a full enjoyment 
 of his intellectual vigour, he had the gratifica- 
 tion of contemplating a body of science entirely 
 
 new as its results, and a variety of useful ap- 
 plications scarcely less astonishing, which might, 
 in one sense, be called his own creation. The dis- 
 coveries of Ampere, Seebeck, and Mr Faraday, were 
 all based upon his; and during those thirty years, this 
 elegant and interesting branch of experimental phy- 
 sics underwent an' almost uninterrupted extension, 
 such as hardly any other affords an example of. The 
 Electric Telegraph is one of its most direct and practi- 
 cal results ; nor should we omit that Oersted himself 
 proposed, as far back as 1818, the application of elec- 
 tricity to blasting rocks by the very same process in 
 which it has of late years been so usefully applied^ 
 namely, that of heating a fine wire to incandescence. 
 
 Though Oersted was the author of numerous (804.) 
 papers connected with science down nearly toHisexperi- 
 the close of his life, they do not contain any impor- ments on 
 tant discovery, and with reference to electro-mag* pressim of 
 netism, he appears to have contented himself princi* water, 
 pally with repeating and expounding the observations 
 of his contemporaries. But some of his experiments on. 
 other subjects deserve mention, especially those on the 
 compressibility of water. This fact, which the Flo- 
 rentine Academicians had vainly sought to establish 
 in the 17th century, had been clearly demonstrated 
 by Canton in the middle of the 18th, but Oersted 
 first devised a compendious and effective apparatus 
 for producing and measuring it more effectually. His 
 result, that the compression amounts to46-millionths 
 of the bulk, for a pressure equal to one atmosphere^ 
 agrees almost precisely with Canton's. In 1845, he 
 considered that he had established that the heat de- 
 veloped by the same amount of compression is •0203 
 of a centigrade degree. He also made some experi- 
 ments on the Law of the Compressibility of Air and 
 upon other subjects. 
 
 The desideratum of a clear expression of the mani- (805.) 
 fest alliance between Electricity and Magnetism had Oersted re- 
 been so long and so universally felt, that the discovery ppj^e of 
 placed its author in the first rank of scientific men. the Insti- 
 There was not even, so far as I am aware, a sus- *^*® "^ 
 picion that he had been, however remotely or dimly, 
 anticipated. The prize of the French Institute which 
 had been awarded to Davy for his galvanic discoveries, 
 was bestowed upon Oersted, and so far as I am inform- 
 ed, has not been since adjudicated. He was elected first 
 Correspondent, and finally Associate of the Academy 
 of Sciences. He was personally known to many of 
 the philosophers of Europe, having made repeated 
 journeys in France, Germany, and England. His His scien- 
 agreeable manners and general information rendered tificcharac- 
 him popular. Sir H. Davy, who visited him at Co- '*''• 
 penhagen, describes him as " a man of simple man- 
 ners, of no pretensions; and not of extensive re- 
 sources." Niebuhr, however, who viewed his cha- 
 racter in a different light, says, " I scarcely know 
 another natural philosopher with so much intellect, ■ 
 and freedom from prejudice and esprit de corps." His 
 writings were indeed too discursive. Professor Forch- 
 
Chap. VII., § 5.] 
 
 ELECTRICITY. — OERSTED— DR FARADAY. 
 
 179 
 
 hammer has enumerated above 200 of his publica- 
 tions or articles, on a vast variety of subjects ; but 
 of all these, only a single tract of a few pages will 
 perhaps be ultimately remembered. As I before 
 remarked, his mind, though capable of continued 
 application, appears to have wanted the sort of con- 
 centration which prolonged physical researches re- 
 quire, and the school of philosophy in which he was 
 considered by his own countrymen as a proficient, has 
 
 never been fruitful in researches based on Induc- 
 tion. 
 
 In November 1850, the fiftieth anniversary of his (806.) 
 connection with the University of Copenhagen was ^'^ ^^^'"^ 
 celebrated by a jubilee. Though in his 74th year, 
 his activity was unimpaired, and he continued his 
 lectures and other employments until within a few 
 days of his death, which occurred on the 9th of March 
 1851, closing a life full of years and honour. 
 
 § 5. Dr Faraday. — Progress of the Theory of Electro- Chemical Decomposition — Volta-Electric 
 Induction — Magneto-Electricity — Diamagnetism — Optical Changes induced by Magnetism. — 
 Professor Fliicker^Magneoptic Action. 
 
 (807.) 
 Eminent 
 discoveries 
 of Dr Fara- 
 day. 
 
 (808.) 
 His early 
 history, and 
 connection 
 witli Davy 
 and the 
 Royal In- 
 stitution. 
 
 ■) 
 
 Variety of 
 his publi- 
 cations — 
 his Re- 
 searches on 
 Electrieitv. 
 
 Immeasurably the larger part of what we know 
 with regard to the nature and laws of electricity and 
 of its connection with Magnetism, so far as it has been 
 developed since the discovery of Oersted, is due to 
 the genius and perseverance of one man — Michael 
 Faraday. 
 
 This eminent philosopher was born, I believe, in 
 1791. He was originally " a bookseller's apprentice, 
 — ^very fond of experiment and very averse to trade." 
 In 1812 he sent to Sir H. Davy, then at the height 
 of his reputation, a copy of a set of notes taken at his 
 lectures, desiring his assistance "to escape from trade, 
 and enter into the service of science." To the credit of 
 the popular and distinguished chemist, he gave Mr 
 Faraday a courteous answer, and appointed him as 
 chemical assistant in the Laboratory of the Royal In- 
 stitution in March 1813. Leaving England to travel 
 in the autumn of the same year, Davy engaged Mr 
 Faraday to accompany him as secretary and scien- 
 tific assistant; they returned in April 1815, and 
 from that time to the present Mr Faraday has 
 been constantly engaged in the scientific business 
 of the Royal Institution, which is as completely 
 associated with his, numerous and splendid dis- 
 coveries as Cambridge is with those of Newton, 
 and Slough with those of the elder Herschel. By 
 a rare, perhaps unexampled good fortune, that esta- 
 blishment, founded principally for the promotion 
 of original research and the promulgation of dis- 
 coveries, has been indebted during the first fifty 
 years of its existence to the talents of two men only, 
 for a succession of new scientific truths which might 
 have done credit to a whole academy; indeed, if 
 to the names of Davy and Mr Faraday we add 
 that of Young, who here first promulgated the doc- 
 trines of the Interference of Light, there is scarcely 
 an academy in Europe which has within the same 
 period added so extensively to our choicest stock of 
 original science. 
 
 Partly in consequence of his official duty of bring- 
 ing forward and explaining the most important cotem- 
 porary discoveries, partly also in consequence of his 
 own matchless talent of elucidating, by original illus- 
 trations, if not by new facts, whatever he undertakes 
 
 to expound, the variety of subjects on which Dr Fara- 
 day has made essential additions to our knowledge 
 is so great that it is difficult to comprehend them 
 under one section. In conformity, however, with our 
 plan of suppressing minor facts, and insisting on the 
 most important, I shall confine myself to a summary 
 statement of his main discoveries connected with 
 Electricity and Electro-Magnetism as contained in a 
 continuous series of " Researches," published in the 
 Philosophical Transactions between 1831 and the 
 present time ; which, when collected (as they have 
 been in a distinct form), now fill three closely 
 printed octavo volumes. It would be difficult to 
 name in the history of any progressive experimental 
 subject so large an amount of research prosecuted 
 for so long a time in so methodical a manner and 
 with such remarkable uniformity in plan, and with 
 such unvarying success. 
 
 I shall only farther premise that Dr Faraday's (810.) 
 earliest essays were naturally of a chemical charac- Electro- 
 ter. In 1820 he assisted Davy, in prosecuting Oer- ^^|°.^*j° 
 sted's researches on the relations of Electricity and 
 Magnetism, and the following year he himself suc- 
 ceeded in producing, for the first time, the continuous 
 rotation of a magnet round an electric conductor, and 
 the converse rotation of the conductor round the 
 magnet (798). These experiments were the germ 
 of others which continued to interest philosophers as 
 well as the curious public for a long time after. But 
 it was in 1831 (when the author had attained his 40th 
 year) that the genius of Dr Faraday was displayed 
 in a commanding manner by the appearance of his 
 First and Second series of the Researches on Electri- 
 city, which have not perhaps been surpassed by even 
 the most brilliant of their successors. The subject was 
 the Induction of Electric Currents from other Currents 
 and from Magnets. But we shall find it most con- 
 venient to take an order different from that of the 
 discovery, and to present the main results of Dr 
 Faraday's electrical labours under the following jjeads of 
 heads :- — his chief 
 
 I. The law of definite Electro-chemical Decompo- electrical 
 sition, and the theory of the pile connected therewith. neticTf dis- 
 
 II. The Induction of Electric Currents from other coveries. 
 A 
 
180 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI, 
 
 (811.) 
 Electro- 
 chemical 
 deoomposl 
 tion, and 
 theory of 
 the pile. 
 
 Definite 
 character 
 of decom- 
 position — 
 electrical 
 equiva- 
 lents. 
 
 (812.) 
 Inferences 
 as to the 
 identity of 
 electrical 
 and chemi- 
 cal forces. 
 
 Currents and from Magnets, or the discovery of 
 Magneto-Electricity. 
 
 III. The influence of the Magnet on all bodies, 
 and the consequent division of substances into two 
 classes. Magnetics and Diamagnetics. 
 
 IV. Optical changes induced by Magnetism. 
 
 I. With regard to electro-chemical decomposition 
 and the theory of the pile, the great extent and intri- 
 cacy of the subject require us to restrict our analysis 
 to a few of the leading conclusions. The most im- 
 portant of these may be summed up in the following 
 propositions : — 1st, The amount of a decomposable 
 substance (or electrolyte^ analysed into its elements 
 by a current of electricity depends solely on the 
 amount of electricity passing through it, and is in- 
 dependent of the form of apparatus employed, the 
 dimensions of the poles (or electrodes), the strength 
 of the solution, or any other circumstance. It is 
 thence inferred, with respect, for instance, to water, 
 that the amount of it decomposed in a given time is 
 an exact measure of the quantity of electricity set in 
 motion in that time. 2d, When a substance is thus 
 decomposed, it is a necessary, or at least a highly 
 probable, consequence of Dalton's laws, that the 
 elements separated are in atomic proportions to one 
 another. But Mr Faraday also found that when 
 several decompositions are effected at the same time 
 by interposing different electrolytes in intervals of 
 the same circuit, the whole of the series of elements 
 separated bear the atomic relations to one another. 
 Thus, to take a single case ; an electric current de- 
 composes in the same time 0*497 grain of water 
 and 3-2 grains of protochloride of tin. Now, these 
 are exactly the proportions of the atomic weights of 
 those bodies. From this and numerous other cases 
 Mr Faraday infers, that universally the amount of 
 electrical action required to dissolve a combination is 
 in a constant proportion to the force of chemical affi- 
 nity by which its elements are united. The corollary 
 seems therefore highly probable that it is one and the 
 same force which is exerted in eithei; case. But the 
 conclusion as to their identity becomes almost irre- 
 sistible when we add to these propositions the follow- 
 ing: 3dly, That the oxidation of one atom of zinc by 
 the acid of the battery generates precisely so much 
 electricity as would resolve one atom of water into 
 its elements. Thus, 8'45 grains of zinc dissolved 
 occasioned the analysis of 2"35 grains of water ; but 
 these numbers are in the ratio of 32-5 to 9 ; the 
 equivalents or atomic weights of zinc and water. 
 
 From these strictly experimental laws, Dr Fara- 
 day considers that he is entitled to draw these im- 
 portant inferences : First, that the source of voltaic 
 electricity in the pile is chemical action solely; 
 Secondly, that " the forces termed chemical affinity 
 and electricity are one and the same.'"- Itis needless to 
 add that these conclusions, involving the very essence 
 
 of the science of voltaic electricity, are supported by 
 Mr Faraday by a great variety of collateral proofs ; 
 and, on the whole, I cannot see that they admit of any 
 reasonable doubt. The contact theory of Volta still, 
 however, holds its ground in Germany, where the 
 number of influential writers on electricity is con- 
 siderable ; and so persevei-ingly is it maintained, that 
 it is dijEcult to perceive how it is ever to be dis- 
 lodged. But on this wide and not very profitable 
 controversy we cannot here enter. 
 
 There are a great many other considerations (813.) 
 connected with the action of the voltaic battery ^'^ ^ara- 
 which are independent of these primary ones, and ^ucy™ 
 which are scarcely less important. Dr Faraday and Con- 
 has entered into a most elaborate experimental diction, 
 argument to show that induction always precedes 
 both conduction and decomposition, and that de- 
 composable bodies or electrolytes must be all more 
 or less perfect conductors. His views may be thus 
 concisely summed up in his own words : — " The first 
 effect" of the electrifying influence, whether of fric- 
 tional electricity or of voltaic electricity, upon bodies, 
 is " the production of a polarized state of their par- 
 ticles which constitutes induction ; and this arises 
 from its action upon the particles in immediate con- 
 tact with" the excited body, " which again act upon 
 those contiguous to them, and thus forces are trans- 
 ferred to a distance. If the induction remain un- 
 diminished, perfect insulation is the consequence ; 
 if the contiguous particles" thus polarized " have 
 the power to communicate their forces, then con- 
 duction occurs, conduction being a distinct act of 
 discharge between neighbouring particles." " In the 
 inductive condition assumed by water" when about 
 to be decomposed, " the discharge between particle 
 and particle is not, as before, a mere interchange of 
 their powers and forces, but an actual separation of 
 them, the oxygen travelling in one direction and 
 carrying with it its ainount of force acquired during 
 polarization, and the hydrogen doing the same thing 
 in the other direction, until they each meet the next 
 approaching particle, which is in the same electrical 
 state with that they have left, and by association of 
 their forces with it produce discharge. This action 
 may be regarded as a carrying one performed by the 
 constituent particles of the dielectric."^ Again, 
 " the current is an indivisible thing ; an axis of 
 power, in eveiy part of which both electric forces are 
 present in equal amount."* 
 
 These views respecting the molecular progress of (814.) 
 conduction and decomposition, though perhaps never 
 so categorically stated as by Dr Faraday, have been, 
 I imagine, substantially held by a majority of those 
 who have considered the subject since the time 
 of Davy, who first gave them a partial expression. 
 And when Davy and others speak of the electric 
 forces in decomposition as if they emanated from the 
 
 1 Retearches, Art. 918. 
 
 lb., Arts. 1338, 1347. 
 
 ' lb., Art. 1642. 
 
Chap. VII., § 5.] 
 
 ELECTRICITY. — DR FAEADAY. 
 
 181 
 
 (815.) 
 Uniform 
 nature of 
 electricity 
 from what- 
 ever source, 
 
 rsie.) 
 
 Induction 
 of electric 
 currents — 
 magneto- 
 electricity, 
 
 poles of the battery and became enfeebled with dis- 
 tance from them, they used a -language not quite 
 rigorous indeed, yet expressing the actual pheno- 
 mena with that general accuracy which we can alone 
 expect in the first stages of so new and difficult an 
 inquiry. " The sum of chemical decomposition is 
 constant for any section of a decomposing conductor" 
 is Dr Faraday's expression.^ So is the sum of illumi- 
 nations arising from light radiating from a point, 
 when taken across any section of its path, yet the 
 influence is said to vary inversely as the square of 
 its distance from the origin. The part of Dr Fara- 
 day's conclusions, however, most open to excep- 
 tion, is what refers to electric action at a distance, 
 which he conceives to depend solely upon induction 
 acting on intervening particles, which induction may 
 take place along curved lines. It is indeed true that 
 he has shown, by a beautiful experiment, that the in- 
 terposition of different substances between an excited 
 electric and a body capable of being electrified by in- 
 duction, occasions different degrees of excitement in 
 the latter, even when the interposed bodies are glass, 
 sulphur, and other "non-conductors;" and this he 
 justly refers to a peculiar power or property of bodies 
 Called "specific inductive capacity." But this is 
 rather different from the general proposition above 
 referred to. 
 
 In conclusion of this part of the subject, I must 
 add that Mr Faraday has, with great pains and suc- 
 cess, demonstrated the fundamentally identical nature 
 of electricity from whatever source derived, and how- 
 ' ever differing in its usual manifestations ; — such as 
 electricity of the pile, of the common machine, or that 
 induced by magnetic, thermal, and animal electricity. 
 These have all common properties, producingthe shock, 
 the spark, and magnetic, chemical, and heating effects ; 
 and, except two, also producing sensible attraction 
 and repulsion. But the disproportion of the effects 
 of electricity, varying so much in intensity when re- 
 ferred to unit of quantity, is astonishing and para- 
 doxical. The electricity which so silently and speedily 
 decomposes a single grain of water would, when its 
 intensity is sufficiently exalted, produce, according to 
 Mr Faraday, " a very powerful flash of lightning," 
 or 800,000 times the contents of a well charged Ley- 
 den battery. Again, zinc and platinum wirfes half an 
 inch long and one-eighteenth inch diameter, dipped 
 into slightly acidulated water, produce in three se- 
 conds as much electricity as a man can easily bear 
 in the form of a shock. 
 
 II. Induction of electric currents from other cur- 
 rents and from magnets. — This splendid research, 
 which dates from 1831, constitutes the discovery of 
 magneto-electricity. 
 
 The discovery by Ampere of the attraction and 
 repulsion of conductors conveying electric currents 
 rapidly followed (as we have seen in Art. 796) Oer- 
 
 sted's discovery of the power of electricity to affect 
 the magnet, and the corollary from it of the mag- 
 netizing agency of electricity. This being achieved, 
 very striking analogies led to the expectations — 1. 
 That a wire conveying a current ought to excite by 
 induction a current in another wire near it ; and, 2. 
 That a magnet ought, under some circumstances at 
 least, to be capable of exciting electric action. But 
 attempts in these directions had repeatedly and sig- 
 nally failed, and for a reason which Mr Faraday first 
 rendered apparent. 
 
 Having made a compound helix of two copper (817-) 
 vnres wound parallel to one another, but not touch- ^""■f-^^^'^' 
 ing, and rolled one within the other upon a cylin- tion. 
 der, he found that when he transmitted a continu- 
 ous voltaic current through one wire, a momen- 
 tary current (tested by a galvanometer) took place 
 in the independent helix opposed in direction tp that 
 of the primary current ; but it ceased to exist in- 
 stantaneously, although the primary current conti- 
 nued to act ; and it was only on the cessation of 
 that current that a new momentary induced current 
 appeared, but in the contrary direction to the previ- 
 ous one. The same effect occurred when a wire 
 conducting a current was mechanically brought into 
 the presence of another wire ; the approximation of 
 the two induced an oppositely directed current, their 
 separation a similar one. Whilst the wires were 
 immovable no induced current took place. This 
 he termed Volta- Electric Induction. 
 
 Mr Faraday next took a ring of soft iron, disposing 
 two copper-wire coils round opposite portions of the 
 ring. In passing a current through one coil, and 
 thus magnetizing the ring, a current was induced in 
 the other copper coil, but, as in the former case, only 
 for an instant. When the primary current stopped, 
 and tlie magnet was unmade, an opposite current 
 shot through the secondary coil. 
 
 The transition to the next experiment was natu- 
 ral, but highly important. The primary coil was Magneto- 
 suppressed ; and the piece of soft iron embraced by «lB'='>^io»ty" 
 the secondary coil was now magnetized by the in- 
 ductive action of a powerful bar magnet, with 
 which contact was alternately made and broken. 
 At the instant of making contact a momentary 
 current of electricity was produced in the remain- 
 ing coil, and on breaking it a reversed current, 
 also of instantaneous duration. No current ex- 
 isted whilst the magnet continued to be applied. 
 The direction of the current at making contact 
 was opposite to that which would have produced 
 the magnetism present in the iron core ; on break- 
 ing contact the current was similar to that which 
 would have magnetized the iron. The electricity 
 momentarily induced in the coil was tested by its 
 action on the galvanometer, by its power to mag- 
 netize steel, to convulse a frog, and finally by the 
 
 (818.) 
 
 (819.) 
 
 ^ Researches, Art. 504. 
 
182 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (820.) 
 
 (821.) 
 Arago's 
 rotation- 
 magnet- 
 ism ex- 
 plained. 
 
 (822.) 
 
 (823.) 
 Dr Fara- 
 day's dis- 
 covery of 
 diamag- 
 netism. 
 
 Classifica- 
 tion of 
 magnetic 
 and dia- 
 magnetic 
 bodies. 
 
 production of a spark. This, then, was the disco- 
 very of magneto-electricity. 
 
 The mere motion of a permanent magnet was now 
 substituted for the induction of magnetism in soft 
 iron. By pushing one end of a bar-magnet into the 
 coil, electricity was developed so long as the motion 
 continued; on withdrawing it an opposite current 
 took place. Even the feeble magnetism of the 
 earth induced a sensible electric current in a wire 
 moved transversely to the direction of the dipping- 
 needle. 
 
 By making a copper plate revolve in the neigh- 
 bourhood of a powerful magnet, a continuous cur- 
 rent of electricity may be detected passing from the 
 centre to the circumference of the plate, and may be 
 collected by proper means. Here, then, is a mag- 
 neto-electric machine. This current perpetually pre- 
 sent in a conducting plate revolving beneath a mag- 
 net, cannot fail (by the common laws of electro- 
 magnetism) to react on that magnet. Dr Faraday 
 showed in the most satisfactory manner that its 
 action is exactly what is required to explain M. 
 Arago's experiment of " transient magnetism by 
 rotation" — namely, to cause the magnet (if free) 
 to follow the direction of motion of the plate 
 (515). 
 
 On the whole, this research of Dr Faraday may be 
 cited as one of the most original and admirably 
 conducted which the annals of science present, 
 and as such may be usefully recommended to the 
 student, 
 
 III. The influence of the magnet on all bodies, and 
 their consequent division into two classes ; Magnetics 
 andDiamagnetics. — By many, perhaps most persons, 
 this will be regarded as the greatest of Dr Faraday's 
 discoveries. It dates from 1846. By using electro- 
 magnets of very great power, and suspending bodies 
 of a somewhat elongated form between the poles, he 
 has proved that every substance, solid, liquid, or 
 gaseous which he has put to the test, is either drawn 
 into a line joining the poles of the magnet, as soft 
 iron would be, returning to that line if displaced, or 
 else it settles in a position at right angles to this, or 
 across the line of poles. The former he calls para- 
 magnetic or simply magnetic bodies, and their posi- 
 tion axial ; the latter diamagnetic bodies, and their 
 position equatoreal. Bodies may be arranged in a 
 list commencing with those most paramagnetic, dimi- 
 nishing to neutrality, then feebly diamagnetic, and 
 finally the strongest diamagnetics. The following 
 is such a list of a few solid and liquid bodies thus 
 classified : — 
 
 I 'Iron. 
 Nickel. 
 Cobalt. 
 P 11 fl' 
 Crown glass. 
 Platinum. 
 Osmium. 
 Zero Vacuum. 
 
 Diamagnetics . 
 
 Arsenic. 
 Ether. 
 Alcohol. 
 Gold. 
 Water. 
 Mercury. 
 Flint glass. 
 Tin. 
 
 " Heavy glass." 
 Antimony. 
 Phosphorus. 
 . Bismuth. 
 
