ALBERT R. MANN LIBRARY New York State Colleges OF Agriculture and Home Economics Cornell University Date Due MAY i: : 1976 c ■ i 1 Library Bureau Cat. No. 1137 Cornell University Library QC 171.C77 Elements of chemical physics. 3 1924 002 948 259 Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002948259 Makch, 1860. LIST OF BOOKS PUBLISHED BY LITTLE, BmW^ AID COMPANY. 112 WASHINGTON STREET, BOSTON. ^^^ Any of the following Books will be sent by mail, postage free, on receipt of the publication price. Adams's Life and Works. THE LIFE AND WORKS OF JOHN ADAMS, Second President of the United States, Edited by his Grandson, Charles Eeancib Adams. 10 vols. 8vo, cloth, $22.60. Agassiz's Natural History. CONTRIBUTIONS TO THE NATURAL HISTORY OF THE UNITED STATES 01' AMERICA. By Prof LoDls AoASSlz. 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BOSTON: LITTLE, BROWN, AND COMPANY. 1860. QC17 Entered according to Act of Congress, in the year 1860, by JOSIAH P. COOKE, JR., in the Clerk's Office of the District Court of the District of Massachusetts. University Press, Cambridge : £lcctrotypcd and Printed by Welch, Bigelow, & Co. PREFACE. The history of Chemistry as an exact science may be said to date from Lavoisier, who first used the balance in investigating cliemical phenomena, and the progress of the science since his time has been owing, in great measure, to the improvements which have been made in the processes of weiglaing and measur- ing small quantities of matter. These processes are now the chief instruments in the hands of the chemical investigator, and it is evidently essential that he should be familiar with the causes of error to which they are liable, and should be able to deter- mine the degree of accuracy of which they are capable. All this, however, requires a theoretical knowledge of the principles which the processes involve ; and the chemical investigator who, without it, relies on mere empirical rules, will be exposed to constant error. This volume is intended to furnish a full development of these principles, and it is hoped that it will serve to advance the study of chemistry in the colleges of this country. In order to adapt the work to the purposes of instruction, it has been pre- pared on a strictly inductive method throughout ; and any stu- dent who has acquired an elementary knowledge of mathematics will be able to follow the course of reasoning without difficulty. So much of the subject-matter of mechanics has been given at the beginning of the volume as was necessary to secure this object ; and for the same reason, each chapter is followed by a large number of problems, which are calculated, not only to test the knowledge of the student, but also to extend and apply IV PREFACE. the principles discussed in the work. Regarding a knowledge of methods and principles as the primary object in a course of scientific instruction, the author has developed several of the subjects to a much greater extent than is usual in elementary works, solely for the purpose of illustrating the processes and the logic of physical research. Thus, the means of measuring tem- perature and the defects of the mercurial thermometer have been described at length, in order to show how rapidly the difficulties multiply when we attempt to push scientific observations beyond a limited degree of accuracy ; so also the history of Mariotte's law has been given in detail, for the purpose of illustrating the nature of a physical law, and the limitations to which all laws are more or less liable ; the condition of salts when in solution, and the nature of supersaturated solutions, have in like manner been fully discussed as examples of scientific theories ; and, lastly, the method of representing physical phenomena by empirical for- mulas and curves, which are the preliminary substitutes for laws, has been illustrated in connection with Regnault's experiments on the tension of aqueous vapor. Although, for the reason just given, it has not been the aim of the author to make a mere digest of facts, care has been taken to include the latest results of science, and where it was impos- sible to enter into details, references arc given to the original memoirs. The author would earnestly recommend the advanced student to extend his study to these memoirs, and not to spend much time in reading text-books. All compcndiums are unavoid- ably incomplete. They can only give general resxilts, which are necessarily stated in definite terms, and are apt to convey a false notion of the true character of the phenomena and laws of nature. A student who desires to train his powers of observation cannot expend labor more profitably than in looking up fully in a large library one or more of the subjects mentioned above, and reading all the original memoirs that have been written upon it. It is only in this way that he can learn what scientific investigation has really done, as well as what can be expected from it, and can thus prepare himself to work vrith advantage in extending the bounda- PREFACE. V ries of knowledge. Moreover, that peculiar scientific power which is so essential to the successful interpretation of natural phenom- ena can be acquired only at these fountain-heads of knowledge. In preparing the work, the author has used freely all the ma- terials at his command. Most of the woodcuts in the book have been transferred from the pages of different standard works, but especially from the TraitS de Physique of Ganot. The excel- lent work of Buff, Kopp, and Zamminer has been repeatedly consulted, as well as those of Miller, of Graham, of Daguin, of Jamin, of Miiller, of Bunsen, of Dana, and of Silliman, and aU that is suitable for the illustration of his subject has been borrowed from them.* Whenever it was possible, the original memoirs were consulted, especially those of Eegnault in the twenty-first volume of the MSmoires de I'Academie des Scien- ces. Indeed, this distinguished experimentalist has so greatly improved the methods of investigation in this department of Physics, that any text-book on the subject must necessarily be in great measure an abstract of his labors. A large number of valuable tables are included in an Ap- pendix at the end of the volume. Several of these have been re-calculated ; but the rest are selected with care from standard authors. The authority for each table, and the page on which the method of using it is described, are given at the commencement of the Appendix. A list of numerous other tables distributed througia the body of the work will be found, under the word " Tables," in the Index. The author is in- debted to Captain Charles Henry Davis, Superintendent of * Buff, Kopp, und Zamminer. Lehrbuch der physikalischen und theoretischen Chemie. Braunschweig, 1857. Miller. Elements of Chemistry. Part I. Chemical Physics. London, 1855. Graham. Elements of Chemistry. Vol. I., London, 1850. Vol. II., 1857. Daguin. Traits de Physique. Tom. I. Paris, 1855. Jamin. Cours de Physique. Tom. I. Paris, 1858. Miiller. Lehrbuch der Physik und Meteorologie. Braunschweig, 1856. Bunsen. Gasometry. Translated by Koscoe. London, 1857. Dana. System of Mineralogy. Vol. I. New York, 1854. Silliman, First Principles of Physics. Philadelphia, 1859. a* Vi PREFACE. the Nautical Almanac, for the use of a table of logarithms of natural numbers to four places of decimals, which wiU be found sufi&cient for solving most of the problems in this book. The greater number of the problems were prepared by the author ; the rest have been selected from various works, but especially from Kahl's Aufgaben aus der Physik, and from the Appendix to Ganot's Traite de Physique. Solutions of these problems will be published hereafter, though for an obvious reason they are not included in this volume. For the purpose of ready reference, the sections and equations have been num- bered ; the numbers of sections are given in parentheses, those of equations in brackets ; and in order still further to facilitate reference, a list of the formulse is included in the Index. Great pains have been taken in the printing of the book to avoid errors, and the author is under especial obligation to his friend. Professor Henry W. Torrey, for a careful revision of the proof-sheets. The difficulties of securing perfect accu- racy in printing formulae and tables are almost insurmountable, and many misprints have undoubtedly occurred. Such as may be discovered will be corrected in the next edition ; and the author will feel under obligations to any of his readers who will have the kindness to send him a note of such as they find. Although the present volume is a complete treatise in itself of the principles involved in the processes of weighing and meas- uring, it is also intended to serve as the first volume of an extended work on the Philosophy of Chemistry. The arrange- ment of the chapters and sections has been adopted with this view, and the inductive method begun in this volume will be con- tinued through the whole work. The second volume will treat of Light in its relations to Crystallography (including Mathemat- ical Crystallography) , and also of Electricity in its relations to Chemistry. The third and last volume will be on Stoichiometry and the principles of Chemical Classification. This volume is now in preparation, and will be published next. J. P. C. Cambbidge, February 1, 1860. CONTENTS. CHAPTER I. INTEODUCTION. (1.) Matter, Body, Substance, 3. — (2.) General and Specific Properties, 3. — (3.) Pliysical and Chemical Changes, 4. — (4.) Physical and Chemical Proper- ties, 5. — (5.) Chemistry and Physics, 5. — (6.) Porce and Law, 6. CHAPTER II. GENERAL PEOPERTIES OF MATTER. (7.) Essential and Accidental Properties, 10. — (8.) Extension and Volume, 10. — (9.) The Measure of Extension, 11. English System of Measures .11 (10.) tJnitsof Length, 11. — (11.) Units of Surface and of Volume, 13. French System of Measures , . . . . . , 14 (12.) Histoid, — the Metre, 14. — (13.) Subdivisions and Multiples of the Metre, 17. — (14.) Units of Surface and of Volume, 17. — (15.) Density and Mass, 18. — (16.) Impenetrability, 19. Problems I to 11 19 Motion 20 (17.) Position, 20. — (18.) Mobility, 21. — (19.) Time and Velocity, 22. — (20.) Uniform and Varying Motions, 23. — (21.) Uniformly Accelerated Mo- tion, 23. — (22.) Uniformly Retarded Motion, 26.— (23.) Compound Motion, 27. — (24.) Parallelogram of Motions, 27. — (25,) Curvilinear Motion, 29. Problems 12 to 24: 31 Force 82 (26.) Force, 32. — (27.) Direction of Force, 32. — (28.) Equilibrium, 34. — (29.) Measure of Forces, 34. Composition of Forces ......... 38 (30.) Components and Resultant, 38. — (31.) Forces represented by Lines, 38. — (32.) Point of Application, 38. — (33.) Resultant of Forces acting in same Direction, 39. — (34.) Parallelogram of Forces, 39. — (35.) Decompo- sition of Forces, 40. — (36.) Composition of several Forces, 42. — (37.) Com- position of Parallel Forces, 43. — (38.) Couples, 47. — (39.) Composition of several Parallel Forces, 47. — (40.) Centre of Parallel Forces, 48. — (41.) Ac- tion and Reaction, 49. — (42.) Power, or Living Force, 52. Problems 25 to 50 54 VlU CONTENTS. Gravitation 56 (43.) Definition, 56, — (44.) Direction of tlie Eartli's Attraction, 57. — (45.) Point of Application, 58. — (46 ) Centre of Gravity, 60. — (47.) Position of Centre of Gravity, 61. — (48.) Conditions of Equilibrium, 62. — (49.) In- tensity of the Earth's Attraction, 64 — (50.) Pendulum, 66. — (51.) Simple Pendulum, 66. — (52.) Isochronism of Pendulum, 68. — (53.) Formula of Pen- dulum, 68. — (54.) Compound Pendulum, 69. — (55.) Centre of Oscillation, 70.— (56.) Use of the Pendulum for Measuring Time, 71. — (57.) Use of the Pendulum for Measuring the Force of Gravity, 73. — (58.) Value of g, 76. — (59.) Centrifugal and Centripetal Force, 77. — (60.) The Spheroidal Figure of the Earth, 83. — (61.) Variation of the Intensity of Gravity, 85. — (62.) Law of Gravitation, 86. — (63.) Absolute "Weight, 87. — (64.) French System of Weights, 89. — (65.) System of Weights of the United States and of England, 89. — (66.) Specific Weight, 90. — (67.) Unit of Mass, 90. — (68.) Density, 91.— (69.) Specific Gravity, 91.— (70 ) Unit of Force, 93.— (71.) Relative Weight, 94. — (72.) Lever, 97. — (73.) Balance, 100. Problems 51 to 90 106 Accidental Properties of Matter . . . . . . .109 (74.) Divisihility, 109. — (75.) Porosity, 110. — (76.) Compressibility and Expansibility, 113. — (77.) Elasticity, 115. CHAPTER III. THE THREE STATES OF MATTER. (78.) Molecular Forces, 117. Molecular Foeces betateen Ho.hogeneous Molecules. I. Chakacteristic Pkopektibs of Solids. Crystallography . . .119 (79.) Crystalline Form, 119. — (80.) Processes of Crystallization, 119.— (81.) Definitionsof Terms, 121. — (82.) Systems of Crystals, 121.— (83.) Cen- tre of Crystal, and Parameters, 124. — (84.) Similar Axes, 125. — (85.) Similar Planes, 126. — (86.) Holohedral Forms, 127. — (87.) Hemihedral Forms, 128. — (88.) Tetartohedral Forms, 129.— (89.) Simple and Compound Ciystals, 129.— (90.) Dominant and Secondary Forms, 130.— (91.) Definition of Terms, and Laws of Modification, 131. — (92.) Forms of Crystals belonging to the va- rious Systems, 132. — (93.) Irregularities of Crystals, 170. — (94.) Groups of Crystals, 173. — (95.) Determination of Crv.?tals, 174. — (96.) Goniometers, 177. — (97.) Identity of Crystalline Form, 183. — (98.) Dimorphism and Poly- morphism, 184. Elasticity 185 (99.) Elasticity of Solids, 185. — (100.) Elasticity of Tension, 185. — (101.) Coefficient of Elasticity, 186. — (102.) Elasticity of Compression, 187. — (103 ) Elasticity of Flexure, 187. — (104.) Applications, 189. — (105.) Elasticity of Torsion, 191. — (106.) Applications, 193. — (107.) Limit of Elasticity, 193. — (108.) Elasticity of Crystals, 195. — (109.) Collision of Elastic Bodies, 196. Resistance to Rupture . . . . . . . . .201 (110.) Measure of Resistance, 201. — (111.)' Tenacity, 203. — (112.) Cleav- age, 204. — (113.) Ductility and Malleability, 205. Hardness ........... 208 (114.) Scale of Hardness, 208, — (115.) Sclerometer, 209.— (116.) Anneal- ing and Tempering, 211. Problems 91 to 105 213 CONTENTS. IX II. Characteristic Properties of Liquids. Mechanical Condition of Liquids 215 (117.) Fluidity, 215. — (U8.) Elasticity of Liquids, 215. Consequences of the Mechanical Condition of Liquids . • .218 (119.)" Divisions of the Subject, 218. — (120.) Liquids transmit Pressure in all Directions, 218. — (121.) Direction of Liquid Pressure, 219. — (122.) Hy- drostatic Press, 220. — (123.) Pressure of Liquids caused by Weight, 223. — (124.) Upward Pressure, 225. — (125.) Lateral Pressure, 226. — (126.) Grener- alization, 227. — (127.) Pressure proportional to Specific Gravity, 227. — (128.) Hydrostatic Paradox, 228. Equilihrium of Liquids 228 (129.) Conditions of Equilibrium, 228.— (130.) Connecting Vessels, 230.— (131.) Heights of Liquid Columns in Connecting Vessels, 231. — (132.) Spiiit- Level, 232. — (133.) Artesian Wells, 233. — (134.) Salt Wells, 234. Buoyancy of Liquids ......... 235 (135.) Principle of Archimedes, 235. — (136), (137), and (138.) Demonstra- tions of Principle of Archimedes, 237. — (139.) Centre of Pressure, 240. — (140.) Floating Bodies, 241. — (141.) Equihbrium of Floating Bodies, 242. — (142.) Stable and Unstable Equilibrium, 243. — (143.) Neutral Equilibrium, 246. Methods of determining Specific Gravity 247 (144.) Definition of Specific Gravity, 247. — (145.) Specific-Gravity Bottle, 247. — (146.) Hydrostatic Balance, 248.— (147.) Hydrometers, 249. Problems 106 to 175 257 ni. Characteristic Properties op Gases. Mechanical Condition of Gases . . . . . . .263 Properties Common to Gases and Liquids ..... 264 (150.) Pressure independent of Gravity, 264. — (151.) Pressure depending on Gravity, 265. — (152.) Pressure of the Atmosphere, 266. — (153.) Buoyancy of the Air, 268.— (154.) Weight of a Body in Air, 268.— (155.) Balloons,270. Differences between Liquids and Gases ..... 273 The Barometer 275 (157.) Experiment of Torricelli, 275. — (158.) Theory of the Barometer, 278. — (159.) Kegnault's Barometer, 280. — (160.) Barometer of Fortin, 282. (161.) Common Barometer, 284. — (162.) Uses of the Barometer, 285. Mariotte's Law . 287 (163.) Statement of Mariotte's Law, 287. — (164.) Experimental Illustra- tion, 288. — (165.) History, 290. — (166.) Limit to the Compressibility of Gases, 301. Application of Mariotte's Law ....... 301 (167.) Pressure of the Atiliosphere at different Heights, 301. Instruments illustrating the Properties of Gases .... 307 (168.) Manometers, 307. — (169.) Pneumatic Trough, 311. — (170.) Gas- ometers, 314. — (171.) Safety-Tubes, 315. — (172.) Siphon, 320. — (173.) Ma- riotte's Flask, 323. — (174.) Wash-Bottle, 325. Machines for Rarefying and Condensing Air 325 (175.) The Air-Pump, 325. — (176.) Degree of Exhaustion, 327. — (177.) Air-Pump with Valves, 329. — (178.) Condensing-Pump, 333. — (179.) Water- Pump, 334. Problems 176 to 239 3S6 x contents. Molecular Forces between Heterogeneous Molecules. Adhesion. Solids and Solids ... .... . .342 (181.) Adhesion between Solids, 342. — (182.) Cements, 343. Solids and Liquids . . . • . . . . ■ . 344 (183.) Adhesion of Liquids to Solids, 344. — (184.) Capillary Attraction, 346. — (185.) Form of the Meniscus, 349. — (186.) Molecular Pressure, 349. — (187.) Amount of Molecular Pressure, 351. — (188.) Effects of Molecular Pres- sure, 352. — (189.) Numerical Laws of Capillarity, 355. — (190.) Verification of the Laws, 357. — (191.) Influence of Temperature, 360. — (192.) Spheroidal Condition of Liquids, 361. — (193.) Examples and Illustrations of Capillarity, 362. — (194.) Absorption, 363. — (195.) SoIution,365. — (196.) Determination of Solubilities, 369. — (197.) Solution and Chemical Change, 371.— (198.) Su- persaturated Solutions, 376. Solids and Gases ......... 379 (199.) Absorption of Gases, 379. Liquids and Liquids ......... 383 (200.) Liquid Diffusion, 383. — (201.) Experiments of Graham, 384. — (202.) Osmose, 387. Liquids and Gases ......... 391 (203.) Adhesion of Liquids to Gases, 391 — (204.) Solution of Gases, 392. — (205.) Variation with Temperature, 393. — (206.) Variation with Pressm-e, 394. — (207.) Influence of Salts in Solution, 398. — (208.) Determination of Coefiicient of Absorption, 398. — (209.) Partial Pressure, 405. — (210.) Analy- sis of Mixed Gases by Absorption Meter, 409. Gases and Gases .......... 412 (211.) Effusion, 412.— (212.) Application of the Law of Effusion, 414.— (213.) Transpiration, 417. — (214.) Diffusion, 419. — (215.) Passage of Gases through Membrane, 425. Problems 24.0 to 271 426 CHAPTER IV. HEAT. Action of Beat on Matter, and Theories concerning Heat . . 430 Thermometers . . . . . . . . . .432 (217.) Mercnrial Thei-mometer, 432. — (218.) Graduation of Thermometer, 433. — (219.) Defects of Mercurial Thei-mometer, 436.— (220.) Change of the . Zero Point, 441. — (221.) Standard Thermometers, 442. — (222) and (223.) Con-oction of Observation, 448. — (224.) House Thermometers, 450. — (225.) Thermometers filled with other Liquids, 451. — (226.) Maximum and Mini- mum Thermometers, 452. Thermoscopes .......... 455 (227.) Air Thermometers, 455. — (228.) Thermo-multipUer, 457. ProUems 272 to 290 461 Specific Heat 463 (229.) Temperature, 463. — (230.) Thermal Equilibrium, 463. — (231.) Unit of Heat, 464. — (232.) Specific Heat, 464.— (233.) Determination of Specific Heat, 466. — (234.) General Results, 471.— (235.) Specific Heat of Gases, 476. — (236.) Specific Heat of Gases under Constant Pressure, 477. — (237.) Specific Heat of Gases under Constant Volume, 480.— (238.) Mechan- ical Equivalent of Heat, 484. Problems 291 to 310 489 CONTENTS. Xi Expansion 491 (239.) Coefficient of Expansion, 491. — (240.) Eelation of Cubic to Linear Expansion, 493. — (241.) Volume of a Vessel, 493. Expansion of Solids 494 (242.) Measurement of Linear Expansion, 494. — (243.) Determination of Coefficient of Cubic Expansion, 495. — (244.) General Results, 496. — (245.) Expansion of Crystals, 498. — (246.) Force of Expansion, 499. — (247.) Illus- trations of Expansion of Solids, 500. — (248.) Applications of Expansion of Solids, 504. Expansion of Liquids ......... 507 (249.) Absolute and Apparent Expansion, 507. — (250.) Absolute Expan- sion of Mercury, 508. — (251 .) Correction of Barometer for Temperature, 511. — (252) and (253) Apparent Expansion of Mercury, 513. — (254.) Relation between Apparent and Absolute Expansion, 515". — (255.) Laws of the Expan- sion of Liquids, 516, — (256.) Expansion of Liquids above the Boiling-Point, 519. — (257.) Expansion of Water, 520. — (258.) Point of Maximum Density, 520. — (259.) Volume of Water at different Temperatures, 526. — (260.) Co- efficient of Expansion of Water, 527. Expansion of Gases 528 (261 . ) Experiments of Eegnault, 528. — (262.) General Results, 532. — (263.) Air-Thermometer, 533. — (264) and (265.) Regnault's Air-Thermometer, 534. — (266.) Air-Pyrometer, 539. — (267.) The True Temperature, 539. — (268.) Effects and Applications of the Expansion of Air, 540. Problems 311 to 351 544 Change of State of Bodies. — 1. Solids to Liquids . . . 548 (269.) Melting-Point, 548. — (270.) Vitreous Fusion, 548. — (271.) Ereezing- Point, 548. — (272.) Effect of Salts on the Freezing-Point of Water, 549. — (273. ) Effect of Pressure on the Melting-Point, 550. — (274.) Change of Volume attending Fusion, 551. — (275.) General Results, 553. — (276.) Determination of the Melting-Point, 554. — (277.) Heat of Fusion, 555. — (278) and (279.) Person's Law, 560.— (280.) Absolute Zero, 564. Change of Staie. — 2. Liquids to Gases 565 (281.) Boiling-Point, 565. — (282.) Variations of the Boiling-Point, 568.— (283.) Determination of the Boiling-Point, 569. — (284.) Formation of Aque- ous Vapor of Low or High Tension, 570. — (285 ) Dalton's Apparatus, 572. — (286.) Marcet's Globe, 574. — (287.) Apparatus of Gay-Lussac, 574. — (288.) Apparatus of Regnault, 575. — (289.) Discussion of Results, 580. — (290.) Formation of Vapors of different Liquids, 582. — (291.) Maximum Ten- sion of Vapors, 584. — (292.) Gases and Vapors, 585. — (293.) Distillation, 588. — (294.) Steam-Bath, 591. — (295.) Papin's Digester, 591. — (296.) Con- densation of Gases, 592. — (297.) Greatest Density of Vapor, 600. — (298.) Smallest Density of Vapor, 602. Heat of Vaporization 603 (299.) Latent Heat of Vapor, 603. — (300.) Latent Heat of Steam, 606. — (301.) Illustrations of Laws of Latent Heat, 608. — (302.) Applications of the Latent Heat of Steam, 611. — (303.) Spheroidal Condition of Liquids, 611. Steam-Engine 615 (305.) TheBoiler, 615.— (306 ) Dimensions of Steam-Boilers, 620. — (307.) Watt's Condensing-Engine, 621.— (308.) Single-acting Engine, 626. — (309.) Non-condensing Engine, 628. — (310.) Mechanical Power of Steam, 631. — (311.) Low and High Pressure Engines, 633. Prollems 352 to 317 634 Hygrometry ........... 636 (312.) Formation of Vapor in an Atmosphere of Gas, 636. — (313.) Hy- grometers, 639.— (314.) Drying Apparatus, 646. Xii CONTENTS. Origin of Heat 647 (315.) Sourcesof Heat, 647. — (316.) Physical Sources, 648. — (317.) Chem- ical Sources, 649. Propagation of Heat ........ 650 (318.) Divisions of the Subject, 650. — (319.) Laws of Radiation, 651. — (320.) Laws of Conduction, 654. — (321.) Illustrations of the Laws of Conduc- tion, 657. — (322.) Coefficient of Conduction, 659. CHAPTEK V. WEIGHING AND MEASUEING. Solids 661 (324.) Weight, 661. — (325.) Specific Gravity, 662. — (326.) Volume, 664. Liquids ........... 665 (327.) Weight and Specific Gravity, 665. — (328.) Volume, 666. Gases and Vapors ......... 667 (329.) Weight, 667. — (330.) Specific Gravity of Gases, 670. — (331.) Spe- cific Gravity of Vapors, 674. — (332.) Volumes of Gases, 679. Problems 378 to 420 682 Tables .687 Index .729 ELEMENTS OF CHEMISTRY. PART I. CHEMICAL PHYSICS. PART I. CHEMICAL PHYSICS. CHAPTER I, INTRODUCTION. (1.) Matter, Body, Substance. — That of which the universe consists, which occupies space, and which is the object of our senses, is named matter. Any limited portion of matter, whether it be a grain of sand or the terrestrial globe, is called a body ; and the difierent kinds of matter, such as iron, water, or air, are termed substances. The number of distinct substances already described is exceedingly large ; but they are all formed by the combination of a few simple substances, called Elements, or else consist of one element alone. The tendency of science for the last fifty years has been to increase the number of the elements ; at present sixty-two are admitted. But those recently discovered exist only in minute quantities on the surface of the globe, and appear to play a very subordinate part in the economy of na- ture. In regard to the essential nature of matter, or of the elements of which it consists, we have no knowledge ; but we have observed the properties of almost all known substances, as well elements as compounds, have studied their mutual rela- tions and their action on each other, and have discovered many of the laws which they obey. (2.) General and Bpecific Properties. — If we study the properties of iron, we shall find that they may be divided into two classes ; — one class, which iron possesses in common with all substances ; the other, which are peculiar to iron, and dis- tinguish it from other kinds of matter. A mass of iron occupies space, — or, in the language of geometry, possesses extension ; 4 CHEMICAL PHYSICS. it gravitates towards tlie earth, that is, it has weight. But ev- ery other substance as well as iron, gases and liquids as well as solids, possess both extension and weight. Such properties as these, which are common to all kinds of matter, are called General Properties. Besides these general properties, iron is endowed with other qualities, which are pecTiliar to itself. Thus iron not only possesses extension, but it has a peculiar crystal- line form. It not only possesses weight, but every piece of iron weighs 7.8 times as much as the same bulk of water. It has also a certain hardness and a familiar lustre. Properties like the last, which are peculiar to a given sxibstance, and serve to distinguish it from other kinds of matter, are called Specific Properties. (3.) Physical and Chemical Changes. — If, next, we study the various changes to which all substances are liable, we shall find that they also may be divided into two classes ; — first, those changes by which the specific properties are not altered ; and, sec- ondly, those by which the specific properties are essentially modi- fied, and the identity of the substance lost. Thus a mass of copper may be transported to a distant part of the globe, it may be di- vided into exceedingly small particles, it may be melted and cast into nails, it may be coined ; but yet, although the position, the size, or the external shape is thus entirely changed, those quali- ties which distinguish copper, which make it to be copper, are not altered. Water may be frozen by cold or converted into steam by heat, yet the water is not destroyed ; for if the ice be melted, or the steam condensed, fluid water reappears, with all its characteristic properties. A bar of iron, when in contact with a magnet, becomes itself magnetic, and acquires the power of attracting small particles of iron. So also a stick of sealing- wax, if rubbed with a silk handkerchief, becomes electrified, and endowed with the power of attracting light pieces of paper ; but the peculiar properties of iron and sealing-wax are not essentially modified by these changes. Such changes, which do not destroy the identity of substance, are called Physical Changes. On the other hand, if copper filings are heated for some time in contact with the air, they fall into a black powder (oxide of copper) ; if heated with sulphuric acid, they are converted into a blue crystalline solid (sulphate of copper) ; and in either case the properties of copper entirely disappear. If steam is passed INTRODUCTION. 6 over metallic iron heated to a red heat, it yields a combustible gas (hydrogen)'. If an iron bar is exposed to moist air, it slowly crumbles to a red powder (iron-rust). If sealing-wax is heated to a red heat, it burns, and is apparently annihilated ; but, as we shall hereafter see, it changes by burning into invisible gases (vapor of water and carbonic acid). Changes like these, by which the distinguishing properties of a substance are altered, and the substance itself converted into a different substance, are called Chemical Changes. (4.) Physical and Chemical Properties. — Corresponding to the two classes of changes above described are two classes of properties, into which we may divide the specific properties of a substance. Those properties which a substance may manifest without undergoing any essential change itself, or causing any essential changes in other substances, are generally called Phys- ical Properties. On the other hand, those properties which " re- late essentially to its action on other substances, and to the permanent changes which it either experiences in itself, or which it effects upon them," * are called Chemical Properties. Thus, among the physical properties of iron we should include its great tenacity and malleability, its specific gravity, its peculiar lustre, its great infusibility, the facility with which it may be forged at a high temperature, its power of transmitting electricity and of assuming magnetic polarity. Among its chemical properties, on the other hand, we should enumerate the ease with which it rusts in the air, the readiness with which it dissolves in dilute acids, its combustibility in oxygen gas, and many others. This last class of properties evidently cannot be manifested by iron with- out its losing its essential properties and ceasing to be iron. The first class, on the other hand, do not involve any such radi- cal changes. (5.) Chemistry and Physics. — It is the province of Chemistry to observe the chemical properties of substances, and to study the chemical changes to which they are liable. Physics, on the other hand, deals with the physical properties and the physical changes of matter. The study of Chemistry involves the discus- sion of at least three questions in regard to each substance. The chemist asks, in the first place. What are the specific properties * Miller's Elements of Chemistry, Part I., page 2. 1* 6 CHEMICAL PHYSICS. of the substance ? in the second place, What are the chemical changes to which it is liable, or which it is capable of producing- in other substances ? and, in the third place, What are the causes of these changes, and according to ivhat laws do they take place ? An answer to the first of these questions must ob- vioiisly be obtained before the chemist can approach the other two, and indeed the whole of Chemistry is based upon the accu- rate observation of the specific or distinguishing properties of substances. These properties, as we have seen, are physical as well as chemical, and when the substances can only be observed in a state of chemical rest, the chemist is obliged to depend on the physical characteristics alone in distinguishing between them; and under all circumstances he relies upon these characters to a greater or less degree. Hence the study of Chemistry necessa- rily implies some acquaintance with Physics, and a thorough knowledge of Physics will always be found useful to the investi- gator of chemical phenomena. There are, however, some portions of the subject which are more closely connected with Chemistry than the rest, and which, therefore, it is particularly convenient to study in connection with this science. This portion of Phys- ics, which is frequently called Chemical Physics, is the subject of Part I. ■ of this work. Chemical Physics is entirely an arbitrary division of the science, including a variety of subjects which are only grouped together because they are closely connected with Chemistry in its present condition. It treats more especially of those physical properties of matter which are used by chemists in defining and distinguishing substances, and which, therefore, it is exceedingly important for the student of Chemistry thor- oughly to understand. It treats also of the action of heat on matter, and of the various methods by which the weight and volumes of bodies, whether solids, liquids, or gases, are accu- rately measured. (6.) Force and Law. — The axiom, that every change must have an adequate cause, leads us to refer all the phenomena of nature to what we term forces ; thus, we refer the falling of bodies towards the earth to the force of gravitation, the motion of a steam-engine to the expansive force of heat, and the burn- ing of a candle to the force of chemical affinity. The only clear conception of the origin or nature of force to which man can attain, is derived from studying those limited phenomena of INTBODUCTION. 7 matter which can be traced back to human agency. These phe- nomena, as we are conscious, result from the mysterious action of mind on matter ; and we are thus led to infer that the grand phenomena of nature result in like manner from the action of the Infinite Mind on matter. In this view, force is only another name for the volition either of man or of God, and the varied phenomena of nature are only the manifestations of His all- pervading will. A careful study of material phenomena frequently leads us to the discovery of unexpected analogies between those which seemed at first sight entirely disconnected. No two phenomena are apparently less related than the motion of our planet throiigh space and the falling of a stone to its surface ; and yet it has been discovered that all the phases of both phenomena can be per- fectly explained, by assuming that every particle of matter in the universe attracts every other particle with a force varying directly as the mass and inversely as the square of the distance. So also the ripples on the surface of a still lake have no apparent resem- blance to the rays of light which play upon them ; but neverthe- less it has been found that all the phenomena of light can be folly explained, by the assumption that they are caused by a sim- ilar undulatory motion in an ethereal medium. Such generaliza- tions as these, by which the phenomena of nature are linked together and in a measure explained, are called laws. A law is the mode of action of some assumed force ; thus, the law of gravi- tation is the mode of action of the force of gravitation, and the law of undulations is the mode of action of the force which produces light. But if force is, as above considered, a direct emanation of Divine Power, then law must be regarded as the uniform and unchanging mode of action of the Divine Mind. It must be no- ticed, however, that what we call a natural law is merely our human expression of the Divine mode of action in the universe, and that this is accurate in proportion to the extent and clear- ness of our knowledge of the phenomena and of their relations. The great differences which exist in this respect are implied in the very language of science. The words hypothesis, theory, and law stand for the same thing, that is, our conception of the mode in which G-od acts in nature, and we use the one or the other according to our own conviction of the accuracy of our conception. If we suppose that it is merely possibly correct, or 8 CHEMICAL PHYSICS. only in part true, we call it an hypothesis or a theory ; but if we are fiilly convinced of its truth, we say that it is a law of nature. One criterion by which we judge of the correctness of our ideas of the Divine mode of action in the material iiuiverse, and by which we determine whether a proposed explanation of mate- rial phenomena should be regarded as an hypothesis, a theory, or a law of nature, is the completeness with which it explains the class of phenomena in question. A law of nature must not only cover all known phenomena of the class, but must also include all those which may hereafter be discovered, and even predict their existence before they are actually observed. This has been the case with the laws of nature already discovered, and with none more remarkably than with the law of gravitation, which may be regarded as the most perfect of all. This law was first advanced by Newton to explain the phenomena of planetary motion then known, by connecting them with those of falling bodies on the surface of the earth. As Astronomy advanced, this law was not only found able to explain all the complicated perturbations of lunar and planetary motions as they were successively discovered, but it even went before the observer, and enabled the astronomer to calculate with absolute exactness the extent and the periods of these irregularities of motion, although.it will require centuries on centuries to verify his results. The same is also true of the not less remarkable law of undulations advanced by Huyghens to ex- plain the comparatively few facts of optics known in his time. As these facts have been rapidly multiplied by the wonderful discov- eries of Mains and of Young, the law has not only been found fully adequate to explain all, but it has also predicted the existence of phenomena, which, like that of conical refraction, would hardly have been noticed had they not been thus pointed out. To hy- potheses and theories we do not look for the same full explana- tion of all the facts which we require of a law. They are re- garded as merely provisional expedients in science iintil the law shall be discovered, as guesses at truth before the truth is known. Laws have been said to be the thoughts of God manifested in nature and expressed in human language. Hypotheses, flien, are our first imperfect comprehensions of these thoughts. They are also the shadowing forth of laws, and the progress of science has always been from the dim glimmerings of truth in the INTBODUCTION. 9 hypothesis and the theory, to the full light of knowledge in the law. Another criterion of the validity of a law, no less important than the one we have considered, is to be found in the analogies of nature. The force of omalogy is the great directing principle in the mind of the successful student. It is this which leads him to pronounce some theories unsound, although apparently sustained by facts, and to accept others, which, although not fully verified by experiment, are yet in harmony with the general plan and order of creation, and with those convictions of the truth which are based on an enlarged knowledge and an extended ob- servation of natural phenomena. In thus defining law as the thoughts of God manifested in na- ture, and force as the constant action of his infinite will, we must be careful to remember that this is a conclusion of metaphysical rather than of physical science. The demonstrations of physical science unquestionably point to the same result ; but it is the goal towards which they tend, rather than one which they have attained. In the present condition of science, we are obliged to use language which implies the existence of separate and dis- tinct forces ; but this is unimportant so long as we keep the truth in view, and do not allow ourselves to be led into materialism by the unavoidable imperfections of scientific language. CHAPTER II. GENEEAL PEOPEETIES OF MATTEE. (7.) Essential and Accidental Properties. — Of the general properties of matter, I shall consider in this chapter the follow- ing, which are common to all bodies, solids, fluids, and gases, and which it is important for ns to study early in our course : — Essential Properties. Accidental Properties. 1. Extension, implying, 4. Weight. a. Volume. 5. Divisibility. b. Density. 6. Porosity. 2. Impenetrability. 7. Compressibility and Expansibility. 3. Mobility. 8. Elasticity. The first three of these properties are evidently more essential than the rest. We cannot conceive of a kind of matter which would be destitute of them. Attempt to conceive of a variety of matter which would not occupy space, which would not resist an effort to condense it into a smaller volume, or which would be incapable of motion, and it will be seen at once that these prop- erties form an essential part of the very idea of matter. The last five are as universal properties of matter as the first three ; but they do not seem to our minds to be so essential, for we can conceive of matter which would not possess them. It is not difficult to conceive of matter without weight, so hard as to be indivisible, at least in a physical sense, without pores, incom- pressible, and therefore unelastic. Indeed, some physicists refer the phenomena of light and heat to an imponderable variety of matter, and the Atomic Theory supposes that the assumed atoms are indivisible, incompressible, and without pores. (8.) Extension and Volume. — When we say that matter has extension, we merely mean that it occupies space, and the amount of space which a given body occupies we call its volume. We may study extension without any reference to the matter of GEffERAL PBOPEETIES OP MATTER. 11 which it is a property, and we shall thus arrive at the principles of Geometry. — This science distinguishes three degrees of ex- tension : the solid, or extension in three dimensions ; the surface, or extension in two dimensions ; and the line, or extension in one dimension. Only the first of these, however, can be said to be represented in matter, for a surface is only the boundary of a solid, and a line the boundary of a surface. (9.) The Measure of Extension In order to measure the Volume of a solid, the Area of a surface, or the Length of a line, we adopt some arbitrary unit of extension of the same order, and by the principles of Geometry compare all other extensions with it. The unit of length is the only one which must be arbitrary, because we can use a square of this unit in measuring surfaces, and a cube of this unit in measuring solids. Various units both of length and of volume have been adopted in different countries. . Of the numerous systems of measure there are two which it is important for us to study. ENGLISH SYSTEM OP MEASURES. (10.) Units of Length. — The unit of length which has been adopted in this country is the same as that of England. It is called a ya/rd, and is said to have been introduced by King Henry the First, " who ordered that the ulna or ancient ell, which corresponds to the modern yard, should be made of the exact length of his own arm, and that the other measures of length should be based upon it. This standard has been maintained without any sensible variation, and is the identical yard now used in the United States, and is declared by an act of Parliament, passed in June, 1824, to be the standard of linear measure in Great Britain." * The clause in the act is as follows : — " From and after the first day of May, 1825, [subsequently extended to the first of January, 1826,] the straight line, or the distance between the centres of the two points in the gold studs in the straight brass rod now in the custody of the clerk of the House of Commons, whereon the words and figures ' Standard Yard, 1760,' are engraved, shall be the original and genuine standard of length or lineal extension called a yard ; and the * Hunt's Merchant's Magazine, Vol. IV. p. 334. 12 CHEMICAL PHYSICS. same straight line, or distance between the centres of the said two points in the said gold studs in the said brass rod, the brass being at the temperature of sixty-two degrees by Fahrenheit's ther- mometer, shall be and is hereby denominated the ' Imperial Yard,' and shall be and is hereby declared to be the unit and only standard measure of extension, wherefrom or whereby all other measures of extension whatsoever, whether the same be lineal, superficial, or solid, shall be derived, computed, and ascer- tained ; and that all measures of length shall be taken in parts or multiples or certain proportions of the said standard yard ; and that one third part of the said standard shall be a foot, and the twelfth part of such foot shall be an inch ; and that the pole or perch in length shall contain five and a half such yards, the furlong two hundred and twenty such yards, and the mile one thousand seven hundred and sixty such yards." And the act further declares, that " if at any time hereafter the said imperial standard yard shall be lost, or shall be in any manner destroyed, defaced, or otherwise injured, it shall be re- stored by making, under the direction of the Lords of the Treas- ury, a new standard yard, bearing the proportion to a pendulum vibrating seconds of mean time in the latitude of London in .a vacuum and at the level of the sea, as 36 inches to 39.1393 inches." The event contemplated by the last clause of the act actu- ally happened in less than ten years aftei: its passage, for the standard was destroyed by the fire which consumed the Par- liament House in 1834. It was then found that this clause was entirely nugatory, and that the country was left without a legal standard ; for the restoration of the lost yard could not be effected with any tolerable certainty in the manner prescribed by the act. The measurement of the seconds pendulum, which was made the basis of the peremptory enactment, was executed with extraordinary precaution and skill by Captain Kater ; but this measurement was subsequently found to be incorrect, owing to the neglect of certain precautions in the determination of the length of the pendulum, which more recent experiments have shown to be indispensable. On account of these sources of error, the yard could not be restored with certainty in the prescribed manner within one five-hvindredth of an inch, an amount which, although inappreciable in all ordinary measurements, is a large GENEEAL PROPERTIES OP MATTER. 13 error in a scientific standard. The commissioners appointed, in 1838, " to consider the steps to be taken to restoi-e the lost standard," recommended the construction of a standard yard, and four " Parliamentary copies" from the best authenticated copies of the imperial standard yai'd which then existed. They also prescribed the manner in which the standard and the four Par- liamentary copies should be preserved, and recommended further that authenticated copies, prepared with all the refinements of modern art, should be distributed throughout the realm, and placed in the custody of certain government officers. The recom- mendations of this commission have in general been followed,* and by an act of Parliament, which received the royal assent July 30, 1855, the restored standard yard was legalized. The actual standard of length of the United States is a brass scale eighty-two inches in length, prepared for the survey of the coast of the United States, by Troughton of London, in 1813, and deposited in the Office of Weights and Measures at "Wash- ington. The temperature at which this scale is a standard is 62° Fahrenheit, and the yard measure is between the 27th and 63d inches of the scale. f From recent comparisons of this scale with a bronze copy of the new British standard, presented to the United States by the British government, it appears that the Brit- ish standard is shorter than the American yard by 0.00087 of an inch, — a quantity by no means inappreciable. Carefully adjust- ed copies of the United States standard yard have been prepared, by the order of Congress, under the direction of Professor A. D. Bache, Superuitendent of Weights and Measiires, and distributed to the different States of the Union ; but up to 1859 the standard had not been defined by any act of Congress. The subdivisions and multiples of the yard are given in Table I. at the end of this volume, with their respective numerical relations. (11.) Units of Surface and of Volume. — All the English units of surface are squares whose sides are equal to the units of length, with the exception of a few, which, like the perch or the acre, are used in the measurement of land, and in other coarse measurements. The square inch is the most convenient unit of * Account of the Construction of the New National Standard of Length and of its principal Copies. By G. B. Airy, Esq., Astronomer Eoyal. Philosophical Transac- tions of the Royal Society of London, Vol. CXLVII. p. 621. t Report of the Secretaiy of the Treasury on Weights and Measures, 34th Congress, 3d Session. Ex. Doc. No. 27, 1857. 2 14 CHEMICAL PHYSICS. surface for scientific purposes. The circular inch is also some- times used by engineers. When volume can be calculated from linear measurements by the principles of Geometry, it is usual to estimate it in cubic yards, cubic feet, ov cubic inches, and it is in this way that earth- work and masonry are measured. In measuring the volume of gases, liquids, and of many varieties of solids, liowever, an arbitrary unit is more frequently employed. Several such units, entirely independent of each other, were formerly used in dif- ferent trades ; but the Imperial Gallon, established by an act of Parliament, has been substituted for all other arbitrary meas- ures of volume. It is equal to 277.274 cubic inches, and con- tains ten avoirdupois pounds of water at 62° of the Fahrenheit thermometer. A table showing the relations of the units both of surface and of volume, will be found in connection with the table of linear measure. FRENCH SYSTEM OP MEASURES. (12.) History. — The decimal metrical system of France origi- nated with her Revolution. " It is one of those attempts to improve the condition of human kind, which, should it ever be destined ultimately to fail, would in its failure deserve little less admiration than in its success." * Previous to the Revolution, the metrical system of France was even more complex than that of England, almost every province having distinct standards of weight and measure of its own, — a condition of things which was productive of the most serious inconveniences in trade and commerce. The first effective movement to reform this extreme diversity was made by Talleyrand in the Constituent Assembly of 1790, and the new system was developed by a commission of members of the Academy of Sciences, consisting of Borda, Lagrange, Laplace, Monge, and Condorcet. In their report, which appeared in the following year, they proposed that the ten-millionth part of the quadrant of a meridian of the globe should be adopted as the basis of a new metrical system, and called a Metre ; that the subdivisions and multiples of all measures should be made on the decimal system ; that, in * Report upon Weights and Measures, by John Quincy Adams, which may be con- sulted for a full history of this subject. GENEEAL PBOPERTIES OP MATTER. 15 order to determine the metre, an arc of the meridian, extend- ing from Dunkirk to Barcelona, six and a half degrees to the north and three degrees to the south of the mean parallel of 45°, should be measured, and that the weight of a cubic decimetre of distilled water at the temperature of melting ice should be deter- mined and adopted as the unit of weight. They also proposed a new subdivision of the quadrant into one hundred degrees, the degree into one hundred minutes, and the minute into one hundred seconds. This report was accepted, and the execution of the great work was intrusted to four separate commissions, including the names of the most celebrated men of science of France. The measurement of the arc was assigned to De- lambre and M^chain, and the determination of the weight of water to LefSvre-Gineau and Fabbroni. Delambre met with great difficulties in the measurement of the French portion of the arc. The work was commenced at the most violent period of the Revolution, and was repeatedly ar- rested by the suspicions of the people and the fickleness of the government. But, after repeated interruptions, the work was completed in 1796, when the whole of the records of the survey were siibmitted to a special commission, consisting of Delambre, M^chain, Laplace, and Legendre, of France, Von Swinden, of Holland, and TralMs, of Switzerland, who found the length of the. metre to be 443.259936 lignes* The determining of the unit of weight led to a most impor- tant discovery. The commission discovered that water was most dense, not, as had been previously supposed, at the temperature of melting ice, but at a temperature nearly five degrees of the centigrade scale higher. They therefore determined the weight of a cubic decimetre of distilled water at its greatest density, and not, as had been first proposed, at 0° ; and to this weight was given the name of Kilogramme. On the 19th of August, 1798, the original metre and kilogramme were presented, with an ad- dress, to the two councils of the legislative body. In order to avoid sources of error which might arise from the ellipticity of the earth, the measurement of the arc from Dunkirk to Montjouy (Monjuich), near Barcelona, was subsequently ex- tended by Biot and Arago, in accordance with the original design * The French standard then in use. 16 CHEMICAL PHYSICS. of M^chain, to Formentera, one of the Balearic Isles, so as to com- prehend an arc of more than twelve degrees between the extreme stations, which would be almost exactly bisected by the parallel of 45° ; it being well known that from the length of any given arc which is bisected by the parallel of 45° may be deduced a length of a quadrant of a meridian, and therefore of the metre, which would be independent of the earth's ellipticity. The observations of Biot and Arago were calculated by the same methods prescribed by Delambre in the previous survey, and tlie result appeared to verify the accuracy both of the method and of the original work, since the length of the metre, which was the result of the entire arc between Dunkirk and Formentera, was found to be almost identical with that which had been previously determined. The perfect accuracy of the base of the French metrical system seemed thus to be established ; but, unfortunately, later exam- inations have not verified this conclusion. In. the year 1838, Puissant, who was then engaged in con- structing the Carte Geographique de la France, announced that there existed an important error in the calculated length of the arc of the meridian on which the length of the metre was based, and that the calculated metre differed from the one ten-millionth part of the quadrant — the metre by definition — by s-i^s of the whole ; and that the provisional metre hastily adopted on the 1st of August, 1793, during the heat of the Revolution, and based on an old measurement of an arc of the meridian by Lacaille, was in reality more accurate than that which was established by the labors of the great commission. Puissant's results were sub- sequently verified by a careful re-examination of the calculations of the commission, when it appeared that the error he had de- tected, great as it was, resulted from two greater errors, which had in part balanced each other in the final result. It was not, however, thought best to correct the length of the actual metre, and it still remains the same as that adopted by the commission. Thus, then, it appears that the metre of France is no less an ar- bitrary standard of measure than the English yard, and that, like the last, if destroyed, it cannot be restored in conformity to its definition. Like all other results of human labor, it bears the mark of imperfection and fallibility; and the singular history* * See the Edinburgh Eeview, Vol. LXXVII. page 228, for a full account of this subject. GENEEAL PROPERTIES OP MATTER. 17 of the -work teaches most impressively the limitation and uncer- tainty of the best human powers of observation and reasoning. (13.) Subdivisions and Multiples of the Metre. — The subdi- visions and multiples of the metre are all decimal. The names of the multiples are derived from the Greek numerals, and those of the sxibdivisions from the Latin. They are as fol- lows : — Measures of Length. Kilometre = 1000 metres. Metre (m.) = 1.000 metre. Hectometre = 100 " Decimetre (d. m.) = 0.100 " Decametre = 10 " Centimetre (c. m.) = 0.010 " Metre = 1 " Millimetre (m.m.)= 0.001 " In this work, the abbreviations in the table will be used to desig- nate these units of length. (14.) Units of Surface and of Volume. — The French units of surface are squares whose sides are equal to the units of length. They are named squares of these imits, and will be designated by the abbreviations as above with an exponent 2 ; thus, 5 m^' stands for five square metres, and 3 cm.' for three square centimetres. The common French measure of land is the square decametre, which is called an are, and the names of its decimal multiples and subdivisions are formed like those of the metre. The units of volume are in like manner cubes of the units of length, and are named cubic metres, cubic centimetres, etc. They will be designated as before, using the exponent 3 ; thus, 5 cm." stands for five cubic centimetres. The cubic decimetre is the common measure of liquids, and is called a litre = 0.001 m.^- So also the cubic metre, which is the measure for bulky materials, such as fire-wood, has received the separate name stere. Both the litre and the st^re have decimal multiples and subdivisions named like those of the metre. The very simple decimal relations of the French system render it exceedingly valuable in all scientific calculations, and it will therefore be exclusively used in this book. The relation between the French and English units is given in Table I., and with the aid of the annexed logarithms the reduction from one to the other can easily be made. A similar table has also been added, which gives the means of reducing the metre to several of the most important standards in use on the continent of Europe. 2* 18 CHEMICAL PHYSICS. The methods of determining approximately length, surface, and solidity, by means of the units of measure just described, are known to all who have studied Geometry, and need not there- fore be described. When great accuracy, however, is required, as in most scientific investigations, these methods become less simple, and cannot be fully understood until the student is famil- iar with the action of heat on matter. This will be described in the chapter on "Weighing and Measuring. (15.) Density and Mass. — The idea of volume involves that of density, since a given volume may be filled with a greater or a less amount of matter. The amount of matter contained in a cubic centimetre of hydrogen gas, for example, is many thousand times less than that whicli fills a cubic centimetre of gold. As used in Physics, the word density means the amount of matter contained in the unit of volume. This quantity will always be represented by D. The amount of matter which a body contains is termed its mass, and is represented by M. For example, the amount of matter which the sun, the earth, a locomotive, a cannon-ball, or a grain of sand contains, is called the mass of that body. When the body is homogeneous, there is a very simple relation between its mass and its density. Its density, as we have seen, is the amount of matter which one cubic centimetre of the body contains. Its mass is the amount of matter which the whole body contains. If, then, we represent by Fthe volume of the body, that is, the number of cubic centimetres which it occupies, it follows that M=Dr. [1.] This, translated into ordinary language, means that the amount of matter which a body contains is equal to the amount of matter which one cubic centimetre of the body contains, multiplied by the number of cubic centimetres which the body occupies. The mass of a body is determined from its weight ; for it will be hereafter proved that the weight of a body is proportional to the amount of matter it contains. It must, however, be carefully kept in mind, that weight, although proportional to mass, is not the mass, just as the arc of a circle is an entirely different quan- tity from the angle which it measures. M From equation [1] we obtain D = ^ ; that is, the density is the mass of the unit of volume, or, as above, the amount of GENERAL PROPERTIES OP MATTER. 19 matter in the unit of volume. In order to estimate mass and density, we assiime a certain amount of matter as a unit of mass and compare all other amounts with it. When ve say that the mass of a given volume of iron is 10, we mean that the amount of matter it contains is ten times as great as the amount of matter contained in this assumed unit of mass. In like manner, when we say that the density of mercury is eqiial to 1.386, we mean that one cubic centimetre of mercury contains 1.386 times as much matter as the unit of mass. In every case, the numbers express- ing mass and density stand for units of mass. The unit of mass is derived from the unit of weight, as will be explained in the section on Gravitation. The terms Mass and Density will be constantly used through- out this work, and their meaning should, therefore, be clearly impressed upon the mind. (16.) Impeneir ability. — Matter not only occupies space, but it also resists, with differing degrees of force, any attempt to reduce it into a smaller volume. Thus, one litre of air can be made to occupy a volume, so far as we can see, indefinitely smaller, but only by great mechanical force. This resistance which all bodies offer to any attempt to condense them, is termed Impenetr ability. PROBLEMS. 1 . What is the length of one degree on the meridian at the latitude of • 45° in French linear measure ? 2. The latitude of Dunkirk was found by Delambre to be 51° 2' 9"; that of Formentera, as determined by Biot, is 38° 39' 56". What is the distance between these parallels in metres ? 3. The distance between the parallels of Dunkirk and Formentera, as determined by triangulation, is 730,430 toises of 864 lignes each. What is the length of a metre in fractions of a toise, and in lignes ? 4. The equatorial and polar diameters of the globe are to each other in the proportion of 299.15 to 298.15. What is the length of each in metres ? 5. Had the decimal division of the circle mentioned on page 15 been adopted, what would have been the length of one degree, one mmute, and one second in metres ? 6. To how many cubic centimetres do five litres correspond ? To how many do 3.456 litres, 0.0034 Utre, and 5.674 litres correspond? 7. To how many cubic metres do 564.82 htres, 3240.85 htres, 0.675 litre, and 0.032 litre correspond ? 8. A box, measuring ten centimetres in each direction, wiU hold how many litres, and what portion of a cubic metre ? 20 CHEMICAL PHYSICS. 9. Reduce, by means of the table at the end of the book, — a. 30 inches to fractions of a metre. h. 76 centimetres to English inches. c. 36 feet to metres. <^. 10 metres to feet and inches. 10. Reduce, by means of the table at the end of the book, — a. 8 lbs. 6 oz. to grammes. h. 7640 grammes to English apothecaries' weight, c. 45 grains to grammes. 11: Reduce, by means of the table at the end of the book, — a. 4 pints to litres and cubic centimetres. h. 5 gallons to litres and cubic centimetres. c. 5 litres to English measure. d. 4 cubic centimetres to English measure. MOTION. (17.) Position. — We conceive of a body, not only as occupying a certain portion of space, but also as existing in space, and there- fore as being in a determinate Position with reference to other bodies. A book, for example, not only fills a certain amount of space, but also holds a certain position with reference to the surface of the table on which it lies, or with reference to the walls of the room in which the table stands. If we select a point of that book, its position on the table can easily be de- fined by measuring its distance from each of two adjacent edges of the table along a line parallel to the other of the two edges, and its position in the room can, in like manner, be defined by measuring its distance from two adjacent walls and the ceiling along lines parallel to the three edges formed by the meeting of these three surfaces. This is the method most commonly used in Geometry of defining the position of a point. The distances which determine the position of a point are called co-ordi- nates, and the edges and sur- faces to which the position is referred are called co-ordinate a£es and co-ordinate planes. In Fig. 1, the position of the ^^^^^^^^^^™ point p is determined by the GENERAL PROPERTIES OP MATTER. 21 Fig. 2. distances pb = b and p a = a from the two co-ordinate axes o x and y ; and in Fig. 2, the position of the same point is determined by the distances pc==c,pb = b, and pa = a from the planes xy, X z, and y z. In Part II. of this work, the use of co-ordi- nates -will be fully illustrated in their application to the study of crystallography. The position of points on the surface of the globe is referred to the equator and the meridian of Greenwich. In this case, however, the position is not defined by the distance from these planes, as in the example just taken, but by the latitude and longitude ; the jSrst being the angular dis- tance of the place from the equator measured on its own merid- ian, and the second the angle made by its meridian with that of Greenwich. In like manner, the position of a body in the solar system is defined by stating its distance from the sun and its angu- lar position with reference to the ecliptic and the vernal equinox, to which its heliocentric latitude and longitude are referred. (18.) Mobility. — The idea of position necessarily involves that of change of position, which we call motion. We cannot, for example, conceive of the book as having a definite position on the table, without also connecting with it the idea that its posi- tion could be changed, or, in other words, that it could move. A body is said to be moving when it is constantly changing its position with reference to the co-ordinate lines to which its posi- tion is referred ; and when no such change is taking place, it is said to be at rest. Rest and motion are relative terms ; for abso- lute rest is not known in nature. Every body on the surface of the globe partakes, not only in a motion of revolution roimd the axis of the earth, but is also moving round the sun, and per- haps accompanying the sun in its revolution round a more dis- tant centre. All known matter is in motion, and when, in any case, we say that it is at rest, we merely mean to assert that it is at rest with reference to certain lines or planes, which were arbitra- rily assumed for co-ordinates. A body on the deck of a steamboat may be at rest with reference to the boat, but in rapid motion with 22 CHEMICAL PHYSICS. reference to the earth. In like manner, a body on the surface of the globe, which is said to be at rest because it is not changing its position with reference to the equator and first meridian, is yet in very rapid motion with reference to the ecliptic and the vernal equinox. So, on the other hand, a body may appear to be in rapid motion, and yet at rest with reference to the earth or the sun. For example, a ship, which is sailing through the ocean at the rate of ten kilometres an hour, while the ocean current is flowing at the same rate in the opposite direction, is at rest with reference to the earth, although it would appear to be in motion to persons on board the ship. Again, any point on the surface of the globe at the latitude of 50° is moving from west to east, in con- sequence of the rotation of the globe on its axis, about 289 metres each second, but is, relatively to the surface of the globe, at rest. If a cannon-ball is, at the same latitude, moving 289 metres each second from east to west, it will appear to be in rapid motion to an observer at this point, while it is at rest with reference to the sun. Experience teaches us that a body may m-ove on the surface of the globe with equal readiness in any direction, and therefore that this motion is not influenced by the motion of the earth itself. The same amount of gunpowder which would drive the cannon- ball 289 metres each second from west to east, would drive it with the same velocity from east to west, or in any other direction. It is evident, from these and similar considerations, that a body may partake of several motions at once, and yet that each may be entirely independent of the rest. (19.) Time and Velocity. — All the phenomena of nature may be referred to motion ; and the succession of natural phe- nomena gives us the idea of duration, or tivie. In order to measure the duration of phenoinena, we select the duration of some one as our unit, and compare the duration of others with it. It is essential that our unit should be invariable, and such invar riable units of time we find in the motions of the heavenly bodies and in that of the pendulum. The duration of a single oscilla- tion of a pendulum 0.99394 m. long, at the latitude of Paris, is a second, the smallest unit in use, and the one which we shall have most occasion to use in this book. Therefore, when the unit of time is spoken of, it is always to be understood to mean one second. The duration of the revolution of the earth on its GENERAL PBOPEETIES OF MATTER. 23 axis is the next larger unit, ■which we call a day, and that of the reyoliition of the earth round the sun-, the largest unit in com- mon use, is called a year. The distance passed over by a moving body in the unit of time is called its Velocity, which we will represent by Jb. When, then, a body is said to have a velocity of ten metres, we merely mean that, if it continue to move at the same rate, it will pass over ten metres in each second of time. (20.) Uniform and Varying Motions. — The motion of a body is said to be uniform when its velocity does not change. In such motion the body will pass over the same distance in each second, or, in other words, the distance passed over in uniform motion is proportional to the time. Denoting, then, by d the distance passed over, and by T the niimber of seconds, we have d = bT, or t) = ^, and T^-^. [2.] We have an example of uniform motion in a railroad train moving with a constant speed. In varying motions, the distances passed over in successive seconds are unequal. The body has no longer a constant ve- locity, and its velocity at any moment is the distance it would pass over in each second, if, with the velocity then acquired, its motion suddenly became uniform. The motion of a body may vary according to different laws. There are twoJcinds of varying motion which it is important to study. They are called uniform- ly accelerated motion and uniformly retarded motion. (21.) Uniformly Accelerated Motion. — The motion of a body is said to be uniformly accelerated, when its velocity increases by an equal amount each second. This amount is called the ac- celeration, and will be represented by V. The most familiar ex- ample of such a motion is that of the fall of a stone to the earth. Starting from the state of repose, its velocity at the end of the first second is 9.8088 m., which we may call in round numbers 10 m. ; at the end of the second second, its velocity is 20 m. ; at the end of the third, 30 m.; at the end of T seconds, its velocity is 10 X T metres. To make the case general, if, starting from a state of rest, the body acquires a velocity each second represented by V, then its velocity, Jb, after T seconds will be, 24 CHEMICAL PHYSICS. In order to find the distance passed over at the end of T seconds, we make use of the principle proved by Galileo, that this distance is the same as if the body had moved at a uniform rate "with a mean velocity. In the case of a falling stone, the velocities at the end of successive seconds are, — 0" 1" 2" 3" 4" 5" 6" 7" n" Om. 10 m. 20 m. 30 m. 40 m. 50 m. 60 m. 70 m (10«)m. At the end of five seconds, the velocity is 50 m. ; at the com- mencement, the velocity is m. According to the principle just stated, the distance passed over is the same as if the body had moved uniformly during the five seconds with the mean velocity of 25 m. In like manner, the distance passed over between the end of the third and the end of the seventh second will be J (30 + 70) 4 = 200 metres. Eepresenting, then, the accelera- tion of velocity during each second by c, as above, we shall have, for the distance passed over during T seconds by a body moving with a uniformly accelerated motion, and starting from a state of rest, rf=J(0-f To) T=ii) T^ [4.J The truth of this principle can be proved in the following way . Let us suppose the time T divided into a large number (n) of very T small intervals. Each of these intervals will be represented by — . These intervals we will take so small, that the motion during this minute fraction of a second may be regarded as uniform, and as having the same velocity which it really has only at the end of the interval. Representing the velocity at the end of one second T T by t), the velocity at the end of — seconds will be, by [3], — t) ; T T the velocity at the end of 2 — seconds will be 2 — u : at the n n ' T T end of 3 — seconds, 3 — t), etc. n n Regarding this velocity as uniform during the interval, we have, by equation [2] , for the distance passed over during the first in- terval, the value c?i = -^ o. In the same way, we shall find, for the second interval, c?i = 2 -y d ; for the third, (?j = 3 -j- o ; and for the last, d„ = n-^'D. The space passed over during the whole time T will be equal to the sum of these values. GENERAL PROPERTIES OP MATTER. 25 rpz ij^2 rp2 y2 «^ = -2t) + 2-2-t> + 3 -5-*'+ +»*-2-t); or, rf=^D (1 + 2 + 3 + 4+ +«). The quantity within the parenthesis, being the sum of the terms of an arithmetical progression, is equal to f (w + 1) w ; and substituting tliis value, we obtain. This value of d will be the more accurate the smaller are the intervals of titne, or the larger the number into which T is divided ; and it will be absolutely accurate when the number is infinitely large. In this case # = 00, and the last equation be- comes the same as [4] , d = \vT\ [5.] For another time T', we should have d' = \v T'^, and, com- paring the two equations, d:d' = ^ii T^ : I » T" = T» : T'= ; that is,'tw a uniformly accelerated motion, the distances passed over by a moving body starting from a state of rest are propor- tional to the squares of the times employed. By substituting in [5] the value of T obtained from [3] , it gives, I b'2 for another velocity v', we should have d' = s— , and comparing this equation with the last, d-d' — ^ .y1 — ll= • Jb'" • which shows that, in a uniformly accelerated motion starting from a state of rest, the distances passed over by a moving body are proportional to the squares of the final velocities. By trans- position we obtain from [6] , which is an expression for the final velocity in terms of the dis- tance passed over, and the constant increment of velocity for each second. 3 26 CHEMICAL PHYSICS. Returning to the previous illustration, if Tve represent by a the distance through which a stone falls in the first second, -we can easily find the following values for the distances it will fall through during each succeeding second, and also for the whole distance it will have fallen through at the end of each second. 1" 2" 3" 4" 5" 6" 7" n" Successive distances, a 3a ba la 9a Hot 13 a.... (2 » — 1) a. Whole distances, a 4 a 9 a 16 a 25 a 36 a 49 a n^ a. The co-efficients in the last series are to each other as the squares of the times ; — which has already been proved. Those in the first series are as the series of odd numbers, and can be deduced from the last series, by subtracting from each of its terms the one next preceding it. (22.) Uniformly Retarded Motion. — A motion is said to be uniformly retarded, when its velocity diminishes by an equal amount each second. The motion of a stone, thrown perpendic- ularly into the air, is an example of a uniformly retarded motion. The velocity of the stone rapidly diminishes until it becomes zero, when for a moment it is at rest ; and then it falls back to the point where it started. If we now use d to denote the amount by which the velocity is diminished each second, or its retardation, it is evident that, at the end of T seconds, it will have been diminished t) T. If next we use Jb' to denote the initial velocity, it is also evident that the residual velocity at the end of T seconds will be expressed by the equation, t) = b' — t) T. [8.] The body will evidently come to rest when » T equals ll' ; when T= F- [9-] In the case of the stone, v is equal, as before, to about ten metres ; so that a stone thrown perpendicularly with a velocity of one hun- dred metres a second, would come to rest in ten seconds. At the end of five seconds, its velocity would be 100 — 10 X 5 = 50 metres. The distance passed over by a body moving with a uniformly retarded motion, at the end of T seconds, is evidently equal to the distance it would have gone in virtue of its initial velocity, less the amount by which it has been retarded. The distance it would have gone in virtue of its initial velocity is, by [2] , equal GENERAL PROPERTIES OP MATTER. 27 to V' T. Ill order to determine the amount by ■vrhich it has been retarded, we must remember that the distance lost each second is proportional to the diminution of Telocity. At the end of T sec- onds, the velocity lost is t) T, and the distance corresponding to this loss of velocity may be proved, by the same course of reason- ing used in (21), to be equal to | b T". Hence, d = \)' T—^vT\ [lO.J The height to which the stone of the previous example would rise in five seconds is then 100 X 5 — ^ 10 X 25 = 375 metres. We have found that a body moving with a uniformly retarded motion will come to rest when T= — . By substituting this value in [10] , we shall find that, when at rest, 21) 100^ The stone will then rise to -^ = 500 metres, before it begins to fall. (23.) Compound Motion. — It has already been stated, that a body may be moving in several directions at once, and moving with perfect freedom in each. The movements of the passengers on the deck of a vessel sailing over a calm sea preserve the same relations of direction and velocity, relatively to the different parts of the vessel, as if it were at rest. So also, the motions on the surface of the globe are not influenced by its rotation on its axis, or its motions through space. A point on the rim of a wagon- wheel partakes of the forward motion of the wagon, while it is also revolving roimd the axle. The actual motion of a body which is the result of two or more motions, is termed a com- pound motion ; and we will now inquire what must be the path and velocity of such motions, commencing with the simplest case, where there are but two motions, and where both are uniform. (24.) Parallelogram of Motions. — Let us then sup- pose that a body, starting from a, is moving towards m, with a uniform motion, and that at the same time the line a f is moving par- allel to itself, and also with Fig 3." 28 CHEMICAL PHYSICS. a uniform motion, towards e s, the point a always keeping on the line a e. Let iis also suppose that the velocities are so adjusted, that, when the body reaches the point £, the line will have reached the position e s. It is easy to show that the path described by the body is the diagonal a 5 of the parallelogram, of which a s and e s are two sides. Lay oif, in the direction a m, a line, a £, equal to the velocity of the moving body, and on the line ana. distance, a e, equal to the velocity of the moving line. Divide both of these lines into the same number of equal parts. Each of these will be equal to the space passed over by the moving body or line in a small frac- tion of a second, which we may take as small as we choose. At the end of the first of these intervals, the body will evidently reach the point p ; at the end of the next, the point q ; at the end of the third, r ; and so on, until the end of the second, when it will reach the point s. By making the number of intervals larger and larger, we can prove that the body will pass succes- sively a larger and larger number of points on the line a s ; and by making the number of intervals infinite, that it will pass every point on the line, or, in other words, that it will move on the line itself. It will be noticed, that the proof is general for any velocities when the two motions are uniform ; and moreover, that the line a s represents, not only the direction, but also the velocity of the moving body. Hence follows the well-known proposition, first enunciated by Galileo, and generally termed the Composition of Velocities : — The velocity resulting from two simultaneous ve- locities is represented, both in direction and in amourit, by the diagonal of a parallelogram constructed on two straight lines, which represent the direction and amount of these velocities. The reverse of this must also be true ; and any given motion may be considered as resulting from two others which stand in the same relations to it, both as regards direction and velocity, that the sides of a parallelogram do to its diagonal. Hence the converse proposition: — A velocity in any given direction may be resolved into two others, represented both in direction and amount by the tivo sides of a parallelogram, of which the first velocity is the diagonal. As the same line may be the diagonal of an infinite number of different parallelograms, it follows that a given motion may be GENERAL PROPERTIES OF MATTER. 29 composed of, or may be resolved into, an infinite number of dif- ferent pairs of uniform motions. We liave considered, above, a motion as resulting from two other uniform motions ; but a motion may result from three or more motions. As these motions are entirely independent of each other, we can obviously find, by the above method, what would be the result of two alone ; and then, by combining this resultant with the third motion, we shall obtain a second result- ant, which would be the result of three alone ; and by combining the second resultant with the fourth motion, we should obtain a third resultant ; — and so we can proceed until we obtain the final resultant of all the motions. What has been proved to be true in regard to the resultant of two or more uniform motions, is also true in regard to two or more uniformly varying motions, provided the variations of both follow the same law. This truth can easily be proved in the case of two uniformly accelerated or uniformly retarded motions, by laying off, on two lines representing the directions of the motions, the spaces passed over during successive intervals of time, taken so small that the motion during each interval may be considered uniform. We can thus find the points at which the moving body will be at the end of these successive intervals, as above ; and it will then be easy to prove that the resulting motion may be rep- resented, both in direction and velocity, by the diagonal of a parallelogram, of which the two sides represent the velocities at the end of one second. In the case where the original motion is uniform, it is easy to prove that the resulting motion is also uniform ; and where it is varying, that the resulting motion varies according to the same law as its two components. Thus, in the last example, the result- ing motion will be uniformly accelerated or retarded, as the case may be. (25.) Ourvilinear Motion. — In the cases above considered, the resulting motion is reclilinear ; if, however, any one of the motions of which a compound motion is composed obeys a differ- ent law from the rest, the resulting motion is curvilinear. As the velocity of a moving body may vary according to many dif- ferent laws, and as an infinite number of combinations of such varying motions may be made, an infinite variety of curvi- linear motions may result. We can only consider here one, and 3* 30 CHEMICAL PHYSICS. Fig. i- that one of the simplest cases, which will serve as an example of the rest. Let us, then, suppose a body moving from a to m (Fig. 4) with a uniform motion, and at the same time moving in the direction a n with a uniformly accelerated motion. An ex- ample of such a motion would be that of a cannon-ball, fired horizontally from the embra- sure of a fort, at some height above the general surface of the ground. In virtue of the projectile force, it would move horizontally along the line a m with a uniform motion, while in obedience to the force of gravity it would rapidly fall to the earth, in the direction a n, with a uniformly accelerated motion. To find the path of the re- sulting motion, let V be the velocity of the uniform motion, and V the acceleration of velocity of the falling body for each second. Lay off on the line a m the distances a ^, ^y, yS, etc., each equal to t). Lay off on the line a n the distances ab,b c,cd, etc., equal to ^ t), f t), I V, etc., the distances through which the ball will fall in successive seconds. Draw through each of the points ^, y, 8, etc., lines parallel to a n, and through b, c, d, etc., lines parallel to am. The points P, Q, R, etc., where the first set of lines inter- sect the second, are evidently points through which the ball must pass. Join these points by a curved line, and this line will repre- sent the path of the ball. It is easy to show that this path is a parabola. For tliis purpose, let the lines a m and an he the axes of co-ordinates. The co-ordinates of any point, as s, are s e = a; and s £=^1/; and we know that x^s a^V T, and also ^z = e o = iv T\ Equating the values of T obtained from these equa- tions, we have, by reduction, ^. 2 ll2 Since 2t)2 parabola, inyiiich 4jo=: is a constant quantity, this is the equation of a 2t)2 1) GENERAL PROPERTIES OP MATTER. 31 PROBLEMS. Velocity and Uniform Motion. 12. A locomotive runs 36 kilometres in l*"' 20'. What is the velocity of the locomotive ? 13. A horse trots 11 kilometres in one hour. What is his velocity? 14. A man walks 5.6 kilometres in I''- 10'. What is his velocity? 15. From the extremities, A and B, of a straight line 24,000 m. long, two bodies start at the same time. The one from A moves in the direc- tion A B with a velocity of 2 m.; the other from B, in the direction B A, with a velocity of 3 m. At what distance from A, and after what time, will they meet ? 16. From the extremities, A and B, of a straight line am. long, two bodies start ; the one from A, t" after the one from B. The one from A moves with a velocity of c m., the one from B with a velocity of Ci m. At what distance from A will they meet ? Uniformly Accelerated or Retarded Motion. 17. Find the space through which a body falls in 7", and the velocity acquired. The increment of velocity each second is I) = 9.8 m. 18. A stone falls from the top of a tower to the earth in 2.5". How high is the tower when B = 9.8 m. ? 19. On the surface of the moon, the increment of velocity of a falling body is B = 1.654 ; on the surface of the planet Jupiter, t) = 26.243. Find the answers to the last two problems with these values. 20. A stone is let fall into a pit 100 m. deep. With what velocity will it strike the bottom of the pit ? With what velocity would it strike the bottom of a similar pit on the moon, and on Jupiter ? 21. A stone is projected vertically with a velocity of 50 m. How high wiU it rise from the earth ? How high would it rise from the moon, and from Jupiter ? After how many seconds will it again reach the ground in the three cases ? 22. A body is projected vertically from the bottom of a tower 80 m. high, with a velocity of 48 m. In what time will it reach the top, and what will be its velocity at that time ? Also, to what height above the top of the tower wiU it rise, and after what time will it again reach the bottom ? 23. A body is projected vertically with 30 m. velocity. A second later, another body, with 40 m. velocity, is projected vertically from the same point. At what point of elevation will the two meet ? 24. A cannon-ball, being projected vertically upwards, returned in 20" to the place from which it was fired. How high did it ascend, and what was the velocity of its projection ? Solve the problem also for B = 1.654, and B = 26.243. 82 CHEMICAL PHYSICS. FORCE. (26.) Force. — Matter, of itself, is incapable of changing its state, either of rest or of motion. If a body be at rest, it cannot put itself in motion ; if a body be in motion, it can neither change that motion nor reduce itself to rest. Any such change ' must be produced by some external cause independent of the body. This quality of matter we term Inertia ; and the external cause we term Force. In discussing the origin and nature of force in the introductory chapter, we used this word for the cause of all the phenomena of nature. We shall use it, in this section,, in a more limited sense, as meaning " any agency which, applied to a body, imparts motion to it, or produces pressure upon it, or causes both of these effects together." In studying the action of a force vipon a body, we must consider three things. First, the point of the body to which it is applied, its point of application ; secondly, its intensity ; thirdly, its direction. The action of forces on bodies is the subject-matter of Mechanics. We shall only be able to consider here those elementary principles of this science which we shall have occasion to use in this book, referring the student to works on Mechanics for a full exposition of the subject. (27.) Direction of Force. — When a force applied to any point of a body causes it to move, the direction of the motion is the direction of the force. If the point cannot move, the direc- tion of the force is the direction of the pressure exerted by it, or the direction in which the point would move if it were free. When two or more forces are applied to any point of a body, each of these produces the same effect as if it were acting alone. This is a necessary consequence of what has already been stated, in regard to the perfect freedom with which a body may move in several directions at once. Each of these motions may be the result of a separate force, which thus acts in producing motion as if it were acting alone. Hence, also, the action of a force, upon a body is not affected by its condition of rest or motion, because the result which it produces is by the above principle entirely in- dependent of the motions which other forces have impressed upon it. For example, if a body moving with a given velocity, under the influence of a given force, is suddenly acted upon by another and equal force, in a direction at right angles to the first, it will GENERAL PROPERTIES OP MATTER. 33 move in the new direction with the same velocity as if it had been previously at rest. The path it describes can be found by combining the two motions according to the principles already described. It follows from this principle, that a body under the in- fluence of a force which is constant, both in direction and intensity, moves with a uniformly accelerated velocity. That this must be the case can be seen by reflecting that, if this force imparts to the body a velocity B during the first second, it will, from the principle just stated, impart the same velocity during each succeeding second. At the end of the second second, the body will then have the velocity gained during two seconds, or 2 t) ; at the end of the third second, it will have the velocity gained during three seconds, or 3 D ; and so on. In other words, the velocity will be proportional to the time, which is the characteristic of uniformly accelerated motions. The reverse of this also must be true ; that is, a body moving; with a uniformly accelerated velocity in a straight line, must be under the influence of a force of constant intensity acting in the direction of its motion. If, when a body has acquired a given velocity, the force ceases to act, the body will continue to move with the same velocity and in the same direction which it had when the action of the force ceased ; in other words, it will have a uniform motion, and the motion will continue until it is arrested by an equivalent force, acting for an equal time in the opposite direction. This, which is a necessary consequence of the principle of inertia, is illus- trated by many familiar facts. A train of cars continues to move after the action of the steam has ceased, and until the fric- tion of the wheels and the resistance of the atmosphere destroys the motion. Were it not for these opposing forces, a body once set in motion on the earth would continue to move indefinitely with the same velocity, and in the same direction, which it had when the force which produced the motion ceased to act. This does not admit of direct experimenta,l illustration ; because, on the surface of the earth, we can never entirely remove a body from the influence of the resistance of the air or of friction. But even here, the more completely these influences are removed, the longer motion continues ; and in the heavenly bodies, where they do not exist, at least to any sensible degree, the motion is per- 34 CHEMICAL PHYSICS. petual. A uniform motion does not, tlierefore, imply the exist- ence of a force still acting ; it only shows that a force has acted at some previous time.* (28.) Equilibrium. — "When two or more forces are acting on a body, or on a system of bodies, in such a way that they exactly balance each other's eifects, they are said to be in equilibrium. Forces so adjusted will not communicate motion to a body at rest, or alter its motion, if already in motion. That portion of the science of Mechanics which treats of the conditions of equilibri- um, is termed Statics ; that part, of which the object is to deter- mine the motion which a body assumes when the forces which are applied do not constitute an equilibrium, is called Dynamics. (29.) Measure of Forces. — We conceive of forces as having different intensities, and hence as quantities, which can be ex- pressed in numbers, selecting one of them as the unit. As, however, we only know forces through their effects, we can only compare them together by comparing their effects ; that is, by comparing together the amounts of motion they cause, or the amounts of pressure they exert. Let us then seek for a measure of force in the amount of motion which it causes. In discussing this subject we can assume as axioms, — first, that two forces are equal which will give equal velocities to equal amounts of matter in the unit of time ; secondly, that two forces are equal which, when applied in opposite directions to any point of the same body, or to any two points situated in the line of the forces and inseparably united, leave it at rest. The following proposi- tions can now be easily proved. Proposition 1. Two constant forces, which in the unit of time impart to unequal masses of matter equal velocities, must be to each other as these masses. Let us suppose that we have n equal masses of matter, each represented by m, on which are acting n equal forces in directions parallel to each other, each represented by /. By the axiom above, each of these masses * This statement does not apparently agree with the principle of the introductory chapter, in which it is maintained that all phenomena imply a continuously acting cause ; but it must bo remembered that the word force is used here in its mechanical sense, and that although in this limited sense present motion does not imply acting force, yet it by no means follows that the motion is not maintained by the very will of which what we term mechanical force is but another manifestation. The subject is involved, however, in philosophical difficulties, which cannot be discussed in this con- nection. GENERAL PKOPEETIES OP MATTER. 35 will receive the same velocity in the unit of time ; they will, there- fore, all move in the same direction and with the same velocity, and must preserve the same relative position. We may then regard them as united in a single body, whose mass is equal to n X m, on which is acting a force equal to w X /. Hence it follows, that the force n X f will give to the mass n X m the same velocity that the force / will give to the mass n. It is evi- dent that n X f '■ f ^=^ n X m : m. To make this proof more general. Let M and M' represent the two masses of matter, which we will suppose to be commensu- rable, and let m be their common measure ; so that M= n m, and M' = n' m. Represent by/ the value of the force which will impart to m the given velocity in the unit of time ; then, by what precedes, nf will give the same velocity to n m, or M, and n'f " " " n' m, or M'. Represent nf by F, and n'f by F', and we have nf:n'f=nm:n'm, or F : F' = M: M', [11.] which was to be proved. If the masses are not commensurable, we can take m infinitely small. Proposition 2. Two constant forces , which in the unit of time impart to equal masses of matter unequal velocities, must be to each other as these velocities. Represent the two forces by F and F', which we will suppose to be commensurable, and let / be their common measure ; so that F= nf, and F' = n' f. Represent also by t) and tj' the velocities which these forces re- spectively impart to the common mass, M, in the unit of time. The force / will be capable of imparting to ilf a velocity, which we will represent by t)". It follows now, from the last proof, that F = w/ will impart to ilf a velocity n V" = n, and that F'=^ n'f " " " n'v" = v'; ' nf:n'f=nv" :n'v", or F: F' — v :v'. [12.] Proposition 3. Two constant forces are to each other as the products of the masses by the velocities which they impart to these masses in the unit of time. Let F and F' be the two forces 36 CHEMICAL PHYSICS. acting on the masses 31 and M', and imparting to them the velocities v and v' in the unit of time. Eepresent by / a force which imparts to the mass M the velocity t)' in the unit of time. F and / are, then, two forces which, in the unit of time, impress on equal masses, M and 31, unequal velocities, t) and v' ; hence, from Prop6sition 2, F:f=v : »'. Moreover,/ and F' are two forces which impress on unequal masses, itfand 31', equal velocities, v' andu' ; hence, from Prop- osition 1, f:F' = 3I: 31'. Multiplying the two proportions, term by term, we obtain F: F' = 3In: M'V, [13.] which was to be proved. In order to measure a force, we have then only to select some one force for our imit, and, by the principles of the above propo- sitions, compare all other forces with it. We will then assume, as the unit of force, that force which, acting on the unit of mass during one second, will impress upon it a velocity of one metre, or that force which causes an acceleration of one metre in the velocity of the unit of mass each second. If then a given force, F, acting during one second, impresses on a given mass of mat- ter, 31, a velocity, o, we can easily find the relation it bears to the imit of force by the above proportion, F: F' = 3In: 31' V. If F' is the unit of force, then, by definition, 31' and d' are both equal to unity ; and the proportion gives F=3Ixi. [14.J It will be remembered (21), that the quantity D is termed technically the acceleration. Hence, the measure of a force is the product of the mass moved by the acceleration,. For example, if the mass moved is equal to four units of mass, and the accel- eration is equal to six metres, the intensity of the force is equal to twenty-four ; that is, the intensity of the force is twenty-four times as great as the unit of force. If a constant force continues to act upon a body during a given time, it imparts to it each second, as we have seen, as much ve- locity as it gave to it the first. This velocity we have called the GENERAL PROPERTIES OP MATTER. 