 The equatoreal pointing of diamagnetic bodies evi- 
 dently presupposes that they are longer in one di- 
 mension than in the others. A small bar of sili- 
 cated borate of lead, or " heavy glass," about two 
 inches long, and from a quarter to half an inch 
 broad and deep, suspended in a stirrup of paper by 
 six or eight lengths of cocoon silk, was the appa- 
 ratus first employed by Dr Faraday. When a 
 sphere or a cube is used, of course it cannot point. 
 The diamagnetic action is shown in that case by the 
 little body being rebelled indifferently from either 
 pole of the magnet, in the same manner as soft iron 
 is indifferently attracted by either. This repulsive 
 tendency includes the phenomenon of equatoreal 
 pointing, and its law is thus comprehensively ex- 
 pressed : " The diamagnetic tendency is to move the 
 body from stronger to weaker places of magnetic 
 force." 
 
 The behaviour of diamagnetics in the presence of 
 a magnet may be thus further illustrated. It is 
 what would occur if a body absolutely inert were 
 suspended in a fluid pressing upon it, that fluid 
 being at the same time more or less magnetic, that 
 is, more or less attracted by either pole of the mag- 
 net. The result would evidently be, that the body 
 would seem to be repelled, and would set equato- 
 really for the same reason that a piece of wood 
 plunged in water rises to the surface as if repelled 
 by gravity. Thus Dr Faraday suspended feebly 
 paramagnetic bodies in ferruginous solutions more 
 magnetic than themselves, when they acted as dia- 
 magnetic bodies would do. 
 
 It is impossible for the most part to guess before- 
 hand to which class a substance will belong. China- 
 ink, porcelain, silkworm gut, shell-lac, and charcoal, 
 rank amongst paramagnetic substances ; whilst sul- 
 phur, resin, wood, leather, and most animal sub- 
 stances, are diamagnetic. Thus, if a living man 
 could be delicately enough suspended between the 
 poles of a huge magnet, he would settle equato- 
 really. 
 
 philosophers are not yet entirely agreed as to the 
 precise nature of the Diamagnetic relatively to the 
 Magnetic actions, of bodies. Besides Dr Faraday, 
 MM, "Weber andEdmond Becquerel abroad, and Pro- 
 fessors Tyndall and William Thomson in this coun- 
 try, have examined the subject both practically and 
 theoretically in great detail. The more probable 
 opinion seems to be, that bismuth and its analogues 
 
 (824.) 
 Fundamen- 
 tal experi- 
 ment and 
 definition 
 of diamag- 
 netism. 
 
 (825.) 
 Farther 
 illustra- 
 tions. 
 
 (826.) 
 
 (827.) 
 Discussion 
 on the 
 nature of 
 diamagnet- 
 
Chap. VII., § 5.] 
 
 ELECTRICITY. — DR FARADAY — M. PLUCKER. 
 
 183 
 
 (828.) 
 Obscure 
 anticipa- 
 by Brug- 
 mans and 
 Lebaillif. 
 
 (829.) 
 Father 
 Bancalari 
 discovers 
 the dia- 
 magnetism 
 of flames. 
 
 (830.) 
 Dr Para- 
 day on the 
 magnetism 
 of oxygen. 
 
 (831.) 
 Professor 
 PlUcker on 
 magne- 
 optic force, 
 
 acquire a true polar condition under tlie action of 
 magnets, tut opposed to that which iron and para- 
 magnetics do in Jike circumstances. 
 
 Like almost every other great discovery, some 
 feeble traces of this may be found amongst the vo- 
 luminous records of almost forgotten experiments. 
 Brugmans observed, in 1778, the repulsion of bis- 
 muth by a magnet, which was rediscovered by Le- 
 baillif in 1827 ; and something like the equatoreal 
 pointing of sheU-lac and wood was noticed in the 
 same year by Becquerel, and may also be traced in 
 the writings of Coulomb. The present writer recol- 
 lects very distinctly to have had pointed out to him 
 by M. Becquerel, at Paris, about 1835, the pointing 
 of minute chips of wood placed near a common steel 
 magnet. But these incidental facts having been suf- 
 fered to remain in complete obscurity for so many 
 years, without even an attempt to connect and ex- 
 plain them, can scarcely be said even to touch the 
 originality of Dr Faraday's discovery. 
 
 The year after the announcement of diamagnet- 
 ism, Father Bancalari of Genoa discovered the 
 powerful diamagnetic quality of flame. It is easily 
 shown by placing the flame of a wax taper between 
 two blunt conical terminations of a powerful electro- 
 magnet. The flame spreads equatoreally, becoming 
 fish-tailed. Dr Faraday, zealously taking up the in- 
 quiry, proved that this depends upon hot air being 
 diamagnetic relatively to the surrounding cold air, 
 but that atmospheric air is always absolutelt/ para- 
 magnetic. Analyzing the efiect still farther,- he 
 found that the oxygen of the air is a very powerful 
 paramagnetic, whilst nitrogen is relatively diamag- 
 netic, but in all probability is a neutral substance, 
 one at the real zero of this singular scale. By a most 
 ingenious application of the torsion balance, he was 
 enabled to compare the relative actions of magnet- 
 ism on the gases with admirable skiU and precision. 
 (^Philosophical Transactions, 1851.) 
 
 These experiments demonstrate a paramagnetic 
 (or iron - like) attraction in oxygen really aston- 
 ishing. A small mass of oxygen appears to be 
 attracted at the distance of an inch from the axial 
 line of the electro-magnet by a force equal to 
 its own weight ! Since heat diminishes this qua- 
 lity, the acute perception of Dr Faraday rapidly en- 
 tertained the idea that the apparent magnetism of 
 the earth might partly at least reside in the atmo- 
 sphere, and that the changes of terrestrial magnetic 
 intensity and direction might be explained by the 
 action of the sun expanding the atmosphere. The 
 26th series of his researches is devoted to an elabo- 
 rate exposition of this theory, which, however inge- 
 nious, is still involved in great difficulty. 
 
 Professor Pliicker — Attraction and Repulsion of 
 Optic Axis of Crystals.— Soon after Dr Faraday's dis- 
 covery of diamagnetism, Professor Pliicker, of Bonn, 
 annoimced the important fact, that the optic axis of 
 Iceland spar is repelled by the magnet. A sphere 
 
 friiJo cystallic 
 •■■"^^ force. 
 
 (833.) 
 
 of that substance suspended by a thread, and having 
 its axis horizontal, being placed between the poles, 
 notwithstanding the perfect symmetry of external 
 figure, the axis ranges itself in the equatoreal position. 
 In some other crystals the axis is directed in the 
 line of poles. The law of the phenomena is not yet 
 completely made out ; but so strong is the latter qua- 
 lity in crystals of kyanite, that a piece of that sub- 
 stance properly suspended wUl actually show a direc- 
 tive power under the influence of the earth's mag- 
 netism. 
 
 Probably closely allied to this fact is a similar (832.) 
 directive tendency observed in well crystallized spe- Magne- 
 cimens of bismuth, antimony, and arsenic, 
 M. Pliicker calls the magne-crystallic, as the for- 
 mer may be termed the magne-optic force ; and 
 it is often so intense as to oppose and even reverse 
 the directive tendency which the body would have 
 had between the poles in its massive or uncrystal- 
 lized state. 
 
 It wiU be easily conceived that the interest crea^ 
 ted by these admirable discoveries, revealing not only 
 new and general properties of matter, but also rela- 
 tions between very difierent branches of science, soon 
 became general, and raised the reputation of Dr 
 Faraday to the very highest rank as an experimental 
 philosopher. If we compare his two greatest works, 
 that on magneto-electricity, and this on diamag- 
 netism, we find in the former perhaps a more perfect 
 specimen of inductive sequences ; in the latter, facts 
 more independently novel and unlooked-for, and an 
 unrivalled skill in the application and invention of 
 experimental methods. 
 
 Passing over many less important matters, there (834.) 
 yet remains one interesting discovery to be men- Dr Fara- 
 tioned, which in point of time preceded the last, ^^^. °° 
 namely— _ changes 
 
 IV. Optical Changes induced by Magnetism. — induced by 
 In his 19th Series of iJe«earcAe*, published in 1845, ™*g"«t'™- 
 Dr Faraday announced " The Magnetization of 
 Light and the Illumination of the Magnetic Lines of 
 Force," — a title which, though intended to express 
 exactly the author's idea of his discovery, perhaps 
 excited undue anticipations in the public mind. For 
 here we have no direct, or even apparently direct, 
 action of the magnetic force on a luminous ray, but 
 only that a peculiar state is induced by magnetism 
 in some transparent bodies which produces an action 
 on light which they did not possess before, and which, 
 indeed, difiered in some respects from any similar 
 action previously recognised. 
 
 Dr Faraday's leading experiment is the following : (835.) 
 — A piece of "heavy glass," or siliceous borate of ^°'**"'" °*^ 
 lead, was placed lengthwise between the poles of apoiariza- 
 powerful electro-magnet. A ray of plane-polarized of a ray of 
 light was transmitted through the glass parallel to '•S'"'- 
 the line of the magnetic poles ; when the magnetic 
 energy was fully applied, the plane of polarization of 
 "the light was found to have twisted round, similarly 
 
184 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 the action j^^^ there be a medium on wMch the magnetism im- 
 
 ■ ^ Some molecular change, no 
 
 (apparently) to what occurs when, polarized light 
 passes through quartz or oil of turpentine. It is 
 found that a great number of solids and liquids are 
 subject to the magnetic influence in the same man- 
 ner as in the case of " heavy glass," though to a 
 smaller amount. 
 (836.) Now, in reasoning on this experiment, it is to be 
 
 Resembles observed that no rotation of the ray takes place un- 
 
 the action 
 
 of quartz, 
 
 but with a presses its energy. 
 
 difference, doubt, results, such as that which pressure gives to 
 glass, rendering it doubly refracting and depolariz- 
 ing, or, to take a stiU closer analogy, when heat ap- 
 plied to it conveys similar properties. Yet no one 
 imagines that these experiments show a direct reac- 
 tion of heat, still less of mechanical compression, upon 
 light. Yet, with all abatements, Dr Faraday's dis- 
 covery is novel and singular ; the more so, that this 
 constrained state differs from that naturally pos- 
 sessed by quartz and certain liquids. The state mag- 
 netically induced in a body causes the rotation of the 
 ray to be reversed when it moves in the contrary 
 direction ; that is, its rotation is right-handed when 
 the ray moves from the north to the south pole, but 
 left-handed when it moves from S. to N. But in 
 bodies in the natural state the rotation takes place 
 towards the same hand whatever be the path of the 
 body. Mr Airy has shown that this peculiarity ad- 
 mits of being mathematically expressed in a manner 
 somewhat analogous to that imagined by Professor 
 MacCuUagh in the case of quartz (512) ; but it is 
 not pretended that these formulae convey informa- 
 
 tion as to the physical conditions on which these 
 singular phenomena depend. 
 
 Amongst Dr Faraday's contributions to science (837.) 
 not connected with electricity, the most remarkable ^^ ^fra,- 
 perhaps is the condensation of many gases into the g^J ^"^"®' 
 liquid form by cold and pressure, of which he is the tain gases. 
 undoubted discoverer. This fact is highly interest- 
 ing both in a scientific and practical point of view. In 
 the latter it was early applied by the late ingenious 
 Sir M. I. Brunei as a new moving power (375), and 
 it may not improbably yet be resorted to for that 
 purpose. The subsequent discovery of a mode of 
 solidifying carbonic acid by M. Thilorier is not only 
 interesting in itself, but affords a method of produc- 
 ing more intense cold for experimental purposes 
 than any other previously known. 
 
 Dr Faraday still continues his laborious and fruit- (838.) 
 ful inquiries. Whilst he has attained almost every ^'^ ■^'^® 
 titular honour which the world of science has to "'^'^ * "'°' 
 bestow (including that of associate of the French 
 Academy of Sciences), he has preserved a modesty 
 of character and a simplicity of life which enhance 
 the respect in which he is held by all who are ad- 
 mitted to his nearer acquaintance. No one has more 
 successfully escaped the contentions which literary 
 rivalry so often produces ; and by his extraordinary 
 skill in expounding the most difficult researches, 
 whether made by himself or by others, he has main- 
 tained (as I have already said) the early reputation 
 of the Royal Institution, and has immensely enlarged 
 the circle of those who are able to admire and appre- 
 ciate his successes. 
 
 § 6. Ohm — Daniell — Mr "Wheatstone — M. Jacobi. — Laws of Electrical Conduction; — Constant 
 Battery; — Applications of Electricity to Telegraphs — Clocks — Motive Engines — the Electrotype. 
 
 , 9-) We have traced in the last section the progress of 
 
 ^f^th*^*^'*'^ electrical and of electro-magnetic discovery since the 
 science of days of Davy and Oersted, as well exemplified in 
 electricity, the pre-eminent researches of Dr Faraday. In con- 
 Its nume- foj-mity with the plan of this Dissertation (13), 
 vators. " (14) > i have, on account of their immense interest 
 and importance, analyzed them more fully than 
 could possibly have been done were I to render 
 similar justice to all who have distinguished them- 
 selves in the same career. Thus, France has pro- 
 duced in M. Becquerel one of her most inge- 
 nious and indefatigable experimentalists, fuU of de- 
 votion to science, and giving lip conscientiously the 
 whole of a long life to the cultivation of this parti- 
 cular department. His discovery of the efficacy 
 of long-continued and very feeble voltaic actions 
 
 to produce crystallized earthy and metallic com- 
 pounds not obtainable by chemical means is highly 
 important. Switzerland is proud of her two De la 
 Rives,'' and Italy of not a few disciples of Volta. In 
 Germany the number of electricians is greater than 
 in any other country; and as they have taken the lead 
 in obtaining correct measures of the electric forces, 
 and in determining (in many cases) the numerical laws 
 which regulate the efficiency of batteries and conduc- 
 tors, and have applied these to many important 
 practical purposes, I shall devote a section to some 
 account of these, as well as to the beautiful experi- 
 ments of our countryman Mr Wheatstone. 
 
 Ohm's Law of Electrical Conduction. — Geobg (840.) 
 Simon Ohm was bom in Bavaria in 1787, and was O'""'^ 
 successively professor at Cologne, Niirnberg, and ^^^ "^'J^" j 
 conduction 
 
 ^ I may here record that before the year 1835, I suspected that there might be some immediate action between circularly polar- 
 ized light and a magnetized body, and made experiments in consequence in May 1836, which, however, led to no result. I 
 rather think, however, that these experiments deserve careful repetition under more varied circumstances. 
 
 ^ MM. Becquerel and A. De la Uive have both published elaborate works on Electricity, to which the reader is referred for 
 details on this inexhaustible subject. 
 
Chap. VII., § 6.] 
 
 ELECTRICITY. — OHM — DANIELL. 
 
 185 
 
 Munich. He died on the 7th July 1854. His 
 theory of electrical conduction was not highly appre- 
 ciated in Germany until it had received, in 1841, an 
 eminent mark of approval from the Royal Society of 
 London, by the award of their Copley medal. His 
 principal work on the Galvanic Circuit {Die galvan- 
 ische Kette mathematisch bearbeitet ; Berlin; 1827) 
 has had a somewhat peculiar fate. Accepted by only 
 a few persons as a great discovery, it met with com- 
 paratively little attention, at least until recently ; yet 
 notwithstanding the long anticipation by Ohm of his 
 results, it has been his misfortune to have theii: ori- 
 ginality contested. 
 (841.) It seems not difficult to account for the diversity 
 
 Its merits of estimation in which this work has been held. The 
 fects ^' primary fault is the author's own. He deduces the 
 strength of a voltaic current in any given circuit, and 
 the electroscopic excitement of each part of the cir- 
 cuit, by means of reasoning seemingly a priori, from 
 certain assumed axioms submitted to mathematical 
 reasoning. The axioms are very simple ; the theory 
 founded on them is intended to correspond to Fourier's 
 theory of heat, of which, indeed, in point of form, it is 
 a mere and literal copy ; but as every circumstance 
 which introduces real complication is soon left on 
 one side, the leading propositions are almost self- 
 evident results of the axioms. In short, the pa- 
 rade of mathematics is uncalled for, and the whole 
 structure of the theory seems so slight and ques- 
 tionable that one is surprised that it should ever 
 "have been regarded as more than a clever expres- 
 sion of some approximately true experimental laws. 
 It appears, indeed, that this is the simple fact ; — 
 that the axioms were obtained from the results 
 which they seem to predict, and that Ohm was an 
 experimentalist before he became an author. In 
 this guise we understand how to treat the so-called 
 " Laws of Ohm." They are truly important empi- 
 rical laws, calculated to guide the practical man in 
 applying and measuring galvanic forces, to enable 
 the theorist to form clearer notions of the diiferent 
 (often confusing) effects of these forces, and to reduce 
 their varying energy to calculation ; but we must be 
 allowed to doubt whether Ohm has thrown any new 
 light on the real first axioms of electrical excitement 
 or transmission. 
 (842.) The most important of these laws refer to the 
 
 The prin- numerical measure of the voltaic stream circulating 
 of^TOiidutf- ill *^6 conductor of a closed circuit. Such a closed 
 tion. circuit may be imagined to consist of — (1.) an exciter 
 
 or battery ; (2.) a conductor homogeneous or other- 
 vrise, but necessarily continuous, uniting the ends of 
 the battery. The exciting force is derived (we will 
 assume) from the chemical or thermo-electric action 
 present in the battery. The electric equilibrium 
 being disturbed, is restored more or less speedily 
 through the medium of the conductor which connects 
 the poles. If the conductor be good, the electricity 
 passes rapidly through it, and does not accumulate in 
 
 the battery ; if the reverse, it accumulates until it ac- 
 quires power to overcome the resistance, and then it 
 passes through in a stream less abundant, but of a 
 higher intensity. If the construction of the battery 
 does not permit that degree of intensity to be reach- 
 ed, the electricity stagnates in the battery, the con- 
 ductor cannot perform its office, no efiect results. The Illustra- 
 whole maybe compared to a spout of water discharged *''"'• 
 into a trough, from the bottom of which extends a 
 long narrow horizontal pipe. The water is the elec- 
 tricity, the trough is the battery, the pipe is the con- 
 ductor. If the pipe be very long and narrow, no 
 water at all will pass through it until the water in 
 the trough has attained a certain height, or has a 
 head of pressure sufficient to overcome the resistance 
 in the pipe. If the trough be filled to the brim 
 without the resistance being overcome, the trough is 
 as good as plugged, no motion takes place, the stream 
 regurgitates. The longer the pipe the feebler the 
 stream that passes; shorten the pipe indefinitely, 
 and the efflux depends only on the construction of 
 the trough. Indeed, the illustration might be pushed 
 considerably farther. The depth of the cistern re- 
 presents the electro-motive force of the voltaic com- 
 bination ; its area the size of the plates. By in- 
 creasing the latter, we do not give the means of 
 overcoming more resistance; but when the resist- 
 ance is small, we affi)rd a larger supply without 
 lowering the level — i. e., the intensity. 
 
 Ohm regards the current as proportional to the elec- (843.) 
 tro-motive force directly, and to the resistances in- Resist- 
 versely ; and the latter are divided into (a) the re- estimated, 
 sistance of the battery itself to the passage of the cur- 
 rent ; (6) the resistance of the conductor. Now the 
 latter varies as the length of the wire completing the 
 circuit: We may therefore double its amount by 
 doubling the length of wire joining the poles ; and 
 if we observe the strength of the current passing 
 before and after this has been done, we have a mea- 
 sure of a -I- 6 in the first experiment, and oi a + 2b 
 in the second ; and b being assumed to be known, a, 
 or the comparative resistance within the battery, 
 becomes known also. 
 
 The resistance of a standard copper wire a foot (844.) 
 long may be taken as the unit of resistance. Mr Standard 
 Wheatstone finds it convenient to assume a copper "^^J'^^ ^*' 
 wire a foot of which weighs 100 grains. M. Jacobi 
 prefers a metre of copper wire one millimetre in dia^ 
 meter. The resistance is as the length, and inversely 
 as the sectional area. 
 
 To measure the current two methods have chiefly (§45.) 
 been used, and the results agree closely. One is Force of 
 the tangent compass. A voltaic current is allowed *^ current 
 to pass through a thick wire arranged in a vertical 
 circle. At the centre of the circle is placed a very 
 short magnetic needle. When a current passes the 
 needle is deflected ; and it is easy to show that the 
 deflecting forces are as the tangent of the angle of 
 deflection. A double or treble force in the circuit 
 
 compass. 
 
18S 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 produces a deflection of the needle whose tangent is 
 double or treble the first. 
 (846.) The other method is by Dr Faraday's Voltameter. 
 
 Voitame- The amount of water decomposed is directly as the 
 '°'^' quantity of the current. The unit in this case is 
 
 one cubic centimetre of gas produced from water in a 
 minute. 
 (847.) These two measures agree. After being once com- 
 
 pared, we may in all cases deduce the decomposing 
 force of a current from its effect iipon a tangent com- 
 pass. 
 (848.) Mr Wheatstone has facilitated the measurement 
 
 Eheostat of voltaic effects by the invention of the rheostat, a 
 Whe t- simple contrivance for introducing any desired length 
 stone and of wire into a circuit, and thus estimating resistances 
 Jacobi. both of conductors and of batteries, and also the 
 electro-motive forces of different batteries. The re- 
 sults appear to be extremely satisfactory. (Phil. 
 Trans., 184:S.) The conducting power of different 
 metals drawn into wire will be inversely as the 
 lengths required to be introduced into the circuit to 
 reduce the strength of the current in a given pro- 
 portion. The principle of the rheostat was inde-* 
 pendently applied to similar inquiries by M. Jacobi 
 of St Petersburg, in 1840. 
 (849.) The laws of Ohm farther proceed to expound the 
 
 Farther effect of the size and number of the elementary cells 
 from Ohm's combined in a voltaic battery. The size of the plates 
 theory. increases the quantity of electricity which escapes 
 through a short conductor, but has little effect upon 
 a long current. On the other hand, the multiplica- 
 tion of elements produces no increase in the voltaic 
 stream when the connecting wire is short and when 
 it is also a good conductor, for the chief resistance 
 in the circuit is in that case the battery itself, which 
 resistance increases with the number of elements, just 
 as the force which overcomes it increases. If, on 
 the other hand, the chief resistance be extraneous to 
 the battery, the addition of more elements increases 
 the power without much increasing the resistance. 
 All this scarcely requires mathematical proof. It is 
 very evident, and very just, and it is borne out by 
 experiment, 
 f 850 ) Ohm's theory farther gives the partial effects of a 
 
 current branching into varioue unequally good con- 
 ductors, and into other details, particularly as to the 
 electric tension in different parts of a circuit. It is, 
 however, to be observed, that the whole is based on 
 the assumption that the dissipation of electricity from 
 the surface of the conductor is insensible. 
 (8.51.) It is only justice here to add, that the theory of 
 
 Fechner's Ohm owes much, if not most, of its value to the ex- 
 experi- periments of Fechner in Germany ; and that its re- 
 
 ception in France and England is mainly due to the 
 ingenious and (in many cases) independent experi- 
 ments of M. PouiUet and Mr Wheatstone. 
 