87 acceleration, and represented by jj. At the end of T seconds the velocity is T », which has been represented by t). If now the force ceases to act, the motion becomes uniform, and the body continues to move with the velocity t) = T t). In order to stop this motion, it would be necessary to apply to the body, in an op- posite direction, a force of the same intensity, for an equal time. If M represents the mass of the body, M » represents the inten- sity of the original force ; and hence it would require a force of the intensity Mv acting during T seconds to destroy the mo- tion. Evidently, however, the same effect could be produced by a force of T times the intensity, acting for one second. The intensity of this force would be TMx) = M{). [15.J Hence the product of the mass of a body by its velocity repre- sents the intensity of a force which, acting during one second, will bring the body to rest. This product is usually called the viomentum of a moving body. We say, for example, that a body whose mass is equal to five tmits, and which is moving with a velocity of four metres, has a momentum equal to 20 ; and we mean by this, that it would require a force twenty times as intense as the unit of force, and acting for one second in a direc- tion opposite to that of the motion, to bring the body to rest. The momentum is also frequently called the moving force of the body, because it not only represents the intensity of the force re- quired to overcome its motion, but also -because the body itself would exert a force of this intensity against any obstacle tending to resist its motion. In this view, momentum may be regarded as representing the accumulated intensity of force in a body ; the product M t) representing the intensity of force in a body after one second ; the product M t) representing the accumulated in- tensity after T seconds. It must be carefully noticed, that we have considered in this section solely the measure of the intensities of forces, and not the measure of their quantities. The quantity of a force, or, as this is frequently called, its power, is measured in a different way, as will be shown in (42). In this work, we shall have to deal almost solely with the intensities of forces, and when the measure of force is referred to, it must be always understood to mean the measure of its intensity, luiless the reverse is ex- pressly stated. 4 38 CHEMICAL PHYSICS. COMPOSITION OF FORCES, (30.) Components and Resultant. — In mechanical problems we frequently have two or more forces acting at once on the same point of a body, or on several points which are immovably united together ; and it becomes important to consider what will be their combined effect. This problem, which is termed the composition of forces, reduces itself to that of finding the direction and amount of a single force which would produce the same motion as that resulting from the action of all the forces combined. This single force is called the resultant, and the forces to which it is equivalent in effect are called its components. It follows, from this definition, that a force is mechanically equivalent to the sum of its components, and, on the other hand, that any number of forces are mechanically equivalent to their resultant ; because, as we only know forces through their effects in pro- ducing motion, any forces which produce the same motions are to us equivalent. (31.) Forces may be represented hij Lines. — The unit of force has been defined as that force which causes an acceleration of one metre in the motion of the unit of mass each second ; and, further, it has been shown that the product of the mass moved, by the acceleration, is the number of units of force to which any given force is equivalent. If, then, we represent the unit of force by a line one centimetre long, any other force will be repre- sented by a line as many centimetres long as the number which is obtained by multiplying the mass it moves by the acceleration it imparts each second. Moreover, since these lines may be made to represent the directions as well as the amounts of the forces, the problems of resolution of forces may be reduced to problems of geometry. (32.) The point of application of a force may be changed to any other point of the body on the line of the direction of the force, loithout altering- in any respect the action of the force on the body, provided only that the two points are immovably united tog-ether. The truth of this proposition seems almost self-evident ; for it amounts only to this, — that a given force acting in the direction A B (Fig. 5) will pro- '^' ' duce the same effect, whether it is applied GENERAL PBOPERTIES OF MATTER. 39 in pnsliing the body forward at A, or in pulling it forward from B. The following illustration may make the matter still clearer. "We will assume that the force applied at A is equal to five units of force, and is in the direction A B. "We will now apply two forces, each of the same value as the last, to the point B ; one in the direction A B, and the other in the direction B A, as we can obviously do, without changing the condition of the body. The second of these forces will, by the axiom of (29), exactly coimter- balance the force applied at A, and we shall then have left a force of five units applied at B, and acting in the direction A B, producing an equivalent effect to that of the first force. (33.) Resultant of Forces in the same Straight Line. — The resultant of a number of forces acting in the same straight line on a point of a body, is obviously equal to the sum of the forces acting in one direction less the sum of the forces acting in the opposite direction ; and this resultant is in the direction of the largest sum. If, for example, we have three forces applied to the point A (Fig. 5) in the direction A B, equal respectively to 4, 6, and 7 units, and two forces in the opposite direction equal to 18 and 10 units, then the resultant force will be eqiial to (4 ■+ 6.+ 7) — (18 + 10) = —11 units, and, as the nega- tive sign indicates, will act in the direction B A. The validity of this principle follows from the fact, that each force acts as if it were the only force acting (27). As was shown in the last .section, it is unimportant whether all the forces are applied at A, or whether they are applied at difierent points along the line A B. (34.) Resultant of Forces acting in differ- ent Directions, but applied at the same Point, or Parallelogram of Forces. — Let us sup- pose that we have two forces, F' and F", applied to the point A (Fig. 6), in the di- rections A b and A b' respectively, and let us inquire what will be their resultant. It has already been proved, that two forces acting on the same or equal masses of matter are to each other as the accelerations ; or, F' : F" = t)' : t)"- "What therefore is true in regard to the two Fig. 6. 40 CHEMICAL PHYSICS. velocities must be ti-ue relatively in regard to the two forces, so that if -we can, by any method, find tiie resultant of the two velocities, this same method will give us the resultant of the two forces. Now it has been proved (24), that the resultant of two velocities is represented, both in direction and amount, by the diagonal of a parallelogram whose sides represent the directions and velocities of the two motions ; and hence it follows, that the resultant of two forces is represented, both in direction and in- tensity, by the diagonal of a parallelogram whose sides represent the directions and intensities of the component forces. The re- sultant of two forces can, therefore, always be found by a very easy geometrical construction. It can also be calcvilated ; for we have, by a well-known principle of trigonometry, from Fig. 6, A C = AB -\- B C — 2 AB . B C . cos AB G ; or, since B A B' == 180° — ABC, and therefore cos A B C = — cos B A B', we have ATC" = AB" + BC' -i- 2 AB .BC cos BAB'. Representing the two component forces by F' and F", their re- sultant by F, and the angle between the components by a, the last equation becomes F'= F"-\- F"'-{-2 F' F" cos a. [16.] In many cases with which we meet in nature, the directions of the two components make a right angle ; then the last term of [14] disappears, and the equation becomes F^^F'^ -\- F"\ [17.] (85.) Decomposition of Forces. — As any given motion may be the result of an infinite number of pairs of motions (24), so any given force is the equivalent of an infinite number of pairs of forces. It follows from what has been proved above, that we can replace a given force acting on the points (Fig- '7^)? S'Hd represented in direction and intensity by A P, by the two forces represented by either of the pairs of lines A B and AB', AG and AG', AD and AD, AE and A B, or indeed by any other pair of forces which can be represented by the sides of a par- allelogram, of which the line representing the given force is the diagonal. As the sides of a parallelogram may have any GENERAL PROPERTIES OE MATTER. 41 Fig. 7. angular position whatsoever with reference to tlie diagonal, it follows that a given force may be decomposed into two others in any required directions. If, then, the value of a force in units, and two directions, are given, the value in units of , two components in these direc- tions can always be found. The problem can be solved geometrically thus. Draw a line, A C (Fig. 6), as many centimetres long as there are units in the given force. Draw two indefinite lines, A b and A b', in the required di- rections, making the given angles with A C. Finally, draw through C lines parallel to A b and A b'. These lines will intersect the first at the points B and B', and the length in centimetres oi AB and A B' thus determined will be the values in units of the required forces. The problem can also be solved by trigonometry. Denote the value in units of the given force by F, and those of the required components by x and p. Denote also the angles which x and y are required to make with i^ by a and ^ respectively. In the triangle AB Cj'we have AB: A C= sin A CB: sin ABC; and also, since A B' = B C, AB' : AC=sinBAC: sin ABC. Substituting in these proportions the equivalent values A B= x, AB'=y, BA C=a, A C B = ^, A B C;=180'' — S and i? S will be applied to the point in in op- posite directions ; and since, by construction, J. jS is equal to B S, these two components must also be equal, and will therefore neutralize each other. The two components parallel and equal to A P and B Q will also both be applied at the point m. In Pig. 10, where the original forces were in the same direction, tlie two components will be in the same direction, and will conspire to move the point m in the direction m C. In Fig. 11, where the original forces were in opposite directions, the two compo- nents will be in opposite directions, and will tend to move the point m in the direction of the greater component with a force equal to their difference. Hence, the final resultant will be a force in the direction m C, -parallel to the original forces, in the one case equal to their sum, and in the other to their difference. The point of application of this force may obviously be transferred to the point C, without altering the conditions of its action. To find the position of the point C. By construction, the sides of tlie triangle A Pr are parallel to those of the triangle m C A, and liliewise the sides of the triangle B Qt are parallel to those GENERAL PROPERTIES OP MATTER. 45 of tlie triangle m C B, and hence their homologous sides are pro- portional ; so that we have the proportions, AC:mC=rP:AP, and B C : m C = t Q : B Q. We have, hy construction, rP=AS = t Q = B S=f', AP==F', and BQ = F"; hence, by substitution, AC:mC=f'iF', and B C : m C =f" : F" \ or, mG=ACj, = BC^,, or A Cx F'= B C X F"; or, AC: BC = F": F'. [20.] Hence it appears that, when the two forces have the same direc- tion, as in Fig. 10, the point of application, C, of the resultant force divides the straight line A B, which joins the points of ap- plication of the components, into two parts, which are inversely proportional to the amounts of the given forces. When, on the other hand, the forces are in opposite directions, as in Fig. 11, the point of application of the resultant is still on the same line, but beyond the point of application of the larger of the compo- nents, and at distances from the points A and B, which are, as before, inversely proportional to the intensities of the two forces. Our general result, then, is the following : — I. In regard to the resultant of two parallel forces acting in the same direction. 1. The intensity of this resultant is equal to the sum of the intensities of its components. 2. The direc- tion is the same as the common direction of the components. 3. The point of application divides the line joining the points of application of the components into two parts, which are inversely proportional to the intensities of the forces. II. In regard to the resultant of two parallel forces acting in opposite directions. 1. The intensity of this resultant is equal to the difference of the intensities of its components. 2. The direction is the same as that of the larger component. 3. The point of application is on the line joining the points of applica- tion of the components, produced beyond the point of application of the larger of the two, and is at distances from these points which are inversely proportional to the intensities of the given forces. 46 CHEMICAL PHYSICS. Fig. 12. It follows, from the nature of a resultant force, that a force applied at C, Figs. 10, 11, which is equal and opposite to the re- sultant of the two forces F and F', ought exactly to balance this resultant. This obvious truth will enable us to put the validity of our conclusions to the test of experiment. The experiment may be arranged as in Fig. 12. P and P' are two points at the ends, for example, of a wooden rod. To these points are attached cords, which, passing over the two pulleys M and M', are at- tached to the two weights A and A'. A third weight, R, is suspended by means of a looped cord to the rod, so that its position can be easily shifted. In this ex- periment the weights cor- respond to the forces F' and F" of Fig. 10, while the cords indicate the directions in which the forces act. By varying the amount of the weights, and also the position of the weight R on the rod, it will be found that equilibrium can be maintained only when the conditions above stated are fulfilled. Thus, if the weight R be 20 grammes, the sum of the weights A and A' must also be 20 grammes. If A' is equal to 12 grammes, then A must equal 8, and the position of the loop on the rod must be siich, that O P' shall be to OP as 8 is to 12. If, then, the distance P P' is equal to 20 c. m., the distance P O will be 12 c. m., and P' O will be 8 cm. This same experiment also illustrates the case represented in Pig. 11, where the two components are acting in opposite direc- tions ; for, as the system of weights is in equilibrium, it follows that the force exerted by any one may be regarded as equal in intensity to the resultant of the other two ; this resultant, how- ever, acting in the opposite direction to the force exerted by the weight. Hence, we may consider the forces exerted at the points O and P' to be the components of a force equal to that exerted by the weight at P, but in a direction opposite to P M. Taking the values of the weights when the system is in equilibrium, as given above, it is evident that the amount of the resultant, and GENERAL PROPERTIES OF MATTER. 47 the position of its point of application, S, are the same as would be found by the rule ; for, in the first place, the weight A is equal to the difference of the two weights R and A', and, in the second place, the distances P O and P P are inversely propor- tional to the values of the two weights R and A'. (38.) Couples. — When the two parallel forces are exerted in opposite directions, there is one set of conditions which presents a case of peculiar interest ; and that is, when the two compo- nents are equal. In .this case, the value of the resultant is evi- dently equal to zero ; and, moreover, the point of application is at an infinite distance from the points of application of the two equal components. The last fact follows from the proportion [20] , A C : B C = F" : F'. This, by the theory of proportions, may be written, AC—BC:F" — F' = AC:F" = BC:F'; or, substituting (see Fig. 11} AB = A C—BC, nndF=F"—F', A B : F = A C : F" = B C : F'. Hence, A C = -Q , and BC=^^-^. [21.] Wlien the two components are equal, the resultant F ^0, and both the distances A C and B C become equal to infin- ity. In this case, therefore, there is no single resultant, and therefore no tendency to produce in a body any progressive mo- tion. Such a system of forces is termed a couple, and its ten- dency is to make the body rotate. The theory of couples is of great importance in mechanics ; but as we shall not have occasion to apply it in this work, we shall not dwell upon it. (39.) Composition of several Parallel Forces. — We can evi- dently find the resultant of several parallel forces, by combining them two by two, as in the case of forces acting in different directions. In Pig. 13, the points m, m', m", and m"' are the points of application of the parallel forces F, F', F", and F'", all acting in the same direction. In order to find a common resultant, we first combine F with F' ; let o be the point of appli- cation of the first resultant. We next 48 CHEMICAL PHYSICS. combine the first resultant with F", and let o' be the point • of application of the second resultant. Lastly, we combine the second resultant with F'", and we shall then find a final result- ant of all the forces. This is evidently equal in amount to the sum of all the components, and its point of application will be on the line o' m'", at an intermediate position between the two points, which may be determined by means of the proportions given above. Where all the parallel components are not in the same direc- tion, we combine each set separately, and thus obtain two partial resultants, acting in opposite directions. If these are equal, we shall have a couple, and no final resultant. If they are not equal, we can find a resultant by the method already described. (40.) Centre of Parallel Forces. — By referring to Figs. 10, 11, and the demonstration following, it will be seen that the position of the point G does not depend on the common direction of the forces represented by j1 P and B Q, but only on their rel- ative intensities. If we suppose these components to revolve round their points of application, A and B, the resultant will still pass through C in any position they may assume, provided only that they remain parallel. Moreover, it will be seen that the point of application of the resultant, which we transferred for convenience from m to C, may be at any point on the line of its direction. In other words, it is not fixed by the conditions of the problem, except so far as this, that it must be on the linem C R. It follows, then, that if, in the system of parallel forces of Fig. 13, we suppose the components to revolve about their points of ap- plication, their resultants will always pass through the point G, provided only that they remain parallel. In Fig. 14, all the components have been revolved through an angle equal to P' G P. The direction of the resultant has changed from P'G to P G, but it still passes through the point G. In the posi- tion of the components represented by Fig. 13, the point of application may be at any point of the body on the line G P which corresponds to the line G P' of Fig. 14. In the second position of the components in Fig. 14, it may be at any point on the line G P. The point G, in GENERAL PROPERTIES OP MATTER. 49 •which all the successive directions of the resultant intersect When its components revolve about their points of application, is called the centre of parallel forces. It follows, from this definition, that if the forces remain parallel, and their points of appli- cation invariable, this system of points may be turned round the centre of parallel forces without changing the point of appli- cation of the resultant ; so that, if this point were supported, the system would remain in equilibrium in any position we could give it in turning it round this point. (41.) Action and Reaction. — The simplest case of the action of one body upon another, is when a body in motion, which we may call M, strikes upon another at rest, which may be termed M'. If M' is free to move, it will be put in motion by the action of M, and in any case the reaction of M', in retarding ilf 's mo- tion, will be precisely equal to the action of ilf in communicating motion to M'. This principle, which is a necessary result of the inertia of matter, is generally expressed thus : — Action and re- action are always equal and opposite. The changes in the motion and in the moving force of both bodies, which result from collision, are in general of a complicated kind, and depend on the degree of elasticity of the bodies, their form, mass, and other circumstances. To simplify the question, we shall consider the bodies as completely devoid of elasticity, and so constituted that after the collision they shall move as one body. Let us then inquire what will be the direction and velocity of the united mass after the impact. The mass M', being previously at rest, can have no motion save what it may receive from the mass M, and consequently must move in the same direction as the mass M moved in before the collision. Again, since bodies cannot generate or destroy motion in themselves, it follows that whatever motion the mass M' may acquire must be lost by the mass Jf ; and also, that the total momentum of the united masses after the collision must be exactly equal to the momentum of the mass M before it. If t) and Jb' represent the velocities before and after impact, then, by (29), Mb and (ilf -f- M') tj' represent the momentum before and after impact ; and since these are equal, we have Mb = (iM-\-M')b', whence ^' = ^ m+M' ' ^^^'^ Let us next suppose that the two bodies are both moving, and 5 50 CHEMICAL PHYSICS. in the same direction ; the mass M with a velocity V, and the mass M' with a velocity t)', less than t). What will be the com- mon velocity after impact ? The momenta of the two bodies are M\) and M' V'. Since these motions are in the same direction, they cannot be either diminished or increased by the collis- ion, and hence the momentum of the united bodies will be Mb -j- M' b'. If, then, Jb" be the unknown velocity of the united masses, we have Mb + M'b' = iM+ M'-) b", and b" = — ^V^!^' - [23.] Let us now suppose that the two bodies are both moving, but in opposite directions, and that the momentum of M is greater than that of M'. On their collision, the momentum of M' will destroy just so much of that of M as is equal to its own amount ; for it is evident that equal and opposite momenta must destroy each other. The momentum left after collision must, therefore, equal Mb — M' b', and, using b" as before, we shall have Mb—M'b' = QM+M')b", and b" = ^=;^'. [24. j In the last case, as in the first, the reaction of the mass M' is equal to the action of the mass M. The action of the mass M has consisted, first, in destroying the momentum of M', eqxial to M' b' ; second, in giving to it the momentum M' b". The total action is therefore expressed by M' b' -\- M' Jb". The reaction of M' has consisted, first, in destroying a portion of the momentum of M, equal to M' b' ', and second, in subtracting from the re- mainder of the momentum of M the amount which it has after the collision, or M[ b". The total reaction is therefore, as before, M' b' -f M' b'. We will now suppose that the two masses are moving in differ- ent directions ; M in the direc- tion A B, Fig. 15, with a velocity b, and M' in the direction A' B', with a velocity b'. The direc- tion of the motion after collision, and the momentum of the united masses, can be easily ascertained by the application of the prin- ciple of the parallelogram of '^'K-i^- forces already explained (33). GENERAL PROPERTIES OF MATTER. 51 Let the distance CD represent the momentum Mh, and the dis- tance C D' the momentum M' V', and complete the parallelogram CD ED'. Draw its diagonal CE. This diagonal will then represent the direction of the common motion and the momen- tum of the combined masses, which is equal to (M-{- M'~) t)". To find the velocity, it will be necessary to divide the niimber expressed by this diagonal by the sum of M and M'. If, in the first case, we suppose the body M', at rest, to be in- finitely large, as compared with the moving mass M, then the value of lb' [22] becomes 0, which shows that the whole momen- tum is destroyed. This is practically the case when the moving mass impinges against a fixed obstacle, which is either very much larger than itself, or which is firmly fastened to the earth. The body must, however, be supposed to strike the surface of the ob- stacle from a direction at right angles to this surface. Should it strike the surface at an oblique angle, we may have a different result. Let us suppose an unelastic sphere impinges against an unyielding surface, D B C, in the direction A B, with a velocity t) and a momentum M 13 ; what would be the result ? By the principle of the parallelogram of force, the momentum ilf l) is equiv- alent to two others, one in the di- rection A D, and the other in the ' jj^ ^ direction D B. The first will be destroyed at the impact ; but the second, which is equal to M t) cos a, will give the sphere a motion with the velocity tj cos a in the direction B C. In the figure the surface is a plane, but the demonstration is true for any curved surface ; in such cases, however, the plane D B C of the figure is the tangent plane to the surface at the point of contact. It follows from the above discussion, that the loss of mo- mentum in a mass, M, impinging on another mass, M', is always proportional to its velocity. In the first case, for example, the u MM' loss, as can easily be deduced from [22], is equal to V ^| ^„ a quantity whos§ value is evidently proportional to that of \). The same truth can easily be established in all the other cases. In all the above cases, it can easily be shown that the re- 52 CHEMICAL PHYSICS. action of the body M' is always exactly equal and opposite to the action of the body M. The same is also true, when the body M acts on the body M' through the forces of gravitation, electri- city, magnetism, etc., and not by direct impact. A needle, for example, attracts a magnet with exactly the same force with which the magnet attracts the needle ; and were both free to move, the magnet would move towards the needle as well as the needle towards the magnet. It is also true, when a body does not strike, but merely presses against, an obstacle, — as, for example, when a weight rests on a table, — that the reaction of the obstacle is exactly equal to the pressure. (42.) Power, or Living Force. — It has been shown (14), that the intensity of a force is measured by ilf j) . In the case of a loco- motive, for example, ilT represents the whole mass of the locomo- tive and train, and v the acceleration of velocity imparted by the moving force each second. Were the motion not retarded by friction and other causes, its velocity would increase indefinitely, according to the laws of uniformly accelerated motion already de- scribed. In fact, holrever, with a given force, F, this velocity soon comes to a maximum, which it does not exceed ; and so long as the force and the resistance do not vary, the train moves with a uni- form motion. During this time the action of the force is exactly balanced by the resistance arising from friction and other causes, and the train moves in virtue of the momentum, MV, previously acquired. In the space passed over by the train each second, the counteracting forces just neutralize the force F, exerted by the moving agent during the same period. It might now be supposed, that, if this force were suddenly quadrupled, so as to equal 4 F, the velocity would again increase until it attained to four times its present amount. In fact, however, its velocity rapidly increases, but only to twice its present amount ; and then it is found that the resistance is again just balanced by the greater force. That this must be the case can be seen by reflecting, that, with a double velocity, the moving train passes over double the space each sec- ond, and therefore encounters 'twice as many points of resistance. Moreover, it strikes each of these points with double the velocity, and hence meets at each point twice the resistance. It there- fore meets, during a second, twice as many points of resist- ance, and suffers at each point twice as miich resistance. The resistance during a second is thus four times as great as before, GENERAL PROPERTIES OP MATTER. 53 and must require four times as much force to overcome it. In order to obtain three times the velocity, it would be necessary to increase by nine times the force ; and in general the force re- quired will be proportional to the square of the velocity to be attained. What is true of the motion of a train of cars is true also of the motion of a steamboat through the water, and indeed of any motion on the surface of the earth, since all such motions encounter resistance. Hence, the work accomplished by a force is proportional, not to the velocity, but to the square of the ve- locity which it imparts to the moving body. The space passed over during a secomd by a body starting from a state of rest, is equal to 1 1) [6] . The intensity of the force which has moved it over this space is equal to Mv The product of the intensity of the force by the space passed (the number of points at which it has acted), represents the work accomplished by the ~ force. This product, equal to ^ M v', was named by Leibnitz vis viva, or living- force, to distinguish it from force which does not produce motion, biit only pressure ; and which he named dead force. A discussion was excited by Leibnitz on this subject, in which all the mathematicians of the eighteenth cen- tury took part, and which continued for more than forty years ; — one party claiming, with Leibnitz, that force was proportional to the square of the velocity ; and the other, that it was propor- tional to the simple velocity, — the first party measuring force by the vis viva, and the other by the momentum. As not unfre- quently happens in such cases, both parties were right ; and their two opinions were harmonized by introducing the element of time. For, as we have seen, the living- force represents, not the intensity of the force at any instant, which is always meas- ured by Mv, but the work which the force will accomplish dur- ing a second of time. It represents, in other words, the power or quantity of the force, in distinction from the intensity of the force. The intensity of a •force has been represented by F. The power or quantity of a force may be denoted by P. Hence, F=Mv, and P=^i-i»ft)^ [25.J The ■word force is generally used in a restricted sense, as in (29), to denote only the intensity of any effort, the quantity of the force exerted being called power. These terms will be adopted with their usual sense in this volume. 5* 54 CHEMICAL PHYSICS. PROBLEMS. Note. The following problems should be solved both by geometiical constraction and by trigonometry, whenever both methods are applicable. Measure of Force. 25. A mass of matter equal to 10 units of mass receives an acceleration from a given force of 5 metres. What is the intensity of the force ? 26. A mass of matter equal to 7 units of mass receives an accelerar tion from a given force of 9.8 metres. What is the intensity of the force ? 27. A mass of matter equal to 15 units of mass receives an accelera- tion from a given force of 1.654 metres. What is the intensity of the force ? 28. A mass of matter equal to 20 units of mass receives an accelera- tion from a given force of 26.243 metres. What is the intensity of the force ? Momentum. 29. A railroad train whose mass equals 1000 units is travelling with a velocity of 50 kilometres an hour. What is its momentum ? How many units of force would be required to stop the train in ten minutes, supposing the moving power to cease acting ? 30. A vessel whose mass equals 120,000 units is moving with a ve- locity of 2.25 metres. What is its momentum ? How many units of force would be required to stop it in five minutes, supposing the moving power to cease acting ? If the resistance of the water and other causes of retardation are equivalent, on an average, to a force of 900 units, how soon would the vessel come to rest after the moving power ceased ? Composition of Forces. 31. Three forces are acting on a point in the direction A B, equal re- spectively to 20, 35, and 70 units. In the opposite direction, B A, are acting four forces, equal respectively to 10, 45, 15, and 30 units. What is the intensity, and what the direction, of the resultant ? 32. A force equal to 1000 units is acting on a point in the direction B A. What is the intensity of each of two components, which are to each other as 3 : 5, and both of which are acting in the same direction as the resultant ? What is the intensity of each of two components, one of which acts in the direction of the resultant and the other in an opposite direction, and which are to each otlier in the relation of 3 : 5? 33. It is required to resolve a force equal to 441 units into six compo- nents, in the same direction as the resultant, whose intensities shall be to each other as 1 : 2 : 2^ : 2^ : 2^ : 2*. 34. It is required to resolve a force equal to 44 units into six compo- GENERAL PEOPEKTIES OP MATTER. 55 nents. Three of these, which have the same direction as the resftltant, are to each other as 1 : 3 : 5 ; while the three others, which have an op- posite direction, are to each other as 1 : 2 : 3. Moreover, the sum of the first is 5.4 times greater than the sum of the last. 35. Two forces are acting at right angles to each other on one point. The force F' == b units, and the force F" = 5 /s/'s units. What is the intensity of the resultant ? and what is the angle which its direction makes with the direction of F' ? 36. Two forces acting at right angles on one point are equal, F' to 3 units, and F" to 4 units. What is the intensity of the resultant ? and what is the angle which its direction makes with the direction of F'? 37. It is required to resolve a force, F = 100 units, into two compo- nents, F' and F", making with F the angles 65° and 25° respectively. What must be their intensities ? 38. It is required to resolve a force, F = 100 units, into two compo- nents at right angles to each other, one of which which shall be equal to 30 units. What must be the value of the second component ? and what the values of the angles which both components make with the resultant ? 39. Two forces, each equal to 100 units, act on one point. The angle made by the directions of the two forces equals 45°. What is the value of the resultant ? 40. The directions of two forces, F' = 100 and F" = 50, acting on one point, make an angle of 145°. What -is the value of the resultant F ? and what are the angles which ^ makes with F' and F"l 41. It is required to decompose a force, F = 125, into two compo- nents, the direction of each of which shall make, with the direction of F, an angle of 25°, What will be the value of each component ? 42. It is required to resolve a force, J?'= 100, into two components, F' and F", whose direction shall make, with the direction of F, the an- gles of 10° and 20° respectively. What will be the value of each com- ponent ? 43. Five forces, whose directions are in the same plane, act on one point. The intensities of the forces, and the angles which their directions make with a fixed direction passing through the point of application in the same plane, are given in the following table : — Intensity of the Foicea. Inclination to the fixed Direction. 90 50° 100 120° 120 170° 50 250° 40 290° What is the intensity of the resultant ? and what is the angle which its direction makes with the fixed direction ? 56 CHEMICAL PHYSICS. 44.' The force F = 100 is resolved into, two components, F' = 100 and F" = 150. What are the angles which the directions of these com- ponents make with the direction of F? 45. At the extremities of a straight line 44 c. m. long, two parallel forces, F' = 15 and F" = 7, are acting in the same direction. "What is the intensity of the resultant ? and what is the position of the centre of the two forces ? 46. At the extremities of a straight line 12 cm. long, two parallel forces, F' = 19 and F" = 13, are acting in opposite directions. What is the intensity of the resultant ? and what is the position of the centre of the two forces ? Action and Seaction. 47. A mass M = 20 units, moving with a velocity of 5 m., meets a second mass M' =15 units, which is at rest. What will be the ve- locity of the combined masses after collision ? In this and in the few succeeding problems the masses are supposed to be unelastic, and so constituted that after the collision they will move on together as one body. 48. A mass Jf = 500 units, moving with a velocity of 15 m., meets another mass M' = 50 imits, moving with a velocity of 10 m. in the same direction. What will be the velocity of the combined masses after the collision ? 49. A mass M= 250 units, moving with a velocity of 20 m., meets another mass M' = 300 units, moving with a velocity of 2 m. in the op- posite direction. What will be the velocity of the combined masses after the collision ? 50. A mass M= 25 units, moving with a velocity of 5 m., meets an- other mass M' = 30 units, moving with a velocity of 2 m. The direc- tions of the two motions before collision make with each other an angle of 75°. What will be the velocity of the combined masses after the collision ? and what will be the angle made by the direction of the resulting motion with the directions of the two motions before coUision ? GRAVITATION. (43.) Definition. — When bodies near the surface of the earth are left unsupported, they fall to the ground ; or, if supported, they exert a downward pressure, which we term their weight. The cause of these phenomena is called the force of gravity. This force is the attraction which the earth exercises upon all bodies on or near its surface, and is only a particular case of a GENERAL PROPERTIES OF MATTER. 57 general force of nature, in virtue of wliicli all bodies in the iini- verse attract each other, with a force depending on their masses and their mutual distances. Astronomy exhibits tlie grandest examples of this force, in the motions of the heavenly bodies ; but it can also be shown that the same force acts upon the smallest masses of matter with which we experiment on the surface of the globe. The existence of this force of attraction between the heav- enly bodies was first recognized by Newton, who discovered the law which it obeys, and gave to it the name of Universal Gravi- tation. In this work, we shall only have occasion to study tliose phenomena of gravitation which are caused by the attraction whiph the earth exerts for bodies on or near its surface. Let us then inquire what is the direction, what the point of application, and what the intensity of this force. Compare (26). (44.) Direction of the Earth's Attraction. — It has been stated (27), that the direction of a force is the direction of the motion which it causes, or the direction of the pressure which it exerts. When bodies fall freely, they move on a line which, if extended, would pass through a variable point near the centre • of the globe, called its centre of gravity. Hence, the direction of the force of gravitation is that of a line joining the centre of gravity of the earth to the point of application of the body. This direction is given by a plumb-line, which is merely a small weight, generally of lead, suspended by a light and flexible thread (Fig. 17). When the weight thus freely suspended is at rest, it is easy to show that the pressure exerted by the force of gravitation is in the direction of the line. In Fig. 18, for example, this pressure must be in the direc- tion A C. To prove this, suppose for a moment the force exerting the pres- sure were in any other direction, as A B ; then the force in the direction A B could be decomposed into two components, one in the direction A C, which would be neutralized by the resistance of the point of suspension, the other in the direction A D, which would cause motion. As by supposition the weight is at rest, it follows that the direction of the pressure, and hence 9 Fig. 17. Fig. 13. 58 CHEMICAL PHYSICS. also the direction of the force qi gravitation, must be tliat of the plumb-line. If several plumb-lines be placed near each other, it will be found that the lines when at rest will all be sensibly parallel to each other ; because their distances apart are inconsiderable in comparison with the length of the radius of the earth. Hence the directions of the forces of gravity exerted by the earth on neighboring bodies are parallel. The direction of the plumb- line at any place is called the vertical direction, and the di- rection perpendicular to this the horizontal direction. The surface of a liquid at rest, as will be proved hereafter, is always horizontal, and therefore perpendicular to the plumb-line. (45.) Point of Application of the Earth's Attraction. — As every particle of a body is similarly situated towards the earth, it follows that every particle must be equally attracted, and that there must be as many points of application as there are parti- cles of the body. The action of the earth's attraction may there- fore be regarded as the action of an infinite number of parallel and equal forces on as many distinct points of application. The resultant of these forces can be easily found by extending the method, discussed in (39), of finding the resultant of several parallel forces, to the case where the number of forces is infinite. As the general conclusions of (39) are independent of the num- ber of parallel forces, it follows that the direction of the result- ant of the forces of gravity, acting on the particles of a body, is parallel to the common direction of the forces, and also that the intensity of the resultant is equal to the sum of the intensities of the components. If, for example, A B (Fig. 19) represents a mass of matter, and the small arrows pointing vertically downwards represent the directions of the gravitating forces acting on the particles com- posing such mass, then it follows, from what has been explained, that the resultant of all these forces will have a direction, D E, parallel to their common direction, and will have an intensity equal to their sum. The position of this resultant remains yet to be determined. The principles of mathematics enable us, in many cases, to combine together the forces acting on all the particles of a body, by extending the method used in (39), Fig. 13, and thus to calculate the exact position of the resultant ; but its posi- tion can in most cases be determined more readily by experi- ment. GENERAL PROPERTIES OP MATTER. 59 If, in Fig. 19, we suppose tliat the line represented by the large arrow is the direction of the resultant, it is evident that, if any point, such as G, on that line, is supported, the body will remain at rest ; because the resultant of all the forces acting upon tlie body having the direction D E, will be expended in pressure on the fixed point C. It is not essential that the point of support should be in the body, for the same would be true for any point in the direc- tion of the arrow D E. If, for example, D were a pin, from which the body was suspended by a thread attached to the body at any point in the line D C, then the body would still remain at ^'s- ^^ rest ; for, as before, the resultant having the direction D E would be expended in pressure on the pin at D. It would be different, however, with a point of support not in the direction of the arrow, such as P- If the body be connected with this point by a string attached at C, it will no longer remain at rest ; for the resultant D E, acting at the point C, can be decomposed into two compo- nents, — the first in the direction of C H, which would be ex- pended in pressure on the point P, and tlie second in tlie direction CI, which would move the body towards the vertical line. It follows, therefore, that, if a body be supported by a fixed point, it cannot remain at rest, unless the resultant of all the parallel forces which gravity exerts upon its particles passes through that point. Tliis fact gives us the means of ascertaining experimentally the position of the resultant of the parallel forces which gravity exerts upon the particles of a body. We have only to suspend it by a string attached to any point of the body, and the direction which the string assumes will be the direction of the re- sultant of the forces of gravity when the body is in that position. In Pig. 20, for example, the resultant of the forces which gravity exerts upon the particles of the chair is the line A B, when the chair is in the position represented in the figure. If we attach the string to another point, the chair will take another position, and the resultant will also change its position to the ^.^ ^_^_ 60 CHEMICAL PHYSICS. line CD, Pig. 21. We should find, by experiment, that for every point of suspension there would be a different position of the chair, and also a different position of the resultant. When, in any given position of a body, we have determined the position of the resultant of the forces of gravity, we have also determined a line on which the point of application of the earth's attraction must be ; because, by (32), this point may be any point on the line of the resultant. The position of the line, however, will depend on the position of the body ; and there- j. fore, in order to determine it, the position of the body must be given. (46.) Centre of Gravity. — When a body is turned round in any direction, it is easy to see that the lines of direction of the par- allel forces, which gravity exerts on its particles, revolve about their points of application, retaining their parallelism. Hence it follows, from (40), that, in any position which the body may as- sume, the resultant of these forces will always pass through the same point. This common point of intersection of the resultants of the forces of gravity, in any position which the body may as- sume, is termed the centre of gravity. This point has several important relations, which we will now consider. The centre of gravity may always be regarded as the point of application of the resultant of the forces tvhich gravity exerts upon the particles of a body, because it has been proved, first, that the point of application may be any point on the line of the resultant ; secondly, that the centre of gravity is a point common to all the resultants. When the centre of gravity is supported, the body remains at rest. If the centre of gravity be supported on a point or axis, and the body is free to turn round such axis, the body will re- main at rest in any position in which it can be placed. This result follows necessarily from the last ; for, as the point of appli- cation of the resultant is fixed, the whole intensity of the forces of gravity must be expended in pressure against this point. The whole attractive force exerted by a mass of matter may be regarded as emanating from its centre of gravity. The prin- GENEBAL PROPERTIES OF MATTER. 