 Daniell's Constant Battery. — ^This seems the pro- (852.) 
 per place to mention an invention which has exer- ^°^° ^'^' 
 cised a remarkable influence on the progress of prac- nieli— the 
 tical electricity — I mean the Constant Battery. I constant 
 believe that the merit of this application is entirely battery. 
 due to the late Professor Daniell,i although the Ger- 
 man writers (who manifest throughout a singular 
 sensibility with regard to their national claims to 
 electrical improvements) seem to claim it for their 
 countrymen. Every battery previously constructed 
 diminished rapidly in energy from the instant of being 
 charged. This was chiefly due to two causes ; first, to 
 the acid becoming gradually charged with oxide of 
 zinc ; and, secondly, to the appearance of " nascent" 
 hydrogen arising" from the decomposition of water at 
 the copper surface where it prevented effectual con- 
 duction of the electricity. These sources of di- 
 minished effect were prevented in the following 
 way : — Instead of a single cell containing one fluid 
 moistening both the copper and the zinc, a double 
 cell was formed by means of a partition of bladder 
 or porous earthenware. The partition next the zinc 
 was filled with dilute sulphiiric acid ; the partition 
 next the copper with a solution of sulphate of cop- 
 per, also acidulated. When galvanic action proceeds, 
 both fluids are decomposed ; but whilst that in the 
 zinc cell becomes charged with oxide of zinc, it is 
 at the same time continually acidulated by the 
 electro-chemical transfer of acid from the decom- 
 position of sulphate of copper in the copper cell ; 
 and the copper set free from the same combination 
 in the form of oxide is metallically reduced by com- 
 bining with the "nascent" hydrogen (the oxygen 
 derived from the water decomposed having combined 
 with the zinc), and the metallic copper is deposited in 
 an ever fresh film on the surface of the copper plate. 
 This beautiful invention was described in 1836. 
 Many other batteries on the same principle have 
 been since contrived and described ; several are more 
 powerful, but none perhaps are so constant in their 
 action. 
 
 Application of Electricity to the Arts — MM. (853.) 
 Wheatstostb and Jacobi. — I have selected Messrs Applica- 
 Charles Wheatstone and M. H. Jacobi as the repre-*j°"j.°f .. 
 sentatives of a numerous class of ingenious men who to the arts. 
 have shown great felicity of invention in applying in- 
 genious mechanism to render electric agency available 
 in the arts. We here again find the reciprocal influ- 
 ence of art upon science, to which I have elsewhere 
 
 ^ John Frederic Daniell, Professor of Chemistry in King's College, London, was horn in 1790. He was the author of a work 
 on Chemical Philosophy, of Meteorological Usaays, and of numerous papers in the Philosophical Transactions, many of which were 
 connected with Voltaic Action. His work on Meteorology contributed materially to the progress of that science, as did the in- 
 vention of his Hygrometer (notwithstanding certain defects in that instrument) to the theory and practice of Hygrometry. For 
 his Constant Battery Mr Daniell received the Copley medal of the Royal Society, His death took place from apoplexy while 
 attending a council meeting of the Koyal Society on the 13th March 1845. 
 
Chap. VII., § 6.] ELECTRICITY.— MM. WHEATSTONE AND JACOBI. 
 
 isr 
 
 (854.) 
 
 (855.) 
 Mr Wheat- 
 stone on 
 the velo- 
 city of eleC' 
 trie con- 
 duction. 
 
 adverted (32, &c.) The Requirements of practice 
 are magnificent experiments, such as no indivi- 
 dual and no scientific Society would thinks of exe- 
 cuting for the illustration of theory. It is not in 
 the least my purpose to transfer to these two gentle- 
 men an exclusive merit which they need not be un- 
 willing to share with other energetic and able com- 
 petitors in the hard-run race of scientific applications. 
 They occupy, however, perhaps the most marked and 
 distinguished place, and the field is so wide and in- 
 cludes so many minute details, that it requires all 
 our resolution to fix our eyes steadily on the most 
 considerable acquisitions — ^the nobler sheaves of so 
 prolific a harvest. 
 
 I shall connect, then, with the name of Mr 
 Wheatstone, (1), the apparatus for determining the 
 velocity of electrical conduction, (2), the electric tele- 
 graph and clock, — with that of M. Jacobi, (3), elec- 
 trodynamic machines, and (4), the electrotype. 
 
 I. The apparatus used by Mr Wheatstone in 1834 
 for measuring the velocity of the passage of the elec- 
 trical impulse through a good insulated conductor 
 . such as a copper wire, deserves particular notice 
 from its great ingenuity, and from its general appli- 
 cation to the measurement of short intervals of time. 
 Let a copper conducting wire of half a mile long be 
 so convoluted that the middle and the two ends of 
 the wire may be brought near together, the whole 
 being perfectly insulated. Let the wire be slightly in- 
 terrupted at these three places, and the whole put 
 into connection at pleasure with an electric machine 
 or battery. When contact is made, three sparks will 
 take place. Let the two end sparks be called A and C 
 and the middle one B. As the three sparks take place 
 close to each other, they can easily be seen at once 
 reflected in a small plane mirror. Let now this small 
 mirror be put in very rapid rotation round a hori- 
 zontal axis so placed that the sparks (if they occur in 
 the suitable part of the revolution) may be reflected 
 together to the eye. Imagine the rotation to become 
 immensely rapid: — ^in Mr Wheatstone's apparatus 
 the velocity reached 800 times in a second ; conse- 
 quently the mirror described 1° in eooxaw ^^ P^'^ of a 
 second; i. e., in ■n^s^iss ^^ ^ second. But for 1° of 
 rotation of a mirror the reflected image will describe 
 an arc of 2°. Supposing then that all the sparks occur 
 at the same absolute instant of time, they wiU be 
 seen in one line (supposing the points of the inter- 
 rupted circuit in a line), but if either spark occur 
 later than the others by only tsssI^tts °f * second, 
 the mirror will have revolved so much in the interval 
 as to displace the image of that spark relatively to 
 the others by the very palpable angular amount of 
 2°. In the copper wire half a mile long, the end 
 sparks occurred simultaneously, whilst the middle 
 spark occurred later by about one millionth of a 
 second ; giving a velocity of transmission (according 
 
 to Mr W.) of 288,000 miles a second, or somewhat 
 greater than that of light.^ The velocity in an iron 
 telegraph-wire, ascertained lately in America with 
 much greater accuracy, and by a different method, is 
 only 1 6,000 English miles a second ; but doubts have 
 been thrown upon the correct interpretation of these 
 experiments. Those of M. Fizeau on the telegraphic 
 lines of France give results more conformable to 
 Mr Wheatstone's, namely, about 70,000 English 
 miles per second for iron, and 120,000 for copper 
 wire. The duration of a spark drawn immediately 
 from the battery is insensible, but in Mr Wheatstone's 
 experiment it lasted ^-^^^sj, of a second when trans- 
 mitted by a copper wire half a mile long. 
 
 II. Electric Telegraph and Clocks. — The idea of (856.) 
 using the transmission of electricity to communicate f'®"*"". 
 signals is so obvious as hardly to deserve the name _itg e^iy 
 of an invention, the prodigious velocity of common history, 
 electricity in wires having been established by Watson 
 before the middle of the last century. The earliest 
 proposal of the kind appears in the Soots Magazine 
 for February 1753, where a correspondent from Ren- 
 frew, who signs himself C. M., proposes several kinds 
 of, telegraphs acting by the attractive power of electri- 
 city, conveyed by a series of parallel wires correspond- 
 ing in number to the letters of the alphabet, and in- 
 sulated by supports of glass or jeweller's cement at 
 every twenty yards. Words are to be spelt by the 
 electricity attracting letters, or by striking bells cor- 
 responding to letters. One Lesage, in 1782, and even 
 long before, proposed to convey twenty-four insulated 
 wires in a subterranean tube, and to indicate the letters 
 of the alphabet by means of the attraction of light 
 bodies. In 1811 Sommering suggested a similar ap- 
 plication of voltaic electricity, chemical decomposition 
 being the effect observed. Oersted first, and then Am- 
 pere (1820) suggested the use of magnetic deflections 
 for the same purpose, which is nothing else than the 
 needle telegraph in general use in England ; but they 
 contented themselves with the suggestion merely. 
 MM. Gauss and Weber communicated signals at 
 GiJttingen in 1833 or 1834 to a considerable dis- 
 tance, and gave them the signification of letters. 
 This was the first accomplishment of telegraphic com- 
 munication by means of electricity, and it realized 
 the fancy of Strada, quoted by Addison, of sym- 
 pathetic magnets. It was, however, a mere appen- 
 dage to a magnetic observatory, and its application 
 and diffusion on a great scale seems to have required 
 a distinct effort ; for several years elapsed before we 
 hear more of the telegrapli. 
 
 The year 1837 is the date of the realized electric (857.) 
 telegraph. We find three distinct claimants, of whose Telegraphs 
 independent merits there is no reason whatever to^^j.^^' 
 doubt, though how much of the merit of all must besteinh'eil, 
 considered due to MM. Gauss and Weber, who first and Wheat. 
 made the experiment, though they did not offer it'*""*- 
 
 I The numerical value is of course only a very rude estimation. 
 2b 
 
J 
 
 188 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 for general adoption in a convenient form, is a matter 
 which we need not here decide. The three indepen- 
 dent inventors (I name them alphahetically) are Mr 
 Morse of the United States, M. Steinheil of Munich, 
 and Mr Wheatstone of London. The telegraph of 
 the two last resembles in principle Oersted's and 
 Gauss's ; that of the first is entirely original, and con- 
 sists in making a ribbon of paper move by clockwork, 
 whilst interrupted marks are impressed upon it by 
 a pen or stamp of some kind brought in contact with 
 the ribbon by the attraction of a temporary magnet, 
 which is excited by the circulation of the telegraphic 
 current of electricity. In the telegraphs of MM. 
 Wheatstone and Steinheil the needle moves only to 
 the right or left ; and by the combination of a certain 
 number of right and left motions, either with one or 
 with two independent needles acted on at once by 
 distinct currents, the alphabet is easily, though some- 
 what tediously constructed. Such, however, is the 
 dexterity which practice gives, that forty or even 
 ■more of such complex signals are transmitted and 
 registered per minute.^ 
 
 (858.) It has already been said that we claim the exclu- 
 sive invention of the electric telegraph for no one in- 
 dividual. But of the several inventors none pro- 
 bably has shown such perseverance and skill in over- 
 coming diiEculties as Mr Wheatstone.^ His telegraph 
 accordingly was in general use in England before M. 
 Steinheil was able to obtain a similar success in 
 Germany. The telegraphs of Mr Morse are naturally 
 preferred in America, and they have this inestimable 
 advantage, that they preserve a permanent record of 
 the despatches which they convey. 
 
 (859.) There is one circumstance connected with the elee- 
 
 The earth- ^.pjg telegraph deserving of particular notice — I mean 
 the apparently infinite conducting power of the earth 
 when made to act as the vehicle of the return current. 
 Setting aU theory aside, it is an unquestionable fact, 
 that if a telegraphic communication be made, sup- 
 pose from London to Brighton, by means of a wire 
 going thither, passing through a galvanometer, and 
 then returning, the force of the current shown by 
 the galvanometer at Brighton will he almost ex- 
 actly doubled, if, instead of the return wire, we 
 establish a good communication between the end of 
 the conducting wire and the mass of the earth at 
 Brighton. The whole resistance of the return wire 
 is at once dispensed with ! This fact was more than 
 suspected by the ingenious M. Steinheil in 1838 ; 
 but, from some cause or other, it obtained little 
 publicity ; nor does the author appear to have ex- 
 erted himself to remove the reasonable prejudices 
 
 circuit. 
 
 with which so singular a paradox was naturally re- 
 ceived. A most ingenious artist, Mr Bain, estab- 
 lished for himself the principle, and proclaimed its 
 application ' somewhat later; and in 1843, perhaps- 
 the first entirely convincing experiments were made 
 by M, Matteucci at Pisa. From this time the double 
 wire required to move the needle telegraph was 
 reduced to a single one. The explanation of this 
 curious fact appears to be, — ^not that the electricity 
 is conducted back by the earth to its origin at the 
 battery, — ^but that the molecular disturbance po- 
 larly communicated along the conducting vrire to its 
 farther end being effectually relieved by perfect com- 
 munication with a vast reservoir of neutral electri- 
 city like the earth, conduction proceeds in an unin- 
 terrupted manner, and to an unlimited extent. 
 
 Of submarine telegraphs, it is sufficient to state (860.) 
 that the isolation is obtained by inserting the con- Submarine 
 ducting wires in a mass of gutta percha, and that ^ "^'^^ ' 
 the first on a considerable scale was sunk between 
 Dover and Cape Gris Nez, on the French coast, in 
 August 1851. 
 
 The applications of electricity to the measurement (861.) 
 of time are so numerous, that I can only refer ge- 
 nerally to the principal contrivances. 
 
 1. The simple electric clock of Mr Bain derives its (862.) 
 maintaining power from two large plates of copper ^'^'1'"° 
 and zinc (or more simply zinc and charcoal) sunk in 
 
 the earth, which affords for a very long time a con- 
 tinuous supply of voltaic electricity. The current is 
 conveyed into the bob of the pendulum, where it 
 traverses a long coil of wire ; and as the pendulum 
 oscillates, the current (by a simple shifting contriv- 
 ance) is reversed at each vibration. A stationary 
 bar-magnet is placed so that when the pendulum 
 moves, the voltaic coil of the bob embraces the mag- 
 net, and the direction of the current is such as by 
 the electro-magnetic reaction to strengthen and main- 
 tain the vibratory movement, which is by this means 
 perpetuated. 
 
 2. Sympathetic clocks By means similar to those (863.) 
 
 just explained, one standard clock anyhow regulated Sympathe- 
 may, by means of magneto-electric currents, convey *'° "'<"='''• 
 absolutely isochronous movements to any number of 
 afiiliated clocks at any distance. Probably the first 
 application of the kind was made by M. Steinheil. 
 
 3. American electric-registration clocks. — .Mr (864.) 
 Locke proposed to register the instant of an event American 
 occurring in the following way : A ribbon of ^gg'i^jj,^ 
 paper being put in imiform motion, as in Morse's tion clocks, 
 telegraph, a dot is imprinted on it every second by 
 
 ^ Occiisionally 18 or 20 worda per minute have been telegraphed. 
 
 ^ I ought to mention that the practical introduction of the electric telegraph in England is in no small degree due to the 
 energy of Mr Fothergill Cooke, joint patentee with Mr Wheatstone for the invention. The question of the respective shares of 
 these gentlemen in the merit of telegraphic communication was submitted, in 1841, to the arbitration of Sir Marc Brunei and 
 the late Mr Daniell, the result of which appears to leave the preponderance of merit in some respects ambiguous j neverthe- 
 less, in a history of Science, Mr Wheatstone is clearly entitled to the pre-eminent place. Several pamphlets have also been sub- 
 sequently published by the parties. It is significant that Mr Cooke admits having borrowed his idea from becoming acquainted, 
 at Heidelberg, in March 1836, with Gauss's experiments. 
 
Chap. VII., § 7.] 
 
 ELECTRICITY. — M. JACOBI — CAVENDISH. 
 
 189 
 
 means of a simple connection with an astronomical 
 clock. A separate marking apparatus under the con- 
 trol of the experimenter enables him to interpolate a 
 dot or mark corresponding to the instant of any 
 event happening — such, for instance, as the transit of 
 a star. This method has the great advantage of 
 leaving the observer at entire liberty to watch the 
 object without having to attend to the beats of the 
 clock, whilst it renders mistakes next to impossible. 
 It has been successfully applied to the determination 
 of longitudes, and more recently to all kinds of astro- 
 nomical observations, by Mr Bond in America, and 
 by Mr Airy at Greenwich (231). 
 (865.) 4; Chronoscopes, or instruments for the measure- 
 Chrono- uJg^^. ^f excessively short intervals of time, such as 
 the flight of military projectiles, and even the trans- 
 mission of sensation and motion along nervous 
 fibres.- — Such instruments have been constructed on 
 a great variety of principles. Those of M. Pouillet, 
 Mr Wheatstone, and Mr Siemens, deserve especial 
 mention. 
 (866.) III. Of electro-magnetism used as a moving 
 
 Electro- power, we need say little. No one can witness the 
 magnetism astonishing experiment of the sudden creation of 
 
 as a prime . ° ^ „ . 
 
 mover. magnetic power sufhcient to sustam one or two tons 
 by the voltaic dissolution of a few grains of zinc, 
 without having the idea suggested of a continuous 
 moving force; This enormous power is, however, 
 exerted through a space so excessively minute, that 
 its dynamical effect is always small ; and, though it 
 is, of course, possible to produce an engine by a 
 sufficiently gigantic arrangement, the success has 
 hitherto not been encouraging. 
 (867.) The rotations of Mr Faraday and Dr Eitchie were 
 
 electro-dynamic machines on a small scale. They M. Jacobi's 
 were (probably) first mechanically applied by M. dal ™a<!^i"es. 
 Negro in 1833, but more systematically by Mr. M. H. 
 Jacobi, of St Petersburg, the following year. It is 
 stated that the latter gentleman moved a boat on the 
 Neva with an electro-dynamic motor equivalent to 
 three-fourths of a horse power. He has also inves- 
 tigated the theory of these machines, and the most 
 advantageous circumstances of their employment. 
 The principle is the alternate attraction and repul- 
 sion of two temporary magnets (one of which re- 
 volves), the current of electricity being suddenly 
 changed at the critical part of the revolution. 
 
 IV. To M. Jacobi — almost simultaneously with Mr (868.) 
 Spencer of Liverpool — we are also indebted for one Electro- 
 of the simplest and most elegant applications of elec- voltatype • 
 tricity, the Galvano-plastic art, or Voltatype. In— MM. Ja-' 
 this, advantage is taken of the perfectly metallic state ^oti and 
 in which the base of a metallic salt is deposited at Spencer, 
 the negative pole of a voltaic combination. In the 
 case, for example, of the decomposition of sulphate 
 of copper, the sulphuric acid unites with the positive 
 wire, or remains suspended, while the metallic cop- 
 per is slowly and homogeneously deposited on the 
 surface of any object (rendered conducting by the 
 application of black lead or otherwise), of which it 
 forms a perfect mould, from which a fresh cast or 
 fao-simile in metal of the original object may be ob- 
 tained by a repetition of the process. To see the 
 veins of a leaf, or the delicate wing of an insect, thus 
 metallized, is certainly an astonishing thing ; and 
 the applications to the useful arts are far too nume- 
 rous to be noticed here. Daniell's invention of the 
 Constant Battery evidently suggested the Voltatype. 
 
 7. Cavendish — Coulomb — Eayperimental Laws of the Distribution of Statical Electricity; — 
 Mathematical Theory of the same. — Poisson — Mathematical Theory of Statical Electricity 
 and of Magnetism generalized. Green ; Professor William Thomson. 
 
 (869.) 
 Statical 
 theory of 
 Electricity, 
 
 (870.) 
 .Spinas, 
 Cavendish, 
 and Cou- 
 lomb. 
 
 Having thus brought down the history of'galvanic 
 or voltaic electricity, and that of the wonderful dis- 
 coveries connected with it, to our own time, I shall 
 in this section briefly notice the more intermitting 
 progress during the same period of our knowledge 
 of the quantitative laws which regulate the distribu- 
 tion of statical electricity on bodies charged with it. 
 
 " .fflpinus and Coulomb," says Dr WheweU,^ " were 
 two of the most eminent physical philosophers of 
 the last century." They laid the foundations of an 
 exact science of statical electricity ; and a third, and 
 still more eminent name, deserves to be connected 
 with theirs, — ^that of Cavendish, of whose general 
 labours I have already given some account in the 
 Second section of the chapter on Heat. The labours 
 of .SIpinus belong rather to the period embraced in 
 the previous Dissertation, where they have been re- 
 ferred to by Sir John Leslie. 
 
 Perhaps the most elaborate of the memoirs not ,^1 -. 
 strictly chemical which Cavendish published werecaven- 
 those on electricity. The Franklinian hypothesis of tlisb's 
 a single fluid in excess or in defect of its average '°^'"^y^and 
 state producing the phenomena then known as elec- ments. 
 trical, offered a tempting field to an experimental 
 philosopher well trained in the mathematical know- 
 ledge of the day ; and his paper on this subject shows 
 extreme care in its conception and execution. He 
 assumes, as a matter of necessity, the repulsion of 
 matter for matter at sensible distances, considered 
 apart from the electricity always combined with it in 
 greater or less quantity. The indifference of matter 
 under ordinary circumstances is held to arise from 
 the union with it of a sufiicient amount of electricity 
 to neutralize the repulsion of the matter. In short, 
 the electric fluid is considered as a second kind of 
 matter repelling its own particles, and attracting those 
 
 ^ History of the Inductive Sciences, vol. iti., p. 34, 2d edition. 
 
190 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 OaTen- of other matter with a force varying inversely as some 
 electrical ^®*® power of the distance than the cube. Common 
 theory and Blatter repels its own particles and attracts electric 
 experi- particles according to the same law. The limitation 
 '"*''**• as to a power below the inverse cube of the distance 
 is necessary, since were the decrease of force more 
 rapid, a particle would not be sensibly affected by the 
 repulsion of any portion of the fluid except what was 
 placed close to it. The hypothesis of Cavendish and 
 his mode of reasoning from it were in general the 
 same as those of ^pinus ; but Caveiidish was not 
 aware of the researches of the Swedish philosopher 
 until his own memoir was completed. The number 
 of facts accurately ascertained concerning electricity 
 was at that time too small to admit of very precise 
 numerical comparisons, but the ordinary cases of at- 
 traction, repulsion, and induction, were perspicuously 
 explained by the theory ; and had the inverse square 
 of the distance been assumed (as it very safely might 
 have been) to represent the law of diminishing re- 
 pulsion, several of the theorems would have as- 
 sumed a much more definite character, as was 
 shown by Robison. Cavendish first demonstrated 
 in his paper of 1771 that electricity must be 
 confined close to the surface of a spherical body. 
 This memoir also includes a correct theory of 
 the Leyden phial, a just approximation to the law 
 of attraction as the inverse square of the distance, 
 a theory of conduction, and of the distribution of 
 electricity on insulated conductors placed at a dis- 
 tance but connected by a fine wire or electric canal ; 
 and it was only the prelude to other researches never 
 published, but of which some remarkable fragments 
 exist amongst his manuscripts. Professor William 
 Thomson, who has partly examined these, informs 
 me that they contain the experimental solution of 
 problems such as the following i " To compare the 
 quantities of electricity on a spherical conductor, 
 and a plane disk of equal diameter connected by a 
 long conducting wire." Cavendish found that the 
 sphere holds 1-57 times the electricity of the plate, 
 a result exactly coincident with the deductions of 
 theory. 
 (872.) I may here (for the sake of biographical connection) 
 
 He makes mention Cavendish's paper on the Torpedo, as a re- 
 fieial markable instance of the explanation of an obscure 
 
 torpedo, natural phenomenon, by the analogous efiects of an 
 artificial imitation. The experiments of Walsh on the 
 Electrical Pishes have been cited in the preceding Dis- 
 sertation. Cavendish undertook the bold task of prov- 
 ing, that all the external effects of the shock under 
 varied circumstances, might be reproduced by a com- 
 bination of Leyden jars duly protected. He made an 
 artificial torpedo, consisting of 49 jars in a frame 
 
 covered with leather, and he succeeded in obtaining 
 shocks in air as in water, exactly comparable to those 
 obtained from the live fish by Walsh. But perhaps the 
 most striking part of the paper is the incidental men- 
 tion of several laws of electricity then certainly new, and 
 which he had deduced from experiment. Thus, he af- 
 firms the conducting power of iron for electricity to 
 exceed 400,000 times that of distilled water, which he 
 states to be equivalent to the fact, that a conductor of 
 equal diameter will transmit as much electricity if the 
 iron be 400,000 times longer than the water — a law 
 conformable to that of Ohm. He farther estimates 
 the conducting power of sea-water at 100 times, but 
 of saturated brine at 720 times that of pure water. 
 Again, the quantity of electricity required to raise the 
 charge on different jars or plates to the same inten- 
 sity he finds to be directly as the area of the coating, 
 and inversely as the thickness of the plate, and he 
 applies this just conclusion with great ingenuity toi 
 explain the surprising power of the torpedo's shock 
 by the extreme fineness of the membranes separating 
 the columns of the electrical organs. 
 