61 ciple, that action and reaction are always equal and opposite, applies to the attraction of gravity exerted by one mass of matter over another. The earth is attracted, by a body near its surface, ■with a force exactly equal to the attraction exerted by the earth on this body. Now, since the attraction of the body must be equal and opposite to that of the earth, it follows that the re- sultant of the force must be on the same line with the centre of gravity, and hence may always be regarded as emanating from it. Hence, also, the attraction of the earth may be regarded as emanating from its centre of gravity, which is not, however, the same as the centre of its figure, and, moreover, it is variable. A singular result follows from the principle of reaction above stated, since it must be, when a body falls to the ground, that the earth must rise to meet the body, — and this is true ; but the extent of the motion of the earth is as much less than that of the body, as the mass of the earth is greater than the mass of the body. Representing by m the mass of the body, we have for the intensity of the earth's attraction m u ; and representing by M the mass of the earth, we have for the intensity of the body's at- traction for the earth M »' ; and since these are equal, we have m t) = Mv', or v' -.M = 1)1 : M that is, the velocity acquired by the earth at the end of one sec- ond is as much less than that acquired by the body, as the mass of the body is less than that of the earth. (47.) Position of the Centre of Gravity. — For the methods of calculating the position of the centre of gravity, we must refer the student to works on Mechanics, since these methods depend on the principles of the higher mathematics. The position of the centre of gravity can be found experimentally by suspending the body by a cord from two points successively, as represented in Figs. 20, 21. 'The point where the line of the cord produced In One position intersects the line of the cord produced in the second, is, by (46), the centre of gravity. It can thus be proved, that, when a homogeneous body has a regular form, the centre of gravity is at the centre of the figure. This is the case with the sphere, the cube, the octahedron, and the other regular solids of geometry. So also, when a homogeneous body has a symmetrical axis, the centre of gravity will be a point of this axis. Thus, in a cone, the centre of gravity is in the axis of the cone, and it can 6 62 CHEMICAL PHYSICS. easily be seen that, if a cone be suspended by a string from its apex, the direction of the line of suspension -should coincide -with the direction of the axis of the cone ; because, as the matter is uniformly distributed round this axis, tlie gravity of its particles, acting equally on every side, ■will have no tendency to move it ■when in this position. The centre of gravity is not necessarily in the body. Thus, the centre of gravity of a hoop is at its centre, and the cen- tre of gravity of a hollow sphere, an empty box, or a cask, is within it. The centre of gra'vity of two separate and independent bodies immovably united is a point between them. This point can be very easily determined mathematically, from principles already established. Let A and B, Fig. 22, be the two bodies, and let a and b be their centres of gravity. Connect the two by a line. From what has been said, it follows that the attraction of the earth on this system may be regarded as the action of two parallel forces at a and b. Hence, the point of "° "' application of the resultant, the centre of gravity of the system, must be on the line a b, and must divide the line into two parts, which are inversely pro- portional to the intensities of the forces. It will be shown in (49) that the two forces are proportional to the masses, and hence the centre of gravity must divide the line a b into two parts which are inversely proportional to the masses of the two bodies A and B. (48.) Stable, Unstable, and Neutral Equilibrium. — It is a necessary consequence of what has been said, that the centre of gravity of a body has always a tendency to move into the lowest position of which the conditions will admit. Hence, if the body is supported at only one point, it cannot remain at rest, unless this point of support is either at the centre of gravity or is in the same vertical with it. If the centre of gravity is below the point of support, the body is in a stable equilibrium ; because, if by any means the centre is displaced, the force of gravity will tend to restore it to its original position. If, however, the centre of gravity is above the point of support, the body -will be in an GENERAL PROPERTIES OP MATTER. 63 unstable equilibrium ; for the slightest displacement will remove the centre out of the vertical, and it will then move to the lowest possible position. The chair suspended by a string in Pig. 20 is in a stable equilibrium, because the centre of gravity is below the point of support. The same chair could, with great care, be balanced on the end of one of its legs, but its equilibrium would then be unstable ; because the centre of gravity would be above the point of support, and the slightest displacement of the centre of gravity would cause the chair to fall. When a body rests on a base, it is stable, when the vertical passing through the centre of gravity falls within the base. The stability of the body in such a position is estimated by the mag- nitude of the force required to overturn it. If its position can be disturbed or deranged without raising its centre of gravity, the slightest force will be sufficient to move it ; but if its position cannot be changed without causing its centre of gravity to rise to a higher position, then a force will be required which would be sufficient to raise the entire body through the height to which its centre of gravity must be elevated. This is illustrated in Pigs. 23, 24, 25. To turn the cylinder over the edge B, it would be Fig. 23. Fig. 24. Fig. 25. necessary in either case to move the centre of gravity, G, over the arc G E, and hence to raise it through the height HE. This distance is greater, and hence the force required to over- turn the cylinder is greater, the larger the base of the cylinder relatively to its height. It can also easily be seen that the sta- bility is greatest when the vertical, passing through the centre of gravity, passes also through the centre of the base. If it passes 64 CHEJIICAL PHYSICS. through the edge of the base, as in Fig. 26, the slightest force will overturn it. If it passes outside of the base (Pig. 27), then Fig. 27. the centre will be unsupported, and the cylinder will fall. These principles, which have been illustrated by a cylinder, may be readily extended to other bodies. "When a body rests on two or more points, it is not necessary for its stability that its centre of gravity should be directly over one of these points ; it is only necessary that its vertical should fall between them. If a body rests on two points, it is supported as effectually as if it rested on an edge coinciding with the straight line which unites the two. If it rests on three points, it is supported as firmly as it would be by a triangular base coinciding with the triangle of which the three points are vertices. A familiar condition of equilibrium is presented by a sphere resting on a level plane. Such a sphere has but one point of support, and this is directly under the centre of gravity. If the sphere is rolled upon the plane, the centre of gravity will neither rise nor fall. Hence any force, however slight, will cause it to move ; and, on the other hand, the body will have no tendency, of itself, to change its position when it is disturbed. This condi- tion is called neutral equilibrium. A cylinder resting with its edge on a plane and level surface is another example of neutral equilibrium. (49.) Intensity of the Earth'' s Attraction. — The falling of a stone to the earth is, as has been stated (21), an example of a imiformly accelerated motion. Hence, the force of gravitation GENERAL PEOPEKTIES OP MATTER. 65 must be a force of constant intensity (27). The amount of ac- celeration, as was also stated (21), at the latitude of Paris, is u = 9.8088 metres. This acceleration is the same for all masses of matter, whether large or small. The apparent contradiction to this statement in common experience arises from the fact, that the fall of light bodies is more retarded by the resistance of the air than that of heavy bodies. If, however, the experiment is made in a vacuum, it will be found that a gold eagle and a feather will fall with equal rapidity. The intensity of a force is, as we have seen, equal to Mx). Representing the intensity of the force of gravity, which acts on a given mass of matter, M, by G, we shall have, for the latitude of Paris, ■G = M 9.8088 (units of force). [26.] For any other mass of matter, M!, we shall have, in the same way, G' = M' 9.8088 (units of force). Hence, G: G' = M: M'. [27.] The intensity of the earth's attraction is therefore proportional to the quantity of matter on which it acts. In other words, the force increases with the quantity of matter to which it is applied. In this respect gravity differs from many other forces with which we are familiar, from muscular force and the force of a steam- engine, for example, since these have a constant value, and do not vary with the amount of matter to which they are applied. "We assumed (45) that the earth's attraction acts equally on every particle of matter. If this is true, it follows that the. re- sultants of all the forces of gravity acting on the separate parti- cles of two bodies must be proportional to the number of par- ticles in each ; in .other words, to the masses of the two bodies. That this is the case, is proved by the experiment on falling bodies alluded to above, and by the proportion [27] which fol- lowed. Hence the assumption of (45) was correct. As tlie intensity of the force of gravity varies with the amount of matter on which it acts, we must, in estimating the strength of this force in different places, always compare the intensities of the force when acting on equal masses of matter. It simpli- fies the subject, to take a quantity of matter equal to the unit of mass in each case. Representing then by g the intensity of the 6» 66 CHEMICAL PHYSICS. attraction of gravitation for the unit of mass, we can easily de- duce from [26], g = 9.8088 (units offeree') ; [28.] and also G == Mg- (units of force). [29.] In tliis book, g ■will always be used to express the intensity of the force of gravity acting on the unit of mass, or, in general, the intensity of the force of gravity ; and G will always be used to express the intensity of the force of gravity acting on a given mass, M. In eveiy case they both stand for a certain number of xinits of force. The intensity of the earth's attraction varies slightly at different points of its surface ; thus, at the equator, g = 9.7806 ; at the latitude of Paris, as above, g = 9.8088 ; and at the pole, g = 9.8314. In order to determine the intensity of gravity at different places, it might be supposed that we could measure the dis- tance through which a heavy body would fall the first second, and then, by the principles of uniformly accelerated motion (21), twice this distance would be equal to the value of g at tlie given place. On account of the great rapidity with which bodies fall, it is impossible to measvire this distance with any accuracy ; nor is this necessary, since we have in the pendulum an instrument by which we can determine indirectly the value of g with great precision. (60.) Pendulum. — A pendulum is a heavy body, suspended from a fixed point by a rod or cord. If the centre of gravity of the body is directly under the point of support, the body remains at rest ; but if the body be drawn out of this position, so that the centre of gravity will be on either side of the vertical line passing through the point of support, then the body, when disen- gaged, will fall towards the vertical line, and in consequence of its inertia will contume its motion beyond the vertical line until it comes to rest. It will then return to the vertical, and thus oscillate from side to side. In order to investigate the phe- nomena of this kind of motion, the mathematicians study at first an ideal pendulum, which they call a simple pendulum, to distin- guish it from the actual material pendulum, which they call a compound pendulum. (51.) Simple Pendulum. — A simple pendulum consists of a material point suspended to a fixed point by means of a thread GENERAL PROPERTIES OP MATTER. 67 ■without mass or weight, perfectly flexible and inextensible. Such a pendulum is of course only a mathematical abstrac- tion ; but we can approach sufficiently near to it, for purposes of illustration, by suspending a small lead bullet to a fixed point by means of a fine silk thread. Let O A, Fig. 28, be such a simple pendulum, in a vertical po- sition, and therefore at rest. If we now withdraw it to the posi- tion O B, the force of gravity act- ing on the point B in the direction B g may be decomposed into two components ; one, B a, which will be destroyed by the resistance of the thread and of the fixed point O ; the other, B b, perpendicular to O B, which, being unresisted, will move the point B towards the vertical O A. If the line B g represents the intensity of the force of grav- ity, then B h represents the in- tensity of the second component. Hence, if we suppose the amount of matter concentrated at B to be equal to the unit of mass, and represent the angle BOA by a, we shall have, for the value of the second component, g sin a. This component will evidently diminish in intensity as the pendulum approaches the vertical, and at the vertical will become nothing. It appears, therefore, that this force will be continuous, but not constant ; and hence, that the pendulum will move with an accelerated, but not with a uniformly accelerated motion (20), in the arc of a circle whose radius is equal to O B. Having reached the vertical O A, the pendulum, in virtue of its momentum, will rise with a retarded motion toward O B' ; and since the action of gravitation in retarding the motion must be exactly equal to its previous action in accelerating it, it follows from (27) that the momentum will not be destroyed until the pendulum has moved over an arc, A B', equal to A B. At B' it will be for an instant at rest, and then fall back again to A, re- mount to B, and thus continue indefinitely, supposing there were no resistance. In actual practice, however, with a compound pendulum, the resistance of the air, the rigidity of the thread, Fig. 28. 68 CHEMICAL PHYSICS. and the friction at the point of support, rapidly diminish the arc through which it moves, and finally arrest the motion al- together. By diminishing these resistances, the motion may be made to continue for a proportionally longer time ; and a pendu- lum has been known to continue oscillating in a vacuum for several hours. Each motion of the pendulum from B to B', or from B' to B, is called one oscillation, and the angle B O B' is called the ampli- tude of the oscillation. (52.) Isochronism of the Pendulum. — It is evident that the length of time required for a single oscillation of the pendulum O A, Fig. 28, must be absolutely the same, so long as the ampli- tude of the oscillation remains constant ; but also, what is more remarkable, it is true that the time required for each oscillation of the pendulum is but little influenced by the amplitude of the oscillation; and, for all practical purposes, the time of oscilla- tion may be regarded as equal for all amplitudes not exceeding three or four degrees. This singular property of the pendulum is termed isochronism, from two Greek words signifying equal time, and the oscillations of the pendulum are said to be iso- chronous. Two oscillations of the pendulum are not, however, absolutely isochronous, unless the difference between their am- plitudes is infinitely small. (53.) Formula of the Pendulum. — If we represent by T the time of oscillation of a pendulum in seconds, by I its length in- fractions of a metre, by g- the acceleration produced by gravity each second, and by n the ratio of the circumference of a circle to its diameter, the value of T may be found to be T=^]\, [30.J when the amplitude of the oscillation is infinitely small. If the amplitude is not infinitely small, but only very small, then we have ^^'^JK' + r^)' ^'^-^ when a is the length of the arc A B, Fig. 28. The truth of these formulae cannot readily be demonstrated without the aid of the higher mathematics, and we must therefore refer the student to works on Analytical Mechanics for the demonstration. GENERAL PROPERTIES OP MATTER. 69 Several important truths are expressed in these formulae : — 1. The duration of an oscillation does not depend on its ampli- tude when this is infinitely small, and is but slightly influenced by the amplitude even when it is as large as three or four de- grees. By substituting, in [30], 1 = 1, and g- = 9.809, we should obtain, for the time of vibration of a pendulum one metre long, at the latitude of Paris, T= 1.003085. By sub- stituting in [31] the same values, and also a = 3.1416 -^ 90 = 0.0349, we should obtain, for the time of vibration when the am- plitude was eight degrees, T= 1.003161, which differs from the first value by only the 0.000076 of a second. 2. The duration of the oscillation is proportional to the square root of the length of the pendulum. Substituting, in equation [30] , C= — , which is a constant quantity at any given place, the equation becomes T= C a/T. For a pendulum of another length, as /', we have T' = C s/v, and, comparing the two, T -.^ = ^7 : V"F; [32.] and also l:V = T^: T'\ [33.] 3. The duration of the oscillation of a pendulum of an inva- riable length is inversely proportional to the square root of the intensity of gravity . Substituting, in equation [30], G = /s/nFl, wliich is a constant quantity when / is supposed invariable, we obtain T= C _. For another place, where the intensity of gravity is g', we have T = C |_L ; hence, \g' (54.) Compound Pendulum. — We have hitherto supposed that the pendulum is a heavy mass, of indefinitely small magni- tude, suspended by a string or a rod, having no weight. Such a pendulum is, as has been stated, a pure abstraction, and can never be realized in practice. The pendulum which must be used in all our experiments is a compound pendulum, consisting of a heavy weight, suspended to a fixed point or axis, by means of a rigid i-od of wood or metal. The particles of such a pendu- 70 CHEMICAL PHYSICS. lum must necessarily be at different distances from the point of suspension, and must therefore tend to oscillate in different times. Hence, the time of oscillation of the whole pendulum will not be the same as that of a simple pendulum of the same length, and the diflFerence becomes of much importance. The theory of the simple pendulum may bo extended to the compound pendulum, by regarding the last as consisting of as many simple pendulums as it contains material particles. Were these free to move, they would oscillate in different times, deter- mined by their distances from the point of suspension ; but they form parts of a rigid system, and they are therefore all compelled to oscillate in the same time. Consequently, the oscillations of the particles near the point of suspension are retarded by the slower oscillations of those below them ; and, on the other hand, the oscillations of the particles near the lower end of the pendu- lum are accelerated by the more rapid oscillations of those above them. At some point on the axis of the pendulum, intermediate between these, there must be a particle whose natural oscillation ' is neither accelerated nor retarded, and where the several effects will be all balanced, all the particles above it having exactly the same tendency to oscillate faster that the particles below it have to oscillate slower. This point is called the centre of oscillation, and it is obvious that the time of oscillation of a compound pen- dulum is exactly the same as that of a simple pendulum whose length is eqiial to the distance of tlie centre of oscillation from the point of suspension. This distance is the virtual or acting length of the pendulum, and equations [30] and [31] will apply to compound pendulums, by substituting for / their virtual length. By the length of a pendulum, no matter what may be its form, is always to be understood the virtual length, unless the reverse is expressly stated. (55.) Position of the Centre of Oscillation. — When the form of the pendulum is given, the position of the centre of oscillation can be calculated ; but as the methods of calculation involve the principles of the higher mathematics, they cannot readily be ex- plained in this connection. The centre of oscillation can also be found experimentally, by making use of the following remarka- ble property of the compound pendulum, first demonstrated by Huyghens. If a pendulum be inverted and suspended by its centre of os- GENERAL PEOPERTIES OP MATTER. 71 cillation, its former point of suspension -will become its new centre of oscillation, and the time of vibration will remain the same as before. This property is usually expressed by saying, that the centres of oscillation and suspension are interchangeable. This property of the pendulum may be verified by means of a reversible pendulum. Fig. 29. This pendu- lum is furnished with two knife-edges, a and b, which, i when the pendulum is in use, rest on plates of steel or agate. If a is the axis of suspension, and b the axis of oscillation, determined by calculation, the penduluni will be found to oscillate in the same time on either knife- edge. If the position of the axis of oscillation is not known, it can easily be foiind by shifting the position of the lower knife-edge, until, on trial, the pendulum is found to oscillate in equal times on both. The lower knife-edge is then in the axis of oscillation. A pen- dulum of this kind was used by Captain Kater, in his determination of the length of the seconds pendulum, mentioned on page 12. When the pendulum consists of a fine thread and a heavy ball, the centre of oscillation very nearly coin- cides with the centre of gravity, and such a pendulum can be used for ascertaining approximatively the virtual length of a compound pendulum. By shortening or lengthening the thread, a length can easily be found with which the pendulum will oscillate in the same time with the compound pendulum. This length will then be approximatively the virtual length sought. (56.) Use of the Pendulum for Measuring Time. — If in .the equation T = it — , we substitute for T unity, and for tc and g the values already given, we shall find, for the length of a pendulum vibrating seconds at Paris, the value I = 0.993781 m. The lengths of pen- dulums vibrating in 2, 3, and 4 seconds would be by (33) 4, 9, and 16 times this length. In order to use the ^'^'^' seconds pendtilum for measuring time, it is only necessary to con- nect with it a mechanism by which its beats may be recorded and its motion maintained. Such a mechanism constitutes a common clock, the essential parts of which are represented in Fig. 30. 72 CHEMICAL PHYSICS. The toothed wheel R, called the scape-wheel, is turned hj a weight or spring, either directly, as in the figure, or through the intervention of other wheels. The revolution of the scape-wheel is regulated by means of a peculiar contrivance, a b, called the escapement, which oscillates on an axis o o'. The oscillations are commiini- cated to the escapement by the pen- dulum P, through the forked arm of. When the pendulum hangs vertically, one of the teeth of the scape-wheel, cut obliquely for the purpose, rests on the upper side of the hook b, and the clock remains at rest. If now the pendulum is set in motion, so that the hook b is moved from the wheel, II mill J jti .■PiM ,ijii *^'® tooth which rested upon it is set III 1\ ir/J ri'l ■'"''®®' ^"*^ ^^^ wheel begins to revolve ; iilil n^JitE 111 but it is soon arrested by the hook a, which has moved up to the wheel as b moved from it, and catches on its under surface the tooth immediately below. As the pendulum oscillates back the hook a moves away, the wheel again commences to revolve, but is arrested a moment after on the opposite side by the hook b, which catches the tooth next to the one it held before ; and thus contin- uously, so that each oscillation of the pendulum allows the scape- wheel to move forward through a space equal to one half of one of its teeth. If, then, the wheel has thirty teeth, it will com- plete one revolution in sixty beats of the pendulum, moving for- ward one sixtieth of a revolution at each beat. This wheel is the one on whose axis the second-hand is placed. It is connected by cogs with another wheel, which is made to occupy sixty times as long in revolving, and this carries the minute-hand ; and this is connected with another wheel, which revolves in twelve times the period, and carries the hour-hand. Thus the second-hand regis- ters the beats of the pendulum up to sixty, or one minute ; the minute-hand registers the number of revolutions of the second- hand up to sixty, or one hour ; and the hour-hand registers the GENERAL PROPERTIES OF MATTER. 73 number of revolutions of the minute-hand up to twelve, or half a day. If the pendulum and escapement were removed from a clock, there would be nothing to prevent the train of wheels from being turned round with great rapidity by the weight or spring acting on it, and the clock would speedily run down. On the other hand, were there not some means of communicating to the pen- dulum occasional impulses, it would soon be brought to rest by the resistance of the air and the resistance due to the mode of suspension. To prevent this, the escapement is so constructed as to give a very slight additional impulse to the pendulum at each oscillation. The ends of the two hooks, a, b, are cut so as to pre- sent to the teeth of the scape-wheel inclined surfaces. As the tooth of the wheel leaves one of these hooks, its extremity slides over this inclined plane with a considerable; force, commu- nicated by the weight, so as to throw the escapement forward with a slight impulse the moment the tooth is set free. This im- pulse is communicated, through the axis o o' and the arm o f, to the pendulum. If the weight is increased, the force with which the impulse is given will be greater ; and the pendulum, receiv- ing a greater impulse at each oscillation, will swing through a greater arc. As this will slightly increase the time of each oscil- lation (53), the addition of weight will make the clock go slower. The change of rate in a clock caused by the expansion and con- traction of the pendulum, will be considered in the chapter on Heat. (57.) Use of Pendulum for Measuring- the Force of Grav- ity. — By transposing, we obtain from equation [30] the value of g-: g = i"^.; [35.] from which, when we know the length of a pendulum which os- cillates in a given time, T, we can easily calculate the value of g- for the place of experiment. If, in the last equation, we place T=l, then I denotes the length of the seconds pendulum, and we obtain for the value of g, g = lTt'- [36.] In order, then, to measure the intensity of gravity at any place, we have only to oscillate a pendulum whose virtual length is known, 7 74 CHEMICAL PHYSICS. and observe the length of a single oscillation. This observation is readily made by counting a large number of oscillations, and observing the time occupied by the whole number. This time, divided by the number of oscillations, gives the duration of a single oscillation with great accuracy, because any error we may have made in observing the time is thus greatly divided. By this method Borda and Cassini, in 1790, measured with great accuracy the intensity of gravity at the Observatory of Paris. The pendulum which they used consisted of a sphere of platinum, suspended to a knife-edge by means of a fine platinum wire. The knife-edge rested on an agate plate, and the whole pendulum was about four metres long. Instead of counting di- rectly the number of oscillations, Borda compared the motion of his pendulum with that of a clock placed behind it. On the ball of the clock's pendulum a vertical mark indicated the position of its axis, and a small telescope, placed a few metres in front, enabled him to observe when the wire of his pendulum exactly coincided with the vertical mark. Starting from a moment when the two coincided, he observed the number of seconds before such coin- cidence occurred again ; and knowing this, he was able at once to calculate the number of oscillations of the pendulum which oc- curred during an observed number of seconds by the clock. Let V be the number of oscillations of the seconds pendulum between the coincidences, then v ± 2 will be the number of oscillations of the experimental pendulum in the same interval, that is, in V seconds, and will be the number in one second. Hence, if p is the number of oscillations of the pendulum, and t the number of seconds observed by the clock, we shall have p = t^y-=,±?J; [37.] an equation by which we can calculate the number of oscillations in a given time, without being obliged to count them. In these experiments, the pendulums were enclosed in glass cases to pro- tect them from currents of air, and separated from each other by glass, so that they should not react on each other through this fluid. As the amplitude of the oscillations is not infinitely smaU, but only very small, in such experiments, it is important to correct the number of oscillations observed as above, and substitute for GENERAL PROPERTIES OP MATTER. 75 it in the calculation the number which would have occurred had the amplitude been really infinitely small. If we call the duration of an oscillation which is infinitely small T, and that of one which is onlyvery small T', we have from [30] and [31] T'^T^l +|^ Y where, a is equal to one half the arc which measures the am- plitude. Now, as the number of oscillations in a given time is inversely as their duration, we have T' : T=ni n'; aiid hence. •'(i+n). [38.] where n is the required number of oscillations, and n' the ob- served number. The amplitude is measured by means of a hori- zontal scale placed behind the pendulum, and, as it sensibly diminishes during the experiment, we take for tiie value of a in [38] the mean amplitude during the time of observation. Tlie value of g found by the above formula is a little too small, owing to the fact that the force of gravity acting on the mass of the pendiilum is balanced to a slight degree by the buoy- ancy of the air, and it is necessary to correct the result for this cause of error. The principles from which this correction may be calculated will be explained in Chapter III. It will there be shown that a body is buoyed up in a fluid by a weight equal to the weight of fluid which it displaces. Hence, if W represents the weight of a body in a vacuum, and w the weight of air it displaces at a .given temperature and under a given pressure, then W — w is the weight of the body in the air at this temper- ature and pressure. If we put 8 = ^, the small fraction which represents the ratio of the weight of the air to the weight of the body, we shall easily obtain W—w = W—S W= W(l — S). Representing the weight of the body in air ( TT — w) by W, we obtain, for the relation between the weight of a body in air and in a vacuum, the equation W'= W (1 — 5). It will be shown, in one of the following sections, that the weights of the same body under different circumstances are proportional W s' to the intensities of gravity, and hence that -^ = ■§- ; substi- tuting this, we have, for the relation between the actual intensity 76 CHEMICAL PHYSICS. of gravity, g, and the apparent intensity when the experiments are made in air, g', It appears, however, from the experiments of Bessel, which were confirmed by the calculations of Poisson, that the loss of weight which the pendulum suffers in air is much greater when it is in motion than when at rest, so that a still further correction must be made to eliminate this source of error ; but for the details of this and of the other corrections which are required, we must refer the student to Bessel's original Memoirs. (58.) Value of g. — By the method described in the last sec- tion, Borda and Cassini found for the intensity of gravity at the Observatory of Paris the number g = 9.8088. This value has since been redetermined by Biot, Arago, Mathieu, and Bouvard, who used the same process, except that they employed a shorter pendulum, and obtained almost absolutely the same results. Bessel, by correcting for the loss of weight in the air due to the motion of the pendulum, found for the value of the intensity of gravity at Paris, g = 9.8096, which is probably the most accurate. The value of g has also been determined at different points on the earth's surface, with more or less accuracy, by different ob- servers. Some of these results are collected in the following table, which has been taken from Daguin's TraiU de Physique. The length of the seconds pendulum is easily calculated from the values of g by means of equation [36] . stations. Latitudes. Value of g. Seconds Pendulum. Observers. Spitzbcrgen, 79 49 58k. 9.83141 0.99613 Sabine. Stockholm, 59 20 34 9.81946 0.99492 Svanberg. Kiinigsberg, 54 42 12 9.81443 0.99441 Bessel. Paris, 48 50 14 9.80979 99394 Biot, etc. He Rawak, 1 34S. 9 78206 0.99113 Freycinet. He de France, 20 9 23 9.78917 0.99185 Dupeney. Cape of Good Hope, 33 55 15 9.79696 0.99264 Freycinet. Cape Horn, 55 51 20 9.81650 0.99462 Foster. New Shetland, 62 56 11 9.82253 0.99523 Foster. It appears from this table, that the intensity of the force of gravity gradually increases with the latitude as we go from the GENERAL PROPERTIES OP MATTER. 77 equator towards either pole. In general, the value of g for any latitude can be determined sxifficiently near for all purposes of Physics, by means of the formula, g = 9.80604 (1 — 0.00259 . cos 2 A), [40.] in which A is the latitude of the place, and 9.80604 the value of g- at the latitude of 45°. By substituting for A, 0° or 90% •we obtain at the equator g = 9.78062, and at the poles g = 9.83146. It does not appear, however, that the intensity of gravity is rigorously the same at all points on the same parallel of latitude, or at corresponding points in the northern and southern hemispheres. Irregularities in this respect were noticed in the measurement of the arc of the meridian in Prance, and also by Lacaille at the Cape of Good Hope. These variations in the intensity of gravity on the earth's sur- face depend mainly on two causes ; first, on the centrifugal force due to the earth's revolution on its axis, which is at its maximum on the equator, and gradually diminishes towards the poles, where it disappears ; secondly, on the spheroidal character of the earth, in consequence of which a body at the poles is more strongly attracted by the mass of the earth than it is at the equator. We will consider the effect of each of these causes in turn. (59.) Centrifugal and Centripetal Force. — It has already been stated (25), that a curvilinear motion is the resultant of two motions which obey different laws. Thus, in Pig. 31, the parabolic motion of a ball shot horizontally from a fort is the resultant of a uniform motion in the direction of a m, and of a uniformly accelerated motion in the direction of an. We also know that this motion is the result of two forces, one which has acted, and the other which is still acting, on the ball ; first, the projectile force of gunpowder, which has given to the ball a certain momentum', M t), in virtue of which it will rig. 81. 78 CHEMICAL PHYSICS. Fig. 32. continue to move until its motion is arrested by an equivalent force acting for an equivalent time in the opposite direction; second, the force of gravity, a constant force both in direction and intensity. Compare (27) and (29). Let us now consider the conditions of Fig. 31 to be so far changed, that the constant force no longer acts in directions par- allel to itself, but in directions which all converge to one point. Such a force may be regarded as an attractive force emanating from this point, and is there- fore frequently called a cen- tral force. Let us then suppose that in Fig. 32 we have, as be- fore, a ball moving with a cer- tain momentum in the direction a m, communicated to it origi- nally by a force acting for a given time with a given intensi- ty, but whicli has ceased to act. Let us also suppose that the same ball is attracted towards a given point, C, by a force con- stant in intensity. "What will be the resulting motion of the ball ? Let V be the velocity in the direction a m, and » be the accelera- tion of the given force. In a small fraction of a second, which we may take as small as we please, the ball will move in the di- rection am over a space a /3, equal to — , where n is the number of intervals into which the unit of time has been divided. In the same time it will move in the direction a C over a space a b, equal to I -2- [^] • The resultant of these motions, on the principle of (25), will be a curved line passing through the point P, which can be found by completing the parallelogram a ^ Pb. Arrived at the point P, the direction of its original motion has so far changed, that, if the central attraction ceased to act at that mo- ment, the original momentum would cause it to move in the direction P n, tangent to the curve at the point P, which, accord- ing to the principle of geometry, may be regarded as the contin- uation of tlie direction in which it was moving at the instant. The central force, however, does not cease to act, and during the GENERAL PROPERTIES OP MATTER. 79 next small interval of time the same thing is repeated. In virtue of the momentum, the ball will pass over the distance Py, equal to -r^, and in virtue of the central force will move towards the centre by an amount, Pc, equal to J -^. The resultant of these motions will be a second curved line, similar to the first, and a continuation of it, passing through Q. The same thing will be again repeated every succeeding interval of time, and thus the motion resulting from the two forces will be a curved line bending towards the central point C, the central force con- stantly changing the direction of the original momentum. It is easy to see, that, with a certain relation between the momentum and the intensity of the central force, the distance of the ball from the centre would keep always the same, and the path of the ball would be a circle. If the central force were greater rela- tively to the momentum than this, then the ball would be drawn each second nearer to the centre, and the radius of the curvilinear path would as regularly shorten ; if the central force were relative- ly less, the ball would evidently recede from the centre, and the radius of its path would lengthen. If, however, we suppose that the central force diminishes as the body recedes from the centre, and increases as it approaches it, so that the intensity is always inversely as the square of the distance, then it can easily be proved mathematically that the path of the ball will return into itself, and will be an ellipse. We shall have only to deal with that particular case where the path is a circle. In this case, the central force, which tends to draw the ball to the centre of the circle, is evidently just balanced every instant by the inertia of the mass of the ball, which tends to move in a tangent to the circle ; so that the ball moves no nearer to the centre, the whole of the central force being expended in changing the direction of the original motion. The force by which the ball tends to fly off on a tangent to the circle, is termed the centrifugal force, while the central force, by which it is restrained and kept on the circumference, is termed the centripetal force. The term centrifugal force is very liable to be misunderstood, since it would seem to imply a force which, acting alone, would cause the body to fly directly from the centre, which, as we have seen, is not the case. "We must constantly bear in mind, that the only proper use of this term is to express 80 CHEMICAL PHYSICS. the tendency which the momentum of the body has to carry it on in tlie straight line tangent to the circle at the point at which the centripetal force ceases to draw it from that line. The body will, it is true, then recede from the centre ; but it will only do so by passing along the tangent, the distance of which from the centre is continually increasing, and not by flying in a direction opposite to the centre of attraction. Its action, however, will be to cause the particles of a body in rapid revolution to take their places at the greatest possible distance from the centre. The measxire of the centrifugal force in Fig. 32 is obviously the amount of restraint required to keep the ball on the circum- ference of the circle, and it is measured by the intensity of the centripetal force, which, on our supposition, just balances it. Calling, then, the centrifugal force CT, the acceleration of the cen- tripetal force t), and the mass of the ball M, we have, by [14], € = Mxs. [41.J Since, however, we only know, as a general rule, the velocity of the motion of a ball on the circle and the radius of the circle, it is important to obtain, if possible, an expression of the intensity of the centrifugal force in terms of these two quantities. This can easily be obtained by the principles of geometry. Let a P, Fig. 32, be the arc described by the ball in an interval of time so small that the arc may be considered as equal to the chord. Call this interval — of a second, where n may be as large as you please. Represent by v the velocity of the ball on the circumference; then — is equal to the length of the arc a P. Represent next, by t>, the unknown acceleration of the cen- tripetal force ; then the distance a b, through which the ball would move under the influence of this force alone in — of a second, will be, by [5] , | ^ . We have, by geometry, ab : aP = a P : a D ; from this proportion, by substituting the above val- -^•. - = —:2R, or i)=:-^ n^ n n ' H tuting this value oft) in [41], we obtain, for the intensity of the centrifugal force, b^ € = i)f -^. [42.J ues, we obtain i ^ : — = —:2R, or i)=:~; and substi- GENERAL PROPERTIES OP MATTER. 81 We can give this expression another form, which is more con- venient for use. The expression t), vrhich represents the velocity of the ball, denotes the number of metres which it passes over in one second. If, then, we represent by T the number of seconds occupied by the ball in going once round the circle (its period of revolution), and by 2 jR tt, as usual, the circumference of the circle, we shall have b = „, ". Substituting this value in [42] , we obtain (jr = Jfi^, [43.] which is an expression for the intensity of the centrifugal force in terms of the time of revolution, the radius of the circle de- scribed, and the mass of the body. If a weight is whirled round at the end of a string, the action of the centrifugal force is shown in the tension of the string, and the only difference between this and the previous example is, that the resistance of the string takes the place of the attractive force. If the string breaks, the weight flies off on a line which is a tangent to the circle which the weight had described. In like manner, the particles of water on the rim of a revolving grindstone tend to fly ofl" from the surface, but are kept in place by the adhesive attraction of the stone ; when, however, the revolution becomes rapid, the centrifugal force overcomes the adhesion, and the water is thrown off in lines which are tangent to the cylindrical surface. Not unfrequently, when the revolution is very rapid, the centrifugal force overcomes the cohesion between the parti- cles of the stone itself, and serious accidents have resulted from this cause. Since the earth is revolving rapidly on its axis, we should ex- pect to find, especially at the equator, a manifestation of this same force ; and in fact we do. All bodies on the globe not sit- uated exactly at the poles tend to fly off from its surface on lines tangent to the parallels of latitude on which they revolve, and are only prevented by the force of gravity. Were the rapidity of the earth's revolution more than seventeen times increased, the force of gravity would not be sufficient to restrain bodies on the equator from obeying this tendency. As it is, however, the centrifugal force only acts to diminish the intensity of the force of gravity ; and this action, which is greatest at the equator. 82 CHEMICAL PHYSICS. gradually diminishes as we go towards the poles, where it is nothing. We can easily find the intensity of the centrifugal force at the equator, by substituting in [43] , for E, the value of the equato- rial radius, 6,377,398 metres, and for T the number of seconds in a day, 86,400. The value of the centrifugal force then be- comes, for the mass M, (S: = MX 0.03373, and for the units of mass, t = 0.03373 (units of force'). [44.] The apparent value of g at the equator is less than its true value by exactly the amount of this force. Hence the full value of the earth's attraction at the equator is 9.78062 -f 0.03373 = 9.81435. For any other latitude, the value of the centrifugal force is easily found by assuming that the earth is a perfect sphere. In Pig. 33, let m be the position of the body on the globe ; then m O B = A m = am f is the latitude of the place, which we will indicate by A ; also Am^R cos X is the radius of the parallel of latitude on which the body m is revolving. The value of the centrifugal force, in terms of the lat- itude, will be found by substituting this last value for R in [43] . Making this sub- stitution, and using for R the mean rac^ius of the globe, we obtain, for the vakie of the centrifugal force, m/= 0.03367 cos X. This, however, is the value of the centrifugal force acting in the direc- tion mf. The force of gravity acts in the direction m O, and in order to ascertain to what extent the force of gravity is influenced by the centrifugal force, we must decompose the last into two com- ponents. Let j)i/ represent the intensity of the centrifugal force, then m a and ?» b will represent the intensities of two components ; the first of which, being opposite in direction, will tend to neutral- ize the force of gravity, while the second, being perpendicular in direction, will produce no effect on it. The value of the compo- nent ma is m a = mf cos X ; and substitutuig for tnf its value as above, and representing always by t that component of the / --../'. ■/ 1 V / / / ^^■ ■' / \ V ^. / Fig 33. GENERAL PROPERTIES OP MATTER. . 83 centrifugal force which is opposite in direction to gravity, we have t = 0.03367 cos'' A. [45.] We can easily find how rapid the rotation of the glohe must be, 'in order that the centrifugal force at the equator should just balance the attractive force of gravity. For this purpose we have only to substitute for (E, in [43] , the value of the attractive force just found, and calculate the corresponding value of T, which will be found to be 5,065 seconds. Hence, if the earth revolved once in 5,065 seconds, or in l'- 24°'' 25°, — that is, a little more than seventeen times faster than it does, — the force of gravity at the equator would be just balanced by the centrifugal force. (60.) The Spheroidal Figure of the Earth. — The second cause, mentioned in (58), of the variation of gravity with the latitude, is the spheroidal figure of the earth, in consequence of which a body at the poles is more strongly attracted by gravity than at the equator. The form of the earth, as has been before intimated, is not a perfect sphere. It is flattened at the poles, and its figure is best described as an oblate ellipsoid or spheroid. A section of the earth through a meridian circle is therefore not a circle, but an ellipse of very small eccentricity, and the figure of the earth may be conceived as generated by the revolution of such an ellipse round its shorter diameter as an axis. The flat- tening at the poles amounts in round numbers to about si-^ of the equatorial radius ; in other words, the polar radius is about 5^^ shorter than the equatorial. This deviation from a true sphere is so small, that it could not be detected by the eye in a common globe, but in the earth it nevertheless amounts to over thirteen English miles. The dimensions of the earth are accurately as follows : * — Volume of the earth, 1,082,842,000,000.000 cubic kilometres. Surface of the earth, 509,961,000.000 square " Length of a quadrant, 10,000.857 kilometres. Equatorial radius, 6,377.398 " Mean radius (lat. 45°), 6,366.738 " Polar radius, 6,356.079 " Difierence between the equa- torial and polar radius, 21.319 " * These data are all taken from the table of constants in Kohler's " Logarithmisch- Trigonometrisches Handbuch." 