 Coulomb (born 1736, died 1806*) was a person of (873.) 
 less genius and less mathematical attainment than Coulomb's 
 Cavendish, yet he had very considerable geometrical ^^nl-n. ' 
 ability and much facility in applying it to the results men ts. 
 of experiments, which he conducted with the greatest 
 ingenuity and accuracy. In the latter respect he has 
 seldom been surpassed. His methods, and even his 
 numbers, are still, after a lapse of more than half a 
 century, in many cases the best we can quote. 
 Like Cavendish, he was devoted to quantitative esti- 
 mations of phenomena. 
 
 His two greatest inventions were the balance of (874-) 
 torsion and the proof plane. In the course of his J^n^g "f 
 strictly mechanical researches (which, as we have torsion 
 seen in the chapter on Mechanics, Art. 339, &c., were and the 
 numerous and important) he ascertained the laws of Pf™^ 
 torsion. Within the limits of perfect elasticity, he 
 found that the force is as the angle of torsion of the 
 wire or fibre, and inversely as its length. An almost 
 indefinite minuteness may thus be attained in the mea- 
 sure of forces which maybe balanced by the elastic tor- 
 sion of a wire. We have seen (Astronomy, § 1, Art. 
 156) how it was applied by Michell and Cavendish to 
 measure the gravitation of bodies. Coulomb's inven- 
 tion dates at least from 1784, By means of it he 
 established (in a different and perhaps more satisfac- 
 tory way than had been done by Robison in 1769) that 
 the electric and magnetic forces vary according to the 
 Newtonian law;' and with the aid of the "proof 
 plane" he obtained exact measures of the electric 
 tension on any part of an excited body. The " proof 
 plane" consists of a small gilt disk with an insulat- 
 
 ' For a farther account of Coulomb, see the chapter on Mechanics, § 2. 
 
 " Besides this law, Coulomb experimentally proved two others of great importance : — 1. That the electricity of an elec- 
 trified conductor resides wholly on its surface. 2. That the interior of such a conductor is in a condition absolutely undisturbed 
 by the presence of other external excited bodies. 
 
Chap. VII., § 7.] 
 
 ELECTRICITY. — COULOMB — ^POISSON — GREEN. 
 
 191 
 
 ing handle, which being applied flaUwise to the sur- 
 face of an excited body takes off a portion of electri- 
 city, which is found in all cases to be proportioned 
 to the electric excitement of the part which it had 
 touched ; being then presented to the torsion balance 
 properly electriHed, it shows by the repulsive effect 
 produced, the relative tension of the part of the 
 body whence the sample was obtained, 
 ^^^t "^ ^^ *1"S manner Coulomb determined the distribu- 
 
 tion of electricity upon electrified spheres at and after 
 contact with one another ; — on spheres inductively 
 electrified, — on rods and plates and other figures; and 
 his results, so far as they have been compared with 
 theory, give evidence of the care and skill with which 
 they were obtained, allowance being in all cases made 
 for the loss of electricity by imperfect insulation. He 
 also laboured with praiseworthy diligence to compare 
 his results with the theory which he adopted of two 
 fluids, each attracting the particles of the other and 
 repelling their own according to the Newtonian law. 
 The ^pinian theory admits of only one fluid, but as it 
 assumes a repulsion between the elementary particles 
 matter it cannot be said to gain much in simplicity, 
 whilst the mathematical results of either hypothesis 
 are in general .the same. M. Mosotti has endea- 
 voured recently to revive the view of Franklin and 
 of ^pinus, so as to include, after the manner of 
 Boscovich, the entire mechanical properties of 
 matter. 
 (876.) The doctrine of attractions is a complex and difii- 
 
 Theory of p^j^ qj^q gygjj .yrhen the distribution of the attracting 
 attractions matter, as well as the fundamental law of attraction, 
 and repul- is known. But it becomes much more so when the 
 Bions. distribution of the attracting matter is itself the 
 result of the very effect which it is the object 
 of the problem to discover. If two homogeneous 
 spheres attract one another, molecule to molecule, by 
 the law of gravity, the problem is easy, provided the 
 matter be rigid, and the distribution of it therefore 
 unchanged ; but if two such spheres be charged with 
 the mobile electric fluid (using the term as a mere 
 abbreviation), the case is very different, for now the 
 electricity tends to shun the nearest points of each 
 sphere, and to accumulate itself towards the remoter 
 parts of their surfaces. The distribution of the 
 electricity, and also the repulsive effect at any point, 
 are both to be found simultaneously. The calcula- 
 tions of Coulomb were inadequate (as has been said) 
 to such a solution ; he contented himself with comput- 
 ing the effect of certain simple distributions which evi- 
 dently lay on opposite sides of the truth, and com- 
 paring them with the result of experiment. Though 
 any one such comparison might avail little, the 
 cumulative evidence of many imperfect comparisons 
 argued favourably for the truth of the hypothesis. 
 (877.) -A-t the very time that Coulomb was pursuing this 
 
 Its prin- inquiry, Legendre first, and then Laplace, were in- 
 ciplesde- venting and improving those subtle and powerful 
 Codomb''^ mathematical methods at which we have glanced in 
 
 the chapter on Physical Astronomy, Art. 99, &c., Laplace, 
 for estimating attractions by a general method. Le- *"'* ^°^^' 
 gendre's principles of calculation applied to cases of °° ' 
 the symmetrical distribution of the attractive sub- 
 stances, but Laplace escaped this restriction. The 
 problem is reduced to finding a quantity usually de- 
 noted by the letter V, called by some writers the 
 potential, for the given body or surface, the expression Potential. 
 for which may in each case be expanded into a series, 
 the co-efiicients of the terms of which (known as 
 Laplace's co-efficients) are connected by certain rela- 
 tions which are evolved from the conditions of the 
 problem. It was M. Biot first of all, but principally 
 Poisson, who dpplied this method to electrical, and 
 subsequently to magnetical phenomena. Poisson, 
 with great labour, succeeded in representing correctly 
 by analysis the conditions of some of Coulomb's ex- 
 periments on spheres and ellipsoids. But it jnust 
 be owned that the complication of the analysis, the 
 difficulty of applying it to any but the very simplest 
 cases, and the considerable latitude of the errors of 
 experiment, rendered the results rather analytical 
 exercises than solid bases for physical induction ; 
 which may in some degree account for the manner 
 in which Sir John Leslie mentions them in his Dis- 
 sertation. Poisson (as I have elsewhere remarked) 
 had not the talent of conducting his mathematics in 
 a fertile direction, and usually left the fields of ex- 
 perimental physics on which he touched nearly as 
 barren as he found them. But this is no rea- 
 son why other mathematical reasoners may not 
 obtain more pregnant results. We shall see in the 
 next section that Gauss, a distinguished contempo- 
 rary of Poisson, by treating the great problem 
 of the distribution of the magnetism of the globe 
 (in many respects similar to those of the theory 
 of electricity) with the utmost mathematical gene- 
 rality, has obtained results of great novelty and 
 importance ; that he has not only shown experi- 
 menters how to proceed, but has invented instru- 
 ments for them to use. A similar step has not yet 
 been taken in electricity. Notwithstanding the un- , 
 questionable beauty of Sir William Harris's methods 
 of measuring electrical attractions (Pfe7. Trans. 
 1834), they are little adapted for comparison with 
 theory, and Coulomb's experiments still remain the 
 standard ones on the subject. 
 
 The theory of Coulomb has, however, been ably ge- (878.) 
 neralized by Green, a nearly self-taught mathemati- Writings 
 cian of great originality, who died at a premature age. °^ ^"^^^^ 
 In a memoir on electricity privately printed about profeBsor 
 1830 he generalized Poisson's methods and ap-W.Thom- 
 plied them to a number of new cases. His paper ^™* 
 was reprinted a few years since in Crelle's Journal. 
 To him I believe is due the term potential. Several 
 continental mathematicians of eminence have added 
 some steps to the theory of electricity, but probably 
 the most important from its fertility and simplicity 
 is a theorem discovered by Professor William Thorn- 
 
192 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 Electrical 
 images. 
 
 (879.) 
 Applica- 
 tion of the 
 theory of 
 magnet- 
 ism to 
 correct 
 ships' 
 compasses. 
 MM. Bar- 
 low and 
 Airy. 
 
 son of Glasgow, for reducing tte electrical effects of 
 electrified spheres upon points or other spheres with- 
 out them to those of electrified points in certain po- 
 sitions replacing the spheres, which points, from 
 certain analogies to well known optical formulae, 
 Professor Thomson has designated electrical images,^ 
 The mathematical theory of magnetism has re- 
 ceived a highly practical application in the correction 
 of the deviation of compass due to the local attrac- 
 tion of ships. Professor Barlow of Woolwich led the 
 way in attempting practically to correct the errors 
 thence arising. But when ships began to be con- 
 structed almost entirely of iron, the use of his " cor- 
 recting plate" was found to be totally insuificient. 
 To the Eev. Dr Scoresby, practical navigation is 
 indebted for many ingenious observations on the 
 magnetism of ships, and suggestions as to the means 
 
 of allowing for it ; while Mr Airy and Mr Archibald 
 Smith have the merit of applying the Theory of 
 Magnetism to the case in question. Mr Airy's in- 
 vestigations may be found in the Philosophical 
 Transactions for 1839 and 1855; from which it 
 appears that the effects of local magnetism in a ves- 
 sel may be speedily and effectually corrected for a 
 given place by the use of two permanent magnets 
 placed in rectangular positions relatively to the com- 
 pass ; and by the use of a mass of soft iron in a third 
 direction. But grave doubts still remain as to the 
 possibility of rendering such corrections permanent, 
 and applicable in all magnetic latitudes. A great 
 step has, however, been gained by putting the power 
 of readily verifying the compass corrections in any 
 part of the world in the hands of every intelligent 
 captain. 
 
 § 8. Professor Hansteen — Baron A. von Humboldt — Gauss — Major-General Sabine — Captain 
 Sir J. C. Eoss. — Progress of our Knowledge of Terrestrial Magnetism in the present Century. 
 
 (880,) 
 Recent 
 history of 
 terrestrial 
 magnet- 
 
 (881.) 
 Professor 
 Hansteen 
 — Magne- 
 tismus der 
 Erde. 
 
 Variation 
 or decli- 
 nation. 
 
 I could hardly have intentionally selected a more 
 characteristic example of the scientific progress of 
 the nineteenth century than the recent history of 
 terrestrial magnetism, even had it not accidentally 
 formed the closing section of this Dissertation. . The 
 combination of extended methodical research in ob- 
 taining physical data, with mathematical skill in 
 comparing them and in deducing from them the 
 most important results, has been attended with 
 merited success. I regret that the unforeseen extent 
 of this historical sketch compels me to touch with 
 great brevity on the leading points of this research. 
 
 Professor Chkistophee Hansteen, of Christiania, 
 in Norway, is the person who has given pro-- 
 bably the greatest impulse in recent times to 
 the efforts to methodize the facts and laws of 
 the earth's magnetism. M. Hansteen was born 
 26th September 1784, and is Professor of Astro- 
 nomy in the University of Christiania, and Direc- 
 tor of the Observatory. His dissertation, entitled 
 Magnetismus der Erde, published in 1819, which 
 received a prize from the Royal Danish Academy, 
 recapitulated all the authentic facts obtained by 
 voyagers and others from the earliest times. It 
 will be recollected^ that Halley had represented 
 the magnetic variation at different parts of the 
 globe by lines traced on Mercator's chart, and 
 passing through all places where the variation 
 (or declination) of the needle from the true north 
 was equal ; and being well aware of the progressive 
 (or secular) changes in the course of these lines, he 
 
 proposed the hypothesis of two pairs of magnetic 
 poles interior to the globe, of which one pair re- 
 volves slowly. 
 
 This hypothesis, little thought of at the time, (882.) 
 and perhaps of little value except as a help towards Halley's 
 the formal representation of the facts, appears to ^yppt^^^is. 
 have been revived by Wilcke, a Swede, whose la- charts, 
 hours attracted the attention of Professor Hansteen 
 first in 1807. M. Hansteen found the results of his 
 own collections to coincide well with Halley's chart 
 for 1700, and also with the hypothesis of four poles, 
 two in each hemisphere, one stronger than the other. 
 It results from these charts that the Line of No Fa- Line of No 
 riation, which, in 1600, formed a remarkable arch- Variation, 
 like curve, stretching from the Gulf of Mexico to 
 near the North Cape of Norway, then descending 
 through Central Europe to the Gulf of Guinea, had, 
 during the seventeenth and eighteenth centuries, be- 
 come gradually flattened (having passed through 
 Paris in 1669, and through London twelve years 
 earlier), and at present this part of the Hue of No 
 Variation is confined to the American continent and 
 neighbouring seas. Another and more complicated 
 branch of the same line traverses the Pacific Ocean, 
 making a complex serpentine track through East- 
 ern Asia and Siberia. The line of No Variation 
 may be expected to pass through those points of the 
 earth's surface towards which the needle converges, 
 which are sometimes called the magnetic poles (of 
 which more presently), and of which M. Hansteen 
 concludes the position to be as follows :' — 
 
 1 Cambridge MathematicalJournal, 1850. 
 
 2 See Fifth Dissertation, p. 741. 
 
 3 Prom M. Hansteen's recent paper on the Secular Change of the Dip (Copenhagen, 1855). In this ingenious meinoir it is in- 
 ferred, with considerable plausibility, that the annual diminution of the dip is decreaaing, and consequently that a minimum ot 
 dip will occur in Europe before the close of this century. 
 
Position of 
 magnetic 
 centres or 
 poles. 
 
 (883.) 
 Lines of 
 dip. 
 
 (884.) 
 North 
 American 
 pole. 
 
 (885.) 
 Magnetic 
 intensity. 
 
 Chap. VIL, § 8.] ELECTRICITY ^MAGNETISM).— M. HANSTEEN. 193 
 
 Dist.ftom Long. E. from Annual Variation 
 
 Pole of Earth. Greenwich. ' in E. Longitnde. 
 
 jy,or strongest nortliern pole (N. America), for 1838 25° 22' 280° 19' + 15''5 
 
 », or weakest nortliern pole (Siberia), for 1829 7 57 114 33 + 43 ■4-0''153(«_1608)* 
 
 8, or strongest southern pole (S. from Australia), for 1845... 21 9 131 28 — 4 -0 
 
 s, or weakest southern pole (S. from Tierra del Fuego), for 1842. 13 53 216 26 — 16 -5 
 
 * t denotes the current year. This result appears very uncertain. It gives about + 6' '6 of annual change at the present time. 
 The latitudes of these "points of convergence" are also varying. 
 
 Variation maps of a different kind have been con- towards the middle of the last century ; but the ex- 
 structed by the French Admiral Duperrey, in which ploration of its variation on the earth's surface was 
 the actual direction of the needle is represented by first attempted by the officers of Laperouse in 1785, 
 arrows. The above positions of the magnetic poles and later by De Rossel. But it was Baron Hum- 
 were deduced by Mr Hansteen from the apparent boldt who, at the instigation of Borda.i undertook 
 convergenoy of the magnetic needle towards those the earliest observations which have had any perma- 
 four points. The earlier observations appear to be nent influence on this branch of science, and who in 
 more precise than might have been expected. the first years of this century determined the rela- Baron 
 
 Professor Hansteen also constructed charts of the tive intensity of the earth's magnetism at Paris and Hum- 
 lines of equal dip. In certain positions between the at the magnetic equator in South America, to be in toldt's 
 tropics the dip is nothing, or the freely suspended the ratio of 1-3482 to 1-0000 ; « a result which has '"'''■ 
 magnetic needle remains horizontal. The line con- become, so to speak, classical, and which the author 
 necting these places is called the magnetic equator, considered as the most important result of his jour- 
 It is an undulating line inclined somewhere near 12° ney.^ M. Hansteen promoted the same enquiry ex- 
 or 13 to the terrestrial equator, and cutting it in tensively ; he devised a neat and convenient apparatus 
 two points not exactly opposite, but in about 3° 20' for counting the oscillations of the needles, and he 
 and 174° 30' of east longitude from Paris, according investigated the effects of time and temperature in 
 to Admiral Duperre/s observations in 1825. The altering their magnetism.* He made numerous ob- 
 position of these nodes is, however, variable. The servations in the north of Europe, and finally under- 
 north end of the needle (as is well known) dips took, between 1828 and 1830 (by the liberality of 
 more and more in the northern hemisphere, until the Norwegian parliament or Storthing), an adven- 
 in a certain place it becomes vertical, where there- turous journey into Siberia, for the purpose of exa^ 
 fore the horizontal component of the magnetic mining the " region of convergence" of the needle in 
 force is nothing, and the common compass loses that quarter. His account of his journey has mostM. Erman. 
 altogether its directive power. Similar phenomena unfortunately not been published; but his compa- 
 occur in the southern hemisphere. Lines of dip nion. Professor Adolphe Erman, has given the main 
 of 10°, 20°, &c., may be drawn, and where the dip results, together with extensive observations entirely 
 is 90° iAere is a true magnetic pole. The best obser- his own.® This was the first magnetical expedition 
 vations seem to show that there is but one such true of any magnitude, and of a national character. It 
 pole in each hemisphere. yields in importance to none which have succeed- 
 
 If we define as " pole" a spot where the needle ed it. 
 points vertically (which is ,the signification adopted The magnetic intensity then increases from the (886.) 
 
 by Gauss and others), these points do not coin- neighbourhood of the equator towards the Arctic Distribu- 
 
 cide with those of greatest intensity. On the 1st Regions, and there it has two foci of greatest inten-*^™°^ 
 
 Jime 1831 j Commander Eoss (now Sir James sity. A similar arrangement occurs in the southern '°*^°^^'^' 
 
 Clark Eoss) attained the true magnetic pole in the hemisphere, and these four points of maximum at- 
 
 North American continent in lat. 70° 5' 17" N., and traction or convergence of the needle constitute the 
 
 long. 96° 45' 48" W. The dip of the needle was " poles" of Halley and of M. Hansteen. To M. 
 
 sensibly 90°. Hansteen we are indebted for the first good ap- 
 
 A third element not less important than Variation proximation to a general chart of the lines of equal 
 
 and Dip, though more lately brought into notice, is intensity. 
 
 thelntensityoftheearth'smagnetism, andto thisPro- The supposed diminution of the magnetic inten- (887.) 
 
 fessor Hansteen directed special attention. That the sity as we recede from the earth's surface has been^'™''"*- 
 
 intensity of the earth's directive force may be mea- repeatedly made the subject of experiment. The *^°" °^.. 
 
 sured by counting the oscillations of a suspended insulated experiments of Gay-Lussac in a balloon intensity 
 
 magnet in the same way that a pendulum measures (630), and of M. Kupffer at Mont Elbroutz, led to with 
 
 gravity was known to Graham, Lambert, and others, no conclusive result. Prom a numerous series of'^^'S'i*- 
 
 ^ See Koimos, vol. i., note 169. 
 
 ^ On the same scale the intensity at London is 1-3720. 
 
 * lie Mutationibus YirgtB Magneticae, 1842. 
 
 * See his Lines of Equal Variation, reproduced in the Eoyal Society's " Beport on Physics and Meteorology, 1840." 
 
 ^ See Kosmos, ubi. sup. 
 
194 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI, 
 
 . 3.) 
 Variations 
 of mag- 
 netic ele- 
 ments. 
 
 — 1. Secu- 
 lar. 
 
 (889.) 
 — 2. Diur- 
 nal. 
 
 (890.) 
 —3. Irre- 
 gular. 
 
 careful observations made in the Alps and Pyrenees 
 ■mth Hansteen's apparatus, and studiously corrected 
 for temperature, the present writer has found a 
 diminution of one-thousandth part in the horizontal 
 intensity for a vertical ascent of about 3000 feet.' 
 
 Such are the general features of the distribution of 
 the magnetic force upon the surface of the globe. But 
 from an early period the magnetic elements for the 
 same place have been known to be variable. Such 
 deviations from constancy are either — 1 . Secular ; 2. 
 Periodic ; 3. Irregular. All the three magnetic ele- 
 ments (Variation, Dip, and Intensity) probably par- 
 take of these changes. The westerly Variation or De- 
 clination had till 1818 been increasing in Europe since 
 the earliest observations. This results from a com- 
 plicated movement of the line of No Variation and 
 its companion curves. While their common centre 
 or pole in North America has been slowly advancing 
 towards the East, a considerable portion of the sys- 
 tem of curves in this quarter of the globe has been 
 proceeding in a south-westerly direction nearly in a 
 line joining Spain with South America, thus produc- 
 ing a complicated rotatory motion of the lines of Va- 
 riation, of which the first eiSect was to extinguish the 
 singular loop in the curve of No Declination (in- 
 cluding a space of easterly declination) which is 
 shown in M. Hansteen's chart for 1600 to have 
 occupied a large part of Western Europe.^ About 
 1818 the needle began to retrograde towards the 
 east in this part of Europe. The dip has been dimi- 
 nishing in Europe since the earliest observations. 
 
 Graham discovered the Diurnal Variation of the 
 Compass. It occurs in a reversed direction in the 
 southern hemisphere. Near the equator (as at St 
 Helena) the needle partakes at one season of the 
 northern character, at another of the southern, de- 
 pending on the position of the sun. 
 
 To Baron Humboldt and to Arago we are prin- 
 cipally indebted for a knowledge of great and capri- 
 cious fluctuations of the magnetic elements occurring 
 simultaneously over vast regions of the earth. These 
 have been called magnetic storms.' They are often 
 connected with auroral appearances. 
 
 (891.) 
 
 Next to Professor Hansteen, science is mainly in- 
 debted for the recent great extension of our know- 
 ledge of the facts and laws of terrestrial magnetism 
 to two illustrious German philosophers, Baron Alex- 
 ander von Humboldt and the late Professor Gauss. 
 (892.) The name of Alexander ton Humboldt is as 
 
 widely known as science is cultivated. The ardour Baron 
 of his love of nature, the comprehensive interest ''^ hich^^'^^^'^J 
 he takes in every department of knowledge, arid the tpidt. 
 generosity of his disposition, in combination with the 
 fortunate accidents of an imusually vigorous constitu- 
 tion, and an eminent social position, have combined 
 to place him in the foremost rank of natural philoso- 
 phers. 
 
 He was bom on the 14th September 1769, and (893.) 
 consequently is now (1856) in his 87th year. He^///"'^. 
 was a pupil of Werner in 1791, and devoted consi- ^^^^^^^ "" 
 derable attention to metallurgy. An early longing 
 for foreign travel seems to have foreshadowed his 
 future career, but political circumstances were, to- 
 wards the close of the last century, eminently un- 
 favourable to its accomplishment. His celebrated 
 journey to Southern and Central America (under- 
 taken after the failure of several other schemes) lasted 
 from June 1799 until August 1804. We may, per- 
 haps, be allowed to regret that an impression of the 
 duty of presenting to the public the results of that 
 interesting journey in their most complete form 
 should have absorbed the leisure of so many of his 
 most vigorous years, and should have withheld him 
 from other and still more important enterprizes. 
 From 1808 to 1826 Baron Humboldt resided mainly 
 in Paris, in the most intimate companionship with 
 Arago, who, though much his junior, has predeceased 
 him. He then took up his residence at Berlin, in 
 compliance with the wish of the King of Prussia, and 
 he soon after delivered there a course of public lec- 
 tures on Physical Geography which formed the basis 
 of his remarkable work entitled Kosmos, the compo- 
 sition of which has formed the chief occupation of his 
 vigorous old age. In 1829 he made a rapid but in- 
 teresting journey into Asiatic Russia, important in 
 its results, yet imperfectly carrying out the ardent 
 aspiration of his early years to unfold the marvellous 
 physical peculiarities of the Eastern continent. 
 
 Baron Humboldt has contributed more to Physical (89*') 
 Geogrfiphy than any other man now living ; and that, j^ physical 
 not only by his individual efforts, but by the direction Geography, 
 and encouragement which he has given to innumer- 
 able travellers and naturalists. Has career seems to 
 have been more closely modelled upon that of De 
 Saussure than of any other of his contemporaries or 
 predecessors. Those branches of Physical Geography 
 which admit of numerical treatment seem most con- 
 genial to him ; and he has left more of the impress 
 of his personal influence upon the sciences of Meteor- 
 
 ^ Gdinburgh Transactions, vol. xiii, 
 
 2 M. Arago gives, no doubt, an erroneous impression in stating that the westerly movement of the line of No Declination has 
 carried it in 200 years from Paris to Philadelphia. Yet I cannot subscribe to the opinion of his able commentator that the 
 Loop of No Declination which passed over Europe in the seventeenth century moved eastwards, and may still be traced in Asia 
 — (British Association, Fifth Report, p. 63 ; Arago's Meteorological Eataya, translated, p. 330). I conceiv.e that, as stated in the 
 text, the loop moved south-westwards, became successively an oval and a singular point, and was finally worked out previously 
 to 1700. 
 
 ^ In September 1841 a remarkable simultaneous disturbance took place in Canada, Scotland, the Cape of Good Hope, and New 
 South Wales. Such occurrences are now known to be very common. 
 
Chap. \'II., § 8.] ELECTEIOITY (MAGNETISM). — BARON HUMBOLDT — GAUSS. 
 
 195 
 
 Baron ologj and Magnetism than upon any others which he 
 boldt on cultivated. His conception of Isothermal Lines and 
 Meteoro- ^^^ treatment of the subject of Climatology in his re- 
 logy— iso- markable paper of 1817"^ gave a new impulse to the 
 Lin™*^ former subject. His magnetical observations in his 
 voyage to the Equator have already been adverted to. 
 Magnetism. Besides this we are indebted to Baron Humboldt for 
 directing attention to the simultaneous and seemingly 
 accidental disturbances of the magnetic needle which 
 take place over vast portions of the area of the globe. 
 He commenced observations on this subject in con- 
 junction with M. Oltmanns as early as 1806; and 
 during his residence in Paris he no doubt encouraged 
 his friend Arago in those elaborate observations on 
 the hourly variations of the needle which, to the 
 irreparable loss of science, remained unpublished 
 whilst they might have been most useful.^ In 1829 
 simultaneous observations were made in Germany 
 and Russia, and compared by MM. de Humboldt, 
 Dove, and others, with interesting results.* It is 
 probable that the results then obtained instigated 
 Gauss to the enlarged enquiry to which I shall imme- 
 diately refer. M. de Humboldt had already addressed 
 the Russian Government on the same subject, sug- 
 gesting the registration of hourly observations in their 
 vast territories ; and these, the first systematic ob- 
 servations of the kind, have been continued ever 
 since. The suggestion of " Term Days" of continuous 
 registration of the Declination Needle was also due 
 to Baron Humboldt. In 1836 he addressed the 
 President of the Eoyal Society of London on the same 
 subject, and his letter formed the basis of the exten- 
 sive undertakings which have formed the contribu- 
 tion of the British Government to this great enquiry. 
 (895.) Baron Humboldt still lives at Berlin, enjoying the 
 respect of all who know him, and the distinguished 
 favour of his Sovereign. 
 
 (896.) Carl Friedhich Gauss, late Professor of Astro- 
 
 UQ.U.SS • 
 
 nomy at Gottmgen, belonged to that group of cele- 
 brated geometers who illustrated the commencement 
 of this century, and of which he was for some years 
 the last survivor ; but he too has now passed 
 away. 
 (897.) Gauss was born at Brunswick on the 30th April 
 
 His early 1777 ^f bumble parents, and was indebted for a 
 history and , .' , , ,. , ^,, '.,.,,. , 
 
 mathema- liberal education to the notice which his talents pro- 
 
 tical works, cured him from the reigning duke. His earliest 
 
 original researches were in the theory of numbers. 
 
 His Disquisitiones Arithmeticee were published in 
 
 1801, and were as profound and original as they 
 
 have always been considered obscure even by those 
 
 devoted to such studies. Gauss demonstrated the 
 
 possibility of geometrically inscribing a regular poly- 
 
 gon of 17 sides within a circle ; the only extension 
 of geometry in this direction since the time of Euclid. 
 His Theoria Mot-As Corporum Ceelestium, published 
 in 1809, is a very remarkable treatise on the geome- 
 trical theory of the planetary orbits; in which it 
 was shown for the first time how the elliptic ele- 
 ments of a heavenly body may be deduced from 
 three observations only of longitude and latitude, — 
 an important extension of Newton's celebrated de- 
 monstration in the case of parabolic cometary orbits. 
 In the same work the method of least squares 
 (85) was fully unfolded in its applications to astro- 
 nomy. 
 
 These and many other important labours all con- (898.) 
 nected with the higher mathematics, had obtained Researches 
 for Gauss an exalted place among the men of science j "jaf^as- 
 of his time, long before he commenced those re- netism. 
 searches on Terrestrial Magnetism, in virtue of 
 which his name is introduced into the present sec- 
 tion. It can hardly be doubted, however, that by 
 these — scarcely begun before he had entered on his 
 55th year — he will be hereafter chiefly remembered. 
 His first work on the theory of magnetism* was pub- 
 lished in 1833, and excited very general notice, as it 
 contained a remarkable application of the Theory of 
 Attractions to the distribution of magnetism in a 
 steel bar, a singularly ingenious and rigorous proof 
 of the primary law of the magnetic force, and like- 
 wise a new and practical application of a suggestion Magnetic 
 thrown out by Poisson, of a method by which the ^°™^ ^° 
 magnetic directive force of the earth itself may be Measure 
 expressed in absolute measure, irrespectively of the 
 constancy of the magnetism in the bar which is in 
 the first instance used to estimate it. For this purpose 
 two kinds of observation are required, — 1 st, By vibrat- 
 ing a needle or bar of known weight and dimensions, 
 and observing the time of its oscillation, the force 
 pulling it into the meridian is ascertained in terms 
 of the ordinary dynamical units. The time depends 
 jointly on the magnetic force of the earth, and on 
 that of the bar, or it varies inversely as the product 
 of the two. 2dly, Another bar, B, is suspended like 
 the first, A, in the magnetic meridian. A is then 
 brought to act upon B, so as to draw it permanently 
 out of the meridian. The position in which B rests 
 determines the ratio of the magnetic force of the 
 earth and of the bar A. But quantities whose pro- 
 duct and whose ratio are given in known measures, are 
 also known ; whence the separate intensities of the 
 earth's and the bar's magnetism may be eliminated.* 
 
 Having thus fairly entered on a career of mag- (899.) 
 netic experiments. Gauss proceeded, in conjunction •^^T' ™^S- 
 with an experienced physicist of Gottingen, Professor strumenti 
 Wilhelm Weber (420), to invent new apparatus for 
 
 ^ Memoires d'Arceuil, torn, iii., p. 462. " Posthumously published in his (Euvres. 
 
 ^ See abstract in Bibliotheque t/niverselle, Aoiit 1832. 
 
 * Intensitas vis magneticoB terrestris ad mensuram ahsolutam revoeata. Gott. 1833. 
 
 * The Knit of force to which these intensities are referred is that force (in grains) which acting on unit of mass through unit 
 of time (a second) generates in it unit of velocity (a foot). 
 
 2o 
 
196 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 observing the earth's magnetism and its changes. 
 The instruments devised by them were a De- 
 clination Instrument and a Bifilar Magnetometer. 
 The first is a heavy magnetized bar some feet in 
 length, suspended by a bundle of parallel silk fibres. 
 It is suffered to place itself in the magnetic meridian, 
 and the small displacements due to hourly, annual, 
 or irregular fluctuation, are ascertained by viewing 
 with a telescope the reflection of a fixed scale of equal 
 parts placed at some distance in a small mirror 
 which is attached to the magnetic bar. The bifilar 
 instrument is for ascertaining changes of intensity in 
 the earth's magnetism. It is a bar like the last, sus- 
 pended by two parallel threads or wires. By twist- 
 ing round the points of double suspension, the bar 
 is forced by torsion into a position at right angles 
 to the magnetic meridian, where it is held in 
 equilibrium by the force of the earth's magnetism, 
 and that of the torsion of the wires. Supposing the 
 latter force to be constant, if the former vary, the 
 bar will change its position, which is observed by the 
 mirror and telescope as before. 
 (900.) To these instruments. Professor Lloyd, of Dublin, 
 
 added another for measuring the vertical component 
 of the magnetic intensity. It is a magnet suspended 
 horizontally on knife-edges like those of a balance. 
 Its deflection from the horizontal line indicates va- 
 riations in the vertical portion of the earth's mag- 
 netism. 
 (901.) The dip is determined in the usual way ; the va- 
 
 riations of dip, however, are ascertained by comparing 
 the variations of horizontal and vertical intensity. 
 (902.) Gauss did not content himself with suggesting 
 
 The Got- new forms of apparatus, and recommending them to 
 tingen Others. With the active assistance of M. Weber, he 
 observa- erected, in 1833, at Gottingen, a magnetic observa- 
 tions, tory free from iron (as M. de Humboldt and Arago 
 had already done on a smaller scale), where he 
 watched with patience the incessant movements of 
 the newly-constructed needles or bars. It was from 
 the same observatory that he sent telegraphic 
 signals to the neighbouring town, thus showing the 
 practicability of an electro-magnetic telegraph (856). 
 He farther instituted an association (magnetisoher 
 Verein), composed at first almost entirely of Ger- 
 mans, whose continuous observations on fixed Term- 
 days extended from Holland to Sicily.^ The marvel- 
 lous coincidence of the occurrence of even the minute 
 irregularities of the earth's magnetism was thus 
 more fully established. 
 (903.) The Mathematical Theory of Terrestrial Magnetism 
 of Gauss'' is intended to replace all arbitrary assump- 
 
 tions whatever as to the distribution of magnetism Gauss's 
 in or over the earth. It proposes to express by an ™athema- 
 empirical law, involving as little of hypothesis as o'f terres""^^ 
 possible, the direction of the freely suspended mag- trial mag- 
 netic needle and its directive force at any point of the netism. 
 earth's surface, the data being of course derived from 
 a limited number of observations. 
 
 The theoretical assumption with which Gauss (904.) 
 starts is merely this, — that the elementary force of 
 magnetism varies inversely as the square of the dis- 
 tance, and that it is distributed over the matter of 
 the terrestrial globe in a way or according to a law 
 presumed to be entirely unknown. 
 
 Following up the methods employed by Laplace (905.) 
 and others, for representing the attractions of a ''^''^'"'^™^ 
 sphere or spheroid, he proposes to discover the form attractions. 
 of that remarkable function (sometimes called the 
 Pofentiaiy whose difierential coefficients express the 
 resolved components of the total magnetic force. 
 This quantity V, and also its differential coefficients 
 (representing the attractions in given directions), 
 may always be expressed by a series with indetermi- 
 nate coefficients, which is known to converge more 
 or less rapidly ; and since the component forces 
 or attractions are given by observation, the coeffi- 
 cients of the terms of the series representing them 
 may be deduced from a comparison with the data. 
 The convergency is greatest if the magnetic matter 
 be disposed towards the centre of the sphere, least if 
 it reside near its surface. 
 
 Retaining quantities of the fourth order, there are (906.) 
 twenty-four, constants, which, rigorously speaking, 
 may be deduced from complete observations of the 
 three magnetic elements (888) at only eight stations 
 anywhere situated on the surface of the globe. With 
 great patience and skill. Gauss collected as many avail- 
 able data as possible for determining these constants 
 with accuracy, and he thence deduced by calculation 
 the values of V, those of the declination, horizontal 
 and vertical force, and that of the dip for all points 
 of the globe. The beautiful charts which he caused 
 to be constructed show a remarkable general ac- 
 cordance with the complex facts of magnetiem as 
 then known. But in many instances more accurate 
 data have since been obtained applicable to the im- 
 provement of the empirical theory. Perhaps the 
 most surprising fact which Gauss considers to be 
 demonstrated is this, that the average amount of 
 magnetic force associated with every cubic yard of 
 the earth's volume (supposing the distribution uni- 
 form) is equal to that contained in six saturated steel 
 bars each a pound in weight. 
 
 1 The Tolnmea of their publications, from 1836 to 1839, contain much interesting information on the history of this subject. 
 ^ AUgemeine Theorie des Urdmagnetismus. Leipzig, 1839. 
 
 3 See Art. 877. This function V represents the integral / — , were dm is the attracting or repelling element, and f its 
 
 distance from the point acted on. Gauss represents in his charts the values of the function V at different points of the earth's 
 surface. The lines of equal values of V are everywhere perpendicular to the direction of the needle, and the Koriiontal inten- 
 sity is inversely as the distance between two adjacent lines. 
 
Chap. VII., § 8.] ELECTRICITY (MAGNETISM). — GENERAL SABINE — SIR J. C. ROSS. 
 
 197 
 
 (907.) 
 Great 
 merit of 
 Gauss. 
 
 On the whole, it is no small praise to say that the 
 great geometer of Gottingen occupies the same rank 
 in the theoretical science of terrestrial magnetism as 
 Kepler did in the theory of astronomy. That a per- 
 son devoted for the greater part of his life to pursuits 
 connected with the most abstract geometry, should 
 have at last thrown himself with so much zeal into 
 the practical solution of a complicated experimental 
 problem, is a circumstance as rare as it is praise- 
 worthy. Gauss lived long enough to see his methods 
 adopted all over the world, and his name honoured 
 Hia death, amongst every civilized people. Gauss died at Got- 
 tingen (where he had resided since 1807), in great 
 tranquillity, on the 23d February 1855, in the 78th 
 year of his age. 
 
 (908.) 
 
 Import- 
 ance of 
 national 
 expedi- 
 tions. 
 
 (909.) 
 General 
 Sabine. 
 
 (910.) 
 British 
 magnetical 
 expedi- 
 tions. 
 
 But to obtain the data of the empirical theory with 
 exactness, it is evident that expeditions fitted out ex- 
 pressly with accurate apparatus, and directed at once 
 to many points of the habitable globe, are indispen- 
 sable. Powerful governments can alone effect this ; 
 and to Baron Humboldt is due (as has been shown) 
 the praise of having vigorously pressed the import- 
 ance of these upon the governments of England and 
 of Russia. The vast marine resources of the former, 
 and the peculiar magnetic interest of the stupendous 
 Asiatic territory of the latter, rendered their co- 
 operation highly important. In the result. Great 
 Britain has accomplished by far the larger share of 
 this vast enterprise. 
 
 To Major-General Edward Sabine, of the Royal 
 Artillery, is mainly due the judicious management of 
 these magnetic explorations, and the speedy and skilful 
 publication of their interesting results. During the 
 course of an active life he has enjoyed opportunities 
 of making extensive observations with magnetic ap- 
 paratus and with the pendulum (238) throughout a 
 great range of latitude. His experiments (carried on 
 principally between the years 1819 and 1826) were 
 made in Bra,zil, the coast of Guinea, Spitzbergen, and 
 Arctic America. His observations on magnetic inten- 
 sity are particularly valuable, and first indicated the 
 position of a region of maximum intensity in North 
 America considerably to the south of the magnetic 
 pole as indicated by the dipping needle. To him 
 we also owe a valuable Intensity Chart of the Globe, 
 and a Magnetic Survey of the British Islands, pub- 
 lished in the reports of the British Association for 
 1836 and the two following years. 
 
 But his efforts in promoting and directing the 
 system of national magnetical research set on foot at 
 Baron Humboldt's instigation are of still greater 
 importance, to which, in its earlier stages, the exer- 
 tions of Dr Lloyd (550) were also of essential service. 
 Although seconded by young, able, and enthusiastic 
 ofiicers of the service to which General Sabine be- 
 
 ' Captain 
 . Sir J. 0. 
 
 Ross. 
 
 longs, the diflSoulty of starting simultaneously sys- 
 tematic observations (with instruments new and little 
 understood, and dispersed to the widest possible ex- 
 tent over the surface of the globe), was evidently very 
 great. Canada, St Helena, the G!ape of Good Hope, 
 and Van Diemen's Land, were selected for primary 
 stations ; and the vastly voluminous results of hourly 
 or two-hourly observations of numerous instruments 
 continued year by year came pouring in to the central 
 establishment at Woolwich under General Sabine's 
 presidency. Besides these, several nautical expedi- 
 tions were fitted out for similar purposes, the most 
 important of which was sent in 1840 under the direc- 
 tion of Sir James Clark Ross to approach as nearly 
 as might be to the Antarctic Pole. This voyage, whe- 
 ther in respect of the spirit of adventure displayed, 
 the wonderful character of the natural objects re- 
 vealed by it for the first time to human view, or the 
 importance of the scientific results obtained, may 
 rank with any of our memorable polar expeditions. 
 By the aid of an ingenious instrument contrived by 
 Mr Fox, trustworthy magnetical observations were 
 made on dip and intensity (as well as on declina- 
 tion) even in the open sea, and thus the area contri- 
 buting to our knowledge of the earth's magnetism 
 was vastly increased. The results of these researches 
 properly reduced have been gradually laid before the 
 world by General Sabine in a series of memoirs of 
 the utmost interest, contained in the Philosophical 
 Transactions from 1840 to the present time. 
 
 With regard to the geographical phenomena of 
 magnetism, it may now be inferred almost with cer- 
 tainty that the position of the Antarctic magnetic pole 
 is in a region hitherto inaccessible, and to the south 
 of New Holland, placed somewhere near longitude intensity. 
 150° E., and probably not within 17° of the pole of 
 the earth, a latitude which was reached by Sir James 
 Ross in a longitude somewhat farther east.^ It ap- 
 pears also that in the southern as in the northern 
 hemisphere there are two centres of greatest intensity, 
 round which the curves of equal intensity form ovals, 
 and afterwards loops like lemniscates. The stronger 
 magnetic centres of each hemisphere are near, though 
 apparently not coincident with, the two proper mag- 
 netic poles. The following numbers approximately re- 
 present on a scale oi absolute intensity (898), in which 
 the grain, the foot, and the second are units, the 
 magnetic force at the four centres just mentioned ; 
 the second column contains the corresponding values 
 on Baron Humboldt's scale, mentioned in Art. 885. 
 
 (911.) 
 Geogra- 
 phical 
 results — 
 ^ curves of 
 
 Absolute. 
 In North America, . . . li'2 
 
 In Siberia, 13'3 
 
 South from New Holland, . 15-14 
 The other Antarctic centre, 14'9 
 
 On Hamlioldt's Scale. 
 1-88 
 1-76 
 2-00 
 1-97 
 
 The absolute intensity at St Helena, which is not far 
 
 1 See General Sabine's Charts in Fhil Trans., 1844. 
 
198 
 
 MATHEMATICAL AND PHYSICAL SCIENCE. 
 
 [Diss. VI. 
 
 (912.) 
 European 
 magnetical 
 observa- 
 tories. 
 
 (913.) 
 Depen- 
 dence of 
 magnetic 
 periods on 
 the sun 
 and moon. 
 
 from the minimum, is 6'4. These observations also 
 fully confirm the progressive motion of the whole 
 system of magnetic lines on the surface of the 
 globe. 
 
 In Europe national, and even private, observa- 
 tories have contributed largely to our knowledge of 
 the laws of magnetism. Among these observatories 
 may be mentioned Greenwich, Dublin, Makerstoun 
 in Scotland, Munich, Prague, Brussels, St Peters- 
 burg, and the numerous other Eussian stations. At 
 Greenwich and at Kew, near London, the automatic 
 registration of magnetical and meteorological instru- 
 ments, by means of photography, was introduced by 
 Mr Brooke and Mr Bonalds. It would be impossi- 
 ble in this place to give even a summary of the re- 
 sults obtained from these and the Colonial estab- 
 lishments. Besides the valuable deductions by 
 General Sabine already referred to (910), the careful 
 analysis of the formal laws of magnetism obtained at 
 their respective observatories by M. Lamont, M. Kreil, 
 and Mr Broun (Sir Thomas M. Brisbane's observer), 
 merit special notice. 
 
 The primary cause of the earth's magnetism re- 
 mains involved in the greatest doubt. That it is due 
 to electric currents, and not to permanent magnet- 
 ism, is at least probable ; and it is likely that these 
 
 currents may, in part at least, be of a thermo-electric 
 character, or the efiects may possibly depend upon 
 the direct demagnetising influence of temperature, as 
 Dr Faraday supposes (830). The secular magnetia 
 changes will probably ever remain the most unac- 
 countable. The greater portion of those which are 
 obviously periodic seem to depend upon the position 
 and efficiency of the sun in its apparent diurnal and 
 annual course, having their crises at certain hours of 
 the day, and certain seasons of the year. It is un- 
 derstood that the most recent researches leave little 
 doubt as to a like influence arising from the moon's 
 position.^ It appears also to be indicated (although 
 the induction is perhaps yet incomplete) that the 
 diurnal changes, and also those of a capricious and 
 irregular character (magnetic storms), have a period 
 of greatest and least intensity of fluctuation extending 
 to about ten years, a minimum having occurred in 
 1843, and a maximum in 1848. This nearly coin- 
 cides with a period of greatest and least abundance 
 of the solar spots detected by M. Schwabe, and it is 
 possible that there is a real connection between the 
 phenomena. The first recognition of a ten-year mag- 
 netic period appears to be due to M. Lamont, that of 
 a probable concurrence with the frequency of solar 
 spots to General Sabine. 
 
 ^ While correcting the press of this page, I have received an interesting paper by General Sabine (Phil. Trtms,, 1856), in 
 which the dependence of the various magnetic elements on the moon's diurnal place is deduced from a very large number of 
 observations. The change of declination in the course of the lunar day amounts to above 38''. 
 
 Addition to Art, 283, page 860. 
 
 The following is a continuation of the list previously given of the small Planets : 
 
 No. 
 
 Name. 
 
 Date of Discovery. 
 
 Discoverers. 
 
 36 
 
 Atalanta 
 
 1855 Oct. 5 
 
 Goldschmidt. 
 
 37 
 
 Fides 
 
 Oct. 5 
 
 Luther. 
 
 38 
 
 Leda 
 
 1856 Jan. 12 
 
 Chacornac. 
 
 39 
 
 Lastitia 
 
 Feb. 8 
 
 Chacornac. 
 
 40 
 
 Harmonia 
 
 March 31 
 
 ■Goldschmidt. 
 
 41 
 
 Daphne 
 
 May 22 
 
 Goldschmidt. 
 
 42 
 
 Isis 
 
 May 28 
 
 Pogson. 
 