84 CHEMICAL PHYSICS. Fig. 34. Were the earth perfectly spherical, a plumb-line at any point on its surface would point exactly to its centre, and the centre of figure -would then be also the centre of gravity. The earth being spheroidal, the phenomena of gravity upon its surface be- come less simple. The plumb-line does not point exactly to the centre of the earth, except at the equator or at the poles, and, moreover, there is no fixed centre of gravity. In Fig. 34, the line 4 P is supposed to represent a qiiadrant of a meridian, of which O P is the polar, and O A the equa- torial radius. Starting from the equator, let us take stations only one degree distant from each other on this meridian, and at each sta- tion continue the direction of the plumb-line until it intersects the plumb-line similarly produced at the previous station. If, iu the fig- ure B, C, and D are three such points, then a, b, and c are the three points of intersection, and it is easy to see, from the figure, that the ninety points of inter- section, which would be obtained by producing the plumb-lines from all the ninety stations, would form when united a curved line, a b c p. By making the number of stations infinite, we should of course have an infinite number" of points of intersec- tion ; and for every point on the quadrant A P, there would be a corresponding point on the curve a p. The points a, b, c, etc. are termed in geometry centres of curvature ; the lines A a, Bb, C c, etc. are called radii of curvature; and the curve ap is called the evolute of the curve A P. Now it is evident, from the properties of the centre of gravity, that the centre of gravity for any point on the quadrant .4 P is the corresponding centre of curvature on the evolute a p. At A, for example, the attrac- tion of the earth acts as if it originated at the centre of gravity a; at B, as if it originated at the centre of gravity b, etc. The intensity of the force which resides at these different centres is not, however, the same ; the intensity at a, for example, is less than that at b, at b less than at c, etc. It gradually increases at the different points on the evolute from a to p. What is true of the quadrant A P must be true of every GENERAL PROPERTIES OF MATTER. 85' quadrant ; hence, if the evolute ap is revolved on its a.xis, O p, the surface generated would be the locus of all the centres of gravity for points on the upper hemisphere of the globe ; and if the evolute a p' is revolved, the surface generated would be the locus of all the centres of gravity for points on the lower hemi- sphere of the globe. It is evident, from the above, that a body placed at the equa- tor, and a similar one placed at the pole of the globe, stand in different relations to its mass as a whole, and we should natu- rally expect that they would be attracted with different degrees of force. Newton, Maclaurin, Clairaut, and many other eminent geometers, have calculated how great the variation of gravity, owing to the elliptic form of the earth alone, ought to be, in going from the equator to the pole, and the results of their calcula- tions coincide almost precisely with those of observation given above. It has also been proved by the same- mathematicians, that the actual form of the earth is almost precisely that which would re- sult from the revolution of a liquid mass of the same volume and density once in twenty-four hours ; and since we have every reason to believe that the globe was once fluid, and that it is even so now, with the exception of a comparatively thin crust on its sur- face, it follows that the cause of the variation of gravity just considered is itself an indirect result of the centrifugal force. (61.) Variation of the Intensity of Gravity as we rise above the Smrface of the Earth. — The law by which the intensity of gravity varies with the distance from the centre of force, can be discovered by studying the effect of the eairth's attraction on the moon, as compared with its effect on bodies near its surface. The mean distance of the moon from the centre, of the earth, is about sixty times the earth's equatorial radius, and it revolves roimd the earth, in an orbit which is very nearly circular, in 27.322 days.. By (59), it follows that the intensity of the earth'^s attraction at the moon is just equal to the centrifugal force, and it can therefore.' be calculated by substituting in [43] the values of R and T just given. Making these substitutions, we obtain, for the value of the earth's attraction on the moon, where M equals the mass of the moon, G = MX 0.0027. For the unit of mass, then, the intensity of the earth's attraction at the distance of the moon is g-= 0.0027. The intensity of the earth's attraction for bodies on the equator 8 86 CHEMICAL PHYSICS. is, as we have seen, g = 9.7806, -n^hich is about 3,600 times greater than 0.0027. For bodies as distant as the moon, we may consider the attraction of the globe as concentrated at its centre of figure, and lience we may regard tlie moon as about sixty times as distant from the centre of attraction as a body on tlie equator. At sixty times the distance, then, the force is 3600 (= 60') times less ; that is, the intensity of the force of gravity varies inversely with the square of the distance from the centre of attraction. Repre- senting, then, by g- and g' the intensity of gravity at the distances R and R, we have always the proportion, g:g' = R":R\, [46.] It follows from the above discussion, that the intensity of gravity must vary at different heights above the sea-level on the surface of the earth. The amount of this variation can easily be calculated by means of the above proportion. Repre- senting by g the intensity of gravity at the sea-level, by g' the intensity at an elevation, h, and by R the radius of the earth, we have, from [46], neglecting the variation in the centrifugal force at the two heights, g:g' = (R + hy : R^ and g = g' ^^^#. [47.] When h = 1000 m., we have from [47], g = g' 1.0003. The amount of variation is therefore perceptible at any considerable elevation above the sea-level. Hence, in studying the variation of the intensity of gravity on the surface of the earth, it is impor- tant to reduce the results of observations at different elevations to the sea-level before comparing them. This can always be done by [47] , when the elevation is known. (62.) Law of Gravitation. — We proved, in (49), that the intensity of the force of gravitation is directly proportional to the quantity of matter (the mass) on which it acts, and in the last section we have shown that the intensity of the force of grav- itation is inversely proportional to the square of the distance of the masses, on which it acts, from the centre of attraction. By combining the two, we have the well-known law of gravitation, which is expressed in the following terms : — All masses of mat- ter attract one another with forces directly proportional to the quantity of matter contained in each, and inversely proportional to the squares of their distances from each other. GENERAL PEOPEETIES OP MATTER. 87 This law was discovered in 1666 by Sir Isaac Newton, who, while reflecting on the power which causes the fall of bodies to the earth, and considering that this power is not sensibly dimin- ished, even at the top of the highest mountains, conceived that it might extend far beyond the limits of the atmosphere, and even exert its influence through all space. It may be, he thought, this very force by which the moon is retained in her orbit round the earth, and the whole planetary system round the sun. In order to verify his conjecture, he calculated, on the same principle used in the last section, the attraction of the earth on the moon, as- suming that the force must diminish in the inverse ratio of the square of the distance, — an assumption to which he was led by the relation, previously discovered by Kepler, between the times of revolution of the planets and their distances from the sun. The result, at first, did not answer his expectations, because he had" used in the calculation a value of the earth's radius, and hence also of the moon's distance, which was much too small, and he therefore rejected the hypothesis as not substantiated. Several years later, Picard measured, with great accuracy for the times, an arc of the meridian in Prance ; and from his measure- ment it appeared that the radius of the globe was nearly one sev- enth greater than had previously been supposed. Furnished with these new data, Newton resumed his calculations with complete success, and in 1687 published his great work, the Principia, in which the consequences- of this great law were developed as far as the astronomical and mathematical knowledge of the times would permit. (63.) Absolute Weight. — When a body is not free to fall, the force which gravity exerts upon it is expended in pressure, against its support. This pressure is called absolute weight. The abso- lute weight of a book, for example, is the pressure which it exerts against the table on which it rests. It is evident that this pressure is equal to the intensity of the force with which the book is attracl^ ed by the earth. The intensity of the force which gravity exerts on a given mass of matter we have represented by G (49). If, then, we represent the pressure caused by this force, or the absolute weight of the same mass of matter, by tO, we have tO = G. Hence, we can substitute tO for G in [26] and [27], and shall then have ^=M.g, [48.] and \3i:^' = M:M'. [49.] 00 CHEMICAL PHYSICS. In these formulae, tO represents weight or pressure ; "while in [26] and [27] G represents the intensity of the force which is the cause of the pressure. In this work, tU always stands for a certain number of grammes, and G for a certain number of units of force. For example, let us suppose that the quantity of mat- ter in the book just referred to is equal to 50 units of mass ; we should tlien know, from [26] , that the intensity of the force ex- erted by gravity upon it was equal to 490 units of force, and, from [48], that its weight was equal to 490 grammes. In the first case, G = 50 X 9.8 == 490 units of force. In the second case, Id = 50 X 9.8 = 490 grammes. The numbers in the two cases are precisely the same, but they signify different kinds of units. The identity of the numbers arises from the fact that the unit, of force is equivalent to a pressure of one gramme, so that tlie difference between G and tU is rather nominal than real. It follows from [49], that the weights of bodies are propor- tional to the quantities of matter which they contain ; in other words, that a body which contains two, three, or four times as much matter as a given body, wUl also weigh two, three, or four times as much. This fact has a most important bearing on chemistry, since the chemist is enabled, in consequence of it, to compare the various quantities of matter on which he experi- ments, by comparing their weights. So close is this relation, that in common language we confound the weight of a substance with its mass ; thus, we speak of ten grammes of iron, mean- ing thereby a quantity of iron which exerts a pressure of ten grammes. It must be remembered that, in scientific language, weight always means pressure, and not quantity of matter. The word is most commonly used, however, to denote tlie quantity of matter which exerts the pressure. So long as matter is neither taken from nor added to a body, its mass, from the very definition of the term, remains constant. It is not so, however, with the absolute weight. This varies with the force of gravity, and, as follows from [48] , it is directly pro- portional to the intensity of this force. Hence, the absolute weight of a body increases as we go from the equator to the poles, and diminishes as we rise above the surface of the earth. It is very different on the different planets and on the sun. A body weighing a kilogramme on the earth would weigh about 28 kilogrammes on the sun, about 2.6 kilogrammes on Jupiter, and GENERAL PROPERTIES OP MATTER. 89 only about 160 grammes on the moon. On the surface of the globe, however, the possible • variation of weight is but small, amounting at most to y^ of the whole. Calling this in round numbers 2^^^, it will be found that a body weighing one kilo- gramme at the equator would weigh 1 kilog. 6 gram, at the poles. (64.) French System of TFetg-A^s. -r- Weight is estimated by arbitrarily assuming a unit of weight, and then comparing the pressure exerted by other bodies with that exerted by the unit. If, for example, this pressure in a given case is found to be ten times as great as that of the unit, the body is said to weigh ten grammes, or ten pounds, as the unit may be denominated. The French have assumed, as their unit of weight, the pressure ex- erted by one cubic centimetre of -pure water at 4° C. (its point of maximum density) in a vacuum, and at the latitude of Paris. This unit they call a gramme. The gramme is multiplied and subdivided decimally, and the names given to these multiples and subdivisions are analogous to those used in the case of the metre. Thus we have the French System of Weights. Kilogramme, 1000 gram. Gramme, 1.000 gram. Hectogramme, 100 " Decigramme, 0.100 " Decagramme, 10 " Centigramme, 0.010 " Gramme, 1 " Millegramme, 0.001 " It follows from the last section, that a mass of brass whose weight is one gramme at Paris would weigh less than a gramme at a lower latitude, and more than one gramme at a latitude higher than that of Paris. Hence, the weight of one cubic centimetre of water at 4° C, and in a vacuum, is the standard gramme only at the latitude of Paris. The great advantage of this system of weights in all scientific investigations arises froni the very simple relation which exists between it and the system of measures already described. This is so simple, that it is almost always possible to calculate the weight of a substance from its volume, and the reverse, mentally, when the specific gravity of the substance is known. The French system, both of weights and measures, is exclusively used in this volume. (65.) System of Weights of the United States and of Eng- land. — In this country and in England two entirely distinct 8* 90 CHEMICAL PHTSICS. units of weight are in use, called the Troy Potmd and the Avoirdupois Pound, These units are entirely arbitrary, and are represented by certain masses of metal, which have been declared by law to be the legal standard of weight. These units bear to each other the relation of 144 to 175, and do not agree in any of their subdivisions except the grain. The Troy pound contains 5,760, and the avoiiwiupois pound 7,000 grains, all of the same value. The actual legal standard of weight in the United States is the Troy pound, copied by Captain Kater, in 1827, from the imperial Troy pound, for the United States Mint, and pre- served in that establishment. This pound is a standard at 30 inches of the barometer and 62° of the Fahrenheit thermometer.* The English standard of weight is connected with that of meas- ure, by the enactments that 277.274 cubic inches shall constitute the Imperial Gallon, and that the weight of this volume of pure water, weighed in air of 30 inches' pressure at 62° P., shall be taken as 10 avoirdupois pounds, or 70,000 grains. Tables of the subdivisions of the two units, showing their relations to the French system, will be found at the end of this Part, in connec- tion with the other tables of weights and measures. (66.) Specific Weight. — The specific weight of a substance is the weight of one cubic centimetre of the substance, and there- fore bears the same relation to the weight that the density does to the mass (15). If, then, we represent specific weight by ;^. to, we have SpM = Y' [50.] The specific weight of copper, for example, at Paris, is equal to 8.921 grammes. The term specific weight must not be con- founded with specific gravity, which will be explained in (69). The specific weight of a substance is evidently variable, and, like the absolute weight, depends on the intensity of the force of gravity. (67.) Unit of Mass. — In assuming a unit of weight, we have also established a unit of mass. If, in [48], we substitute for M unity, and for g the intensity of gravity at Paris, the value of to becomes * Report on Weights and Measures, by Professor A. D. Bache. Thirty-fourtU Con- gress, Third Session. Ex. Doc. No. 27. GENERAL PROPERTIES OP MATTER. 91 tD = 9.8096 grammes ; [51.] that is, the unit of mass weighs at Paris 9.8096 gram. Any quantity of matter, then, which weighs at Paris 9.8096 gram., is tlie unit of mass. The weight of the unit of mass evidently varies with tlie intensity of gravity ; thus, at tlie poles the unit of mass weighs" 9.8315 gram., at the equator it weighs 9.7806 gram. The differences are very much greater on the surfaces of the sun, moon, and planets ; thus, on the sun the unit of mass weighs about 277.5 gram., on the moon about 1.654 gram., and on the planet Jupiter about 26.243 gram. In gerjeral, a quantity of matter which weighs as many grammes as the number which expresses the intensity of gravity at the place of observa- tion, is equal to the unit of mass. From equation [48] we have, by transposition, M^ — . Hence, in order to find the number of units of mass of which a body consists, we have only to divide its weight in grammes by the in- tensity of gravity at the place of observation. For example, 500 grammes of iron, at Paris contain sf^f^ = 50.98 units of mass. (68.) Density. — The density of a substance has been defined as the mass of one cubic centimetre of the substance (15), and from [1] we have D= ^, or, substituting for M its value, — , to u^ and then for y^ the symbol Sp.w,yfQ obtain D=~ = ^^ (units ofviass-). [52.] 8 921 The density of copper, for example, is equal to ^-^ = 0.909 unit of mass: Density has, therefore, the same relation to spe- cific weight that mass has to weight. It is always equal to the weight of one cubic centimetre of the substance divided by the intensity of gravity. It is evidently a constant quantity, and does not vary with the intensity of gravity. (69.) Specific Gravity. — The specific gravity of a substance is the ratio of its absolute weight to that of an equal volume of pure water at 4° C. and at the sanje locality. If to represents the absolute weight of the substance at any place, and to' the weight of an equal volume of water at the same place, then Sp.Gr.= ^, [58.] 92 CHEMICAL PHYSICS. Moreover, since tO = M. g, and to' = M' . g, ive have, also, Hence the specific gravity of a substance is likewise the ratio of its mass to the mass of an equal volume of water. It is, there- fore, like the density, a constant quantity, and does not vary with the intensity of gravity. In the French system, one cubic centimetre of water at 4° C. weighs at Paris one gramme, and hence at Paris the weight in grammes of a given volume of water at 4° C. is always equal to the number of cubic centimetres. We may therefore substitute in [53], for tD', the volume in cubic centimetres. If we also designate by W the absolute weight of a body at Paris, and by Sp. W. the specific weight at Paris, we can obtain from [53] and [50], &p.Gr.= ^=Sp.W. [55.] From this equation, it appears that the numbers expressing the specific gravity of a substance and its specific weight at Paris are always the same in the French system. The difference, however, between the two is an essential one. Sp. W. always stands for a certain number of grammes, but Bp. Gr. is a ratio. Wlien we say that the specific weight of copper is 8.921 grammes, we mean that one cubic centimetre of copper weighs at Paris this number of grammes ; but when we say that the specific gravity of copper is 8.921, we merely mean that a volume of copper weighs 8.921 as much as the same volume of water. The first number is variable, depending on the unit of weight used; the last is invariable, and hence the same with all systems of weights. It is only in the French system of weights that the two numbers are the same. We can easily obtain from [55], ^=^^.' ""^^ W=y.Sp.Gr. [56.] These simple formulae should be remembered, as they will be constantly used in the course of this work. It is more usual to refer the specific gravity of gases to air, as a standard of comparison, than to water. It will be shown hereafter that the weight of a given volume of air varies very GENERAL PROPERTIES OF MATTER. 93 greatly, both with the temperature and the aftmosplierie pressure to which it is exposed ; and it is tlierefore essential, in using air as a standard of comparison, to adopt arbitrarily a certain tem- perature and pressure, at which it shall be considered as the stand- ard. The temperature which has been generally agreed upon is 0° C, and the pressure which has been adopted is that cor- responding to a height of 76 c. m. of the barometer. We may then define the specific gravity of a gas as the ratio of its weight to that of an equal volume of air at 0° C. and under a pressure of 76 c. m. Representing by W the weight of a given volume of gas at Paris, and by W and W" the weights respec- tively of the same volumes of water and air at the standard teni- peratures and pressure, — also representing by Sp. Or. the spe- cific gravity of the gas referred to water, and by Sp. Gr. the specific gravity referred to air, — we have W W Sp.Gr. = ji^, and Sp.Gr. = ^^. [57.] When the specific gravity of a given substance is referred to one standard, it is frequently required to calculate its specific gravity with reference to the other, or, in technical language, to reduce the specific gravity to the other standard. For this pur- pose, we know that the specific gravity of air with reference to water is equal to 0.00129363, Hence, -^ = 0.00129363, and by substituting the value of W, obtained from this in [57], we can easily obtain Sp. Gr. = Sp. Gr. 0.00129363, [58.] a formula by means of which the reduction can easily be made, A table giving the specific gravities of some common substaaices will be found at the end of this Part. (70.) Unit of Force. — The unit of force has been defined as that force which, acting on the unit of mass during one second, will impress upon it a velocity of one metre (29). Since the unit of mass weighs at Paris 9.810 grammes, we can also define the unit of force as that force which, acting during one second, will impress on 9.810 grammes of matter a velocity of one metre. Moreover, it follows from [14] that a force which will impress during one second a velocity of one metre on 9.810 grammes of matter, is equal to the force which will impress a velocity of 9.810 94 CHKMICAL PHYSICS. metres on one gramme of matter. But this force is the same as the force exerted by gravity on one gramme of matter. In other words, it is equal to the weight of one gramme. "We have, then, a new measure for our unit of force. The unit of force is the force exerted in pressure by the unit of weight. "When a weight of ten grammes, for example, is suspended to a fixed point, the pressure exerted by that weight is equivalent to ten units of force. (71.) Relative Weight. — There are, in general, two methods by which the weight of a body (that is, the pressure which it ex- erts) may be determined. The first method consists in balancing the pressure against a spring, and determining the weight from the amount by which the spring is bent. An instrument for this purpose is represented in Fig. 35. It consists of a steel spring, bent in the form of a "V". To the end of the lower arm is fastened an iron arc, which passes freely through an opening in the upper arm, and ends in a ring. To the end of the upper arm a similar iron arc is fastened, which passes through an opening in the lower arm, and terminates in a hook. In using tlie instrument, the body to be weighed is suspended by the hook, as in Fig. 35, and the number of grammes by which the spring is bent is then read off on the graduated arc. Such an instrument is called a spring bal- ance, and indicates at once the absolute weight of a body. Could it be made sufficiently deli- cate, it would show that the absolute weight of a body varied on the earth's surface, gradually increasing from the equator towards the poles. Such an instrument would give the absolute weight of a body. i''e- 35- The second method consists in preparing a set of so-called weights, which are masses of brass or platinum weigh- ing exactly one gramme, or some multiple or fraction of a gramme, at Paris. The weight of a body is then estimated by balancing it against these weights in a well-known instrument called the bal- ance. The balance is merely a form of the lever, so constructed that, when equal pressures are exerted on its two pans, the beam stands in a horizontal position. The body to be weighed is placed in one pan, and then weights are added to the other until GENEBAL PROPERTIES OF MATTER. 95 the beam of the balance rests in a horizontal position. The sum of these weights then indicates the weight of the body. At Paris the balance indicates at once the absolute weight of a body, but not necessarily so at other places on the earth's surface. To il- lustrate this point, let us suppose that, in weighing at Paris, it required ten grammes' weight in one pan of the balance to equi- poise the body in the other pan. Suppose, now, that we trans- port the whole apparatus to some point on the equator. It is evident that our gramme weights no longer weigh one gramme each, but something less, by an amount easily calculated from the diminution in the intensity of gravity. Nevertheless, since the body has lost weight in the same proportion, it will still be balanced by the ten gramme weights, and so it would be all over the globe. This weight, which is frequently called relative weight, will always be designated in this work by W, in order to distinguish it from the absolute weight at other localities, which we have already designated by ijj. Hence we have, from [48], W= M . 9.8096, and iX) = Jf . g-, [59.] Since the force of gravity at any given locality, and hence ' at Paris, does not vary, it follows that the relative weight of a body, or W, is a constant quantity ; the same at any point on the sur- face of our globe, and the same on the sun, moon, and planets as it is on the earth. We can easily find the absolute weight of a body at any local- ity, when its relative weight is known. Representiag, as above, by W the relative weight of the body, and by to the absolute weight required at the place in question, we have, from [59] , to : W=M.g : M. 9.8096, [60.] and to =^9^96' t^l-] that is, the absolute weight of a body at any place is equal to the absolute weight at Paris (or the relative weight of the body at the place) multiplied by the ratio between the intensity of gravity at the place and that at Paris. In almost all cases the weight of a body is determined by the balance, and hence, when the French system of weights is used, the weight of a body thus estimated is its absolute weight at Paris ; and in this work, when the weight of a body is 96 CHEMICAL PHYSICS. spoken of, it must always be understood to be its relative ■weight, that is, its absolute weight at Paris, unless the reverse is expressly stated. As a general rule, it is unimportant to know the absolute weight of a body at any given place. "We use the balance to estimate the relative amounts of matter in different bod- ies. Now ten grammes of gold relative weight is the same quan- tity of matter in all localities ; but ten grammes of gold absolute weight is a larger amount of gold in Peru than it is in Paris. Hence, if we estimate the quantity of matter everywhere by rela- tive weight, we can compare directly the weights taken in dif- ferent places ; while, on the other hand, if we estimated it by absolute weight, we should be obliged in most cases to correct the weights before comparing them for the difference in the in^ tensity of gravity. This subject may be made still clearer to some persons by put- ting it into a mathematical form. Representing by m the mass of the unit of weight at Paris, we have 1 gr. = m . 9.8096. By comparing this equation with W= M . 9.8096, we obtain W = - ; [62.] that is, the relative weight of a body indicates the quantity of matter which it contains, compared with that contained in one cubic centimetre of water at 4° C. It is, therefore, a legitimate measure of the quantity of matter contained in a body. As we have used W to denote the absolute weight of a body at Paris, so we shall use Sp. W. to denote the specific weight of a substance at Paris, or its relative specific iveight. Substituting W for to in [50] , we obtain Sp. W. = -?. [63.] This quantity, like the relative weight, is evidently constant ; and when the specific weight of a substance is mentioned in this work, its relative specific weight is always to be understood, unless tlie reverse is expressly stated. Substituting in [63], for W, its value, we obtain 8p.W. = y9)Mn = D . 9.8096,, [64.]; • which gives the relation between the relative specific weight of a substance and its density. GENEEAL PROPERTIES OF MATTER. 97 THE BALANCE. (72.) Lever. — Before studying the theory of the balance, it is important to consider the general theory of the lever, of •which the balance is only a single example. A lever is any rigid bar, A B (Fig. 36), resting on a' point, c, round -which two forces tend to turn it in opposite directions. 5 X Fig. 36. Fig. 37. The point c is called i\iQ fulcrum. The force applied at A is called the power, and the force applied at B is called the resistance, or the weight. Levers are commonly divided into three kinds, ac- cording to the position which the fulcrum has in relation to the power and the weight. If the fulcrum is between the power and the weight, as in Figs. 36, 37, the lever is of the first kind. If \ \ Fig. 38. Fig. 39. the weight is between the fulcrum and the power, as in Fig. 38, the lever is of the second kind. If the power is between the 9 98 CHEMICAL PHYSICS. fulcrum and the weight, as in Fig. 39, the layer is of the third kind. In the three kinds of lever, the perpendicular distances from the fulcrum to the lines of direction of the two forces are called the arms of the lever. If the lever is straight, and perpendicular to the directions of both of the two forces, the two portions of the lever, A c and B c, Fig. 36, are themselves the arms of the lever. If, however, the lever is not straight, or is inclined to the direction of one or both of the forces, the arms of the lever are the perpendiculars, a c and b c. Fig. 37, a O and b O, Fig. 40, let fall from the fulcrum on these directions. In order that the two forces applied to the lever should be in equilibrium, three conditions are essential : — 1st. The lines of direction of the two forces must be in the same plane with the fulcrum. 2d. The two forces must tend to turn the lever in opposite di- rections. 3d. The intensity of the two forces must be to each other in- versely as the lengths of the arms of the lever to which they may be regarded as applied. That these three conditions are essential to equilibrium can easily be proved. In the first place, it is evident that the two forces cannot be in equilibrium, unless the direction of their resultant passes through the fulcrum. Now it can easily be proved, that, unless the two forces are in the same plane, they can have no single result- ant; and hence follows the necessity of the first condition. In the second place, let us suppose. Fig. 40, that J. Q and £ P are the lines of direction of two forces in the same plane with the fulcrum O, and that C is the point where these directions in- tersect ; i\pn, in order that the direction of the resultant R should pass through O, it is evident that the directions of the rig. 40. GENERAL PBOPERTIES OP MATTER. 99 components should be sncli that they would tend to turn the lever in opposite directions. The necessity of the third condition will be most readily seen if studied under two cases. In the first place, let us take the case where the two forces are parallel, as in Fig. 37. It has been proved (37) that the point of application of the resultant of two parallel forces divides the line joining the points of application of the components into two parts, which are inversely propor- tional to the intensities of the forces. Hence it follows, that, in order that the direction of the resultant in Fig. 37 should pass through the fulcrum, the two forces applied at A and B must be inversely proportional to A c and B c, and hence also to a c and b c, which are the arms of the lever. In the second place, let us suppose that the .directions of the forces are not parallel, as in Pig. 41. In this figure, A Q and B P represent the directions of the forces, which we will represent by F and F', and 'a O and b O the arms of the lever. By the principle of (32) , the efiFeet of these forces is the same as if they were applied respectively at a and b, points which we may consider as immovably united to the lever. From O as a centre, with a radius equal to O b, the longer arm of the lever, describe an arc which will intersect the direction J. Q at a point c ; then we shall have Oc=Ob. By the same principle as above, the effect of the force F is the same as if it were applied at c. We can now evidently consider this force as made up of two others, one acting in the direction O c, which will be neu- tralized by the resistance of the fixed point O, and the other in the direction c q, parallel to B P. It follows, now, from the equality of O c and O b, that the lever can be in equilibrium only when the force F' equals that component of the force F which acts in the direction c q. Let us suppose that F=c Q, and hence that the component is equal to cq,v?e have then, as the condition of equilibrium, F' = c q. But from the similarity of the triangles c q Q and c O a, we have cq : Oa= c Q : c O, and by substitution, Pig. 41. 100 CHEMICAL PHYSICS. F' : Oa=:F : Ob. [65.] It is, then, also a condition of equilibrium, that the two forces should be to each other inversely as the lengths of the arms of the lever, the point which was to be proved. We have proved the validity of the three conditions of equilibrium for the first kind of lever only ; but this proof can easily be extended to the second and third kinds of lever. Prom proportion [65] we obtain, by multiplying together the extremes and the means, F X O a = F' X Ob. The product of the intensity of a force by the length of the perpendicular let fall from a fixed point to the line of direction of the force, is called the moment of the force with respect to the point. Since O a and O b are such perpendiculars, it follows that, when a lever is in equilibrium, the moments of the power and resistance are equal. It follows from what has been said, that the tendency of the power to turn the lever may be augmented either by increasing the amount of the power, or by increasing the length of the arm of the lever on which it acts ; that is, by increasing the perpen- dicular distance of the direction of the force from the fulcrum. In either case, the effect will be increased in a corresponding proportion. Thus, if we remove the power to double its distance from the fulcriim,,we shall double its effect ; and if we remove it to half the distance, we shall diminish its effect by one half. The perpendicular distance of the direction of a force from the fiil- ■ crura is called its leverage ; and it is evident that the effect of any force applied to a lever will be proportional to its leverage. (73.) The Balance. — The instrument by means of which the weight of a substance is compared with the unit of weight, is called a Balance. It is generally made of brass, and consists essentially of an upright pillar supporting a beam, B B, Fig. 42, which turns upon a knife-edge, placed exactly at the mid- dle of its length. From the two ends of the beam are sus- pended the pans, in which the weights to be compared are placed. The knife-edge is formed by a triangular steel prism passing through the beam, whose axis is exactly at right angles with the plane of the beam. The lower edge of the prism is sharp, and rests upon an agate plane, so as to make the friction as small as possible. For the same reason, the hooks by which the pans are suspended rest also on knife-edges. These knife-edges GENERAL PROPERTIES OP MATTER. 101 are adjusted perpendicularly to the plane of the beam, and on the same level as the fulcrum. The fulcrum is so placed that the centre of gravity of the beam shall be slightly below it, so that Jig. 12. when in equilibrium the beam will tend to come to rest in a horizontal position. The centre of gravity can be adjusted by means of the button C, Pig. 42, which can be moved up or down on the screw to which it is fastened. The long index-rod attached to the beam below the knife-edge indicates, by the graduated arc, when the beam is horizontal. When the balance is not in use, the beam can be lifted off from its bearing, and supported upon the brass arms E, E. These are attached to the cross-piece a a, which can be raised or lowered by turning the thumb-screw O. The motion of the cross-piece is directed by the two pins A, A, which play loosely through holes at its two ends. A balance is evidently a lever with equal arms, and,, according to the principle of the lever, if equal weights are placed in the two pans, they will exactly balance each other. The balance, there- fore, enables us to compare the weight of a substance with the unit of weight. We have simply to place the substance in one pan of the balance, and then add weights, which have been ad- justed by the standard unit^ to the other, until the beam assumes a horizontal position, or until it vibrates to an equal distance on 9* 102 CHEMICAL PHYSICS. both sides of this position, — -as can be observed by the motion of the index over the graduated arc. The sum of the weights re- quired to balance the substance is, then, its relative -weight in terms of the unit of -weight employed. The usefulness of a balance depends upon t-wo points, — 1st, its accuracy^ and, 2dly, its sensibility to slight differences of -weight. An examination of the conditions on -which these depend, -will lead us to understand better the principle of this very important instrument. From the mode in -which the pans of a balance are suspended, it is obvious that -we may regard their -whole -weight as concentrated on the knife-edges at the ends of the beam. In ' a theoretical consideration of the subject, -we may therefore leave the pans entirely out of view, and consider any -weight placed in them as directly applied to the knife-edges, thus reducing the balance to a straight lever. Prom another point of view, the whole weight of the beam and pans may be considered as con- centrated at the centre of gravity, when the balance becomes a pendulum, wjiose point of suspension is the fulcrum of the beam. These two mechanical principles, combined in the balance, have constantly to be kept in view in studying its theory. It will then be easy to understand the folio-wing circumstances, on which the accuracy and sensibility of the instrument depend. 1. It is necessary that the distances of the two knife-edges from the fulcrum should be exactly equal; for if the distance from the fulcrum of the point of suspension of one pan were greater than that of the other, then a weight placed in the first, acting under a greater leverage, would balance a larger weight in the last, and the larger in proportion to the inequality of the two arms of the beam. 2. It is necessary that the centre of gravity of the beam and pans should be beloiv the fulcrum, and as near to it as possible. Were the centre of gravity at the fulcrum, the beam would not oscillate, but remain in whatsoever position it were placed. Were it above the fulcrum, the beam would be overset by the slightest impulse. When it is below the fulcrum, the beam, as already stated, may be regarded as a pendulum, whose axis co- incides with the line joining the fulcrum and centre of gravity. As this line forms right angles with the Jixis of the beam in what- ever position the latter may be placed, and as the pendulum tends always to fall back to the perpendicular position whenever GENERAL PROPERTIES OP MATTER. 103 removed from it, it follows that, if "vre impart an impulse, to the beam of a properly adjusted balance, it will, after vibrating for some time, invariably return to a horizontal position. The centre of gravity of the beam is exactly under the fulcrum, and in a line at right angles to the axis only when the two pans are equally loaded. If unequally loaded, the centre of gravity is to the right or to the left of this line ; and in that case the beam tends to come to rest at an angle to the horizontal position, rapidly in- creasing with the inequality of the weight until the beam is entirely overset. In weighing with a delicate balance, it is not necessary to wait until the beam comes to rest, in order to ascertain whether the pans have been equally loaded. This can be ascertained more promptly by noticing the amplitude of the vibrations of the index on eitlier side of the perpendicular, by means of the graduated arc. They will be equal only when the weights in the two pans are equal. The sensibility of a balance depends in great measure on the nearness of the centre of gravity to the fulcrum. In order that a small weight, placed in one pan of a balance, should turn the beam, it must evidently overcome two forces ; first, the friction of the knife-edges on their bearings, and, secondly, the tendency of the beam to remain in a horizontal position. This tendency depends, as has already been shown, upon the position of the centre of gravity below the point of siipport. Let us now com- pare two cases in which the centres of gravity are at different distances from the fulcrum, and ascertain in which case the force required to turn the beam will be the least: In Fig. 43, suppose the line ffl Z> to be the axis of the beam, O the fulcrum, and g- OT G the centre of grav- ity. We have now to in- quire in what position of the centre of gravity it will require the least force to bring the beam to a new position, a' b'. In order to bring the axis of the beam to this position, it will be necessary to bring the centre of gravity from g to g', or from G to G'. In the first case, it will be necessary to raise the whole Fig. 43. 104 CHEMICAL PHYSICS. weight of the beam and pans, which we suppose concentrated at g, through the perpendicular distance g e ; and in the second case, to raise the same weight through the distance G E. Since the distance g- e is much less than the distance G E, it is evi- dent that it will require a less force in the first case than in the second. Hence, the sensibility of the balance is the greater, the nearer the centre of gravity is to the fulcrum. 3. It is important that the points of suspension of the pans should be on an exact level with the fulcrum. The importance of this condition may be see'n, by remembering that an in- crease of weight in the pans is equivalent to adding just so much weight upon the points of suspension, and therefore tends to draw the centre of gravity towards the line (Fig. 44) connect- ing the two. If this line passed above the fulcrum, as in Fig. 45, then, by increas- ing the weight in the pans, the centre of gravity might be brought to coincide with, or even be carried above, the fulcriim, when the balance would become useless. If this line, as in Fig. 45, passed below the fulcrum, an increase of weight in the pans would tend to draw down the centre of gravity ; and thus, by increasing its distance from the fulcrum, would diminish the sensibility bi the balance. When, however, the line passes through the fulcrum, as in Fig. 46, the points of suspension of the pans are on an ex- act level with the fulcrum, and an increase of load always tends to raise the centre of gravity towards the fulcrum in proportion to its amount ; so that a well-adjusted balance theoretically should turn with the same weight, whatever may be the load placed upon it, from the smallest to the largest of which its construction admits. This last point can bb still further illustrated in the following manner. It has already been shown, that the weight required to rig. 45. Eig. 46. GENERAL PROPERTIES OF MATTER. 105 turn the balance, when unloaded, may be measured by the force required to raise the centre of gravity of the beam and pans through a small arc, G G' (Fig. 43), when applied at b'. Let us suppose that the pans are loaded with a weight of one kilogramme each. It is evident, from what has been said, that this is eqtiiv- alent to condensing a mass of matter equal to one kilogramme at each of the points a and b. The centre of gravity of these masses must evidently be at the middle of the line a b, that is, at the fulcrum of the balance. Since, then, this additional weight is supported in any position of the beam, it follows, that the weight required to turn the balance is still measured only by the foree required to raise the centre of gravity of the beam and pans through the arc G, G', or, to generalize, the absolute weight re- quired to turn the balance is the same, whatever may be the load. This, however, is only theoretically true, for in practice the weight required increases with the load, in consequence of the increased friction and the slight bending of the beam which it causes. While, however, the absolute weight required to turn the balance increases from these causes with the load, the proportion of this weight to the whole load diminishes. This is what is usually meant by the sensibility of the balance, and in this sense, evidently, the sensibility increases with the load. 4. It is important that the friction of the knife-edges on their bearings should be as slight as possible. The importance of this circumstance is so evident, that it does not require illustration. It is secured by a careful construction of the knife-edges, and by making the beam as light as i"s consistent with rigidity. In endeavoring to combine these conditions, the balance-maker meets with many practical obstacles. If he endeavors to increase the sensibility of his balance by diminishing the weight of the beam, he soon finds that he loses as much as he gains, by the in- creased flexure. If, again, he attempts to increase the sensibility by lengthening the beam, he soon comes to a limit, beyond which the increased leverage is more than compensated by the increased friction due to the necessarily increased weight of the beam. Nevertheless, by carefully attending to the, necessary conditions, balances may be constructed with a remarkable degree of sensi- bility. They have been made so delicate, that, when loaded with ten kilogrammes, they will turn with one milligramme, that is, with one ten-millionth of the load. 106 CHEMICAL PHYSICS. PROBLEMS. Centre of Gravity. 51. Two masses of matter are immovably united, A = 14: units of mass, and B = 10 units of mass. "What is the position of their common centre of gravity ? 52. A mass of matter. A, = 15 units of mass, is immovably united to a second mass, B. It is found by experiment that the common centre of gravity of the two masses is nearest to A, and divides the line connecting the masses into two parts, which are to each other as 2 is to 3. What is the mass o{ J3? Intensity of the EartKs Attraction. In these problems, the student is expected to use the values of g given in the table on page 76. 53. What is the intensity of the earth's attraction, at Paris, on a body whose mass is equal to 25 units of mass ? What is the intensity of the force of gravity, at Paris, on bodies whose masses are respectively 20, 60, 720, 430, and 510 units of mass? 54. What is the intensity of the earth's attraction, at Paris, on a body whose mass is equal to 0.1019 unit ? Pendulum. 55. WTiat is the time of vibration, at Paris, of a pendulum which is 0.99394 metre long ? What are the times of vibration of pendulums which are respectively twice, three times, four times, five times, and nine times this length ? The amplitude in each case is supposed to be infi- nitely small, and the pendulum to oscillate in a vacuum. 66. If the amplitude of the oscillation of the pendulum of the last ex- ample is 90°, how much would the duration of an oscillation be increased? Solve the same problem for amplitudes of 10°, 20°, 40°, and 50°. 57. If the pendulum of a clock, beating seconds at Paris, were length- ened by expansion one ten-thousandth of its length, how many seconds would it lose each day ? 58. If a clock, keeping perfect time at Paris, were carried to Spitzber- gen, how much would it gain each day, on the supposition that all the conditions, with the exception of the intensity of gravity, remained the same ? How much would it lose if carried to the equator ? 59. A pendulum on the equator, 0.990934 metre long, was found to oscillate in one second. What is the intensity of gravity ? 60. A pendulum at Paris one metre long was found to oscillate in 1.00304 seconds. What was the intensity of gravity ? 61. A pendulum at Paris four metres long was found to oscillate in 2.00608 seconds. What was the intensity of gravity ? GENERAL PROPERTIES OF MATTER. 107 62. What is the intensity of gravity at the latitude of 42° 21' ? What is the length of the seconds pendulum at this latitude ? 63. What is the intensity of gravity, and what the length of the sec- onds pendulum, on the following parallels of latitude, viz. 15°, 22°, 56°, and 74° ? 64. What is the intensity of the centrifugal force on the parallels of latitude of 5°, 20°, 30°, 50°, and 70° ? What is the absolute intensity of gravity on these parallels ? 65. What is the intensity of gravity at the summit of Mt. Washington, New Hampshire ? Latitude of Mt. Washington, 44° 15'. Height of summit above the sea-level, 2,027 metres. 66. What is the intensity of gravity at the summit of Mt. Blanc ? Lat- itude of Mt. Blanc, 45° 50'. Height of summit' above the sea-level, 4,814 metres. Weight. 67. What IS the weight of a body containing 10 units of mass at Paris ? What is the weight of the same body at Boston ? The latitude of Boston is 42° 21'. 68. What is the weight of a body containing 500 units of mass, at the equator and .at the poles ? 69. What is the specific weight of iron at Paris ? What are the spe- cific weights of lead, tin, mercury, sulphur, sodium, and lithium, at Paris ? and also at Boston ? Mass. 70. What is the masS of 100 kilogrammes of iron ? What are the masses of 50 grammes of sulphur, of 40 grammes of mercury, of 90 kilo- grammes of granite, when the value of g is 9.8J.0 ? 71. What is the mass of 75 kilogrammes of ice, of 20 kilogrammes of common salt, of 50 grammes of air, when g = 9.810 ? 72. What is the mass of a cubic decimetre of lead ? What is the mass of a cubic decimetre of ice ? 73. What is the mass of 1,000 cubic metres of atmospheric air ? What that of the same volume of hydrogen gas ? • Density. 74. What is the density of hammered copper ? What is the density of the following substances, — lead, tin, mercury, sulphur, sodium, and lithium ? Calculate the density from the Sp. W. as obtained by solving the 69th example, and also from the Sp. Or. given in the Table at the end of this Part. 75. What ia the density of air, of oxygen, of hydrogen, and of nitrogen, 108 CHEMICAL PHYSICS. at the temperature of 0° C. and under a pressure of 76 cm.? The relative weight of one cubic decimetre of these gases will be. found in Table 11. at the end of this Part. Relative Weight. 76. The absolute weight of a body at Paris is 500 gram. What is its relative weight ? 77. The relative weight of a body at New Orleans is 460 gram. What is its absolute weight at the same place ? The latitude of New Orleans is 29° 57'. 78. The relative weight of a body at Paris is 1,250 gram. What is its absolute weight at Boston ? 79. The relative weight of a body is 12,300 gram. What is its absolute weight at Quito? The latitude of Quito is 0° 13'.5, and its elevation above the sea-level is 2,908 metres. 80. The relative weight of a body is 5,450 gram. What is its mass ? Find also the masses of the bodies whose weights are respectively 560 gram., 4,945 gram., and 500 gram. 81. The relative weight of a body is 5,255 gram., its volume is 500 cm.' What is its mass ? what is its density ? and what is its specific gravity ? 82. The specific gravity of a body is 7.248, and its volume 500 cm;' What is its density, mass, and weight ? 83. The mass of an iron cannon is 5,000 units, and its specific gravity 7.248. What is its volume and density ? 84. The specific gravity of a gas referred to water is 0.00143028, and its volume 500 m^? What is its density, mass, and weight ? 85. AVhat is the specific weight, the mass, and the density of 500 cm.' of mercury? Unit of Force. 86. A body having a density of 20 units and a volume of 1,000 c. m.' acquires, under the influence of a given force, an acceleration of 8 c. m. each second. What is the intensity of the force ? 87. A body whose weight is 100 kilogrammes acquires an acceleration of 8 m. each second. What is the intensity of the force ? 88. A body whose specific gravity is 2 and whose volume is 50 in".' ac- quires an acceleration of 10 m. each second. What is the intensity of the force ? 89. On a body weighing 100 kilogrammes a force of 15 kilogrammes is constantly acting. What acceleration does it impart to the body ? 90. To a body whose volume equals 10 m.' a force of 300 kilogrammes imparts a constant acceleration of 10 ra. What is the density of the body ? GENERAl, PROPERTIES OP MATTER. 109 ACCIDENTAL PROPERTIES OP MATTER. (74.) Divisibility. — We have now considered the first four of the general properties of matter enumerated in (7). All of these, with the exception of weight, are essential properties, and are necessarily associated with the very idea of matter. The four general properties which remain to be studied do not seem to be so essential, for we can conceive of a kind of matter which should not possess them. This is true, for example, of divisibility. We can easily conceive of a kind of matter so hard as to be physically indivisible, although no such matter is known to exist. In fact, all kinds of matter, even the hardest, can be subdivided, and, so far as we know, indefinitely ; the only limit to our power of sxibdivision being that fixed by the imperfection of our senses. ■ The extent to which, in some cases, the subdivision maybe xjarried is almost incredible. The goldbeater can hammer out a single gramme of gold until it covers a surface of 4,364 c7m;% when the gold-leaf is so thin, that fifteen hundred such leaves placed upon one another would not equal in thickness a single leaf of ordi- nary writing-paper. The surface of gold on the gilt wire used in embroidery is much thinner even than this. It has been calcu- lated that its thickness does not exceed one ten-millionth of a centimetre ; and if so, with the aid of the microscope magnifying five hundred diameters, a particle of gold can be distinguished upon it not weighing more than one forty-two-million-millionth of a gramme. The organic kingdom presents us with examples of the subdi- vision of matter which are still more remarkable. The micro- scope has proved the existence of animals which are as minute as the particle of gold mentioned above, and yet each of these crea- tures is composed of organs of locomotion and nutrition, like the larger animals. The finest human hair is about one two- hundred-and-fortieth of a centimetre in diameter. This is gen^ erally considered very fine ; but the hair is a massive cable in comparison with many animal fibres. The spider's thread is in some instances not more than one twelve-thousandth of a cen- timetre in diameter, and yet each of these threads is formed by the union of from four to six thousand fibrils. It has been calculated that one gramme of this thread would reach about fifty miles. 10 110 CHEMICAL PHYSICS. Science has not succeeded in discovering a limit to tlae divisi- bility of any one kind of matter. Nevertheless, the opinion has been maintained, and is still held by many scientific men, that matter is not indefinitely divisible, and that all bodies are made up of an exceedingly large number of absolutely hard, and hence indivisible particles, called atoms. According to the atomic the- ory, as this hypothesis is called, the ultimate particles of matter' are indestructible and unchangeable, and hence all physical and chemical phenomena are caused by changes in their relative posi- tion or grouping. As these atoms are supposed to be far smaller than the minut^ est portions of matter ■which we can distinguish ■with the micro- scope, they are beyond the limits of direct observation, and their existence is therefore a matter of inference from physical and chemical phenomena. It is not necessary, ho'wever, in order to explain these phenomena, to suppose that these atoms have any absolute size. We may, ■with Newton, regard them as infinitely small, that is, as mere points, or, as Boscovisch called them, va- riable centres of attractive and repulsive forces ; and all the phe- nomena can be as fully explained on this supposition as on the other. According to this vie'w, matter is purely a manifestation of force, and only continues to exist through the constant action of that Infinite Will -with whom all force originates. As it ■will be constantly necessary to refer to these centres of attractive and repulsive forces in matter, ■we ■will, for convenience, term the minute portions of matter in -which they may be supposed to re- side molecules, and the forces themselves molecular forces. (75.) Porosity. — The interstices between the different parts of bodies are called pores. The visible cavities of the sponge, for example, are pores of a large size ; the meshes, of ■which its tissues consist, are pores of a smaller size ; but in addition to these, there are pores between the fibres of the sponge themselves, although they are so minute that they cannot be seen. In like manner, a thin slice of the hardest wood, examined under the microscope, is found to be full of pores (see Figs. 47, 48) ; and the same is true, to a greater or less degree, of all organic struc- tures, as well as of the tissues which are manufactured with animal or vegetable fibres. The porosity of such siibstances is well illustrated by the process of filtering. The filters which are used in the arts and in chemical experiments are simply porous GENERAL PROPERTIES OP MATTER. Ill Kg. 47. bodies, -whose pores are large enough to allow fluids to pass through them, but, on the other hand, small enough to afrest the solid particles, which they hold in suspension. The simplest and most useful form of a filter is a cone of porous paper supported in a glass funnel. The porosity of organic substances jnay also be illustrated by the appa- ratus represented in Fig. 49, It con- sists of a glass tube, A, closed from above by a plug of hard wood cut transversely to its fibres, or by a piece of chamois skin, as is represented at o. The whole is surmounted by a tunnel- shaped cup, which may be filled with mercury. On exh?iusting the tube by means of an air-pump, the pressure of air on the surface of the mercury forces it through the pores of the dia- phragm, so that it falls in showers through the tube. A lump of chalk plunged under water, and placed under the receiver of an air-pump, will, on withdrawing the air, expel a torrent of air-bubbles, which had been concealed -^m gJJMJjrgEll TT^ 112 "CHEMICAL PHYSICS. in the internal pores of the stone. The same is true of many- other varieties of stone. Tliere is a kind of agate, called Iiydro- phane, which in its ordinary state is only semi-transparent, but after being plunged in water takes up about one sixth of its bulk of that iiuid, and becomes nearly as transparent as glass. The porosity of metals was proved by the Academicians of Florence in the year 1661. They filled a hollow ball of gold with water, and submitted it to great pressure, by which the liquid was made to ooze through the pores of the metal. The same exper- iment has since been repeated on different metals, and with like success. ' The porosity of gases' and liquids is proved by their power of penetrating each other without a corresponding change of vol- ume. This is illustrated by an experiment devised by Reau- mur. He filled a long tube closed at one end, half with water and the remainder with alcohol. Having carefully closed the mouth of the tube, he inverted it in order to mix the two liquids, when he found that a contraction of the liquids took place. Another experiment, illustrating the same property in regard to gases, is the following. A globe containing air is so arranged that small quantities of liquids can be introduced into it without allowing the air to escape. If, now, a few drops of alcohol ar6 made to enter the globe, this alcohol will evaporate to as great an extent as if the globe were empty, and the space, which before contained only air, will now contain both air and alcohol vapor. If, next, some ether is forced into the globe, this liquid will also evaporate, and exactly as much ether vapor will be formed as if the globe had contained previously neither air nor alcohol vapor j and we shall then have the space occupied simultaneously by air, alcohol vapor, and ether vapor. In like manner, we may in- troduce any number of volatile liquids into the globe, and yet, sO far as we know, each of these will evaporate to the same extent as if the globe were entirely empty, provided only that these sub- stances do not act chemically on each other. We may thus have, as the result of spontaneous evaporation, twenty or thirty differ- ent vapors, all existing simultaneously in the same space. By the experiments which have been cited, the porosity of most substances can be abundantly proved. The porosity of glass, however, and of many other substances, does not admit of such GENERAL PROPERTIES OF MATTER. 113 proof ; yet in these substances the porosity is rendered quite evi- dent by the changes of bulk which they undergo under tlie inJ- fluence of heat and cold. We make an obvious distinction between the large pores, which exist especially in organized bodies, and the intermolecular spa^- ces. The first arise from the want of continuity of the matter, and may be regarded in a measure as accidental, varying with the structure and organization of the body. They are frequently visible to the naked eye, or at least become evident with the aid of the microscope. The last are the exceedingly minute and in- visible spaces which exist between the molecules of matter. Those philosophers who have admitted the existence of atoms, have gen- erally concurred in the belief that the atoms even of the densest solids are very much smaller than the spaces which separate them. Sir John Herschel asks why the atoms of a solid may not be imagined to be as thinly distributed through the space it oc- cupies, as the stars that compose a nebula ; and compares a ray of light penetrating glass to a bird threading the mazes of a forest. (76.) Compressibility and Expansibility. — The property of porosity necessarily implies that of compressibility and expansi- bility. According to the atomic theory, any body is capable of an indefinite expansion, because we may conceive of the dis- tance between the atoms as being indefinitely increased. It could only, however, be compressed till the atoms come in con- tact. According to the other theory of the constitution of mat- ter, advanced in (74), a body is capable of being both con- tracted and expanded indefinitely. These changes of volume are most readily effected by the action of heat, and, so far as we know, all bodies may be indefinitely expanded by heat and con- tracted by cold. These effects of heat will be considered at length in Chapter IV., and we shall therefore only allude in this place to a few examples of compression, produced by mechanical means. Pieces of oak, ash, or elm, plunged into the sea to the depth of 2,000 metres, and drawn up after two or three hours, have been found to contain four fifths of their weight of water, and to acquire such an increase of density as to indicate the contraction of the wood into about half its previous volume. Some of the metals have their bulk permanently diminished by hammering'; 10* 114 CHEMICAL PHYSICS. and so also in the process of coining, the volume of the metal is sensibly diminished by the pressure to which it is submitted under the die. The stone columns of buildings, also, when they sus- tain great weights, are frequently very sensibly shortened. This was the case with the columns which support the dome of the Pantheon at Paris. It was long supposed that liquids were incompressible ; but they are now known to be compressible, although only to a slight degree. The compressibility of liquids may be illustrated by the apparatus rep- resented in Pig. 50. It consists of a very thick cylindrical vessel of glass, eight or nine centimetres in diameter, which is closed at the bottom and sup- ported on a basement of wood. To the top is cemented a brass cap, into which screws a copper plate, which, when in its place, completely closes the cylinder ; but which can be unscrewed at pleas- ure, in order to remove and replace the tubes A and B within the cylinder. To this plate are adapted the tunnel JJ, for introducing water into the cylinder, and a cylinder with a piston for exerting pressure, which can be moved by the screw P. "Within the apparatus is the elongated glass bulb J., which is filled with the liquid on which the experiment is to be made. This bulb opens into a bent capillary glass tube, whose open end is plunged in the mercury which covers the bottom of the vessel. At the side of this apparatus is a manometer tube, 5, which indicates, in a way wliich will be hereafter described, the amount of pressure. In using the apparatus, the biilb A is first filled with the liquid to be compressed. This is then supported, as represented in the figure, in the interior of the cylinder, with the open end of the tube dipping under the mercury. The cylinder is now filled with water, and the pressure applied by turning the screw P. The mercury will then be seen to rise in the capillary tube, indi- ¥ig. 60. GENERAL PROPERTIES OP MATTER, 115 eating a compression of the fluid contained in the bulb. In order to measure the amount of compression, the capillary tube is graduated into parts of equal capacity, each of which bears a known relation to the capacity of the bulb. The total amount of compression, however, which we can thus produce, amounts only to a few millionths of the original volume. The compressibility of gases is far greater than that of either of the other conditions of matter. If we take a glass cylinder closed at one end, Fig. 61, and insert into it an accurately-fittmg piston, it will be found impossible to force the piston into the tube, if it be full of water ; but if full of air, the force of the arm is sufficient to drive the piston down so as to reduce the volume of air ten or twenty times, if the piston is small. We feel the resistance increase in proportion to the compression ; but, whatever may be the force exerted, we cannot make the piston touch the bot- tom of the tube. The compressibility of many gases is also limited by the fact that they are reduced by great pressure to a liquid state. (77.) Elasticity. — The property which all bodies possess to a certain extent, of resuming their original form or vohime when the force which altered this form or volume ceases to act, is called elasticity. This property is the manifestation of a ten- dency which the particles of bodies possess, to maintain a certain distance or position with regard to each other, and to resume that distance or position when they have been disturbed. The phe- nomena of elasticity may be developed in solids by compression, by tension, hj flexure, or by torsion. In fluids, however, elasticity can be developed only by compression, and it is only this form of elasticity, therefore, which can be regarded as a general prop- erty of matter. All fluids, both liquid and gaseous, are perfectly elastic ; and this elasticity is unlimited in extent, since they resume exactly their original volume as soon as the pressure by which tlais was Kg. 51. 116 CHEMICAL PHYSICS. diminished is removed, however long it may have been ap- plied. Gases tend to expand indefinitely, and, other circumstances being equal, a definite volume always corresponds to a given pressure. If the pressure is increased, the volume diminishes, and if the pressure is diminished, the volume increases. Hence, gases are frequently called permanently elastic fluids. The elasticity of solids is not perfect and unlimited, like that of fluids. In some solids, such as glass, it appears to be perfect ; for no force, however great or long continued, will cause glass to take a set, as it is-called, that is, will cause a permanent change either in form or bulk. But then this elasticity is confined within very narrow limits ; for if the displacement of the particles ex- ceeds a very small amount, the body is crushed. In other solids, as in India-rubber or the metals, the elasticity is less limited-; but in these, if the compressing force exceeds a certain amount, or is continued beyond a limited time, there remains a permanent change of form or bulk. Within these limits, however, which differ very greatly in different substances, all solids appear to be perfectly elastic. It is in the limit of elasticity that we find the great differences between bodies. Thus, a ball of steel or of ivory will be as elastic up to a certain point as a ball of India- rubber, as may be proved by dropping the three balls upon a hard surface from the same height, and then marking the heights to which they rebound ; but while the elasticity of the India-rubber extends to almost any degree, that of the others is very limited. Even lead and pipe-clay, which are generally considered as en- tirely devoid of elasticity, show an elasticity as perfect as that of the best-tempered steel, but within very narrow limits, CHAPTER III. THE THREE STATES OF MATTEE. (78.) Molecular Forcgs. — The forces ■which are supposed to emanate from the molecules of matter, and which we have termed molecular forces, are either attractive, tending to draw togetheC the molecules of a body, or repulsive, tending to drive them apart. The three states of matter seem to depend on the relative inten- sity of these forces. When the attractive forces are in excess, the molecules of a body are held together more or less firmly, and we have the solid state. When the attractive forces are nearly bal- anced by the repulsive forces, the molecules are in equilibrium and endued with freedom of motion among themselves, and we have the liquid state. Finally, when the repulsive forces are in excess, the molecules tend to recede from each other, and we have a state of permanent tension, which we call a gas. In regard to the mode of action of these molecular forces, we have little or no accurate knowledge, and all our theories in re- gard to them are inferences from the phenomena which the aggregations of these molecules, the masses of matter, exhibit. The attractive forces act only through extremely small distances; Several facts may be cited in illustration of this. If, when the flat surfaces of two hemispheres of lead are tarnished, they are pressed together, they will not adhere. If, however, the super- ficial coating of oxide is removed with a sharp knife, and the two clean surfaces are then pressed together, they adhere with great force. The process of welding iron affords an illustration of the same fact. In order to unite two bars of iron, the ends to be joined are first softened, by heating them to a white heat in a forge, and then hammered together on an anvil. The com- plete union of the bars cannot be attained in this process unless the coating of oxide, which forms in the forge on the heated surfaces, is dissolved by sprinkling on the ends of the bars pow- dered borax, or some similar substance. So also pieces of wax, dough, India-rubber, and other soft substances, cannot be made 118 CHEMICAL PHYSICS. to adhere when their surfaces are covered with dust, but can be united firmly together when the surfaces are clean. Finally, plates of polished glass have been known, simply from resting on each other in the warehouse, to adhere so firmly as to resist all efforts to separate them, breaking as readily in any other direc- tion as at the plane of junction. The thinnest film of tissue- paper interposed between them is suiJicient to prevent any such adliesion. The repulsive forces do not appear to ]pe so inherent in the par- ticles of matter as the attractive force. They seem to be due to the action of an external agent, called heat. This opinion is sup- ported by many facts. The first effect of heat on a solid is tq expand it, that is, to separate the molecules from each other ; but as it accumulates in the body, it changes its condition, first into the liquid, and subsequently into the gaseous state. So also, when two plates of glass are pressed firmly together, the minute interval which still separates them is increased by heating. The particles of finely divided and infusible powders repel each other when intensely heated, and the powders roll round in the crticible as if they were liquid ; and lastly, when water is dropped into a heated metallic dish, it does not moisteji the sides of the dish, but is repelled by it and assumes a globular form. The repulsion is so great, that, if the dish is pierced with holes, like a sieve, the water will not run out. Since, tlien, heat evidently increases the repulsive forces between the molecules of matter, it is natural to conclude that it is the cause of these forces, and this hypothesis is generally admitted. In studying the phenomena of matter due to these molecular forces, it will be convenient to class them under two heads: first, those phenomena caused by the action of these forces be- tween homogeneous molecules, siich as the molecules of the same substance ; secondly, those phenomena caused by the action of the forces between heterogeneous molecules, such as those of dif- ferent substances. To the first class belong those phenomena which characterize the solid, liquid, and gaseous conditions of matter ; to the second, the phenomena of capillarity (or adhe- sion) and diffusion. THE THREE STATES OP MATTER. 119 MOLECULAR TORCES BETWEEN HOMOGENEOUS MOLECULES. I. Characteristic Properties of Solids. Among the characteristic properties of solids, we sliall considet the following : — Crystalline Form, Elasticity, Resistance to Rup- ture, and Hardness. Crystallography. (79.) Crystalline Form. — The force which holds together the molecules of solids is called cohesion; and the most ob- vious effect of this force is to retain the molecules in a fixed position with reference to each other, and hence to give to the solid a more or less permanent form. Almost all solids, when they are formed slowly, under circumstances such that tha molecules are free to arrange themselves in accordance with the tendencies of the molecular forces, assume definite external forms. These forms, with certain limitations, are always the same for the same substance, but may differ in different sub- stances. They are, therefore, essential forms, depending upon the nature of the substance. Such forms are called crystals, and the processes by which they are obtained are called processes of crystallization. The larger number of inorganic solids which we meet with iii every-day life, do not appear to have any regularity of outward form. Their form is generally accidental, one which has been given by art, or which is due to the accidental circumstances under which the solid has been placed. In some cases, how- ever, if we break the solid and examine the fracture, it will be seen that the solid is an aggregation of minute crystals closely packed together. This is the case with granite and many other rocks. Other solids split readily along certain planes, called planes of cleavage. Both these classes of bodies are said to have a crystalline structure. In many cases, however, no indi- cations of a crystalline structure can be seen ; but in almost all, the solid can be made to assume a regular crystalline form by one of the processes described in the next section. (80.) Processes of Crystallization. — The conditions of crys- tallization are freedom of motion in the molecules froin which the solid is forming, and sufficient time for the molecules to ar- 120 CHEMICAL PHYSICS. range themselves in obedience to the molecular forces. These conditions are generally obtained in one of four ways. The first consists in dissolving the solid in water or some other solvent, and allowing the liqiiid to evaporate slowly. As the solid is slowly deposited, it assvimes the crystalline form. This method is the most universally applicable, and the one by which crystals are usually formed in natiire. The best method of applying it consists in making a concentrated solution of the substance in water, placing the solution in a shallow dish, covering the dish with porous paper fastened tightly round the edges to prevent dust from settling upon the liquid, and leaving it in a moderately warm place until the crystallization is completed. When the substance is not soluble in water, it can generally be dissolved in alcohol, ether, sulphide of carbon, or melted boracic acid, instead of water. Sulphur, for example, may be crystallized from a so- lution in sulphide of carbon ; and alumina may be crystallized by dissolving it in melted boracic acid, and exposing the solution to the intense heat of a porcelain furnace. At this very high temperature the boracic acid slowly evaporates. Most substances are more soluble in hot water than in cold, and these can also be crystallized by making a concentrated hot solution, and allowing it to cool ; the excess of the solid in solution over that which cold water will dissolve, is deposited in crystals. Unless, however, the quantity of the solution is very considerable, large and per- fect crystals are not so frequently formed in this way as by slow evaporation. A small quantity of solution cools so rapidly, that sufficient time is not afforded for perfect crystallization. The second method consists in melting the solid in a crucible, and allowing the liquid to cool very slowly. When a solid crust forms on the surface, this is broken, and the remaining liquid turned out, when the inside of the crucible is found lined with crystals. Sulphur and many of the metals may be crystallized in this way. The third method consists in converting the solid into vapor, ?ind subsequently condensing the vapor in a cool receiver, — a process which is called sublimation. Iodine, arsenic, arsenious acid, and many other substances, can be crystallized by this method. The fourth method consists in very slowly decomposing some chemical compound containing the substance, either by electricity THE THREE STATES OF MATTER. 121 or by the action of some chemical agent. The crystals of metals formed in the processes of electro-metallurgy are the best exam- ples of this method. (81.) Definitions. — A crystal is always bounded by plane faces, and is therefore a polyhedron. The faces of the diamond and of some other crystals are at times curved ; but in such cases the apparently curved surface can generally be seen to be made up of a large number of very small planes. The terms of solid geometry are used, -without change of meaning, in crys- tallography. Thus we speak of faces, edges, plane angles, inter- facial angles, and solid angles. The axis of a crystal is a line passing through its centre, round which two or more faces are symmetrically arranged. In every crystal, at least three such lines can be distinguished. In Figs. 52, 53, and 54, the axes are indicated by dotted lines. rig. 52. Fig. 53. Fig. 54. (82.) Systems of Crystals. — A crystal is a solid bounded by planes arranged symmetrically round one or another of six sys- tems of axes. 1. The first system (Fig. 55) is called the Monometric System, and consists of three axes, of equal length and at right angles to each other. The length of each semi- axis we shall represent in this work by a, and the system of axes by the symbol a : a : a. It is hardly ne- cessary to observe, that, as crystals may vary very greatly in size, the absolute lengths of the axes must vary to the same extent, and that it is the relative lengths only which are constant. 11 Fig. 55. 122 CHEMICAL PHYSICS. Fig. 56. 2. The second system (Fig. 56) is called the Dimetric System, and consists, like the last, of three axes at right angles to each other. The two axes in the horizontal plane of the figure are called the lateral axes, and are equal to each other. We shall represent the length of each half of these axes by a. The third is called the vertical axis, and is either longer or short- er than the other two. We shall represent the length of each half of this axis by b. The symbol representing this system of axes is a -j a : b. The ratio between a and b is irrational. Thus, in crystals of tin, the ratio between the axes is a : b = 1 : 0.3857. In the monometric system there can be but one set of axes ; but in this system there can be as many sets of axes as tlie number of possible irrational ratios between a and b, which is of course infinite. The ratio for crys- >)^ I^HHIH^S^^HH ^^^^ '^^ ^'^^ same substance is always the same ; but it differs for crystals of different substances, no two substances having the same ratio. 3. The third system (Pig 57) is called the Hexag-onal System, and consists of four axes. Three of these are in the same plane, the horizontal plane of the figure, and are called lateral axes. They are equal in length, and have the same relative position as the diagonals of a reg- ular hexagon (Fig. 58). The common length of the six halves of these lateral axes we shall represent by a. The fourth axis, called the vertical axis, is at right angles to the other three, and is either shorter or longer than their common length. The length of one half of this axis we shall represent by b, and the symbol of the sys- tem of axes is a : a : a : b. The relation be- tween a and b is, as in the last system, irrational. Thus, in crystals of antimony, a •.b = l: 1.3068, and in crystals of carbonate of lime (calcite), a : b = 1 : 0.8543. Here, as in the last system, the ratio is con- rig. 67. rig. 58. THE THREE STATES OP MATTER. 123 Fig. 59. stant in crystals of the same substance, but differs in crystals of different substances. 4. The fourth system (Fig. 59) is called the Trimetric System, and consists of three axes, all at right angles to each other, but all of unequal length. One of these axes is selected as tlie vertical axis, and the length of one half of this axis will be represented in this work by b. The shorter of the two lateral axes is called the brachydiagonal, and its half- length will be represented by a. The longer is called the makrodiagonal, and its half-length will be represented by c. The symbol of this system of axes is a :b xc. The relation between a, b, and c is irrational. In crystals of sulphur, a : b : c = 1 : 2.340 : 1.233. 5. The fifth system (Fig. 60) is called the Monoclinic System, and consists of thi-ee iinequal axes. The two lateral axes are at right angles to each other. The third axis, called the vertical axis, is at right angles to one of the lateral axes, but is inclined to the other. The length of one half of the vertical axis we shall repre- sent by b. The one of the lateral axes which is at right angles to the vertical axis is called the orthodiagonal, and its half-length will be represented by a. The lateral axis which is inclined to the vertical axis is called the klinodiagonal, and its half-length will be represented by c. The value of the acute angle which the vertical axis b makes with the klinodiago- nal c will be represented by a. The symbol of this system is the ratio a : b : c, with the angle a- For the crystals of the same substance, the ratio between a, b, and c, and the value of a, are constant ; but they differ in crystals of different substances. In crystals of sulphate of iron, for example, a:b:c=l: 1.495 : 1.179, and a = 75° 40', while in crystals of gypsum a:b:c^l: 0.413 : 0.691, and a = 81° 26'. 6. The sixth system (Fig. 61) is called the Triclinia System, rig. 60. 124 CHEMICAL PHYSICS. rig. 61. and consists of three unequal axes, which are all inclined to each other. One of these axes is selected as the vertical axis, and the half-length of this axis will be represent- ed by b. The half-lengths of the two lateral axes will be represented by a and c. The angles of inclination between the axes will be represented as follows : — a on 6 by ^, a on c by 3, b on c by a. The symbol of this system is the ratio a : b : c, witli the angles a, /3, y. In crystals of sulphate of copper, a : b : c = 1 : 0.9738 : 1.7683, and « = 82° 21'.5, |8 = 77° 37'.5, y = 73° 10'.5. In crystals of bichromate of potash, a : b : c =: 1 : 0.9886 : 1.794, and a = 82°, |3 =83° 47', ;r = 89° 8'.5. All crystals which have the same system of axes are said to belong to the same crystalline system ; and hence all crystals may be classified under six crystalline systems, corresponding to the systems of axes just described. The systems of crystals have the same names as the systems of axes. (83.) -Centre of Crystal, and Parameters. — The point at which the axes of a crystal intersect is palled the centre of the crystal. If we suppose the axes of a crystal indefinitely produced, it is evident that each of its planes, if also produced, must intersect each of the axes, either at a finite or at an infinite distance from its centre. The distances of the points of intersection from the centre are called the parameters of the planes. Each of the planes of the crystal represented in Fig. 62, for example, would, if produced, intersect the three axes of the monometric system at distances from the centre equal to a : 3 a : 3 a respectively, a representing, as stated above, the length of any semi-axis. These lengths are the parameters of each plane of the crystal. When a plane is parallel to a given axis, it may be regarded as intersecting it at an infinite distance from the centre, and hence f--^— v- Fig. 62. THE THREE STATES OP MATTER. 125 rig. 63. Fig 64. its parameter measured on this axis is infinity. The faces of a cube, for example, intersect one axis of the monometric sys- tem at the distance a from the centre (Pig. 63), and are parallel to the other two. The parameters of each face are therefore a : 00 a : 00 a. So, also, each of the faces of the dodecahedron (Fig. 64) intersects two of the axes of the monometric system at the distance a from the centre, and is parallel to the third axis. Hence the pa- rameters of each face are a : a : oo a. It has already been stated that the crys- tals of a given substance have always axes of the same relative lengths, and with the same relative inclination. It is also true that the parameters of the planes of any crystal of a given substance are always equal, either to the lengths of the semi- axes on which they are measured, or else to some simple multi- ples or submultiples of these lengths. Hence it follows, that the parameters of any plane of a crystal may always be expressed very simply in terms of its axes, as above. (84.) Similar Axes. — In any system, of axes., one axis or one semi-axis is said to be similar to another axis or to anoljxer semi- axis, when the two have the same length and the same inclina- tions to the other axes or semi-axes. It is important to apply this definition to the different systems, and distinguish the similar axes in each. 1. In the monometric system, all the axes and all the semi-axes are similar. 2. In the dimetric system, the two lateral axes are similar, and also, the four halves of these axes are similar. The two halves of the vertical axis are also similar to each other, but they are not similar to the halves of the lateral axes. 3. In the hexagonal system, the three lateral axes are similar, and their six halves are also similar. The two halves of the ver- tical axis are also similar to each other, but not similar to the halves of the lateral axes. 4. In the trimetric system, all three axes are dissimilar, but the two halves of each axis are "similar to each other. By referring 11* 126 CHEMICAL PHYSICS. to the notation given in the previous sections, it will be seen that in the first four systems similar semi-axes have in every case been designated by the same letter, and that the dissimilar semi-axes have been distinguished by different letters. 5. In the monoclinic system, not only the three axes are all dissimilar, but moreover the two halves of the same axis are not in all cases similar to each other. The two halves of the ortho- diagonal are similar, but the two halves of the klinodiagonal, al- though they have the same length, have not the same inclination to any one half, say the upper half, of the vertical axis, and are therefore dissimilar. The same is true reciprocally of the two halves of the vertical axis. In order to distinguish the dissimilar halves of these axes, we will accent the b when it refers to the lower half of the vertical axis, and also accent the c when it refers to the half of the klinodiagonal, which is inclined to b at an obtuse angle. The notation of the monoclinic system of axes is, then, as follows : — a = eitlier half of the orthodiagonal. b E= the upper half of the vertical axis. b' = the lower half of the vertical axis. c = thehalf of the klinodiagonal which is inclined to b at an acute angle. c' = the half of the klinodiagonal which is inclined to b at an obtuse angle. a = angle of b on c. It is evident that the angle of & on c Fig- 65. . ° IS equal to the angle of b' on c', being vertical angles ; and hence, that b and c together are similar in position to b' and c' together. 6. In the triclinic system, all the semi-axes are dissimilar, and the two halves of each axis may be distinguished by accentuation, as in the monoclinic system. (85.) Similar Planes. — Similar planes are those whose param- eters, measured on similar semi-axes, are equal. There is no diffi- culty in distinguishing similar planes, by means of this definition, in any except the last two systems of axes, since in all the other systems those planes are similar which in the notation here adopted have equal parameters, and none others. In the monoclinic and triclinic systems, however, two planes THE THREE STATES OP MATTER. 127 are similar, not only -when they have equal parameters, hut also when the parameters, measured on the dissimilar halves of the same axes, are in both cases oppositely accented. For ex- ample, in the monoclinic system, two planes are similar whose parameters are a : 2b : c, and a : 2b' : c'. In the two symbols, the two halves of the dissimilar axes are oppositely accented. On the other hand, two planes whose parameters are a : 2 b : c, and a : 2 b : c', are hot similar. In the triclinic system, since the six semi-axes are all dissimi- lar, no two planes are similar, unless the three parameters of the one are all accented oppositely to the three. parameters of the other. Thus, two planes are similar whose parameters are a : b : 2 c, and a' : b' : 2 c', respectively. (86.) Holohedral Crystalline Form.— ^^s-^- A holohedral crystalline form is the union of all the possible similar planes which can be arranged around a given system of axes. Thus, the form of Fig. 66 is the union of all the possible planes having the parameters a : a : 2 a, which can be arranged round the monometric system of axes. So also the form of Fig. 67 is the union of all the possible planes having the parameters a : a : CO a : b, which can be arranged round the hexagonal system of axes. Both of these are therefore holohedral forms. It must not, however, be inferred from these examples that a crystalline form is al- ways a crystal, and that it always encloses space. The word form is used in crystal- lography in the technical sense, as defined above. A form may consist of only two planes. Thus, the two basal planes of the hexagonal prism (Fig. 68) are a crystalline form, because they are all the possible planes, having the parameters oo a : CO a : oo a : b, which can be arranged round the hexagonal system of axes. In like manner, the six planes on the convex surface of the prism, being all the planes having the parameters : a : 2 a. Fig. 67. Fig. 68. a: a 00 a : 00 &, which can be arranged round 00 a : 00 a : &, , : coa : cob. 128 CHEMICAL PHYSICS. the same system of axes, form another holohedral crystalline form. In neither case does the form enclose space. It requires the combination of the two forms to complete the crystal. In the triclinic system no crystalline form can consist of more than two planes ; and hence the combination of at least three crystalline forms is required in tliis system to complete a crystal. The parameters of one of the planes are used as the symbol of the holohedral crystalline form. Thus, the parameters printed below the Figs. 66 and 67 not only denote the position of each plane of the form with reference to the axes, but they are also used as the symbol of the form itself. When a crystal consists of two or more crystalline forms, like the one represented in Fig. 68, we use as the symbol of the crystal the several symbols of the crystalline forius of which it consists, written one after the other, or one beneath the other, as convenience may dictate. Examples of these symbols may be seen beneath the figures of crystals on this and the few following pages. (87.) Hemihedral Cri/stalline Form. — A hemihedral crystal- line form is the union of one half of the possible similar planes, which can be arranged round a given system of axes. Tlie form represented in Fig. 69 is the union of all the possible planes hav- ing tlie parameters a : a : a, which can be arranged round the Fig. 69. Fig. 70. Fig. 71. + i (a : a : a). — i {a : a : a). monometric system of axes, and is therefore a holohedral form. The form of Fig. 70 is the union of one half of the planes hav- ing the same parameters, and arranged round the same system of axes. It is, therefore, a hemihedral form. This form is called the tetrahedron, and it may be regarded as derived from the oc- tahedron, by suppressing every other plane of this form and pro- ducing the rest. Hence, it is frequently called the hemihedral form of the octahedron. The form of Fig. 70 is obtained by pro- THE THREE STATES OP MATTER. 129 ducing one set of the alternate planes of the octahedron of Fig. 69. If, now, we suppress this set of planes, and produce the other set of the alternate planes of the octahedron, we shall obtain a second tetrahedron ; differing, however, from the first only in relative position. This form is said to be the negative of the first. We use, as the symbol of a hemihedral form, the symbol of the cor- responding holohedral form, preceded by the fraction i, and we distinguish between the two hemihedral forms of which the holohedral form may be supposed to consist, by means of the signs plus and minus, as shown by the symbols beneath Figs. 70 and 71. (88). Tetartohedral Crystalline Forms. — A tetartohedral crys- talline form is the union of one quarter of the possible similar planes which can be arranged round a given system of axes. Such forms are met with among crystals, but they are of compar- atively rare occurrence. They are designated by writing the fraction \ before the symbol of the corresponding holohedral form. (89.) Simple and Compound Crystals. — A crystal is said to be simple, when it is bounded by the planes of one crystalline form only ; and to be compound, when it is bounded by the planes of several crystalline forms. Thus, the crystals represented by Fig. 74 Fig. 73. a : 00 a : o3 a. Figs. 72, 73, and 74 are simple, because in each case all the planes which bound the crystal have the same parameters. On the other hand, the crystals represented by Figs. 75, 76, and 77 are compound crystals, because there are two or more sets of planes on each crystal, of which the planes have different param- eters. The faces of the crystals are lettered, and below each crystal the parameters of each set of planes are given opposite to the corresponding lettering. 130 CHEMICAL PHYSICS. Fig. 70. Fig. T5. Fig. 77 a = a : oo a : 00 6, = a : a : bf S = a: a:3b. r = + i (a ; a : 00 a ; fc), Y = — \ (a : a : 00 a : i b), 2rl = — i(a:a: a, a : ata. a : 00 rt : oo a, a : ai oo a. a : 00 a : ooa, a : ma: (X a. a : a t Of a : 00 a : oo£ » : a : ff, a : a : 00 a. a : 00 rt : 00 ff, a : CO n : CO 17, + i(^ : a: :"), a : rt : 00 a, a : at a. -Ua; 1 a ; ;a). + i(a;a:a). a: a i CO a. Fig. 97. 142 CHEMICAL PHYSICS. DiMETRic System. Simple Holohedral Forms. a ■ a : Ob. 5. a : a : b. a : a '. m b. 7. a ; a ; 00 8 6. 1 1 1 ■!■ ■ Fig. 98. The most important simple forms of tlie dimetric system are represented in Fig. 98, and the forms have been grouped so that the relation between them can be easily seen. We can study this THE THREE STATES OP MATTER. 143 relation to the best advantage, by commencing with No. 2, which is called the square octahedron, and whose symbol is a : a : b. When the length of the semi-axis b is greater than that of a, as is the case in crystals of sulphate of nickel, where a :b = 1 : 1.906, then the octahedron is acute, like No. 3. When, however, the length of the semi-axis b is less than that of a, as is the case in crystals of acid phosphate of potassa, where a : b =!