PROSPECTUS 
 
 OF THE 
 
 ENCYCLOPJIDIA BRITANNICA, 
 
 EIGHTH EDITIOK 
 
 ADAM AND CHARLES BLACK, EDINBURGH. 
 
 MDCCCLVIII. 
 
LIST OF SOME OF THE CONTRIBUTORS:- 
 
 Thomas Anderson, M.D., Professor of Chemistry in the University of Glasgow. 
 
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 Sir Archibald Alison, Bart. 
 
 D. F. Arago, late Member of the Royal Institute of France. 
 
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 (List of Contributors continued on page 23.) 
 
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 hands of the present editors. The result is in every respect highly satisfactory." — John Bull, 
 August 6, 1853. 
 
 " In a certain sense, notwithstanding the words Eighth Edition, the volume may be 
 reckoned new in substance wherever discovery or time has turned up new facts." — Spectator, 
 August 6, 1863. 
 
 " He might say for tlie Encychpcedia Britannica, that, independently of the articles on 
 cotton and cotton manufacturers, it promised to be a work of extraordinary merit ; and in 
 looking over the first volume the other day, he met with an article on agriculture, which 
 was really deserving the attention of men engaged in manufacturing industry; and he 
 hoped it would be carefully perused by gentlemen who felt an interest, not only in agricul- 
 ture but in the trade and commerce of the country generally." — From Speech of Thomas 
 Bazley, Esq., delivered at a Meeting of the Chamber of Commerce, Manchester, February 10, 
 1855. 
 
 VOL. III. contains — Anatomy, by David Craigie, M.D., F.R.S.E. ; Anchor, 
 by Jonathan Aylen, Greenwich ; Andes, Angle, &c., by Sir John Leslie ; Angling, 
 Animal Kingdom, and Animalcule, by James Wilson, F.R.S.E., Author of various 
 works on Natural History; Annuities, by Joshua Milne; Ant, by P. M. Roget, M.D., 
 
6 ENCYCLOP-^EDIA BRITANNICA, EIGHTH EDITION. 
 
 F.R.S., Author of the Fifth Bridgewater Treatise ; Antrim and Armagh, by 
 Henry Senior ; Apparitions, by James Browne, LL.D. ; Aqueduct, by George 
 Buchanan, C.E. ; Arabia, by D. Buchanan and W. Plate, LL.D. ; Arch, by Sir 
 John Robison, late Professor of Natural Philosophy in the University of Edin- 
 burgh, and William Wallace, LL.D. ; Archaeology, by Daniel Wilson, LL.D. ; 
 Architecture, by William Hosking, Professor of Arts and Construction, King's 
 College ; Aristotle and Aristotle's Philosophy, by Renn Dickson Hampden, 
 D.D., Bishop of Hereford ; Army, by J. Browne, LL.D., and J. H. Stocqueler ; 
 Artillery, by Capt. Spearman and Colonel Portlock ; Arts, by W. Hazlitt and 
 W. B. Johnstone, R.S.A. ; Asia, by H. Murray, P.R.S.E., and W. Plate, LL.D. ; 
 Assaying, by Robert Mushet, of the Royal Mint ; Astronomy (First Part, the 
 remaining portion being in the next volume), by Thos. Galloway, Sir John Playfair, 
 and Thos. Henderson, with Supplement by Rev. Robert Main, Royal Observa- 
 tory, Greenwich, Also numerous other articles, among which are Archery and 
 Arithmetic. 
 
 " The third volume of this noble work begins with ' Anatomy,' and ends with ' Astronomy.' 
 In the former of these treatises we are shown that we are indeed ' fearfully and wonderfully 
 made ;' in the latter, we are raised above the things of this earth to the contemplation of the 
 marvels of the material universe. The one carries us within ourselves, the other to the farthest 
 limits which the eye or the imagination can reach. In the intermediate articles which 
 make up this stately volume, there is much that is scientific and profound, with much that 
 is intensely interesting to the popular reader. The article ' Angling' is so genial and full 
 of gentle enthusiasm, although abounding in useful details concerning lines, fly-hooks, and 
 other mysteries of the angler's craft, that it would have done the heart of old Isaak Walton 
 good to read it. Under the heads ' Animal Kingdom' and ' Animalcule,' we have a vast 
 amount of instructive research and curious speculation. . . . The article ' Annuities' is 
 a very elaborate paper embodying a lucid exposition of the science of probabilities, and full of 
 abstruse calculations on a subject of great practical utility. Passing over many excellent 
 articles in natural history, biography, &c., we arrive at an extremely readable paper on 
 'Apparitions.' . . . ' Arabia,' with its wild and wandering tribes, its immense deserts made 
 habitable by the extraordinary powers of endurance of the camel, and its wonderful religious 
 history, as the birth-country of Mahomet, is very fully and ably described. Then foUows a 
 singularly interesting article, ' Arachnides,' relating to the spider class of insects. . . . One 
 of the most complete treatises in the present volume is the article ' Architecture.' It com- 
 prises the masterly account of the science given in the previous edition of the Encyclopcedia, 
 together with a Supplement from the same pen, disclosing such farther light as the author has, 
 in the course of his investigations, received since 1830. . . . Passing over ' Aristotle' and 
 'Arithmetic' — bothvery learned disquisitions — wearrive at a weightyand eloquent essayunder 
 the head ' Army.' . . . The information embodied in the treatise before us is very full, and 
 
ENCYCLOPiEDIA BRITANNICA, EIGHTH EDITION. 7 
 
 is brought up to the most recent date. Besides its historical digest, the article gives a detailed 
 account of all the armies of all the prominent countries of the world. . . . The article 
 ' Artillery' which follows is profoundly scientific, and written in a spirit of high appreciation 
 of the importance of that arm of the military service. ' Arts,' ' Asia,' and ' Astronomy' com- 
 plete the larger and more elaborate essays in this bulky quarto. Equal care, however, is 
 shown in the preparation of the smaller articles, all of which, where necessary, are brought 
 up to ihe present state of information. . . . The beautiful series of plates appended to this 
 volume are chiefly illustrative of the articles 'Anatomy' and 'Architecture.'" — Glasgow 
 Citizen, November 19, 1853. 
 
 " The various topics are treated with vigorous and masterly skill, and the information is 
 classified and arranged with such ingenuity and system as to be easy of reference, and ac- 
 cessible to the student at the smallest possible expenditure of time and trouble." — Morning 
 Post, November, 1853. 
 
 VOL. IV. contains — Athens and Attica, by James Browne, LL.D., revised 
 by Dr L. Schmitz, F.R.S.E., Rector of the High School of Edinburgh ; Atmometek, 
 Bakometek, and BAnoMETRiCAii Measurements, by Sir John Leslie, with Sup- 
 plements ; Atmosphere, by Thomas Thomson, late Professor of Chemistry in the 
 University of Glasgow ; Atterbury, by the Right Hon. Lord Macaulay ; Attrac- 
 tion, by James Ivory, F.R.S. ; Aurora Borealis, by Robert Jameson, F.R.S., 
 late Professor of Natural History in the University of Edinburgh ; Australasia 
 and Australia, by Sir John Barrow, with continuation by Samuel Mossman, 
 Author of the " Gold Fields of Australia," &c. ; Austria, by Emeric Szabad, 
 Author of " Hungary, Past and Present;" Average, by John Warrack, Average 
 Stater ; Bacon, by William Spalding, Professor of Logic in the University of St 
 Andrews ; Baking, Bleaching, &c., by James Stark, M.D., F.R.S.E. ; Baillie, 
 Barbour, Ballad, Barclay, &c., by David Irving, LL.D. ; Balance op Power 
 and Bibliography, by Macvey Napier, late Editor of the Edinburgh Review, 
 &c. ; Ballot, Bankruptcy, and Bentham, by John. Hill Burton, Author 
 of the "History of Scotland;" Basket-making, by Sir J. G. Dalyell ; Bath- 
 ing, Beccaria, &c., by Thomas Young, M.D. ; Bengal, by Edward Thornton, 
 •Bast India House ; Beauty, by Lord Jeffrey ; Bee, by James Wilson, F.R.S.E. ; 
 Beethoven, by George Farquhar Graham ; Belgium ; Sir Charles Bell, by 
 Sir John M'Neill ; BiblEj by the Very Rev. John Lee, D.D., Principal of the 
 University of Edinburgh ; Bible Societies, by Rev. James Taylor, D.D. ; Black 
 Sea, by Lawrence Oliphant, Author of " The Russian Shores of the Black Sea;" 
 Blasting, by David and Thomas Stevenson, Civil Engineers ; Bohemian 
 
8 ENCYCLOPAEDIA BKITANNICA, EIGHTH EDITION. 
 
 Brethren, by James Montgomery, Author of " Greenland and other Poems;" 
 also Bolivia, Babylon, Baptism, Bernouilli, Block-Machinery, Blowpipe, &c. 
 
 " This volume opens with Parts II., III., and IV. of the great treatise on ' Astronomy,' 
 embracing the theoretical, physical, and practical departments as distinguished from the 
 historical. To Part II. is appended a supplement describing the chief additions which have 
 been made to the planetary, coraetary, and sidereal branches of the subject. The whole 
 treatise has been carefully revised, and embodies all the latest discoveries connected with 
 the wondrous architecture of the heavens. The article ' Athens' has been brought up to 
 the present time. We hasten, however, to the beautiful memoir of ' Atterbury,' contributed 
 to the present edition by Mr Macaulay. The account of that celebrated polemic in the pre- 
 vious issue was a plain matter-of-fact narrative. Mr Macaulay, however, in that style of 
 which he is so great a master, interweaves with the facts of his life a certain brilliant criti- 
 cism, enriched by innumerable lights drawn from contemporaneous biography and events. 
 His account of the controversy between Bishop Atterbury and Eichard Bentley, relative to 
 the letters falsely attributed to the old Greek writer, Phalaris, is a singularly perspicuous and 
 able piece of writing. . . . Passing over the articles ' Attica,' ' Attraction,' and ' Aurora 
 Borealis,' we arrive at an admirable account of ' Australasia,' followed by a new and most in- 
 teresting and instructive paper on ' Australia.' . . . There are few in this country who 
 have not a personal interest in that rich and hopeful region of the globe, and who will not 
 derive valuable information from this comprehensive survey of its history, condition, and 
 prospects. . • . The article ' Austria ' possesses especial interest as regards the existing 
 state of our continental relations. . . . The ' Balance of Power ' is likewise an article 
 which will be found to throw considerable light on the attitude at present assumed by 
 France and England towards Eussia. Commercial men will find the paper on ' Bankruptcy,' 
 by Mr J. H. Burton, very readable and instructive. . . . Lord Jeffrey's celebrated essay 
 on ' Beauty' appears in this volume, together with a variety of other elaborate papers. . . . 
 Altogether, this is a magnificent volume. On all minor topics, biographical, geographical, 
 and scientific, it is much more ample than the previous edition. Some few articles have 
 been condensed so as to occupy less space, but many more topics and terms have been in- 
 troduced, and as a dictionary of arts, sciences, and general literature, it is in every respect 
 much more complete. The engravings at the end of the present volume are chiefly illus- 
 trative of the treatises on 'Astronomy,' 'Attraction,' 'Bleaching,' &c. There are, besides, 
 several admirably executed maps illustrative of the geographical articles." — Glasgow Citizen. 
 
 VOL. V. contains — Bombay, Bukmah, &c., by Edward Thornton, East India 
 House ; Bookbinding, by Charles Martel ; Book-keeping, by Joseph Lowe ; 
 Borneo and Bornu, revised by Augustus Petermann, F.R.Gr.S., &c. ; Botany, by 
 John Hutton Balfour, M.D., Professor of Botany in the University of Edinburgh ; 
 Brahmins, by James Browne, LL.D. ; Brass, by Charles Sylvester, C.E, ; Brazil ; 
 Breakwater, by Sir John Barrow, Bart., revised by John Barrow, Admiralty; 
 
ENCYCLOPEDIA BRITANNICA, EIGHTH EDITION. 9 
 
 Brewing, by James Stark, M.D., P.R.S.E. ; Brickmaking, by Samuel Holmes, 
 Liverpool ; Bridge, by Thomas Young, M.D., F.R.S. ; Britain, by James Browne, 
 LL.D., with continuation ; Brucker, by Sir William Hamilton, Bart. ; Building, 
 by William Hosking, Author of "Architecture;" Bunyan, by the Right Hon. 
 Lord Macaulay ; Burmah, by D. Buchanan and E. Thornton. 
 
 " The smaller articles seem also to have been revised with care, and are remarkable for 
 their fulness and general accuracy. Many new heads have been introduced, or old papers 
 replaced with better from the ablest hands. Among these, we have been most struck with 
 a delightful short biography of Bunyan, which, in a few pages, presents that quaint old 
 worthy to us as a breathing figure, in a sketch admirable for its picturesque and thoughtful 
 treatment, and for those master-touches which bring out the true expression of the man. 
 . . . We have said enough to direct attention to Mr Macaulay's brilhant little sketch, 
 and to suggest the spirit in which the Encyclopcedia must be conducted which has been able 
 to provide for its pages matter of such sterling quality." — Examiner, May 13, 1854. 
 
 "We may point to Professor Balfour's article on Botany as a most complete and 
 masterly exposition of that interesting science." — Morning Post, June 7, 1854. 
 
 " The article ' Botany,' for completeness and scientific accuracy, is perhaps unequalled 
 by any similar treatise on the subject in our language. The articles ' Brazil,' ' Breakwater,' 
 'Brewing,' 'Bridge,' 'Britain,' 'Building,' Burmah,' &c., are worthy of particular study. 
 In each of the articles we have mentioned every care has been taken to bring the information 
 up to the present state of the subject treated of or described. "^G^feg'ow Herald. 
 
 VOL. VI. contains — Bishop Butler, by Henry Rogers, Author of the "Eclipse 
 of Faith," &c. ; Burning-Glasses, by George Buchanan, F.R.S.E. ; Calendar, by 
 Thomas Galloway, F.R.S- ; California; Calvin and Channing, by Rev. W. L. 
 Alexander, D.D. ; Thomas Campbell, by W. E. Aytoun, Professor of Rhetoric and 
 Belles Lettres in the University of Edinburgh ; Canada, by J. B. Brown, Author 
 of " Views of Canada ;" Canary Islands, by J. Y. Johnson, Madeira ; Cannon, 
 by Colonel Portlock, Woolwich ; Capillary Action, by James Ivory, F.R.S. ; 
 Carthage, by James Browne, LL.D., and Dr Schmitz ; Carpentry and Chro- 
 matics, by Thomas Young, M.D. ; Cavan and Clare, by Henry Senior ; Centre, 
 by Sir John Robison, late Professor of Natural Philosophy in the University of 
 Edinburgh ; Ceylon, by J. Capper, Ceylonese Commissioner to the Great Exhibi- 
 tion of 1851 ; Thomas Chalmers, by Rev. William Hanna, LL.D. ; Chemistry, 
 by William Gregory, Professor of Chemistry in the University of Edinburgh ; 
 Chess, by James Donaldson ; Chili, by Charles Bertram Black (Santiago) ; China, 
 by Sir John Barrow ; Chivalry, by Sir Walter Scott, Bart. ; Chloroform, by 
 
10 ENCYCLOPEDIA BRITANNIC A, EIGHTH EDITION. 
 
 J. Y. Simpson, M.D., Professor of Midwifery in the University of Edinburgh ; 
 Chronology ; Civil Law, by David Irving, LL.D. ; Climate, by Sir John Leslie. 
 
 " When we last drew the attention of our readers to the reissue of this great work, we ex- 
 pressed a confident hope that the remaining volumes would not degenerate from the care 
 and liberality which had so remarkably distinguished the publication of the two first vo- 
 lumes. It is a pleasure to be able to say, that, up to the conclusion of the six which are now 
 before us, they have more than fulfilled our expectations. The work is thoroughly well 
 done, as far as it has gone at present ; no pains have been spared to make it complete and 
 satisfactory ; and in all those matters for which we specially want a Cyclopaedia it is now as 
 complete a work as we can ever hope to get. In practical, scientific, and philosophical sub- 
 jects it is especially strong. Such articles, for example, as those on ' Candles,' ' Bridges,' 
 'Bishop Butler,' and ' Campbell' (the poet) leave but little to be desired. We have read those 
 we have named with attention, and they are very good. . . . Some of the geographical 
 papers, such as those on ' Asia,' ' Clare,' ' Chili,' ' Canada,' and the ' Caspian Sea,' have also 
 struck us as very well executed. . . . But we cannot speak too highly of the liberal spirit 
 which has sought to retain the services of the most celebrated men of letters of the day, to 
 make this Cyclopaedia a standard of authority on all the subjects which are treated with any- 
 thing like fulness or elaboration. On purely scientific subjects we are less qualified to speak, 
 but we imagine such a treatise as that on ' Chloroform,' in the sixth volume, to be as com- 
 plete as an article in a book of reference either can or need be. We must not, of course, be 
 understood to assent to all the statements, or agree to all the criticisms in this great book ; but 
 we repeat what we said at the beginning, that on the whole, as far as it has gone, it appears 
 to us the best Cyclopaedia for general use The price is very moderate." — Guardian. 
 
 " We have more than once expressed our opinion as to the merits of this magnificent 
 national work, which is now in course of republication at a price which, even in these times 
 of cheap literature, is perfectly marvellous. Independently of being a book of universal re- 
 ference, articles are to be met with in it, which, in point of style, beauty of illustration, and 
 the undoubted and unassailable character of the facts, are not excelled throughout the wide 
 range of British literature. Such, for instance, are Sir Walter Scott's brilhant essay on 
 ' Chivalry,' and the comprehensive and most able paper on ' Chemistry' in the volume now be- 
 fore us. In the biographical department there are excellent sketches of the lives of Burns, 
 'Byron,' 'Canning,' the 'Empress Catherine,' 'Chalmers,' 'Chaucer,' 'Cicero,' and, in addition, 
 a whole host of minor celebrities. The descriptive or historical subjects, under the heads 
 'California,' 'Canada,' 'Carohna, 'Carthage,' 'Caucasus,' 'Ceylon, ' Chih,' and 'China,' are most 
 ably handled ; and, indeed, we have not anywhere met with a more graphic and readable "* 
 sketch of the ' Celestial Empire,' than that presented in the sixth volume. The article on 
 ' Christianity' is one which even theologians may read with instruction ; and, irrespective of 
 the instruction they supply, the numerous miscellaneous articles afford Kght reading of the 
 most agreeable kind. The paper on ' Chronology' gives us not only an excellent account of 
 the various eras by which time has been computed throughout the world, but also a chrono- 
 logical table, combining remarkable events, from the most remote period of antiquity down 
 
ENCYCLOPAEDIA BRITANNICA, EIGHTH EDITION. 11 
 
 to the declaration of war against Eussia in the spring of the present year. When requisite, 
 the various subjects, especially those referring to countries, arts, and manufactures, are illus- 
 trated by maps and diagrams, executed in the very first style of the art." — Glasgow Herald. 
 
 VOL. VII. contains — Clock and Watch Work, by Edmund Beckett Denison, 
 M.A., Q.C. ; Cohesion, by Thomas Young, M.D., P.R.S. ; Coinage, by Robert 
 Mushet, of the Royal Mint ; Cold and Dew, by Sir John Leslie, late Professor of 
 Natural Philosophy in the University of Edinburgh ; Collision, Combination, 
 Corn-Laws, Corn-Trade, and Cottage System, by J. R. M'CuUoch ; Colliery, 
 by William Alexander, Mining Engineer, Glasgow ; Colony, by James Mill ; 
 Colour-Blindness, by George Wilson, M.D., P.R.S.E. ; Comet, by Thomas 
 Galloway, F.R.S. ; Communism and Corporation, by J. H. Burton ; Conic Sec- 
 tions, by William Wallace, LL.D., late Professor of Mathematics in the University 
 of Edinburgh; Construction, by William Hosking, Author of "Architecture;" 
 Constantinople, by Edward Sang, late Professor of Mechanical Philosophy in the 
 Imperial School, Constantinople ; Copper Smelting, by James Napier, Glasgow ; 
 Cork County, by Henry Senior; Cotton Manufacture, revised by Thomas Bazley, 
 Chairman of the Chamber of Commerce, Manchester; Cowper, by A. Smith, Author 
 of " A Life Drama, &c. ;" Crimea, by James Laurie ; Crusades, Cuvier, Danton, 
 and Defoe, by James Browne, LL.D. ; Crustacea, by John Fleming, D.D., Pro- 
 fessor of Natural Science, New College, Edinburgh ; CunninghaMj Dalrymple, 
 and Dempster, by David Irving, LL.D.; Dairy, by John Wilson, Author of 
 " Agriculture ;" Deaf and Dumb, by P. M. Roget, M.D., F.R.S. ; Demosthenes, 
 by William Spalding, M.A., Professor of Logic and Metaphysics in the University 
 of St Andrews ; Denmaek, by Emeric Szabad, Author of the Article " Austria ;" 
 Dialling, by Henry Meikle, C.E. ; also other articles, among which are Commerce, 
 Constantinopolitan History, Copyright, Crystallization, Deluge, &c. 
 
 " Turning over the ample pages of the volume we come at once upon an elaborate paper 
 on ' Clock and Watch Work,' profusely illustrated with diagrams. The subject is treated 
 of very fully, and contains a vast amount of information, including an interesting chapter 
 on electrical clocks and dials. In a brief memoir of the late Lord Cockburn, allusion is 
 made to the fact of his having, by his ' Life of Lord Jeffrey,' gained 6elebrity as an author 
 after he was seventy years of age. . . . Passing over a learned treatise on the abstruse subject 
 of ' Cohesion,' we meet with a singularly able and comprehensive article on ' Coinage.' In 
 addition to an ample historical review of the subject, a minute and detailed description is 
 given of the actual process of coining, and of everything connected with the Mint. . . . The 
 
1 2 ENCYCLOPEDIA BRITANNIC A, EIGHTH EDITION 
 
 poetical reader will linger over the pleasant memoir of ' Coleridge ;' while readers of a more 
 practical turn will pass on to the admirable article ' Colliery.' In the latter, the whole busy 
 subterranean world, so dark in itself, yet so invaluable as supplying the elements both of light 
 and heat to the world above ground, is laid open to the wonder of the uninitiated. . . . The im- 
 portant subject of ' Colony' is handled in a masterly manner, through the republication of 
 the celebrated treatise of the late Mr James Mill, supplemented, and brought up to the pre- 
 sent time, by a hand which we recognise as that of our friend Mr John Hill Burton, advocate, 
 one of our soundest politico-economical writers. ' Combination,' from the distinguished pen 
 of Mr J. E. M'Culloch, embodies a wholesome argument against workmen's ' strikes.' After 
 an erudite article on ' Comets,' we reach a paper on ' Commerce,' which may be read with 
 great advantage in this time of war. The subject of commercial fluctuations is very intelli- 
 gently explained, and the true principles of trade are discussed in a philosophical spirit. 
 ' Communism' is shown up in capital style by Mr Burton, and the dreams of Fourier, Louis 
 Blanc, and Kobert Owen, are dissipated into thin air. . . . Jumping over the profound treatise 
 on ' Conic Sections,' which, however valuable to the student of geometrical science, has an 
 alarming appearance to ordinary readers, we iind a variety of articles of marked ability and 
 interest." — Glasgow Citizen. 
 
 " The 'Cotton Manufacture' is handled with great felicity and precision, and the article 
 on the ' Corn Laws and Corn Trade' abounds in facts of the most interesting kind." — Glasgoiu 
 Herald. 
 