= 1 : 0.664, then the octahedron is obtuse, like No. 2. In the monometric system, we can have only one octahedron ; but in the dimetric system the same substance frequently pre- sents several octahedrons. In all cases, however, if we reduce the octahedrons to the same base, the lengths of their vertical axes will bear to each other very simple and rational ratios. Thus, for example, on crystals of sulphate of nickel we find octa- hedrons, where the ratio of the two semi-axes is not only 1 : 1.906, but also 1 : 0.953 and 1 : 0.685. The first of these octahedrons has been selected as the principal form of this substance, because it is the one which is the most frequently seen, and which, in com- pound crystals, is generally the dominant form. To the planes of this form we give the symbol a : a : b, and then the symbols of the other octahedrons are a : a : i b, and a : a : i b. When a substance, presents several octahedrons, we are guided in the selection of one of these for the principal form by many circumstances. Among these may be mentioned the frequency of occurrence, the predominance of the planes of the different octahedrons on compound crystals, the position of the planes of cleavage, and the crystalline form of other substances which are analogous in composition and homceomorphous* with it. The selection is in all cases, however, more or less arbitrary, and we must be careful in comparing the crystalline forms of different substances to keep this fact in view, since otherwise we might be led to erroneous conclusions, f Having, then, in the case of a given substance crystallizing in the dimetric system, selected one octahedron as the principal form, and given to it the symbol a : a : b, we may have on crys- tals of this same substance an infinite number of other octahe- drons, having the general symbol a : a : mb, where m is always * Two substances are said to be homceomorphous, when they crystallize in fonna which are closely allied. t See Dana's System of Mineralogy, "Vol. 1 p. 192 and following. 144 CHEMICAL PHYSICS. a very simple rational integer or fraction. Thus we may liaA'c octahedrons whose symbols are hb. ib. a : a : 2 b, or a : a a : a : Sb, " a : a a : a : ib, " a : a : ^b. As the value of m increases, the octahedrons become more and more acute ; and finally, when m = oo, the octahedral planes become parallel to the vertical axis, and we have the square prism whose symbol is a : a : cc b (No. 4, Fig. 98). This we may regard as one limit of the series of octahedrons. On the other hand, as the value of m diminishes, the octahedrons be- come more and more obtiise ; and finally, when m = o, the octa- hedral planes coincide with the basal plane. No. 1, which we may regard as the other limit of the series. The symbol of the basal plane may be written either a : a : ob, or, as is more usual, a: CO a: b, which is obtained from the first by multiplying each parameter by cc, remembering that X <» =1. It will be noticed that neither the square prism nor the basal plane encloses space, and therefore neither can alone constitute a crystal. The two combined form a square prism with its basal plane, which is therefore a compound crystal. In the monometric system, the axes of the octahedron always unite the vertices of the opposite solid angles. In the dimetric system, also, the vertical axis always unites the vertices of the two solid angles forming the summits of the octahedron, but the lateral axes may have two positions. They may either iinite the solid angles or the centres of opposite basal edges. The two posi- tions which these axes may assume are represented in Figs. 99, 100, whicli represent sections through the base of the octahedron. AVe may thus have two octa- hedrons, such as Nos. 3 and 11, of different dimensions, biit yet having axes which are perfectly equal. The fa- ces of the . octahedron whose ^^•'*"- ^'si"*- base is represented by Fig. 100 have the same position as the edges of the octahedron whose base is represented by Fig. 99. We distinguish the two octahe- drons by calling the one represented in No. 3 the direct octahe- THE THEEE STATES OP MATTEU. 145 dron, and the one represented in No. 11 the inverse octahedron. Since the external appearance of the two octahedrons is precisely the same, it is not always possible to determine to which form a given crystal belongs ; and this fact introduces a still further difficulty in determining the principal form of a substance. The general symbol of the iuYorse octahedron is a : co a : mb, where m represents any simple rational integer or fraction. Thus we may have inverse octahedrons on crystals of the same sub- stance, whose symbols are a ; :00a: ■■b, or a ; ; 00 & ■.hb. a : : CO a : ■.2b, (( a : : ix>a : ■ib. a : 00a ; ; 3&, a a : 00 a : ■.ib. The limit of this series of octahedrons on one side is a square prism, No. 12, whose symbol is a : 00 a : co b ; and on the other side the basal plane, whose symbol is a: caa-.ob, or a: coa:b. Between the direct octahedron. No. 3, and its corresponding inverse octahedron, No. 11, there is an intermediate form. No. 7, which may be called the dioctahedron. The parameters of the faces of this form are a : m a : n b. When m = 1 this form becomes the direct octahedron, and when m = 00 it passes into the inverse octahedron. Again, for any constant value of m, for example, m = 2, as in the figure, we may have an infinite series of dioctahedrons with different values of n. As the vahie of n increases, these dioctahedrons become more and more acute ; and when w = 00, they pass into the octagonal prism, No. 8. As the value, of n diminishes, they become more and more obtuse ; and when w = 0, they pass into the basal plane. No. 5. For any other value of tn, for example, m = 8, we may have a similar series ; and hence there may be an infinite number of series of dioctahedrons and an infinite number of forms in each series. Hemihedral Simple Forms. By extending the alternate planes of the square octahedron, two tetrahedrons may be obtained similar to the two tetrahedrons of the monometric system, but difiering from them in the rela- tive length of their vertical axis. We may evidently have a s«ries of either positive or negative tetrahedrons, corresponding with the system of octahedrons, and varying between a square prism on one side and the basal plane on the other. In like 13 146 CHEMICAL PHYSICS. manner, by extending the alternate planes or the alternate sets of planes of the dioctahedron, we may obtain several hemihedral forms. The hemihedral forms of this system, however, rarely occur except as modifying holohedral forms. Compound Forms. Fig 103. Fig. 102. Fig. 101 a : CO a : oo6, a'.a\b^ CT : a : 00 6, o : ooa : 00 6, a : a '. b. a : 00 a : 00 6, a : CO a : 00 6, a : a: ;6, oo a : ooa : b a: a \h. a : aa a : b. a : 3a :3 b. "When the two principal octahedrons combine, the inverse octa- hedron truncates the edges of the direct octahedron, as in Fig. 101, which also presents the two basal planes. Pig. 102 represents a combination of the principal octahedron, o, with an octahedron of the same class, %, and with an octahedron of the second class, 2 d. Fig. 103 represents a combination of the square prism of tlic first class, g-, with the principal octahedron, o. Fig. 104 represents a combination of the square prism of tlie second class, a, with the principal octahedron, o, in which the prism is the dominant form. Fig. 105 represents the same combination, in which th« octahedron is the dominant form, with the addition of the basal planes. Tlie composition of the two remaining crystals can easily be made out from the symbols below the figures. tub three states op matter. Hexagonal System. Simple Holohedral Forms. Ul 1, 2 8. 1 5. ■ 1 1 ■ 1 1 1 1 a:a:c»a:o6. ataicoa: — 6, a:a:Qoa:'&. a:a:coa:m&. a: a: a>a: b. 6. 7. 8. 9. 10 1 ■ ■ ■ L 1 1 ■■■■■ ma: a ip a '.Qb. ma : a :pa: -b. m a : a : p a : b. m a :'a : p a ', nb. ma: a :pa i mb. 11. 12, 13. U. IS. :2a: 06. a : a : 2 a ; Qo &. The simple forms of the hexagonal system are closely allied to those of the dimetric system. They are represented in Fig. 108, and the relation between them is indicated by the arrangement of the forms in the figure. The fundamental form of this system is called the hexagonal pyramid* No. 3. The crystals of the same substance may present a number of these hexagonal pyramids, but we always find that, when they have the same base, the lengths of their vertical axes stand to each other in very simple ratios. As * The tenn pyramid is not used here in the geometrical sense. 148 CHEMICAL PHYSICS. in the dimetric system, we select one of these for the principal form, and give to it the symbol a : a : cc a : b. The general symbol of the other hexagonal pyramids of the same substance is then a: a: od a : mb, in which m is always some very simple integer or fraction. As the value of m increases, the pyramid becomes more and more acute ; and when m = co, it passes into the hexagonal prism, No. 6. On the other hand, as the value of m diminishes, the pyramid becomes more and more obtuse, and finally passes into the basal plane. No. 1 This series of pyramids are called hexagonal pyramids of the first order, to distinguish them from the hexagonal pyramids represented in the lower row of forms in Fig. 108, which are called hexagonal pyramids of the second order. In the hexagonal pyramids of the second order, the lateral axes unite the centres of edges, as in Fig. 110, while in those of the first order they unite opposite solid angles, as in Pig. 109. The lengths of the axes in the two fig- ures are the same. The intersection of one of the faces of the pyramid of the second order with the ^'^■^o^- ^'=™- basal plane, is the line E E, Fig. 110, and it can easily be seen that this plane, if ex- tended, would intersect the three lateral axes at distances from the centre of 2 a, a, and 2 a respectively. The symbol of the principal pyramid of this class (No. 13 of Fig. 108) is therefore 2 a : a: 2 a : b, and the general symbol of other pyramids of the second class 2 a : a : 2 a : m b, where m is always some simple rational integer or fraction. As the value of vi increases or diminishes, this series of pyramids passes through the same va- riations of form as those of the first class. The two limits are the hexagonal prism, where m= , and the basal plane, where m ^0. It will be noticed that the planes of the hexagonal pyramid and prism of the second order have the same position as the edges of the corresponding forms of the first order, and will therefore truncate these edges when the two forms enter into combination. Intermediate between the two classes of hexagonal pyramids THE THREE STATES OF MATTER. 149 ma: a ',p a'.nh. are the dihexagonal pyramids (Fig. 111). Fig.ni. This form is bounded by twenty-four sca- leiie triangles, and the symbol of the prin- cipal form of the class is ma: a: pa: b, in which m and p are so related that p = ^^. When m = 1 then p = x, and this form passes into the hexagonal pyramid of the first order, and when m = 2 then p ==2, and it passes into the hexagonal pyramid of the second order. The general symbol of other dihexagonal pyramids is ma: a: pa: n b, where n is any rational fraction or in- teger. When M = 00, the form passes into the dihexagonal prism, No. 10 of Pig. 108, and when m = o, it passes into the basal plane. No. 6 of Pig. 108. Simple Hemihedral Forms. The hemihedral forms of this system occur more frequently in nature than the holohedral forms, and therefore demand special attention. The most important of them are represented in Pig. 115 (see next page), in which the forms have been grouped so as to show the relations between them. In studying these forms, we will commence with the rhombohedron, Nos. 2, 3, 4 of Pig. 115. Rhombohedron. — The rhombohedron is bounded by six equal and similar rhombs. Its edges are of two kinds ; — first, six sim- Fig. 112. Fig. 113. Fig. 114. + 4 (o ; a ; CO a : B). a'.a: oo a : &. — } (a : a : oc a : 6). ilar terminal edges, marked X in Pig. 112 ; secondly, six similar lateral edges, which are lettered Z. The solid angles are also of two kinds ; — first, two similar vertical solid angles, lettered C, consisting of three equal plane angles ; secondly, six lateral solid 13* 150 CHEMICAL PHYSICS. angles, lettered E, which are similar to each other, but do not consist of equal angles. The vertical axis of the rhombohedron 4. 5 2R' connects the vertical solid angles. The lateral axes connect the centres of opposite edges. The interfacial angles formed at the terminal edges X are all equal to each other. This angle is one of the most important characters of the rhombohedron, and we shall call it the rhombo- hedral angle, and distinguish it by the same letter which we have used to denote the edge. When this angle is acute, the rhombo- hedron is said to be acute, and when it is obtuse, the rhombohe- dron is said to be obtuse. The sections of the rhombohedron passing throvigh two opposite THE THREE STATES OF MATTER. 151 terminal edges are rhombs vrhich are perpendicular to two of the faces of the form. There are three such sections in every rhom- bohedron, and they are called principal sections. One of these, CE C'E', is represented in Fig. 112. The crystals of a given substance frequently present a number of rhombohedrons, both obtuse and acute ; but when these rhom- bohedrons have the same lateral axes, their vertical axes always bear to each other a very simple proportion. One of these rhom- bohedrons, which is selected on the same grounds as those already stated in connection with the dimetric system, is termed the principal rhombohedron. The principal rhombohedron may be regarded as formed from the principal hexagonal pyramid, by extendingthealternate planes until they cover the rest. As there are two sets of alternate planes, it is evident that we can obtain by this method two rhom- bohedrons which are perfectly equal, and which differ from each other only in position. We shall call them the positive and nega- tive rhombohedrons, and distinguish them by writing the signs plus and minug before the symbols. These symbols are given below Figs. 112, 114, and it will be seen that they are formed after the analogy of the symbols of the hemihedral forms in the monometric system. Since every hexagonal pyramid will give by this method two rhombohedrons, it is evident that, corresponding to the series of hexagonal pyramids. Fig. 108, we have two series of rhombohe- drons. The general symbols of these two classes of rhombohe- drons are -}- J (a : a : oaa : m by, and — | (c : o : cca : m i). As the value of m increases, the rhombohedrons become more and more acute, and finally, when m = oo, they pass into the hex- agonal prism. No. 5, Fig. 115. On the other hand, as the value of m diminishes, the rhombohedrons become more and more obtuse, and when m = they pass into the basal plane. No. 1, Fig. 115. Of the series of possible rhombohedrons with any given values of the axes, there are several which stand to each other in an im- portant relation. Commencing with the principal positive rhom- bohedron, -\-i Qa: a: caaib'), No. 3, Fig. 115, we find that the planes of the negative rhombohedron — ^ (a : a : oo a : ^ Z>), No. 2, 152 CHEMICAL PHYSICS. have the same position as its terminal edges, and therefore truncate them This rhombohedron is called the first obtuse rhombohedron. Again, the faces of the positive rhombohedron ■\- \ (a : a : CK a : \ b') truncate the edges of the first obtuse rhomboliedron, and it is called the second obtuse rhombohe- dron, and so on. On the other hand, the faces of the principal rhombohedron truncate the edges of the negative rhombohedron — \ (a : a : coa : 2 b'), No. 4, which is called the first acute rhombohedron. The faces of the first acute rhombohedron trun- cate the edges of the positive rhombohedron + ^ (o : a : <» as : 4 6), which is called the second acute rhombohedron, and so on. The rhombohedrons which form this series are, then, as fol- lows : — Third obtuse rhombohedron. -K« : a : ; 00 a :ib)=-iR. Second " " + K«: : a ; : cc a : :ib}=+iR. First " " -i(_a: : a ; : CO a : ■■hb-)=-hR. Principal rhombohedron, + K«: ; a : CO a : :&) =-fE. First acute rhombohedron. ~i{a: : a : : c» a; ; 2b)= — 2R. Second " " + K«: a : 00 a : 4i)=+4iJ. Third " -i{a: ; a : 00 ft ; ; 8 6^=— 8E. And in this series each rhombohedron truncates the terminal edges of the one wliich follows it. In crystals of the mineral calcite, almost all the above rhombohedrons have been observed, and a large number of others, not belonging to the series, but in- termediate between the members of it. The general appearance of these crystals varies from almost flat plates, where the ter- minal angle X = 160° 42', to sharp needles, where the angle X==60° 20'. As the regular symbol of the rhombohedron is inconveniently long, we frequently abbreviate it in practice, and write, as the symbol of the principal rhombohedrons of a given substance, ± R. For other rhombohedrons we use the general symbol ± m R,m which m is the same quantity as the m in the reg- ular symbol. The abbreviated symbols of the series of acute and obtuse rhombohedrons have been given after the corresponding regular symbols in the above table, and by comparing the two the use of the abbreviation can be easily understood. Intermediate between the obtuse and acute rhombohedrons there is a possible form, wliere X = 90°. This is the case when THE THREE STATES OF MATTEE. 153 Kg. 117. a : mb = 1 : /^f- The rhombohedron then becomes the cube, which may therefore be regarded as a form of the hexagonal system. In like manner, all the other simple forms of the mono- metric system may be regarded as forms of the hexagonal system, but in this system they are compound forms. In consequence of this analogy, the crystals of the two systems frequently resemble each other very closely, especially when they have been irregu- larly formed. Scalenohedron. — By comparing together Figs. 116 and 117, on which the similar parts have been similarly lettered, it will be seen that in the posi- tion occupied by one rig.iie. plane on the hexagonal pyramid there are two planes on the dihex- agonal pyramid ; and hence, that we must extend the alternate pairs of planes on the dihexagonal pyramid, in order to apply to it the same method by which we obtained the rhombohedron from the hexagonal pyramid. If, then, we extend the alternate pairs of planes on the dihexagonal pyramid, commen- cing with the two front upper planes of Fig. 116, we shall obtain the form represented in Fig. 118, and called a scalenohedron; or, by extending the planes suppressed iti the last case, a second scale- nohedron, differing from the first only in position. The two are distinguished, like the rhombohe- drons, as positive and negative scalenohedrons. The scalenohedron, which is derived from the principal dihexagonal pyramid, will be called the principal scalenohedron, and its symbol is ± ^ (ma : a : p a : b'). The general symbol of other scalenohedrons is ± \ (m a : a : pa : nh~). As the value of n diminishes, the scalenohedron becomes more and more obtuge, and finally, when w = o, merges ma : axp a lb. Fig. 118. + i (m a : a : p a :b). 154 CHEMICAL PHYSICS. in the basal plane. On tlie other hand, with increasing values of n, the scalenohedron becomes more and more acute, and when « ^ 00 merges into the dihexagonal prism. By bringing together the rhombohedron and the scalenohedron, as has been done in Pig. 119, it will be noticed that the lateral edges of the two forms have a similar position towards the axes, so that for every scalenohe- dron there must be a rhombohedron whose lat- eral edges coincide with the lateral edges of the other form. This rhombohedron is called the inscribed rhombohedron of the scalenohedron. The scalenohedron may evidently be formed from the inscribed rhombohedron by prolong- ing the vertical axis, and then drawing lines from the ends of the vertical axis thus pro- duced to the lateral solid angles of the rhom- bohedron. It is evident that we may thus make from every rhombohedron an infinite number of scaleuohedrons, Avliose form will depend upon the extent to which the vertical axis has been elongated. We find, however, that the semi-vertical axis of the scalenohe- dron is always some simple multiple of that '^' ■ of the inscribed rhombohedron. Hence we may use, as the abbreviated symbol of the scalenohedron, the ab- breviated symbol of the corresponding inscribed rhombohedron, with an exponent indicating how many times its semi-vertical axis is greater than that of the rhombohedron. If, as in Fig. 119, the inscribed rhombohedron is the principal rhombohedron, -j- R, and the semi-vertical axis of the scalenohedron is three times that of the rhombohedron, the abbreviated symbol of the rhombo- hedron is -|~ •^'- The general symbol for any scalenohedron is ± m il", in which ± w -R is the symbol of the inscribed rhom- bohedron. It has already been stated, that the number of the possible rhomboliedrons on the crystals of a given substance is infinite, and it now appears that for every rhombohedron there may be an infinite number of scaleuohedrons ; so that the num- ber of possible scaleuohedrons on the crystals of a given sub- stance is infinitely greater than the infinite number of possible rhombohedrons. The mineral calcite has a great tendency to THE THREE STATES OF MATTER. 155 crystallize in scalenohedrons (dog-tootli crystals), and no less than thirty-eight rhombohedrons and seventy-six scalenohedrons have been observed among the crystals of this substance.* Besides tlie two hemihedral forms which have been described, there are two other hemihedral forms in tlie hexagonal system, which may be derived from the diliexagonal pyramid. The Jirst of these is obtained by extending the alternate pairs of planes, united at a lateral edge, A E, Pig. 120, where the al- ternate planes are distinguished by the shad- ing. As we extend the shaded or the un- shaded planes of Pig. 120, we obtain one or the other of two hexagonal pyramids, which differ from each other and from the hexagonal pyramids already described only in the position of the axes. The lateral axes of the pyramids thus derived do not unite the opposite solid angles, as is the case with pyramids of the first order (Fig. 109) ; nor yet the centres of opposite edges, as is the case with pyramids of the second order (Pig. 110) ; but points on the lateral edges intermediate between the centre and the ends. The second of these hemihedral forms is obtained by extend- ing the alternate pairs of planes united at a lateral solid angle, Kg. 120. Fig. 121. Fig. 122. Kg. 123. as shown by the shading in Pig. 121. According as the un- shaded or the shaded planes are extended, we obtain the two forms represented in Pigs. 122, 123. They are called the hex- * See Dana's System of Mineralogy, Vol. II. p. 437, for the symbols of these forms. 156 CHEMICAL PHYSICS. agonal trapczohedrons. The two forms derived from the same dihexagonal jjyramid differ from each other, not only in the abso- lute position of the form, but also in the relative position of their planes. They are distinguished as the right and left trapezohe- drons, and their symbols are respectively r i Qnia : a : p a : nb), and I \ (ma ■.pa : nb'). Tetartohedral Forms. By extending the alternate planes of the right hexagonal tra- pezohedron (Pig. 121), we can obtain two forms, differing from each other only in position, whose symbols are d= r \ (m a : a : p a : nb") ; and, in like manner, from the left hexagonal trapezohedron two other forms may be obtained, whose symbols are ± I \{m a : a : p a : nb'). Each of these four forms is bounded by six isosceles trapeziums, and they are therefore called trigonal trapezohedrons. They are evidently tetartohedral forms of the dihexagonal pyramid. These tetartohedral forms are never found isolated in nature ; but they appear very frequently on crystals of quartz in combina- tion with other forms. The crystals of this mineral are usually a combination of a hexagonal prism with a hexagonal pyramid of the same order (Fig. 125), and the trigonal trapezohedrons ap- pear as modifying planes on the solid angles. In Fig. 124, the Fig. 124. Fig. 125. Fig. 126. lateral solid angles are modified by the planes of the positive right-trigonal trapezohedrons, and in Fig. 126, by the planes of THE THREE STATES OP MATTER. 157 the positive left-trigonal trapezohedron. The two negative forms would modify in a similar way the set of solid angles, which are not modified in the figures. The difference of form between the right and left trapezohe- dron is found to be accompanied with remarkable differences of optical properties, which will be explained in the section on the circular polarization of light. Compound Forms. The crystal represented by Pig. 127 is a combination of the hexagonal prism with the basal plane, the symbols of which are given in this order below the figure. On the crystal represented by Fig. 12a Fig. 127. a : a:tjo a : oo &, oa a : CO a : m a : b. — J (a ; o :co a: i b), -\- i {a : a :co a : b). + R —iR +2K. Fig. 131. -f- J (a : o :qo a : 6), -(- j ( oo a : 00 a : oo a ; &)'. Fig. 128 there are evident- ^'e- ^^■ ly the faces of two rhom- bohedrons, the one positive and the other negative. If we assume that the faces let- tered r are those of the prin- cipal rhombohedron, R, then it is evident that the faces lettered Va are those of the +4j£ +k first obtuse rhombohedron, J R, because they truncate the vertical edges of the rhombohe- dron R. As the planes of the first obtuse rhombohedron are much larger than those of the principal rhombehedron, it is not at once evident from the figure that the first are truncating planes ; but on a model this fact could easily be discovered, by noticing that the edges formed by any plane, '/a , with the two adjacent planes, r, are in every case parallel (91). If, in Pig. 129, we assume that the faces r are those of the principal rhom- bohedron, then the faces '/j , which truncate the edges of the prin- 14 158 CHEMICAL PHYSICS. cipal rhombohedron, belong to tho first obtuse rbombohedron, — i R, and the faces 2 r to tho first acute rliombohedron — 2R; because the edges of this form are truncated by the faces r of the principal rhomboliedron. Fig. 130 represents a combination of the principal rhombohedron with its second acute rhombohedron, 4 R. Fig. 131 represents the combination of the principal rhombohedron with the basal plane. It will be noticed how closely this form re- sembles the octahedron of the monometric system, and it, in fact, merges into the octahedron when the angle of a on r is equal to 109° 28' 16", which is the Fig. 132. Fig. 133. case when the axes of the rhombohedron are to each oth- er as 1 : 2.4495. It will be remembered that the cube may be regarded as a rhom- bohedron, in which a : b = 1 : 1.2247. Hence the octa- hedron may be regarded as the first acute rhombohedron of the cube combined with the basal plane. The compound form of Fig. 132 consists of a hexagonal prism of the first order combined with the rhombo- hedron — ^ R. Finally, Fig. 133 represents a combination of a scalenohcdron, R', with the rhombohedron R. -|- A (a : a : a : CO 6), — ^ (a : a : a : i b). + R3 +R. Fig. 134. Trimetric System. Simple Forms. Fig. 135. Fig. 136. a lb : c. The fundamental form of this system is tho rhombic octahedron, so called because the three principal sections made by planes THE THREE STATES OP MATTER. 159 passing through the axis are all rhombs.* This fact is illustrated by Figs. 135, 136, 137, which represent these sections, and which have been lettered to correspond with Fig. 184. The same sub- stance frequently crystallizes in several octahedrons. In such cases we select one of these as the principal octahedron, giving to it the symbol a : b : c, and we then find that the parameters of the planes of the other octahedrons always stand in some simple relation to those of the one thus selected. Besides the octahe- drons, the only other simple forms of this system are rhombic prisms and terminal or basal planes.f The relation of these forms can be best understood by studying their symbols. Having given to the principal form the notation a : b : c, then the other octahedrons which the same substance can present will be expressed by the following symbols : — 1. a ; : m b : c, 3. in a : : b: ; c, 2. a : : b : m c, 4. m a ; ; b: ; nc, in which m and n are always very simple rational numbers. The first three of these symbols may evidently be regarded as partic- ular cases of the third. The number of possible octahedrons in which a given sub- stance may crystallize in the trimetric system is evidently infinite ; but the number which have in any case been observed is ex- tremely limited, including only a few of the possible values of VI and n, together with the rhombic prisms and terminal planes which result when m and n are made equal either to infinity or zero. If in No. 1 we put m = co, the symbol becomes a : cc b : c, which represents a rhombic prism whose axis is the axis of b. If m = 0, the symbol becomes a : ob : c = (x> a : b : ooc, which is the symbol of the basal planes of the same prism. If in No. 2 we put in = 00, we obtain the symbols of a rhombic prism whose axis is the axis of c ; and if we put m ^^ o, we obtain the symbol of the basal planes of the same prism. So also, if in No. 3 we put m equal to infinity and zero, we obtain the symbols of a rhombic prism parallel to the axis of a and of its basal planes. * A section of a ciystal is called a principal section when it contains two of the axes. t Planes placed at the ends of any axis, and parallel to the plane of the other two, are called terminal planes. Such planes, when they form the base of a crystal, aro called basal planes. 160 CHEMICAL PHYSICS. The general symbol No. 4 may be put in the three folio-wing forms : 1. a : nb : mc, 2. n a : mb : c, 3. ma:b:nc. If in No. 1 we put w = oo, we obtain a rhombic prism parallel to the axis of b, whose symbol is a : b : c, g ~ a : a : b : c, 2/ = cna:2b:c. Fig. 143. =■ a '. b : c, a =: a : oo6 : co c, 6 = 00 a : cub ic. e = a : c»6 : :<:. "A; a:ib: CDC, (K a :b : Fig. 144 a>e. /.^ = a : J 6 : a> c. / = 00 o : 6 ; c . c = ao a : b % ooc. Fig. 145. /2 = a : J 6 : e, /= o3 a : 6 : c, « = 00 a : 6 : =!, in the general symbols, we obtain the two symbols oo a : n b : c, and co a : nb : c'. These symbols are not equivalent, and each represents two opposite and parallel planes, which are also parallel to the orthodiagonal. The two planes represented by the first symbol are over the acute * Since h and I' are halves of the same straight line, the parametera oo b and » b' are in all respects equivalent, and may therefore bo substituted for each other. THE THREE STATES OP MATTER. 165 angle a, and are therefore narrower than the two planes repre- sented by the second symbol, which are over the obtuse angle 180° — a. The two sets of planes evidently bear the same rela- tion to each other as the two hemi-octahedrons, and may therefore be called the positive and negative orthodiagonal hemi-prisms. When M = 1, the two symbols become oca : 6 : c, and coa: b:c'. Finally, if we put p = co, and m = i, in the general symbols, we obtain a : nb : co c in both cases, which is the symbol of horizontal rhombic prisms parallel to the klinodiagonal, called the klinodiagonal prisms. When n = i, the symbol becomes a : b : OS c. Substituting tn = o, and multiplying all the parameters by oo, the general symbols become in both cases a : xb : oo c, which is the symbol of a form consisting of two terminal planes parallel to the planes of the axes b and c. In like manner, if we put n = 0, or p = 0, we obtain the symbols of terminal planes par- allel to the planes of the axes a, c or a, b respectively. Kg. 153. t = a : CO 6 : c, = CO a : 6 : oo c. Compound Forms, Fig. 154. t = a ; 03 6 : c, = 03 a : 6 : 00 c, f i' =s a : CO 6 : 00 c. Fig. 165. t = a ; CD b 1 e, = 00 a : 6 : 00 e, ii = 03 a ; tx} b : c. Fig. 153 represents the combination of the principal oblique rhombic prism, with its basal planes. Fig. 154 represents the Fig. 156. i = a : OS b :e, = 00 a : 6 : oo e, - 1 = CO a : 6 ; e'. Fig 157. t = (Z ; 00 d ; e, = CO a : b : OS e, »■ i' = a : 00 6 ; 00 e, Fig. 158. t = a : 00 ft : c, = 00 a : 6 : CD e, + l = a:b:c. 166 CHEMICAL PHYSICS. same combination, with the addition of two terminal planes at the end of the orthodiagonal. Fig. 155 represents the same combina- rig 159. Fig. 160. Fig. 161. i = a : b : Cj t = a : CO 6 : ■ ^» i = a : 00 6 : ' ^t = 00 a : 6 : 00 Cj = coa : b : 00 e, ii> = a: : CO b : 05 e, 1 - « : 6 : c'. it' = a : aa b : 00 e, + l = a: ■.h:c. — 1 = rt : 6 : c', — l = a: ■.b:c>. Fig. 162 tion, with the addition of two planes at the end of the klino- diagonal. Fig. 156 represents still the same combination, with the addition of the two planes of the negative orthodiagonal hemi- prism. Fig. 157 represents the same combination as Fig. 154, with the addition of the two planes of the positive orthodiago- nal hemi-prism. Fig. 158 is the same combination as Fig. 153, with the addition of the positive principal hemi-octahedron. Fig. 159 is also the same combina- Fig. 163. Fig. 164. i = ax CD b : Cf t i = a : CO 6 : 00 c, — 1 = o: 6:c'. i = a : 00 A : c, = oo a : 6 : oDc, 1 1' = a : 03 6 : 05 c, + 1 = a : 6 : e, — 1 = a : 4 : c', 4- 1" = cc a : 6 : c, — i = 00 o : 6 : c', r = a : 6 : 00 c. THE THREE STATES OP MATTER. 16T tion, with the addition of the negative hemi-octahedron. Fig. 160 is the same combination as Fig. 154, with the negative hemi-octahedron. Fig. 161 is the same with both hemi-octahe- drons. Fig. 162 represents the same combination as Fig. 153, with the addition of the four planes of the prism parallel to the klinodiagonal. Fig. 163 is the same combination as Fig. 160, ex- cept that the planes of the negative hemi-octahedron are more dominant, and the basal planes do not appear. Lastly, Fig. 164 represents a combination of all the forms which have appeared on the previous figures of this system. Hemihedral Forms. The hemihedral forms of this system only appear as modifying planes on the edges or solid angles of the holohedral forms, and Fig. 165. Fig. 166. Fig. 167. can easily be distinguished, because they modify only one half of the similar edges or solid angles of the form. Fig. 165 represents a compound form, in which ordinary tartaric acid frequently crys- tallizes. It is a combination of an oblique rhombic prism i with the terminal planes ii and the two hemi-prisms -\-i and — i. On these crystals there are four solid angles, e, which are evi- dently similar, and we should therefore expect that they would in any case be similarly modified. But on the crystal of the variety of tartaric acid which rotates the plane of polarization of light to the right, we find only the two front planes, as on Fig. 166 ; and on the crystals of the variety of tartaric acid which rotate the plane of polarization of light to the left, only two back planes, as on Fig. 167. These two forms are evidently re- lated to each other in the same way as the two forms of Figs. 168 CHEMICAL PHYSICS. 149, 150, and cannot be made to coincide by any cliange of position. Such hemihedral modifications occur chiefly on crystals of sub- stances which have the power of rotating the plane of polariza- tion of light. Common cane-sugar has this property, and on its crystals we find the two back planes of the klinodiagonal prism, without the corresponding front planes. Fig. 186 represents the common form of the crystals of tliis substance. They hare all Fig. 168. Fig, 169; the planes of Fig. 169, with the addition of the planes of the pos- itive hemi-prism -f- (oo a : ft : c), and the two back planes of the klinodiagonal prism a : b : oo c. Triclinic System. In the ti-iclinic system, a simple form consists of only two opposite parallel planes. These planes may have any position towards the three axes, and these axes may have any incli- nation towards each other, and any relative lengths. In all crystals of the same sub- stance, however, the axes have always the same relative length, and are inclined to each other at the same angles. Moreover, of the possible positions in which the two paral- lel planes of a simple form may be placed towards the axes, only a very few are ever observed ; the most frequently seen are those in which the planes are parallel either to one Fig. 1-0 or to two of the axes. Fig. 170 represents an octahedron belonging to this system, and formed by uniting the ends of the axes by planes. It is com- THE THBEE STATES OF MATTER. 169 Fig m. Fig. 172. posed of four simple forms : first, the form consisting of the plane ABC and its opposite, which has the symbol a : b : c, ov a' : b' : c' ; secondly, the form consisting of the plane ABC and its oppo- site, which has the symbol a : b : c', ov a' : b' : c ; thirdly, the form consisting of the plane AB' C and its opposite, which has the symbol a : b' : c, or a' : b : c' ; fourthly, the form consisting of the plane A B' C' and its opposite, which has the symbol a : b' : c', or a' : b : c. Pig. 171 represents an ob- lique prism belonging to this system, in which the axes have the same position as in Fig. 170. It is composed of three forms : first, the form consisting of the plane AB C D and its opposite, which has the symbol a : aab : c, ov a' : aab' : c'; secondly, the form consisting of the plane AA' BB' and its opposite, which has the symbol a: oob :c', or a' : b' : c ; thirdly, the form consisting of the plane BB' CO and its opposite, which has the symbol cc a : b : cc c, ot co a' :b' : ooc'. Since, however, the relative lengths and inclinations of the axes in this system may have any possible values, it is evi- dent that we may suppose the axes of this oblique prism to unite the centres of opposite planes, as in Pig. 172, or in fact to have any other position whatso- ever. Indeed, the position of the axes in the crystals of any given substance is in a great measure arbitrary, and we assign such a position in every case as will render the symbols of the observed forms of the substance as simple as possible. Fig. 173 represents a crystal of sulphate of copper, and the symbols below the figure indicate the position of each pair of parallel faces towards the three lines which have been assumed as the axes of the crystals of this substance. The lengths of these axes are a; b ; c = 1 : 0.974 : 1.768 15 il = a : cob : CO c. { i£ = 00 a : cob 1 e. i — a : cob : c. 1 = a: b : c. = oo a:b I System by 3 or 6 similar planes. ; Number of similar planes at extremities ) Hexagonal of crystal 3 or some multiple of 3. J System, The superior basal modilica- tions in front not similar to the correspond- ing inferior in front or supe- rior behind. 1. All edp;es not modilicd alike. 2. Twoi; or none of the angles trunc. or repl. by 3 or 6 similar planes. Number of similar planes at extremities of crystal nei- ther 3 nor a multiple of 3. Two adjacent or two approximate sim. pi. impossible. Two adjacent or two approximate sim. pi. possible. Tbiclinic System. JIONOCLIN- ic System. N. B. The right rhomboidal prism on its rhorfl- boidal base may be distinguished from the other right prism by the dissimilar modifications of its lat- eral and basal edges and angles. The superior basal modifica- tions in front similar to the corresponding inferior in front or superior be- hind. 1 . Similar planes at each base either 4 or 8 in number. 2. All lat. edges (if modified) simil. trunc. or bevelled. { 1. Similar planes at each base either 2 or 4 in number. 2. All lat. edges (if modified) not simil. truncated or bevelled. { DiMETKIO System. Teimetrio System. The study of the modifications of crystals may sometimes correct deductions from measurements. The interfacial angles of crystals are liable to slight variations, not generally exceed- ing a few minutes, but in extr£iordinary cases amounting to one or two degrees. For example, cubes of common salt have been observed with angles of 92° or 93°, and might be mistaken for rhombohedrons, were it not that the distribution of modifying planes indicated the perfect similarity of the edges and angles. Having determined the system of crystallization, it is next im- portant, if the system is not the monometric, to determine the * Dana's System of Mineralogy, Vol. I. p. 123. t The rhombohedron is the only solid included in this division, any of whose angles admit of a truncation or replacement by three or six planes. X The terminal edges of the octahedrons are here termed lateral, in order that these statements may be generally applicable both to prisms and octahedrons. THE THREE STATES OP MATTER. 177 relative lengths and inclinations of the axes. There is obviously a direct relation between these values and the interfacial angles, and this relation can be expressed mathematically, so that the one can be calculated from the other. It is the especial object of works on the subject of Mathematical Crystallography to ex- plain these relations, and to develop the formulae by which the calculations can be made. The last point in the determination of a crystal is to ascertain the simple forms of which it is composed, so as to give the sym- bol, that is, the parameters of each set of similar planes. In many cases, the forms may be discovered by inspection ; but in other cases the exact parameters of any one form can only be ascertained by calculation from the value of the interfacial an- gles, or from the parameters of other forms already Imown. The method of making these calculations is also explained in the works on Mathematical Crystallography. (96.) Use of Goniometers. — It is evident, from the last sec- tion, that the interfacial angles are the most important elements in the determination of crystals. These angles are measured by means of instruments called Goniometers. The simplest of these instruments, called the Common or Application Goniometer, is represented by Fig. 193. It consists of a semicircular arc, graduated to half-de- grees, and of two arms, ar- ranged as represented in the figure. The first of these arms, a b, is fixed at the ze- ro division ; but the second, d f, turns on c, the centre ""^^ Kg. 193. of the arc, as an axis, and indicates on the limb the angle of the crystal. In using the in- strument, the faces whose inclination is to be measured are applied between the arms, which are opened until they just admit the angle, taking care that the edge made by the two faces is perpendicular to the plane of the instrument. It is easy to de- termine when the arms are closely applied to the faces of the crystal, by holding the instrument between the eye and the light, and observing that no light passes between the arms and the faces of the crystal. The two arms, a b and df, slide in the slits i k, 178 CHEMICAL PHYSICS. g h,l m, and can be shortened at pleasure, a provision which is frequently important in the case of small crystals. Moreover, for measuring crystals partially imbedded, the arc is jointed at t, so that the part a t may be folded back on the other quadrant. Sometimes the arms admit of being separated from the arc, an arrangement which is more convenient than the one represented in the figure. When a regular goniometer is not at hand, approximate results may be obtained by means of an extemporaneous pair of arms made of thin sheet-metal, mica, or even of card. The arms are first applied to the faces of the crystal, as already described ; then, carefully retained in their relative position, they are placed on a sheet of paper, and the ^ngle is laid off by drawing lines with a pencil and ruler parallel with, or in the direction of, each of the arms. This angle may then be measured by means of a common protractor, or a scale of cords. The common goniometer is at best a rough instrument ; for, even when delicately used, it seldom furnishes results within a quarter of a degree of the truth.* For polished crystals we have a much superior instrument, called the Reflective Goniometer. There are several varieties of this instrument, but we shall only describe the one which is most generally used. This was origi- nally devised by Wollaston, and is called by his name. The principle of all reflective goniometers is illustrated by Pig. 194. Let a 6 c be the section of a crystal made by a plane perpendicular to the edge --'*''*^^**»v V formed by the intersection •"•^ r j j s C" ^.-^l^^^^^ ^^ ^^ *^° faces whose S^^\\^ ^^^^^^^^ angle we wish to meas- ^>;:\^^^-;;::;^^ ure, and a b, a c, the sec- ~"PJ ~'ii*'*%^" tions of the two faces. \ i' ■■-,,'""-->~.^_ The angle reqviired is ev- \, ...''•., ^~C,---,jf idently the same as the rig.194. ^ plane angle b a c. Let S S and MM be two ob- jects at some distance from the crystal, which may be used as signals. The eye of an observer at O, looking at the face of the * A more accurate form of the Application Goniometer, devised by Adelmann, is described in Dufr^noy's " Traite' de Mineralogie," Vol. I. This instrument may also be used as a Reflective Goniometer. THE THREE STATES OF MATTER. 179 crystal, sees a reflected image of the upper signal in the direction O M, and coinciding with the lower signal, seen by direct vision. If, now, the crystal is revolved on the edge whose projection is the point a, until it assumes the position a' b' c', it is evident that the reflected image of the upper signal will again be seen in coincidence with the lower signal. But in order to bring the crystal to the second position, it is obviously necessary to revolve the face a c through the arc mnp, which is the supplement of the required angle. If, then, we can measure the angle through which the crystal must be turned in order to reproduce the coin- cidence, we can easily calculate the angle of the crystal. This object is readily accomplished by the goniometer of WoUaston. The instrument consists of a vertical brass circle, L L', Fig. 195, about twelve centimetres in diameter, whose axis is mounted Fig. 195. on a firm support, p g r. The circle is graduated on its rim to half-degrees, and may be revolved by means of the milled head V, which is fastened to one end of the axis. A vernier,* u, per- manently attached to the support at lo, indicates the angle through which the circle is revolved, and also subdivides the half-degrees into minutes. The axis on which the circle revolves is hollow, * The vernier will be described in the chapter on Weighing and Measuring. 180 CHEMICAL PHYSICS. and through it passes, with slight friction, an interior axis, a c. At one end of this interior axis is fastened the milled head 5, by means of which it may be revolved, and at the other end the contrivances for supporting and adjusting the crystal, z, which is fastened with wax to a thin metallic plate, d c. From this con- struction it is evident that, if we turn the milled head v, the circle and crystal will both revolve ; but if we turn the milled head s, the crystal may be revolved independently of the circle. Any distinct horizontal line, such as the bar of a window, may be used for the upper signal ; and for the lower signal, a black line drawn on white paper, placed several feet below, and adjusted parallel to the first. In use, the instrument is placed on a table about ten or twelve feet in front of the signals, and adjusted by means of the level- ling-screws, until its axis is perfectly horizontal and parallel with the lines forming the signals. The crystal, which has been pre- viously attached to the movable plate d c, is next adjusted, so that the edge of the interfacial angle to be measured shall exactly coincide with the axis of the instrument produced. This is the most difficult adjustment, and requires some skill. The crystal should first be brought into place as nearly as possible by the eye, either by shifting its position on the plate d c, or by changing the position of the plate by means of the axis b d and the joint g: When apparently adjusted, the eye should be brought as near the crystal as possible, and directed towards the lower signal. The milled head s should next be turned until the image of the upper signal is seen reflected from one of the faces, which includes the angle to be measured. If the crystal is perfectly adjusted, the image will appear horizontal, and may be brought into perfect coincidence with the lower signal, seen by direct vision. If there is not a perfect coincidence, the adjustment must be altered until it is obtained. The milled head is next revolved until the reflec- tion of the upper signal is seen in the second face, and if this image also coincides with the lower signal, seen in direct view, the adjustment is complete ; if not, the adjustment must be made perfect, by altering the position of the plate d c, and the first face again tried. A few successive trials of the two faces will enable the observer to obtain a perfect adjustment. When the two images are perfectly horizontal, the edge formed by the intersection of the two faces must be parallel to the axis of the THE THREE STATES OP MATTER. 