 " In every instance we observe that scrupulous care has been taken to bring the infor- 
 mation down to the latest period. The value of this edition is also increased by the attention 
 which has been paid to the minor titles." — Morning Post. 
 
 VOL. VIII. contains — Diplomacy and Entail, by John Hill Burton; Distilla- 
 tion, by James Stark, M.D., T.R.S.E. ; Diving and Diving-Bell, by George 
 Buchanan, F.R.S.E. ; Dock and Dock- Yard, by Sir John Barrow, Bart., revised 
 by John Barrow of the Admiralty ; Dollond, Dolomieu, and Duhamel, by 
 Thomas Young, M.D., P.R.S. ; Donegal, Down, and Dublin, by Henry Senior ; 
 Drainage of Towns and Lands, by W. Hosking, Author of " Architecture," &c., 
 and J. Wilson, Author of " Agriculture," &c. ; Drama, by Sir Walter Scott, Bart. ; 
 Drawing and Engraving, by W. H. Lizars ; Dry Rot, by Sir John Barrow, Bart. ; 
 DuMONT, Lord Duncan, &c., by James Browne, LL.D. ; William Dunbar, and 
 English Language, by David Irving, LL.D. ; Dyeing (Calico-Printing), by F. 
 Grace Calvert, Professor of Chemistry, Royal Institution, Manchester ; Dynamics, 
 by Sir John Robison, late Professor of Natural Philosophy in the University of 
 Edinburgh ; Economists, by James Mill; Egypt, by R. Stuart Poole, of the De- 
 partment of Antiquities, British Museum ; Electricity, by Sir David Brewster, 
 K.H., M.A., D.C.L., &c. ; Embankment, by J. C. Loudon ; Emigration, by J. R. 
 
EXCYCLOPJEDIA BRITANNICA, EIGHTH EDITION. 13 
 
 M'CuUoch, Author of " Commercial Dictionary," &c. ; England, by James Browne, 
 LL.D., with Continuation. 
 
 " The present volume includes the titles from ' Diamond' to ' Entail ;' and Sir David 
 Brewster's ' Essay on Electricity' is alone sufficient to stamp the volume as one of no ordi- 
 nary value. The comparative merit of particular contributions is, however, of less impor- 
 tance than the general eificiency with which the whole design, of such a publication is car- 
 ried out." — Morning Post. 
 
 " In every part of the work there are evident traces of revision and enlargement, in 
 order to bring up its contents to the latest date and to the level of the progress made in 
 every department of art and knowledge. Among the numerous articles comprised within 
 the present volume, those which have more particularly attracted our notice are a treatise on 
 'Distillation' byDr Stark; an elaborate account of the processes of 'Dyeingand Calico-Printing' 
 from the pen of Professor Calvert; two papers on the important subject of Drainage, on 'Land- 
 Drainage' by Mr J. Wilson, and on 'Town-Drainage' by Mr Hosking; articles on the Geogra- 
 phy, the History, and Statistics of England and of Egypt ; and two extensive scientific 
 essays of high value, one on 'Dynamics' by Professor Eobison, the other on 'Electricity' by 
 Sir David Brewster. The last-named essay, more especially, is distinguished by the pro- 
 found and comprehensive manner in which its able writer has treated this deeply interesting 
 and daily progressing science." — John Bull. 
 
 " The present volume contains thirty large quarto engraved plates, making a total of 
 232 of such in the eight volumes that have been issued of the present series, affording alone 
 ample evidence of the care and industry, and the capital and skill, that have been expended 
 on this reissue of the Encyclopcedia." — Clerical Journal. 
 
 VOL. IX. contains — Entomology, Fisheries, and Edward Forbes, by James 
 Wilson, F.R.S.E. ; Bphraem Syrxjs, by Rev. Henry Burgess, LL.D. ; Episcopacy, 
 by Rev. George Grleig, D.D. ; Erasmus and Feudal Law, by David Irving, LL.D. ; 
 Equations, by James Ivory, F.R.S. ; Ethnology, by R. G. Latham, M.A., M.D. ; 
 Etruscans, Eugene, Fenelon, &c., by James Browne, LL.D. ; Europe, by Charles 
 Maclaren, F.R.S.E., and James Laurie ; Evil, by Rev. W. L. Alexander, D.D. ; 
 Examinations, by J. F. Maclennan ; Exchange, Exchequer Bills, and Excise, by 
 J. R. M'CuUoch ; Extreme Unction, Fathers, Federal Government, &c., by 
 Rev. J. Taylor, D.D. ; Fable and Fallacy, by William Spalding, A.M., Professor 
 of Logic in the University of St Andrews ; Falconer, Farquhar, and Fairfax, 
 by Robert Carruthers ; Fashion, by Dr Doran, Author of " Habits and Men," &c. ; 
 Fermanagh, by Henry Senior ; Fezzan, revised by Augustus Petermann ; Fichte, 
 by John Colquhoun, F.R.S.E. ; Fifeshire and Forth, by Thomas Barclay ; Figure 
 of the Earth, by Thomas Galloway, F.R.S. ; Filter, by George Buchanan, 
 
14 ENCYCLOPEDIA BKITAJSTNICA, EIGHTH EDITION 
 
 F.R.S.E. ; Flintshire, by John Girdwood ; Florida, by J. Smith Homans, New 
 York ; Fluxions, by William Wallace, LL.D. ; Fontana, Foster, and Fotjrcroy, 
 by Thomas Young, M.D. ; Food, by Thomas Lindley Kemp, M.D. ; Forfar, by 
 James Cowie ; Fortification, by Colonel Portlock, Woolwich ; Foster, by J. E. 
 Ryland, M.A. ; C. J. Fox, by John Allen. 
 
 " The volume opens with a magnificent treatise on ' Entomology/ from the pen of James 
 Wilson, F.R.S.E. When we state that it extends to upwards of 260 quarto pages, our 
 readers will excuse us from attempting to do justice to it in such brief space as we can com- 
 mand. The subject, however, is a large one, and no intelligent person who reads this ela^ 
 borate and deeply interesting paper will consider that it has been treated at too great length. 
 Indeed, the learned author apologizes for its brevity. ' We have somewhere seen it stated,' 
 he says, ' that there were two kinds of beetles, the black and the brown. Naturahsts are 
 now acquainted with not less than 35,000 insects of that order. Above 12,000 different 
 sorts of butterflies and moths have been collected ; and in Britain alone, though with some- 
 what of a cold and cloudy clime, we have about 2000 species of the Lepidopterous order. 
 Several of the other great ordinal divisions contain an equal number of component members, 
 so that the entire amount of insects now described by naturalists may be safely computed as 
 above 72,000. If we were to devote,' he argues, ' a page a-piece to these (and we have no 
 desire to doubt that each deserves it), then we should reqiure to occupy about four times 
 the contents of the present EncyclopcBdia, to the entire exclusion of aU other subjects, 
 which would be inconsistent with the object of this great work.' . . . Although not prepared, 
 however, for any such overwhelming ' plague of flies' as that hinted at, we are in truth 
 most heartily reconciled to the rather more than 260 pages which Mr Wilson has monopolized 
 for the elucidation of his wondrous theme. No science has had more devoted and dehghted 
 followers than that of entomology, and we are much mistaken if this brilHant treatise do 
 not add to the number of its votaries. ... To this volume Mr Wilson likewise contributes the 
 article ' Fisheries.' It extends to 60 pages, and, like the treatise on 'Entomology,' is singularly 
 
 elaborate and complete As a matter of course, the salmon fisheries occupy the first 
 
 place, and are discussed in all their bearings, natural, legal, and commercial." — Glasgmo 
 Citizen, November 3, 1855. 
 
 " To these we have to add an article of high interest on 'Ethnology,' from the pen of Dr 
 E. G. Latham, who may be regarded as the creator of this science. In the department of 
 geography we have, besides an elaborate paper on the figure of the earth, a well-digested 
 article on Europe, accompanied by a neatly executed map. Mathematics claim a large share 
 in this volume ; besides the article on ' Mathematical' Geography already noticed, and a richly 
 illustrated essay on • Fortifications,' which brings down the subject to the evacuation of the 
 south side of Sebastopol, we have articles on ' Equations' and ' Fluxions,' the latter prefaced 
 by a history of the fluxional calculus, including the controversy respecting the conflicting 
 claims of Newton and Leibnitz. The theological department, likewise, has received much 
 attention, and among others a paper on ' Episcopacy,' from the pen of the Eight Eev. Dr 
 Gleig, presents an exceeding fair and conclusive statement of the argument for and against 
 Apostolic Episcopacy." — John Bull, November 3, 1855. 
 
ENCYCLOPEDIA BRITANNICA, EIGHTH EDITION. 15 
 
 " In Wog'rop^ it is particularly rich. . . . The miscellaneous articles are exceedingly at- 
 tractive, and each of them will reward the general reader who may care nothing for science 
 and graver topics. . . . Dr Doran, whose gossiping books have achieved so great a popularity, 
 has discoursed in his own peculiar fashion, or we should rather say chatted, about ' Fashion ;' 
 and Dr Kemp is the author of the very instructive and interesting article on ' Food,' which 
 should be read by everybody." — Critic, 1855. 
 
 " Dr Latham has supplied an article on ' Ethnology,' which places the reader in full pos- 
 session of the existing state of knowledge upon that subject. No man, indeed, could be bet- 
 ter qualified for that ofBce, for his own researches have done much to dignify this new 
 branch of knowledge with the character of a science, and he has spared no pains to describe 
 its various departments, and the progress which has been made in each, clearly and 
 thoroughly, though concisely." — Morning Post. 
 
 " An article on ' Fortification,' by Lieut.-Colouel Portlock, Woolwich, will be read with 
 special interest at a time when the thunder of Sebastopol is still ringing in our ears. The 
 author gives a lucid description of the systems of fortification, both ancient and modern, 
 details, by way of example, the celebrated sieges of Dantzic in 1807, and of Antwerp in 
 1832, and affords biographical sketches of some of the most eminent mihtary engineers of 
 the Napoleonic era." — Glasgow Herald, November 14, 1855. 
 
 VOL. X. contains — France, by A. Y. Kirwan, of the Middle Temple, Barrister 
 at Law ; Benjamin Tbanklin, by Alexander Nicholson ; Sir John Franklin, by 
 Sir John Richardson ; Fuel and Gas Light, by Charles Tomlinson, Editor of 
 " Cyclopaedia of Useful Arts," &c. ; Andrew Fuller, by J. E. Ryland, M.A. ; 
 Funding System, by D. Ricardo, supplemented by J. L. Ricardo, M.P. ; Furnace, 
 by George Buchanan, F.R.S.E. ; Galileo, by James Browne, LL.D. ; Galway, by 
 Henry Senior ; Ganges, by Edward Thornton, India House ; Gassendi and 
 Gibbon, by Henry Rogers, Author of the " Eclipse of Faith," &c. ; Geography, by 
 Rev. John Wallace, D.D. ; Geometry, by William Wallace, LL.D. and Rev. P. 
 Kelland, M.A., Professor of Mathematics in the University of Edinburgh ; Ger- 
 many, by W. Jacob, revised by James Laurie ; Glacier and Fresnbl, by J. D. 
 Forbes, Professor of Natural Philosophy in the University of Edinburgh ; Glasgow, 
 by John Strang, LL.D. ; Glass, by James Ballantyne ; Gnosticism, by John 
 TuUoch, D.D., Primarius Professor of Divinity, St Andrews ; Goethe, by Thomas 
 de Quincey ; Goldsmith, by the Right Hon. Lord Macaulay ; Cape of Good Hope, 
 by Sir B. C. Pine, late Lieutenant-Governor of Natal ; Gotama Buddha, by Rev. R. 
 Spence Hardy, Hon. M.R.A.S., Author of " Eastern Monachism," &c. ; Goths, by 
 Leonard Schmitz, LL.D. ; Government, by P. E. Dove, Author of the " History of 
 Human Progression," &c. ; Grammar, by Dr Doig, revised by W. Spalding, Pro- 
 fessor of Logic in the University of St Andrews. 
 
16 ENCYCLOP-SIDIA BRITANNICA, EIGHTH EDITION. 
 
 " Every part of the volume bears evidence of careful supervision and judicious arrange- 
 ment, while the additions show an endeavour to keep abreast of the advancing science and 
 knowledge of the times. More than ever will the Encyclopcedia Britannica maintain its 
 present place among this class of publications as a standard book of universal reference." — 
 Literary Gazette, March 15, 1856. 
 
 VOL. XI. contains — Geay, Hekriok, and Hogg, by Robert Carruthers ; 
 Greece, by Charles Maclaren, P.R.S.E., revised ; Greek Church, by W. M. 
 Hetherington, D.D., LL.D. ; Gregory of Nazianzum, by John TuUoch, D.D.; 
 Gregory (Dr James), by W. P. Alison, M.D. ; Guinea and Houssa, by Augustus 
 Petermann, F.R.G.S., &c. ; Gun-Cotton, Gunpowder, Gutta Percha, and Hat- 
 Making, by Charles TomlinsOn ; Gunmaking, by P. E. Dove ] Gunnery, by Colonel 
 Portlock; Robert Hall, by Henry Rogers; Harbours, by Thomas Stevenson, 
 C.E. ; C. J. Hare, by W. L. Alexander, D.D. ; Harvey, by Thomas Laycock, M.D., 
 Professor of the Practice of Physic in the University of Edinburgh ; Heat, by T. 
 S. TraiU, M.D., Professor of Medical Jurisprudence in the University of Edinburgh ; 
 Helminthology, by James Wilson, F.R.S.E. ; Hemp, by T. C. Archer, Author of 
 " Popular Economic Botany," &c. ; Heraldry, by T. W. King, York Herald, 
 Herald's College ; Heyne, by Sir "William Hamilton, Bart. ; Hieroglyphics, by 
 R. S. Poole, M.R.S.L., &c. ; Himalaya Mountains, by Joseph D. Hooker, M.D., 
 P.R.S. ; Hindustan, revised by Edward Thornton, India House; History, by 
 David Masson, M.A., Professor of English Literature, University College ; Hol- 
 land, revised by the Rev. James Ingram, M.A. ; Homer, by John S. Blackie, 
 Professor of Greek in the University of Edinburgh ; Homceopathy, by W. T. 
 Gairdner, M.D. ; Thomas Hood, by Richard Monckton Milnes ; Horace, by 
 Theodore Martin ; Horse, Horsemanship, and Hound, by Charles Apperley (" Nim- 
 rod") — Revised by W. H. Langley, Editor of " Bell's Life in London ;". Horticul- 
 ture, by Charles Macintosh, Author of the "Book of the Garden;" John 
 Howard, by Hepworth Dixon ; Royal Household, by Samuel Redgrave. 
 
 " Some articles are new, many are re-written, and nearly all are improved. We are 
 glad to find that the remarks of critics have been received by editors and publishers in a 
 right spirit ; and that this great work of republication, all things considered, the most notable 
 of our time, increases in care and utility as it proceeds." — Athenceum, August 30, 1856. 
 
 VOL. XII. contains — David Hume, by Henry Rogers, Author of the 
 " Eclipse of Faith," &c. ; Hungary,- by Emeric Szabad, late Secretary under the 
 Hungarian National Government of 1849 ; John and William Hunter, and 
 Jenner, by Thomas Laycock, M.D., Professor of the Practice of Medicine in the 
 
ENCYCLOPEDIA BRITANNICA, EIGHTH EDITION. 17 
 
 University of Edinburgh ; Hunting, by Charles Apperley (" Nimrod")— Revised by 
 W. H. Langley, Editor of " Bell's Life in London ;" Hydrodynamics, by Sir David 
 Brewster, K.H., LL.D. ; Hypatia and Iamblichus, by the Rev. Charles Kingsley, 
 Author of " Westward Ho," &c. ; Iceland, by Robert Allan, revised by 
 Robert Chambers ; Ichthyology, by Sir John Richardson, K.B., &c. ; Fossil 
 Ichthyology, by T. S. Traill, M.D., Professor of Medical Jurisprudence in the 
 University of Edinburgh ; Life Insurance, by W. T. Thomson, Manager of 
 the Standard Life Insurance Company ; Fire Insurance, by F. G. Smith, 
 Secretary of the Scottish Union Fire and Life Insurance Company ; Marine 
 Insurance, by John Warrack ; Interest, by J. R. M'CuUoch ; Ionian Islands, 
 by William Blair, late Member of the Supreme Council of Justice of the Ionian 
 Islands, and Author of " Inquiry into Slavery amongst the Romans ;" Ireland 
 (History), by Rev. E. Groves, (Statistics) by Henry Senior ; Iron, by Wil- 
 liam Fairbairn, F.R.S., F.G.S., &c.; Iron Bridges, by Robert Stephenson, 
 M.P., President of the Institution of Civil Engineers ; Irrigation, by James 
 Caird, Author of "English Agriculture in 1850-51;" Italy, by * * * ; 
 Jamaica, by Stephen Cave ; Japan and Java, by John Crawfurd, F.R.S., 
 Author of " A Descriptive Dictionary of the Indian Islands;" Jesuitism, by 
 Isaac Taylor, Author of the " Natural History of Enthusiasm," &c. ; Jesus 
 and Jews, by the Rev. David Welsh, D.D., late Professor of Ecclesiastical 
 History in the University of Edinburgh, revised ; Samuel Johnson, by the Right 
 Hon. Lord Macaulay; Joinery, by Thomas Tredgold, C.E., revised by Arthur 
 Asphitel. 
 
 " This great work is slowly, but now, we believe, steadily advancing. Eapidity, or even 
 certainty, in the delivery of the volumes is not to be expected in the case of a work so large 
 and expensive, and in which writers of such eminence are engaged ; and Messrs Black have 
 met a complaint of want of punctuaHty in delivery by the irresistible answer that great 
 writers cannot and will not be tied to time. On the whole it is well done ; some of it ad- 
 mirably, as, for example, the life of ' Hume,' by Mr Eogers, and that of Dr Johnson, by Mr 
 Macaulay, and the articles on ' Jamaica' and ' Japan,' in this volume." — Guardian. 
 
 VOL. XIII. contains — Kafraria, by Sir Benjamin Pine; Kant, by the Rev. 
 John Cairns, M. A. ; Kars, revised by Dr Sandwith, K.B. ; Knights, Knighthood, 
 Livery, and Lorraine, by Dr Doran ; Labrador and Lapland, revised by Augustus 
 Petermann, F.R.G.S., &c. ; Lagrange and Lalande, by Thomas Young, M.D. ; 
 Language, revised by R. G. Latham, M.A., M.D., &c. ; Law, by J. F. M'Lennan, 
 M.A., Advocate ; Law of Nations and Liberty of the Press, by James Mill ; Lead, 
 
18 ENCYCLOPEDIA BEITANNICA, EIGHTH EDITION. 
 
 Leather, and Life Preservers, by Charles Tomlinson ; Leprosy, by J. Y. Simpson, 
 M.D., Professor of Midwifery in the University of Edinbi^rgh ; Libraries, by 
 Edward Edwards, Free Library, Manchester ; Light, by T. S. Traill, M.D., Pro- 
 fessor of Medical Jurisprudence in the University of Edinburgh ; Lighthouses, 
 by Alan Stevenson, C.E. ; Lock, by E. B. Denison, M.A., Q.C. ; Logic, by William 
 Spalding, M.A., Professor of Logic and Metaphysics in the University of St 
 Andrews; Lombards and Lombardy, by the Author of the Article "Italy;" 
 London, revised by H. G. Reid; Luther, by C. C. J. Buijisen, D.T)., D.C.L., 
 D.Ph., &c.; Madagascar, by the Rev. W. Ellis, Author of "Polynesian Researches," 
 &c. ; Madeira, by J. Y. Jphnson, Author of a " Handbook for Madeira." 
 
 ' " So numerous and important are the improvements and additions in the new edition of 
 this famous JEncyclopcedia, that as to many of the most essential parts of it we may consider 
 it a new work. In the volume now before us there is a most careful and interesting article 
 on 'Public Libraries,' by Mr Edward Edwards of the Free Library at Manchester, which 
 brings their history down to the recent opening of the great Eeading Room at the British 
 Museum, and which contains very much information that deserves to be extensively diffused. 
 We should be glad to see Mr Edwards' articles on ' Libraries and the History of Libraries,' re- 
 printed, in a little volume, like that which contains a republication of Professor Spalding's 
 treatise on ' Logic,' also included in the thirteenth volume of the Encyclopaedia. The essay 
 on ' Language' is by Dr Young and Dr Latham, that on ' Luther' by the Chevalier Bunsen. 
 The volume comprises also full and excellent accounts of London and of Liverpool, and an 
 article on ' Life Preservers' by Dr Young and Charles Tomlinson,in which due attention is paid, 
 to the latest suggestions for the rescue of the crews in the case of shipwreck. In the shorter 
 articles, to which attention is less drawn, we find ample evidence that the reviser's hand has 
 been at work for the removal of all obsolete doctrine, and the introduction of the latest 
 knowledge, and the most recent opinions that have made good their place in science and. 
 philosophy." — Examiner. 
 
 " We notice with pleasure the increased care bestowed on the new edition of this stand- 
 ard Encychpcedia. Many articles in the thirteenth volume excite attention by the new 
 lights they throw on old subjects, or by the power of writing, or of illustration. We may 
 mention, as examples, the papers on 'Logic,' by Mr Spalding; on ' Liberty of the Press,' by Mr 
 James Mill ; on ' Libraries,' by Mr E. Edwards, and many others. Among the other chief ar- 
 ticles of interest we notice 'Kafraria,' by Sir B. Pine; 'Leprosy,' by i)r Simpson; 'Language,' 
 revised by Dr Latham ; and ' Lock,' by Mr E. B. Denison, Dr Doran contributes two or three 
 articles, one of which on ' Knights and Knighthood' is an excellent specimen of his humour. 
 The article on ' Logic' is full of new matter, and is worth notice. But as we see it announced 
 for separate publication, we may reserve discussion of its facts and arguments for another 
 day ." — A thenceum. 
 
 VOL. XIV. contains — Magnetism, Micrometer, and Microscope, by Sir David 
 Brewster, K.H., &c. ; Mammalia, by James Wilson, Author of the Article " Ento- 
 
ENCYCLOPJEDIA BRITANNICA, EIGHTH EDITION. 19 
 
 mology," &c. ; Manchester, by Thomas Bazley, Chairman of the Chamber of Com- 
 merce, Manchester; Manufactures, by J. R. M'CuUochj Mechanics, by W. J. M. 
 Rankine, Professor of Civil Engineering and Mechanics in the University of Glas- 
 gow; Medical Jurisprudence, by T. S. Traill, M.D., Professor of Medical Juris- 
 prudence in the University of Edinburgh ; Medicine, by Thomas Laycock, M.D., 
 Professor of the Practice of Physic in the University of Edinburgh ; Mensuration, 
 by William Swan, Lecturer on Mathematics and Natural Philosophy ; Mental 
 Diseases, by David Skae, M.D., Physician to the Royal Edinburgh Asylum ; 
 Metaphysics, by Rev. H. L. Mansel, Reader in Moral and Metaphysical Philosophy, 
 Magdalen College, Oxford ; Meteorology, by Sir John F. W. Herschel, Bart., 
 K.H., M.A., D.C.L., &c. 
 
 " The new volume of this valuable periodical contains many articles of the greatest in- 
 terest by eminent men ; and the information they contain is uniformly brought down to the 
 latest date. One of the most important articles of the present number is that by Mr Mac- 
 cuUoch on ' Manufactures,' which will be read with the greatest interest and beneiit. The 
 article on ' Magnetism,' by Sir David Brewster ; on ' Manchester,' by Mr Bazley, the Chair- 
 man of the Chamber of Commerce ; on ' Metaphysics,' by the Eev. H. L. Mansell, of Mag- 
 dalen College, Oxford ; and on ' Meteorology,' by Sir John Herschel, — are all very elaborate 
 and valuable." — The Economist. 
 
 This list is to be understood as including only the more prominent articles, 
 the number of shorter contributions being much too large to be embraced by an 
 ordinary Prospectus. Of these articles, by far the greater number are entirely 
 new, and the remainder have been recast, modified, and improved, so as to adapt 
 them to the actual state of knowledge, and the general design of the work. 
 
 THE GENERAL INDEX — which is now in preparation, and will be published 
 as soon as the work is complete — is intended, not merely to facilitate reference, but 
 to serve the important purpose of bringing into view, and directing the inquirer to 
 the miscellaneous information scattered throughout the work. In this way much 
 information upon various topics not indicated under specific heads will be found 
 in these treatises ; and it is obviously of the greatest importance that those making 
 inquiries regarding such topics should be enabled to turn at once to the places in 
 which the scattered information may be found. Besides this, however, there are 
 many other subjects which do not occur under distinct alphabetical heads at all, 
 but which, notwithstanding, are fully explained and discussed in the General 
 Treatises. The utility of a key of this description to a digest of knowledge so 
 varied and comprehensive, will be acknowledged by all who have ever had occa- 
 sion to consult books of reference. 
 
SPECIMEN PAGE OF THE ENCYCLOPEDIA BRITANNICA. 
 
 710 
 
 A M E R I C A. 
 
 America, tlie new continent, though less than half the size of the old, 
 ^"■"V^"' contains at least an equal quantity of useful soil, and much 
 more than an equal amount of productive power. America 
 is indebted for this advantage to its comparatively small 
 breadth, which brings nearly all its interior within reach of 
 the fertilizing exhalations of the ocean. In the old conti- 
 nent, owing to its great extent from east to west, the cen- 
 tral parts, deprived of moisture, are almost everywhere de- 
 serts ; and a belt round the western, southern, and eastern 
 shores, comprises nearly all that contributes to the support 
 of man. How much fruitful land, for instance, is there in 
 Continental Asia? If we draw a line from the Gulf of 
 Cutch (near the Indus) to the head of the Yellow Sea, we 
 cut off India and China, with the intervening Birman em- 
 pire, and the southern valleys of Thibet ; and this space, 
 which comprises only about one-fifth of the surface of Asia, 
 embraces five-sixths of its productive power. Arabia, 
 Persia, Central Thibet, Western India, Chinese and Inde- 
 pendent Tartary, are deserts, with scattered patches of use- 
 ful soil not amounting to the twentieth part of their extent. 
 Siberia, or northern Asia, is little better, owing to aridity 
 and cold together. Anatolia, Armenia, the Punjab, and a 
 narrow strip along the western shores of the Pacific Ocean, 
 north as far as the 60th parallel, compose the only valuable 
 agricultural territory beyond India and China. Europe, 
 which is merely the western margin of Asia, is all fruitfiil in 
 the south ; but on the north its fruitfulness terminates at the 
 60th or 62d parallel. Africa has simply a border of useful 
 soil round three-fourths of its sea-coast, with some detached 
 portions of tolerably good land in its interior. Of the 
 31,000,000 of square miles which these three continents 
 occupy, we cannot find, after some calculation, that the pro- 
 ductive soil constitutes so much as one-third, and of that 
 tliird a part is but poor. 
 
 Now, in estimating the useful soil in America, we reject, 
 1 . all the region northward of the latitude of 53°, amounting 
 to 2,600,000 square miles ; 2. a belt of barren land about 
 300 miles broad by 1000 in length, or 300,000 square miles, 
 lying on the east side of the Rocky Mountains ; 3. a belt of 
 arid land of similar extent situated on the east side of the 
 Andes, between 24° and 40° of south latitude ; 4. the desert 
 shore of Peru, equal to 100,000 square miles ; 5. an extent 
 of 100,000 square miles for the arid country of Lower Cali- 
 fornia and Sonora ; and, 6. an extent of 500,000 square 
 miles for the summits of the Andes and the south extremity 
 of Patagonia. These make an aggregate of 3,900,000, 
 square miles ; and this, deducted from 13,900,000, leaves 
 10,000,000 square miles as the quantity of useful soil in the 
 new world. 
 Ratio of Now, what relation does the fruitfulness of the ground 
 
 TtUity to jjgj^j J.Q j.jjg latitude of the place ? The productive powers 
 of the soil depend on two circumstances, heat and moisture ; 
 and these increase as we approach the equator. First, the 
 warm regions of the globe yield larger returns of those plants 
 which they have in common with the temperate zones ; and, 
 next, they have peculiar plants which afford a much greater 
 portion of nourishment from the same extent of surface. 
 Thus, maize, which produces 40 or 50 for one in France, 
 produces 1.50 for one on an average in Mexico ; and Hum- 
 boldt computes that an arpent (five-sixths of an acre), which 
 will scarcely support two men when sown in wheat, will 
 support fifty when planted with bananas. From a consider- 
 ation of these and other facts, we infer that the productive 
 or rather nutritive powers of the soil, will be pretty correctly 
 indicated by combining the ratios of the heat and the mois- 
 ture, expressing the former of these in degrees of the centi- 
 grade scale. Something, we know, depends on the distri- 
 bution of the heat through the different seasons ; but as we 
 do not aim at minute accuracy, this may be overlooked.' 
 
 inual rain, 
 inches. 
 
 Mean an- 
 nual heat. 
 
 Product. 
 
 Ratio. 
 
 16 
 
 7 
 
 112 
 
 4 
 
 29 
 
 14 
 
 406 
 
 15 
 
 96 
 
 28 
 
 2688 
 
 100 
 
 Latitude. 
 
 60 
 
 45 
 
 
 
 Thus, if the description of food were a matter of indiffer- 
 ence, the same extent of ground which supports four persons 
 at the latitude of 60°, would support 15 at the latitude of 
 45°, and 100 at the equator. But the food prefen-ed will 
 not always be that which the land yields in greatest abund- 
 ance : and another most important qualifying circumstance 
 must be considered, — it is labour which renders the ground 
 fruitftil ; and the power of the human frame to sustain labour 
 is greatly diminished in hot climates. In the torrid zone, 
 in low situations, we doubt if it is possible for men to work 
 regularly in the fields for more than five hours a day, or half 
 the daily period of labour in England. On these grounds, 
 and to avoid all exaggeration, we shall consider the capacity 
 of the land to support population as proportional to the tliird 
 power of the cosine (or radius of gyration) for the latitude. 
 It will therefore stand thus in round numbers : — 
 
 Latitude, 0° 15° 30° 45° 60° 
 
 Productiveness, 100 90 65 35 12^ 
 
 In England the density of population is above 300 per- 
 sons per square mile ; but England is in some measure the 
 workshop of the world, and supports, by her foreign trade, 
 a greater population than her soil can nourish. In France 
 the density of population is about 1 60 ; in Germany it varies 
 from 100 to 200. Assuming, on these grounds, that the 
 number of persons whom a square mile can properly sustain, 
 without generating the pressure of a redundant population, 
 is 150 at the latitude of 50°, we have 26 as the sum which 
 expresses the productiveness of this parallel. Then taking, 
 for the sake of simplicity, 35 as the index of the productive- 
 ness of the useful soil beyond 30° in America, and 85 as that 
 of the country within the parallel of 30° on each side of the 
 equator, we have about 4,000,000 square miles, each capable 
 of supporting 200 persons, and 5,700,000 square miles, each 
 capable of supporting 490 persons. It follows, that if the 
 natural resources of America were fully developed, it would 
 afford sustenance to 3,600,000,000 of inhabitants, a number 
 nearly five times as great as the entire mass of human beings 
 now existing upon the globe ! The novelty of this result 
 may create perplexity and doubt on a first view ; but we are 
 satisfied that those who investigate the subject for themselves 
 will be satisfied that our estimate is moderate. But, what 
 is even more surprising, — there is every probability that 
 this prodigious population will be in existence within three 
 or at most four centuries. We are quite aware of the ob- 
 jections which may be raised to this conclusion, but they 
 all seem to us to admit of an answer. In particular, we would 
 observe, that the expense and difficulty of transporting men 
 from situations where they are redundant, to others where 
 vacant space exists, which is so much felt in the Old World, 
 will be incredibly facilitated by the employment of steam- 
 navigation upon the innumerable rivers which are ramified 
 over four-fifths of the New Continent. 
 
 The imagination is lost in contemplating a state of things ' 
 which will make so great and rapid a change in the condi- 
 tion of the world. We almost fancy that it is a dream ; and 
 yet the result is based on principles quite as certain as those 
 which govern the conduct of men in their ordinary pursuits. 
 Nearly all social improvements spring from the reciprocal 
 influence of condensed numbers and diffused intelligence. 
 What, then, will be the state of society in America two 
 centuries hence, when two thousand millions of civilised 
 men are crowded into a space comparatively so narrow, and 
 when this immense mass of human beings speak only two 
 languages, perhaps only one ! Such a state of things may 
 
 America. 
 
 (From Article hy Charles Maclaren, Esq., F.R.S.E., Sfc., Vol. II.) 
 
SPECIMEN PAGE OF THE ENCYCLOPEDIA BKITANNICA. 
 
 IRON. 
 
 563 
 
 The manu- 
 facture of 
 iron. 
 
 
 Kg. 34.— Elevation. 
 
 ing rolls, where the required form and size is given to it, 
 either round or square bars, &c. These are straightened 
 and cut to the required sizes, and are then ready for 
 delivery. In most large works all these operations are 
 carried on simultaneously with the smelting process, and 
 in some with extensive mining operations for procuring 
 the coal, oi-e, and limestone required to supply a pro- 
 duction of several thousand tons of manufactured iron 
 per month. 
 
 THE FORGE. 
 The forging of iron has entered, of late years, so largely 
 
 into the constructive arts, that the manufactures, how- 
 ever perfect in the rolling-mill, would be very imperfect 
 indeed without the forge. To the discussion of this part 
 of the subject there are many inducements, and we can- 
 not but wonder at the many devices, and the numerous 
 contrivances which present themselves for the attainment 
 of the operations of the forge. In effecting these objects, 
 Mr Nasmyth's steam-hammer is evidently the most efifec- Nasmyth's 
 tive, and to that instrument we are indebted for the Hammer, 
 formation and welding of iron upon a scale previously 
 unknown to the workers in that metal. 
 
 Mi Nasmyth took out his paien'. for this inventioi'. 
 
 {From Article by William Fairhairn, Esq., G.E., Vol. XII) 
 
SPECIMEN PAGE OF THE ENCYCLOPiEDIA BRITANNICA. 
 
 738 
 
 LUTHER. 
 
 Luther. Holy Ghost at the opening of the diet, on which occasion 
 '■^z'"'"-'' an Italian archbishop preached a most fanatical and insult- 
 ing sermon against the Germans, as being worse enemies of 
 God than the Turks. In the imperial opening speech, 
 Charles spoke of the lamentable dissensions which en- 
 croached upon the imperial majesty, and must produce 
 sedition and murder. The Protestants were required to 
 present their confession. The elector signed it first; four 
 other princes and two cities after him, without any obser- 
 vation ; the landgrave of Hesse, however, did not sign it 
 without saying he did not agree as to the doctrine of the 
 communion. The article says, — " That the body and blood 
 of Christ are verily present, and are administered in the 
 Lord's Supper to those who partake of it [and we disapprove 
 those who teach otherwise]." The words in brackets were 
 left out in later editions made during Luther's lifetime. On 
 this occasion the princes took really the lead, and the whole 
 was done as a great national, not as a sacerdotal work, in 
 spite of poor Melancthon's scruples. This good man was in- 
 deed entirely out of his sphere, and lost his time, and com- 
 mitted the cause of Protestantism, by trying to bring about 
 a compromise where there was no possibility of an honest 
 understanding. In the mean time, Luther was left in com- 
 plete and cruel ignorance of all that was going on ; and 
 when at last the letters of Melancthon arrived, they were 
 full of fears and sad misgivings. During all this anxious 
 time, Luther sought and found his comfort in constant prayer 
 and occupation with the Word of God. " Where is Christ's 
 church, if it is not with us? Faith alone is required. I will 
 rather fall with Christ than stand with Caesar." Luther re- 
 primanded Melancthon sharply for his pusillanimity, and 
 some of his letters to him are addressed — " To Master 
 Philip Kleinmuth" (pusillanimous). 
 
 After many tergiversations, the Protestants obtained their 
 just demand ; the confession, drawn up by Melancthon and 
 approved by Luther, was read in public sitting on the 25th 
 June 1530. A great day, worthy of the most glorious days 
 of the apostolic times. Luther was not present ; he was 
 dead as a public man. But he Hived in God, and for his 
 faith and coimtry. Nothing could damp his spirits. " I also 
 have my diet," he said ; " and what lively discussions !" 
 — referring playfully to the rooks which swarmed round his 
 tower. 
 
 The emperor ordered the confession to be read in Latin. 
 " No," said the elector ; " we are Germans, and on German 
 ground. I hope, therefore, yoiir majesty will allow us to 
 speak German." The emperor gave way, recollecting for 
 the nonce he was in Germany, and that the Germans had 
 a language of their own, and the strange fancy of using it 
 even in theological affairs. When the chancellor of the 
 elector had read the first part of that grand confession, which 
 expounds the principlesofthe Reformation, and, in particular, 
 the doctrine of justification by faith, — " that faith which is 
 not the mere knowledge of a historical fact, but that which 
 believes not only the history, but also the effect of that his- 
 tory upon the mind," — there was an indescribable effect 
 visibly produced upon the assembly. The opponents felt 
 that there was a reality before them which they had never 
 imagined ; and others said, such a profession of faith by such 
 princes was a more effectual preaching than that which had 
 been stopped. " Christ," exclaimed Jonas (Melancthon's 
 companion), " is in the diet, and he does not keep silence : 
 the Word of God is indeed not to be bound." And forth 
 these words have gone through a world wider than that to 
 which the apostles preached. After a pause, the second 
 part, the articles about the abuses of the church of Rome, 
 was read and heard with profound silence by the mitred pre- 
 lates of that church who were there assembled. As to the 
 emperor, he slept during the whole of the reading, or 
 seemed to sleep, like a tiger ready to espy the most con- 
 venient moment for leaping upon his prey. In the mean- 
 
 time, he calculated, undoubtedly, what political capital he Luther, 
 could make of the Protestants against the pope. V,»s^*»,^ 
 
 Luther addressed a letter to the cardinal elector of 
 Mainz, demanding nothing but one article, but insisting 
 upon that unconditionally — the liberty of preaching the gos- 
 pel. "Neither emperor," he says, "nor pope has the right 
 of forcing any one to believe." With Melancthon and 
 the other friends he insisted upon their leaving Augsburg 
 immediately. " Home — home — home ! " he exclaimed. 
 " Might it please God that I should be immolated at this 
 council, as John Huss was at Constance !" All the sayings 
 of Luther during this crisis are sublime and of a truly pro- 
 phetic character. He foresaw that now every effort would 
 be made at Augsburg to destroy the principles of the Re- 
 formation by a treacherous compromise and a false peace. 
 " The diet," he said, " is a regular dramatic piece : first, there 
 is the prologue, then the exposition, then the action, — now 
 comes the catastrophe ; but I think it will not be a tragic, 
 but a comic end." And, indeed, so it tiirned out to be, 
 tragical as it was. The first triumphant effect of the confes- 
 sion soon passed away ; the new converts, particularly among 
 the prelates, withdrew ; the fanatical party doubled its efforts, 
 and Charles gave way to it, and aided its ends by all diplo- 
 matic artifices. Melancthon was caught. He entered into 
 conferences in the vain hope they would lead to concord; 
 he declared himself ready to maintain and obey the supreme 
 authority of the pope, if he would, by an act of clemency, 
 connive at, if not approve, some points which they could 
 not change. During the treacherous conferences which now 
 began, the emperor tried to intimidate the elector by threat- 
 ening not to grant him the investiture, which the elector 
 claimed, however, as his hereditary right as brother of his 
 predecessor ; and to frighten all the Protestant princes and 
 the Protestant imperial city of Augsburg with measures of 
 violence, by calling in the imperial troops, and keeping the 
 gates closed. The landgrave escaped. This act caused 
 dismay among the ranks of the Catholics, for a war could 
 not be risked at this moment. The Romanists changed 
 their tactics ; they conceded, or rather feigned to con- 
 cede ; for, meanwhile, the pope had declared solemnly that 
 he would not give up those very points. The Protestants 
 acknowledged the jurisdiction of the bishops and the su- 
 premacy of the pope. A cry of indignation rose among 
 the princes, and, above all, among the brave citizens of 
 Augsburg. " Rather die with Jesus Christ," they de- 
 clared, " than conquer without Him the favour of the whole 
 world." 
 
 At this critical moment Luther's indignation rose to a holy 
 wrath, like that of the prophets of old. " I understand," said 
 he to Melancthon, " that you have begun a marvellous work, 
 namely, to make Luther and the pope agree together ; but 
 the pope will say that he will not, and Luther begs to be 
 excused. Should you, however, after all, succeed in your 
 affair, I will follow your example, and make an agreement 
 between Christ and Belial. Take care that you give not 
 up the justification by faith ; that is the heel of the seed of 
 the woman to crush the serpent's head. Take care not to 
 acknowledge the jurisdiction of the bishops ; they will soon 
 take all. In short, all your negotiations have no chance of 
 success unless the pope will renoimce papacy. Now, mind, 
 if you mean to shut up that glorious eagle, the gospel, in a 
 sack, as sure as Christ lives, Luther will come to deliver 
 that eagle with might." 
 
 But Melancthon was changed : Luther's voice had lost its 
 power over him. The extreme Protestant views main- 
 tained in a declaration which Zwingle had delivered to the 
 emperor, disposed him to cling still more to Rome. All 
 seemed for the moment lost ; but Luther's faith had dis- 
 cerned the way in which God meant to save the Protestant 
 cause, and had said, — " Christ lives ; he who has vanquished 
 the violence of our enemies, can also give us the power of 
 
 {From Article by the Chevalier Bunsen, Vol. XJII.) 
 
LIST OF CONTEIBUTORS — Gontinued . 
 
 John Lee, D.D., Principal of the University of Edinburgh. 
 
 A. H. Layard, LL.D., Author of " Nineveh and its Kemains," 
 
 Sir John Leslie, late Professor of Natural Philosophy in the University of Edinburgh. 
 
 J. C. Loudon, Author of " Encyclopsadia of Gardening," &c. 
 
 Eev. Robert Main, M.A., F.R.A.S., &c.. Observatory, Greenwich. 
 
 H. L. Mansel, Reader in Moral and Metaphysical Philosophy, Magdalen College, Oxford. 
 
 Theodore Martin. 
 
 David Masson, M.A., Professor of English Literature in University College, London. 
 
 Rev. Charles Merivale, B.D., Author of a "History of the Romans under the Empire," &c. 
 
 James Mill, Author of " Elements of Political Economy," &c. 
 
 Joshua Milne, Author of " Treatise on the Valuation of Annuities and Assurances." 
 
 Richard Monokton Milnes, M.P. 
 
 James Montgomery, Author of " Greenland, and other Poems," &c. 
 
 J. D. MoRELL, one of Her Majesty's Inspectors for Schools. 
 
 The Right Hon. Lord Macaulay. 
 
 The Right Hon. Sir James Mackintosh, LL.D., &c, 
 
 Robert Mushet, Royal Mint. 
 
 Charles Maclaren, F.R.S.E., &c. 
 
 Charles Macintosh, Author of the " Book of the Garden." 
 
 J, R. M'CuLLOCH, Author of " Commercial Dictionary," &c. 
 
 James Napier, C.E., Glasgow. 
 
 Right Hon. Sir John M'Neill, K.CB. 
 
 Laurence Oliphant, Author of the "Russian Shores of the Black Sea." 
 
 Richard Owen, F.R.S., British Museum. 
 
 Antonio Panizzi, LL.D., Principal Librarian and Secretary, British Museum. 
 
 Augustus Petermann, F.R.G.S., &c. 
 
 James Pillans, M.A., Professor of Humanity in the University of Edinburgh. 
 
 Sir Benjamin Pine. 
 
 R. S. Poole, M.R.S L., Department of Antiquities, British Museum. 
 
 Colonel PoRTLOCK, R.M.A., Woolwich. 
 
 John Playfair, F.R.S., late Professor of Natural Philosophy in the University of Edinburgh. 
 
 Thomas de Quincey. 
 
 W. J. M. Rankine, Professor of Mechanics in the University of Glasgow. 
 
 J. L. Ricardo, M.P. 
 
 Sir John Richardson, K.B., Author of "Zoology of North America," &c. 
 
 Sir John Robison, LL.D., late Professor of Natural Philosophy in the University of Edinburgh. 
 
 Henry Rogers, Author of the " Eclipse of Faith," &e. 
 
 Peter M. Roget, M.D., Author of "Thesaurus of English Words and Phrases," &c. 
 
 Rev. William Scoresby, LL.D., Author of " Arctic Regions, and the Northern Whale Fishery." 
 
 Sir Walter Scott, Bart. 
 
 Leonard Schmitz, LL.D., F.R.S.E., &c.. Rector of the High School, Edinburgh. 
 
 J. Y. Simpson, M.D., Professor of Midwifery in the University of Edinburgh. 
 
 Sir J. E. Smith, F.R.S., late President of the Linnsean Society. 
 
 Lieut.-Col. Charles Hamilton Smith, F.R.S. 
 
 William Spalding, M.A., Professor of Logic and Metaphysics in the University of St Andrews. 
 
 S. G. SauiER, Author of " History of Nicaragua." 
 
 Robert Stephenson, M.P., President of the Institution of Civil Engineers, &c. 
 
 Alan Stevenson, F.R.S.E., C.E., Author of "Account of the Skerryvore Lighthouse." 
 
 David & Thomas Stevenson, Civil Engineers, Edinburgh. 
 
 DuGALD Stewart, F.R.SS. L. & E.,late Professor of Moral Philosophy in the University of Edinburgh. 
 
 John Strang, LL.D., Glasgow. 
 
 Isaac Taylor, Author of the '' Natural History of Enthusiasm," &c. 
 
 Thomas Thomson, M.D., F.R.S. , late Professor of Chemistry in the University of Glasgow. 
 
 Edward Thornton, Author of " Gazetteer of India," &c. 
 
 Charles Tomlinson, Editor of a " Cyclopaedia of Useful Arts," &c. 
 
 Thomas Tredgold, C.E. 
 
 John Tulloch, D.D., Primarius Professor of Divinity, St Andrews. 
 
 William Wallace, LL.D., late Professor of Mathematics in the University of Edinburgh. 
 
 Rev. David Welsh, D.D., late Professor of Ecclesiastical History in the University of Edinburgh. 
 
 Right Rev. Richard Whately, D.D., Archbishop of Dublin. 
 
 William Whewell, D.D., Trinity College, Cambridge. 
 
 George Wilson, M.D., Professor of Technology in the University of Edinburgh. 
 
 John Wilson, Farmer, Berwickshire. 
 
 Daniel Wilson, LLJ)., F.R.S.A., &c.. Author of " Archseology and Prehistoric Annals of Scotland." 
 
 Thomas Young, M.D., late Corresponding Member of the Royal Institute of France. 
 
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