181 circle, but it will not necessarily coincide with it. A slight vari- ation from exact centring in the position of the edge is not, •however, of importance, when the goniometer is placed ten or twelve feet distant from the signals, so that this adjustment may be made sufficiently near by the eye. The method of adjustment which has been described depends on the laws of reflection, which will be explained in the chapter on Light.* The crystal thus adjusted, the angle is very easily measured. The zero division of the limb is first made to coincide with "the zero division of the vernier. The eye is then brought as near to the crystal as possible, and directed towards the lower sig- nal. The crystal is then revolved by the milled head s until the image of the upper signal, reflected fi-om one of the faces enclosing the required angle, coincides with the lower signal seen by direct vision. This coincidence obtained, the circle and crystal are turned together by means of the milled head v, taking care to keep the eye in exactly the same position until the same coincidence is observed with the second face. The angle through which the circle has been turned may now be read off" by means of the vernier ; and this, as we have seen, is the sup- plement of the angle of the crystal. When the faces of a crystal are highly polished, we can determine its angles by means of the Wollaston goniometer within a few minutes, f Unfortunately, however, the faces of most crystals are not sufficiently polished to give, under ordinary circumstances, a distinct image of the signal. In many such cases, good results can be obtained by making the measurements in a partially darkened room, and using as the upper signal a narrow slit in the screen covering one of the windows, and as the lower signal, a horizontal black line drawn on the casement below. The slit is best made by covering a rectangular aperture in the screen with a parallel ruler, which * Another method of adjusting the goniometer and the crystal is described by Pro- fessor W. H. Miller, of Cambridge, England, in his work on Crystallography, and also in the last edition of Phillips's Mineralogy, London, 1852. This method is preferable to the one described in the text in most cases, and especially when the crystals are mi- nute or the lustre of the faces dim. t For the methods of rectifying the instrument and of determining the probable errors of measurement, the student may consult Naumann, Lehrbuch der reinen und angewandten Krystallographie, Leipzig, 1830, Band II. ; Neumann, Das Krystallsys- tem des Albites (Abhandlungen der koniglichen Akademie der Wissenschaften in Berlin, vom Jahre 1830). 16 182 CHEMICAL PHYSICS. may be opened more or less, as circumstances require. When the faces are very dull, the slit may be illuminated by means ol a heliostat. In such cases, when -we can see no image, we can sometimes get an impression of light imperfectly reflected from the faces of the crystal, and this enables us to measure the angle within ten or twelve minutes. We can sometimes render the faces of crystals reflecting, by fastening on them very thin pieces of mica by means of some interposed liquid, such as water or oil of tui'pentine. The WoUaston goniometer has been modified by Eudberg* and Mitscherlich,! and the instrument, as thus improved, is con- structed by Oertling, of Berlin. The modifications consist chiefly, — First, in an improved apparatus for centring and adjusting the crystal. Secondly, in substituting for the distant signals cross-wires at the focus of the eye-piece of a telescope which is firmly attached to the stand of the instrument. The object-glass, which is directed towards the crystal, is so adjiisted that the rays of light emanating from a lamp placed before tlie eye-piece and illuminating the cross-wires are rendered parallel before they strike upon the face of the crystal, and thus produce the same efiect as if they emanated from a signal ten or twelve feet distant. Thirdly, in directing the eye by means of a second telescope, furnished with cross-wires, whose optical axis is in the same plane as that of the first telescope, and is parallel to the plane of the graduated circle. In iising this instrument, the crystal is first carefully adjusted, and then turned until the re- flected image of the cross-wires of the first telescope is seen to coincide with those of the second, seen by direct vision. The whole circle is then turned until the same coincidence is obtained with the image reflected from the second face. The angle is then read off on the graduated limb, which, in the large goniometer constructed by Oertling, is divided into sixths of a degree, and each of these divisions subdivided by a vernier into sixths of a minute. This goniometer gives very accurate measurements ; but on account of the loss of light produced by the lenses, it can only be used with crystals whose faces are highly polished. In- * Vorschlag zu einem verbesserten Reflexionsgoniometer (Annalen dor Phys. und Chem. von Poggendoif, IX. s. 517). t Abh. der kon. Akad. der Wiss., Berlin, 1825, 1839. Also Dufr^noy, Traite de Mineralogie, Vol. I. THE THREE STATES OP MATTER. 183 deed, it is seldom that such nicety is required, since the angles of crystals are liable to accidental variations amounting to several minutes, and the ordinary WoUaston goniometer will in most cases measure the angles as accurately as they are formed by nature. For descriptions of the various forms of reflective and other goniometers, which have been proposed by Babinet,* Haidinger,f and others, ^ the student is referred to the original memoirs. (97.) Identity of Crystalline Form. — It was stated in (79), that, with certain limitations, the crystalline form is always the same for the same substance, and we are now prepared to under- stand what the limitations are. It is not true, in the ordinary, acceptation of the word, that the same substance always crystal- lizes in the same form ; but the same substance, with the excep- tions hereafter to be noticed, always crystallizes in the same system. Common salt, for example, usually crystallizes in cubes ; but when it is crystallized from a solution containing urea, it takes the form of the regular octahedron, or else a compound form, on which the cube and octahedron are united. Both of these forms belong to the Monometric System. So also, M. le Comte de Bournon, in a monograph of two volumes, has de- scribed eight hundred different forms of the mineral calcite ; but all of these belong to the Hexagonal System. When a substance crystallizes in the Monometric System, the relative lengths of the axes of the different forms must necessarily be the same ; but in the other systems, the relative lengths of the axes of the different forms of the same substance may be different. We have seen, however, that these lengths always bear to each other a very sim- ple numerical ratio (compare pages 143, 147, 159, and 164), and that in the oblique systems the axes of the different forms of the same substance have always the same relative inclinations (com- pare pages 164 and 168). It follows, therefore, that when we say that a substance always crystallizes in the same form, we only mean that it crystallizes in forms belonging to the same system. The number of possible forms in which a given substance may crystallize (although it is restricted to forms of one system) is, * Dufrenoy, Traite de Mineralogie, Vol. I. t Sitzungsberichte der mathera.-naturw. Classe der kais. Akademie der Wissen- schaften zu Wien. Noremberhefte des Jahrganges 1855. t Suckow, Vorschlag zu einem Goniometer (Journal fiir praktische Chemie von Erdmann, Band II.). Gilbert's Annalen der Physik, Jahrgang 1820. Also Kolinati, Elemente der Krystallographie, Brunn, 1855. 184 CHEMICAL PHYSICS. of course, infinite ; but the number of actual forms in ■vrliich it is observed to crystallize is generally very limited, — seldom ex- ceeding two or three. Under similar circumstances, a given substance almost invariably takes the same form; so that this form is one of the most characteristic properties by which a substance may be recognized. Moreover, we also find that in any given system the possible forms of a substance are limited to either holohedral or hemihedral forms. For example, we always find iron pyrites crystallized in the parallel hemihedral forms of the Monometric System, and gray copper in the oblique hemihedral forms of the same system. (98.) Dimorphism and Polymorphism. — There are several substances, which, under widely different conditions, may be made to crystallize in the forms of two systems, and a few which may be made to crystallize in those of three systems. Such substances are said to be dimorphous or polymorphous. Sulphur, for example, at the ordinary temperature of the air, crystallizes in the forms of the Trimetric System ; but at the tem- perature of 113° C. it crystallizes in the forms of the Monoclinic System. Carbon, also, is found in nature as diamond, whose crystals belong to the Monometric System, and as graphite, whose crystals belong to the Hexagonal System. Again, carbonate of lime occurs in forms of the Hexagonal System, when it is called calcite ; and in forms of the Trimetric System, when it is called arragonite. Lastly, titanic acid crystallizes in the forms of the Dimetric System, in which a : b =1 : 0.6442 (rutile) ; in forms of the same system, in which a : b = \ : 1.7723 (^antase') ; and also in forms of the Trimetric System (brookite^ . When, however, a substance crystallizes in the forms of differ- ent systems, we find that in the several states its other properties differ as widely as the forms ; and so much so, that it may be questioned whether they can properly be regarded as the same substances. No two substances could differ more widely than the two states of carbon (diamond and graphite) ,; and similar differences, although not quite so striking, exist between the different states of other substances. It becomes, then, a question of considerable interest, whether these states can properly be re- garded as the same sxibstance. But this discussion must be re- served for another portion of this work. THE THREE STATES OP MATTER. 185 Elasticity. (99.) Elasticity of Solids. — Having considered the effect of cohesion in retaining the molecules of solids in a determinate po- sition with reference to each other (79), we come next to consider the effect of this molecular force in determining phenomena of elasticity. It has been stated (77), that the phenomena of elas- ticity could be developed in all matter by compression, and that in solid matter they could also be developed by tension, by flexure, and by torsion. The laws of elasticity in solid bodies may, for the most part, be developed both by mathematical analysis and by experiment ; but we shall be obliged to confine ourselves, in this work, to a simple enunciation of them, referring the student to the works on Physics which have been previously cited, for a full development of the subject. (100.) Elasticity of Tension. — In experimenting on the elas- ticity developed in solids by tension, we suspend the rod or wire by its upper extremity to a firm support, and attach to its lower extremity a pan to re- ceive weight (Pig. 196) . The elongation caused by the addi- tion of weight to the pan can then be measured by means of a cathetometer.* If the elon- gation does not exceed a cer- tain amount for any given rod, and the experiment is not continued too long, the rod will resume its original length when the weight is removed. If, however, the elongation exceeds the limit of elastici- ty, or if the strain is contin- ued beyond a limited time, a permanent change of length and bulk will ensue. When the limits of elasticity are p. jgg * This instrument will be descHbed in the chapter on Weighing and Measuring. 16* 186 CHEMICAL PHYSICS. not exceeded, it will be found that the following laws will hold true in all experiments of this kind. 1. The elongation caused by, an increase of tension is the same for the same subtance, whatever may have been the original tenr sion. For example, if we are experimenting on a rod of iron, we shall find that the elongation caused by the addition of one kilogramme to the pan is the same, whether the pan was before empty, or was loaded with fifty kilogrammes or any other amount of weight. 2. The elongation is proportional to the increase of tension. If the rod is elongated one millimetre by one kilogramme, it will be elongated ten millimetres by ten kilogrammes, and so on. 3. The elongation is proportional to the length of the rod. A rod of the same substance, of the same size, but twice as long as ajiother, will be elongated twice as much by the same increase of weight. 4. T/ie elongation is inversely proportional to the area of the section made at right angles to the length of the rod. If, for example, two rods of the same substance have the same length, and if the area of the section of the first is twice as great as that of the second, it will only be elongated one half as much by the same strain. (101.) Coefficient of Elas.ticity. — It follows from these laws, that the elongation of a given rod, which we will represent by I, is proportional, first, to a constant quantity, C, depending on the nature of its substance ; secondly, to the weight, tX), by which it is stretched ; thirdly, to its length, L ; and, fourthly, is inversely proportional to the area of the section, S. This, expressed in mathematical language, is 1= C.iD . 1 hence, l=C^, or C='' s ' X to' If in these equations we put K== ^r, they will become, J 1 i^L jr ^ to ran This quantity, K, is called the coefficient of elasticity. If in the last equation we put I = L, that is, if we suppose the elongation 16° to 20O. 1003. 200O. 1,727 1,630 . 5,584 5,408 5,482 7,140 7,274 6,374 10,519 9,827 7,862 15,518 14,178 12,964 20,794 21,877 17,700 19,561 19,014 17,926 17,278 21,292 19,278 THE THREE STATES OP MATTER. ' 187 to be equal to the original length, and also make 8=1 inTm:*, the equation becomes K ={33; which shows that the coefficient of elasticity of any homogeneous substance is equal to the abso- lute weight required to double the length of a bar of that sub- stance, whose section is equal to one square millimetre, supposing such an increase of length were possible, which is not the case except with threads of India-rubber. The following table gives the coefficients of elasticity of a number of metals, as deter- mined by M. Wertheim. Coefficients of Elasticity of Annealed Metals at different Temperatures, Lead, Gold, . Silver, . Copper, Platinum, Iron, . Cast-Steel, English Steel, It appears from this table, that, as a general rule, the coeffi- cients diminish as the temperature rises from 15° to 200°. M. Wertheim has also made experiments on metals which have been submitted to various mechanical agencies, and has found that all circumstances which increase the density increase also the coefficient of elasticity, and the reverse. The coefficient of an alloy is sensibly the mean of the coeffi- cients of the metals which enter into its composition, even when a change of volume accompanies the formation of the alloy. A current of electricity diminishes momentarily the elasticity, inde- pendently of tlie diminution caused by the elevation of temper- ature which it produces. (102.) Elasticity of Compression. — If a bar is compressed in the direction of its length by a force acting at the extremities, it is found that the amount by which it is shortened is exactly equal to the amount by which it would be lengthened, were the force applied so as to stretch it. It follows, from this equality in the effects produced, that the laws of elasticity developed by com- pression are the same as the laws of the elasticity of tension. (103.) Elasticity of Flexure. — The simplest case of elas- ticity developed by flexure is illustrated by Pig. 197. It repre- 188 CHEMICAL PHYSICS. sents a rectangular bar, A B, fastened at one of its extremi- ties in a horizontal position. If, now, we press upon the free extremity of the bar at B, so '^i^^^^ as to curve it a little, the bar will tend to return to its first position, in consequence of the elasticity developed by the flex- ure ; and if left to itself, will resume the horizontal position after a few oscillations. The elasticity of flexure is, in great measure, a mixed effect of the elasticity of compression and tension. Since, by the bending of the bar, the particles of the convex surface A B' are drawn apart, while those of the concave surface CD' are forced to- gether, and it is in consequence of the elasticity thus developed that the bar tends to return to its original position. But, more- over, the particles of the bar have changed their position, inde- pendently of the change of their relative distances apart, since the particles, which were previously situated on a straight line, are now on a curved line ; and we know that such a change of position must be accompanied with a development of elas- i ticity. Starting from these data, the laws of elasticity of fiexiire can be deduced by mathematical analysis. They are comprised in the formula, toZ3 i^ Kale^ or to = ^« -- ; [67.] in which L is the length of the bar ; fcO, the weight acting per- pendicularly, and tending to bend it ; b, the breadth of the bar measured perpendicularly to the direction of this force ; e, the thickness of the bar ; a, the arc described B B' ; and K, a con- stant quantity depending on its substance. If in [67] we put L = 1 m., b = 1 c. m., e = 1 c. m., a = 1 c. m., it becomes ti) z= K. The number K is called the coefficient of the elas- ticity of flexure, and it is evidently equal to the weight which will bend a bar of a given substance one metre long and one centimetre square through an arc of one centimetre. When the values of a, b, e, and L have been determined by experiment in the case of any substance, the value of K for this substance can easily be calculated. THE THREE STATES OF MATTER. 189 Equation [67] shows that the flexure of the bar, or a, is pro- portional to the force tD. It follows from this, that, as the rod is bent, it tends to restore itself to the position of equilibrium with a force which increases with the distance of each of its points from their position of equilibrium. Now it can be proved that, when this condition exists, the oscillations which the bar makes in returning to the position of eqiiilibrium will be isochronous, whatever may be their amplitude. Hence reciprocally it will follow, that, if the oscillations of such a bar are isochronous, the condition under consideration miist exist. It is easy to verify the isochronism of the oscillations experimentally, because, being very rapid, they produce a sound whose pitch depends on the number of oscillations in a second, and hence in any case would vary, if the isochronism were not preserved. Now it is well known that this pitch is constant for a given bar, whatever may be the ampli- tude of the oscillations ; and thus this is at once a consequence and a proof of the law, that the flexure is proportional to the force. It has been assumed in this discussion, that the section of the bar is a rectangle, and that the force is applied in a direction per- pendicular to one of its sides. When these conditions are not fulfilled, the formulae [67] no longer hold true. It has been also assumed that the bar returns exactly to its first position when it is freed, or, in other words, that the flexure does not exceed the limit of elasticity. (104.) Applications. — Almost all springs — for example, watch-springs and carriage-springs — are appli- cations of the elasticity of flexure. The bow is another example. The elasticity of a hair cushion is due to the elasticity of flexure devel- oped in the single hairs. The spring balance. Fig. 198, which has been already described (71), is an application of the law that the flexure is proportional to the weight. The elasticity of flexure has been applied by Bourdon in the construction of a metallic ma- nometer and barometer, which bear his name. It is a familiar fact, that, if we force air into j. jgg a flexible tube, closed at one end, which is flattened and coiled up on its flat side, the pressure tends to 190 CHEMICAL PHYSICS. rig. 199. uncoil it ; and, on the other hand, that, if ■we exhaust the air, the exterior pressure tends to coil it still further. If the tube is also elastic, it is evident that, when the pressure is re- moved or restored, it will return to its fornaer condi- tion, provided that the lim- its of elasticity are not passed. These facts are the basis of the two instru- ments represented in Figs. 199 and 200. The chief object of the manometer (Fig. 199) is to measure the pressure exert- ed by confined steam, al- though it might be used for any similar purpose. It consists of an elastic tube, a b, made of brass, and coiled as represented in the figure. A section of this tube is represented at S. The end of the tube, a, is firmly fastened to the stopcock, m, by which it connects with the steam-boiler. To the closed end of the tube, b, is attached a hand, e, which moves over an index. As the pressure of the steam on the inte- rior surface of the tube increases, it gradually uncoils, and the hand points to the number of atmos- pheres of pressure. When the pressure is removed, the tube, in virtue of its elasticity, resumes its original position, and the hand points to the first division of the scale. The barometer (Fig. 200) is a more delicate instrument, con- structed on the same principle. The tube is here closed at both ends, and when the pressure of the atmosphere is just equal to the tension of the confined air, it Fig. 200. THE THREE STATES OP MATTEB. 191 is in the condition of equilibrium. Wlien, however, the pressure of the atmosphere diminishes, there is an excess of pressure on the interior surface of the tube, and it tends to uncoil ; on the other hand, when the atmospheric pressure increases, there is an ex- cess of pressure on the exterior surface, and the tube tends to coil still morct As constructed, the air is partially exhausted from the tube, and hence the pressure of the atmosphere always tends to coil it more or less, as compared with the condition of equilibrium. The tube is fastened, at the middle of its length, to the upper part of the instrument, and its free ends are connected, by the metallic threads a, b, with the hand, which serves to mul- tiply the motion, while a small spiral spring, c, causes the needle to follow with accuracy any change of position in the ends of the tube. The arc is graduated to correspond with a mercurial ba- rometer, and denotes the number of centimetres of mercury to which the atmospheric pressure corresponds. (105.) Elasticity of Torsion. — It is a fact of frequent obser- vation, that, when a metallic wire, a b (Pig. 201), fastened at one end, is twisted by a force applied at the other, it strives to return to its original position, and when free returns to this po- sition, after having made a number of os- cillations. This of course supposes that the strain has not exceeded the limit of elasticity. It is easy to see how elasticity is devel- oped in a wire by torsion. Suppose m n, Fig. 201, to be a line of particles parallel to the axis of the wire when in a state of equilibrium. It is evident that, when the wire is twisted, these particles will be dis- tributed on the helix m n' ; but in order to assume this position, the distances between the successive molecules must be increased, which will develop the elasticity of tension, ticity is also developed by the fact that the particles resist any change of position, even when the relative distances are pre- served. The angle a, through which a radius of the lower base of the wire is turned, is termed the angle of torsion. The force which, Fig. 201. Besides, this elas- 192 CHEMICAL PHYSICS. applied at the extremity of a lever equal to the unit of length and perpendicular to the wire, will maintain it in a position which corresponds to a certain angle of torsion, is called the force of torsion. And when the angle of torsion is such that the arc described by the extremity of the lever is also equal to unity, the force of torsion is called the coefficient of torsion. The laws of the elasticity of torsion were investigated by Cou- lomb, and are expressed in the following formula : — t = 7tr I ^ , [68.1 or ^ = T7?; [69.J which apply to the case represented in Fig. 201, of a cylindrical weight suspended by a cylindrical wire to a fixed support, a, so that the axis of the cylinder and the wire correspond. In this case, W represents the weight of the cylinder ; r, its radius ; g, the force of gravity ; F, the coefficient of torsion of the wire ; and t, the time of the oscillations which the cylinder makes oil its axis, in returning to the state of rest after the wire has been twisted. The laws of torsion discovered by Coulomb are as follows. 1. The force of torsion is proportional to the angle of torsion. In order to establish this law, Coulomb made experiments on the oscillations of the weight W on its axis caused by the torsion of the wire, using wires of different substances, and loading them with different weights. He found that in each case the times of the oscillations were independent of the amplitudes, or, in other words, that they were isochronous ; and it can readily be shown, by the same course of reasoning used in (103), in regard to the elasticity of flexion, that the law is a necessary consequence of this fact. Tlie isochronism of the oscillations caused by torsion is ex- pressed by [68], since the value of the second member of the equation is independent of the amplitude. 2. The force of torsion is independent of the tension of the wire. It has been proved by experiment, that the square of the time of oscillation is proportional to the weight, W, or, in other W words, that -^ is a constant quantity ; and hence it follows, that THE THREE STATES OF MATTER. 193 the value of F [69] is not changed by any variation of the weight. The coefficient of torsion depends upon the substance of tlie wire, and also upon its diameter and its length, it being inversely proportional to the length and directly proportional to the fourth power of the diameter of the wire. (106.) Applications of the Elasticity of Torsion. — One of the most beautiful applications of the laws of torsion is the tor- sion-balance, contrived for measuring the intensity of feeble attractive and repulsive forces. One form of this balance, which is used for measuring the intensity of the attractive or repul- sive force between electrified bodies, is represented in Fig. 202. The general structure of the apparatus is evident from the figure, and does not require description. The most essential part of it is a fine silver wire, attached, at its upper end, to the brass circle e, and from the lower end of which is suspended a shellac needle. The circle e is movable, and turns on the cap, which is cemented to the glass tube d. This circle is graduated on the exterior rim into degrees, and the index-mark at a, which is fastened to the cap, indicates the angle through which the circle e has been turned. The glass tube also turns in a brass socket, which is cemented to the glass cover of the apparatus. The re- pulsive or attractive force between the two electrified balls m and n, is measured by the angle through which it is necessary to twist the wire (by turning the circle e ), in order to balance it, the force exerted being always proportional to the angle of torsion. A modification of the torsion-balance was employed by Cavendish, and subsequently by Bayly, in the determination of the density of the earth. (107.) Limit of Elasticity. — It has been several times stated in the previous sections, that the laws of elasticity only hold true so long as the strain does not exceed the limit of elasticity, and it was stated in section (77), that, within more or less narrow 17 Fig. 202. 194 CHEMICAL PHYSICS. limits, all solids were perfectly elastic. The phenomena of elas- ticity may be developed by torsion in those substances which seem the most destitute of tliis property. Thus, if we take a leaden wire two millimetres in diameter and three metres long, fix one end of it firmly to the ceiling, and fasten an index to the other, it will be found that, if we twist the wire twice round and let it go, it will, after a number of oscillations, come to rest in its original position ; showing that the elasticity in this leaden wire is perfect up to the point mentioned. But if we twist the wire four times instead of two, it will not return to its first position, but to a position short of that by nearly two revolutions. The particles of a leaden wire of this length and thickness will bear a displacement measured by two revolutions of the index ; but the displacement occasioned by four turns is more than its particles can bear, and they remain permanently displaced, — the wire having taken what is technically called a set. So also, a thin cylinder of pipe-clay (which is generally consid- ered as. destitute of elasticity as almost any substance can be) shows the existence of elasticity as perfect as can be found in the best-tempered steel ; but here again the limit of elasticity is soon reached. A steel wire, similar to the lead one just mentioned, might be twisted a great many times before its particles would receive such a set as to prevent it from completely untwisting again ; but after it had been twisted a certain number of times, the limit of its elasticity would be passed, and it would not come to rest again at its first position. The same phenomena appear in all the cases we have studied. A wire, which, when stretched by a light weight, will resume its original length when the weight is removed, will be permanently lengthened if the weight exceeds a limited amount. So also a steel spring, if bent beyond a certain point, is forced, and re- mains permanently bent to a greater or less extent. It is a remarkable fact, that even when the limit of elasticity has been exceeded, so that the particles have taken a permanent set, the elasticity of the whole mass remains the same as before. Thus, when a wire has been permanently lengthened by a great strain, it is as perfectly elastic in its new condition as before, readily recovering from the eifects of smaller degrees of exten- sion. So also it was found by Coulomb, that, after he had given a set to the lead wire already referred to, by twisting it four THK THREE STATES OP MATTER. 195 times round, the -wire was as elastic in its new condition as be- fore, requiring the same force to give it a further twist, and recovering itself as completely when that force was withdrawn. The limits of elasticity have been determined only in the case of the elasticity of tension. The method of experimenting was to take wires of any length, but whose section was- equal to one square millimetre, and to determine the amount of weight required to extend them permanently 0.05 m. m. for each metre of length. This investigation was more difficult than would appear, on account of the fact that the duration of the strain has an important influence on the permanent elongation which results ; for, when once commenced, this elongation slowly increases, and although it may not be sensible at the end of a few minutes, yet after several hours it may become very evident. This principle is illustrated by the well-known facts, that the best springs are worn out with long use, that the beams of floors bend little by little, and that buildings settle with time. The limit of elasticity is not, therefore, a value which can be rigorously de- termined, and hence the numbers in the following table must be regarde'd as only approximate. Metal9. Limit of Elasticity. Tenacity. T „„;t J Drawn, . Lead, .... < . ' ( Annealed, rp. ( Drawn, . ■*■"' • • • • t Annealed, . „ ,, (Drawn, . Gold,. . . . ■iA„„,^i,a_ _ _ -., (Drawn, . Silver, . . . |^„„,^i,a^ . . _. ( Drawn, . Copper, . . . |^„„,^i,a_ . _ Platinum, . . { ^J°4j / . ' . ' { Drawn, . Iron, .... ^^„„ealed, . . _ _ , ( Drawn, . Cast-Steel, . . [j^^^^^^^^ . . i.. 0.25 0.20 0.40 0.20 13.00 3.00 11.00 2.50 12.00 3.00 26.00 14.00 32.50 5.00 55.60 5.00 k. 2.50 1.80 2.45 1.70 27.00 10.08 29.00 16.02 40.30 30.54 34.10 23.50 61.10 46.88 80.00 65.70 (108.) Elasticity of Crystals. — In most crystalline solids the elasticity is not the same in all directions, as is shown by the phenomena of cleavage (110). By a beautiful application of the 196 CHEMICAL PHYSICS. principles of acoustics, Savart* has determined in a few in- stances the differences of elasticity which the same crystals present, when examined on different lines of direction with reference to their crystalline axes. As neither the methods nor the results of his investigations could be made intelligible in this connection, we must refer the student to the memoirs cited below. These differences of elasticity in crystals give rise to some of the most beautiful phenomena of optics, and we shall have occasion to refer to the subject again in that connection. (109.) Collision of Elastic Bodies. — The effects of collision, described in (41), are greatly modified when the bodies are elas- tic, and in a way which it is im- portant to study. Let us then suppose, in order to make the case simple, that the bodies are two elastic spheres, a and b, Fig. 203, with different masses, Jig. 203. -^ and M', which are moving in the same direction, from left to right, with the velocities 11 and v' re- spectively, V being greater than t)'. When the balls come together, they will flatten each other (Fig. 204), until the velocities of the two become equal. If the bodies are soft, this flattening will lig 204 be permanent, and the balls will move on together with a velocity which, as we have found, [23,] is f — —M~-{r3fr~ ■ L^^-J If the bodies, on the contrary, are elastic, and the limit of elas- ticity is not exceeded during the impact, we have the same result as before up to the moment of greatest flattening, and at that moment the velocity is b", as given above. But after this moment a new set of phenomena appears. The two balls tlnis flattened act as springs, and in resuming their original form impart recip- rocally to each other as much momentum as was expended in producing the compression. At the moment of greatest com- * Annales de Chimie et de Physique, 2" S^rie, Tom. XL. Also Dufre'noy, Traite de Min^ralogie, Tom. I. p. 289. THE THREE STATES OF MATTER. 197 pression, it is evident that the ball a has lost in velocity an amount equal to t) — b" ; and, on the other hand, the ball b has gained in velocity an amount equal to t)" — t)'. In recover- ing its form, the ball b tends to drive a to the left, and therefore to retard its motion ; and, on the other hand, the ball a tends to throw b forward, and therefore to accelerate its motion. More- over, by the principle just stated, this retardation and accelera- tion will be just the same as that caused between the first contact of the balls and the moment of greatest compression. Hence, after the impact, the velocity of a will be diminished by an amount equal to 2 (t) — t)"), and that of b increased by an amount equal to 2 (t)" — t)')- Representing, then, the veloci- ties after the impact by Va and 11,, we have t), = t) — 2(t) — b"), and b, = b' + 2(t)" — b')- [70.J Subtracting the second of these equations from the first, we ob- tain bo — bi = b' — b. [7i.j This equation shows that the difference of velocity is the same after the impact that it was before ; but the relation has been re- versed, the velocity of a being now less than that of b. Hence it follows, that, after the impact, the two balls will recede from each other as rapidly as they approached each other before ; and this is true in every case of the impact of two spheres, when both are perfectly elastic. In order to find the actual velocities after impact, we have only to substitute in [70] the value of b" given by [23], when we obtain u _ {M—M>) b+2Jr'b' ^» — M-\- M' ' and [72.] u _ (M' — ilf ) b' -f 2 J/ b ^' ~~ M+ M' In obtaining these values, we have supposed that both balls were moving from left to right, the mass M, whose velocity is the greatest, being at the left of the other. The same formulse, how- ever, hold true for all cases of direct impact ; except that, when one of the balls is moving from right to left, the sign of its velocity must be changed, A few examples will illustrate the application of the formulse. 17* 198 CHEMICAL PHYSICS. Let us suppose, then, for the first case, that the masses of the two balls are equal, and that the ball b is at rest. "We shall then have M' = M, and \)' = 0. Substituting these values in [72], we have K = 0, and b, = t). [73.] Hence, after the impact, the ball a remains at rest, and the ball b moves on with the velocity which a had before the impact. Let us suppose, as the second case, that the masses are equal, and that the motions are in opposite directions, that of a posi- tive, and that of b negative. We sliall then have M' = M, and b' = — v'. Substituting, we obtain ll„ = _b', and 1)1 = 1). [74.] Here, after the impact, the ball a will move from right to left with the previous velocity of b, and b will move from left to right with the previous velocity of a ; and in general, trhen the masses are equal, the tivo spheres willinterchange velocities. Let us suppose, as a third case, that the velocities are equal, and the motions in opposite directions', as before ; and further, that the mass of b is greater than that of a. We then have v= — v, and M' > M. Substituting, we obtain . _ jM-^M ') 1) ^^^ U_ (3 31-3 1') b ■In this case, after the impact, the ball a must always move from right to left, when, as supposed, M' > M. If 31' < 3 M, the ball b, after the impact, will move from left to right. If, how- ever, M' > 8 ikf, it will move from right to left. "When Jf ' = 3 ikZ, we have t)„=2l), and t). = ; [76.] that is, the ball a will move from right to left with twice its pre- vious velocity, and the ball b will remain at rest. We can also apply the formulse to the case where an elastic ball strikes vertically on a fixed obstacle, as when an India- rubber ball is let fall on the ground. In this case, M' = oo, and {)' = 0. Substituting these values, [72] becomes l)o = — 1) ; that is, the body moves, after impact, with the same velocity as before, but in an opposite direction. Hence the India-rubber ball should, by (22), rebound to the same height from which it fell. THE THREE STATES OP MATTER. 199 This is not practically true, because the surface on which it falls is never perfectly elastic, and, moreover, because the ball does not recover promptly from the compression. Let us next suppose that the sphere strikes the obstacle in an oblique direction (Fig. 205), and that its velocity at the moment of collision is represented by the line i a', which represents also the direction of the motion. This motion is, by (24), equivalent to two others, one in a direction which is tangent to the surface, and whose velocity at the mo- ment of collision is represents ed by the line i c, and another, which is normal to the surface, and whose velocity at the mo- ment of collision is represented by the line i n'. The lines i c ^jg. 205. and i n' are sides of a parallelo- gram, of which i a' is the diagonal. The first motion will con- tinue, after the impact, with the same velocity, without changing its direction. The second motion, as we have jtist seen, will be changed by the impact into a motion in the opposite direction, but with the same velocity. In order to find the resulting path and velocity of the ball after the impact, we need only to combine these two motions. For this purpose, we have already drawn the line i c, which represents the velocity and the direction of the first component. The line i n, drawn equal to the line i n', and in an opposite direction, will represent the velocity and direction of the second component. Completing the parallelogram and drawing its diagonal, we find that the body moves, after the im- pact, in the direction i b, with a velocity represented by the length of this line. Moreover, since the parallelograms c n and c n' are equal, their diagonals are also equal, — proving that the velocity after the impact is the same that it was before. Further, since i n is in the same plane as i n', it follows that the diagonals must be in the same plane, which shows that after the impact the ball moves in the same plane in which it moved before. Lastly, it follows, from the equality of the parallelograms, that the an- gles bin and a' i n' are equal, and consequently the angles bin 200 CHEMICAL PHYSICS. and a in are equal. The angle a i n, which the original direc- tion of the motion makes with the normal to the .surface of the fixed obstacle, is called the angle of incidence ; and the angle bin, formed by the direction of the motion after impact with this normal, is called the angle of reflection. Hence, the angle of incidence is equal to the angle of reflection. The absolute equality of the angles of incidence and reflection is only realized when both the body and the obstacle are perfectly elastic. When this is not the case, the component i n is less than i n', and hence the angle bin greater than a i n, the aiigle of re- flection becoming greater in proportion to the deficiency of elas- ticity ; and when the bodies are unelastic, it becomes equal to 90°, and the ball moves, after the impact, in the direction i c. Compare (41). Finally, let us suppose that two elastic spheres, A and B, Fig. 206, — moving in the same plane with the different velocities D and {)', — meet each other obliquely. In order to find the directions and ve- locities of their motions after impact, we may extend the method adopted in the case just discussed. We first de- compose the velocity of A, repre- sented by the line n v, into two com- ponents at right angles to each other, n U=a, and w F=6. In like man- ner, we decompose the velocity of B ^'^■^*'^' into two components, nU' = a', and n V ^ b'. We next find, by [72], what will be the velocities of the two bodies after the collision in the direction n U, as if they had been moving previously in this direction alone, with the veloci- ties of a and a' respectively. We shall thus obtain for the velocities after the collision, in the direction n U, two quantities, a„ and a,. In like manner, we next seek, by [72], what will be the velocities after the collision in the directions n V' for A, and n V for B, and obtain two quantities, h and 6,. Lastly, by combining together, on the principle of the composition of velocities, the components tto and 6„, we shall obtain the final direction and velocity of A ; and by combining a^ and 6,, the final direction and velocity of B. This calculation can easily be made in any special case, and does not, therefore, require further illustration. When the masses of THE THREE STATES OP MATTER. 201 the two spheres are equal, it follows from [74], that they ex- change velocities in each of the component directions ; that is, do = a', di = a, 60 = b', and bi = b. The final direction and velocity of A will then be obtained by combining a' and b', and those of B by combining a and b, when it will appear that both the directions and the velocities of two elastic spheres are inter- changed by an oblique collision when their masses are equal. The laws of the collision of elastic bodies may be illustrated in a great variety of ways ; but the best of all illustrations is found in the game of billiards, which is based almost entirely upon them. This game is played with balls of ivory, which are in themselves elastic, and on a table whose raised edges are cov-' ered with elastic cushions. The object of the game is to hit one ball with another, set in motion with a stick moved by the hand, so that one or both shall afterwards move toward a certain point or points. To effect this, in the various positions of the balls, requires an empirical knowledge of the laws of the col- lision of elastic bodies, and great skill in their application. The results obtained in this game do not conform exactly to the theory, on account of the imperfect elasticity of the balls and cushions. Thus we have seen [73] that, when an elastic body encounters another of the same mass at rest, the last is set in motion, and the former remains stationary. This is not generally the case with billiard-balls, for usually both balls move after the impact ; but nevertheless, when the stroke is very sharp, this result does at times occur. This is probably owing to the fact, that the friction of the ball on the cloth covering of the table, the imperfect elasticity of ivory, and other causes of disturbance, have the least influence when the ball is moving with a powerful force. So also, when the ball rebounds from the elastic cushion, the angles of incidence and reflection are not exactly equal, but they are very nearly so when the ball is driven with a powerful stroke. Resistance to Rupture. (110.) "When a rod is stretched in the direction of its length, with a gradually increasing force, it finally breaks, the force re- quired to break it depending on the substance of the rod, and its size. The smallest weight required to part it is the measure of 202 CHEMICAL PHYSICS. the resistance of the rod, and the weight required to part a rod of any substance, whose section is equal to one square millimetre, is the measure of the tenacity of that substance. The resistance to rupture can be conveniently determined by means of the dynamometer, represented in Fig. 207. It consists Fig 207. of an iron frame, P, on which slide two carriages, a and b. The first of these is connected with a powerful spring, contained in the box H. When the carriage a is drawn forward, the spring is bent, and communicates motion to the index, C, which moves on a graduated arc, and indicates in kilogrammes the inten- sity of the force. The second carriage, b, is united with the frame at A by means of the screw o, and may be moved for- wards or backwards by turning the handle M. The rest of the apparatus consists of a train of wheels and pinions, which con- nect the spring with the fly-wheel F, and prevent it from flying back too suddenly when the tension is removed. In order to determine the resistance to rupture of a given wire by means of this apparatus, the two ends of it are fastened to the carriages by means of the vices which they carry. The handle, M, is then slowly turned until the wire breaks, when the needle, C, indicates in kilogrammes the amount of force which has pro- duced the rupture. By means of this apparatus, we can easily establish the triith of the following laws : — 1. The force required to produce rupture is proportional to the section of the bar. 2. /;; is inde- pendent of the length of the bar. THE THREE STATES OP MATTER. 203 In determining the resistance of bars to rupture, we meet with the same difficulty already referred to in connection with the determination of the limit of elasticity. The rupture is not caused by the action of a constant force. As soon as the strain exceeds the limit of elasticity, the rod elongates little by little, the particles are at first slowly displaced, but finally they sud- denly separate and the rod breaks ; so that a moderate force applied for a long time will frequently cause the rupture of a rod which would resist a much greater force applied for a short time. This slow diminution of tenacity is a fact to which it is essential to pay regard in the construction of buildings. (111.) Tenacity. — The tenacity of a substance is the resist- ance to rupture, measured in kilogrammes, which a rod will ex- ert, whose section is just one square millimetre. In determining the tenacity of solids, we may obviously experiment on rods or wire of any convenient size, the area of whose section is known, and then calculate the tenacity by the principles of the last sec- tion. The tenacity of the different metals differs very greatly, between that of lead, in which it is very feeble, and that of steel, which has the greatest tenacity of all, as will be seen by referring to the table on page 195, in which the tenacity of the useful metals is given at the side of the numbers expressing the limit of elasticity. It will also be noticed, that there is a very great difference between the tenacity of the same substance when drawn into wire and when annealed, it being greatest in the first condition. The process of drawing wire will be described in (113). The change of form which it produces is accompa- nied by another very curious result. Although the particles of the wire are really less close together after the operation of drawing than they were before, yet they hold together more firmly, so that the tenacity of the wire is greatly increased. The cohesion of iron is increased, in drawing, to a very remark- able degree, so that fine iron wire is the most tenacious of all materials. " Thus a bar one inch square of the best cast-iron may be extended by a weight of nine tons and three quarters ; a bar of the same size of the best wrought-iron will sustain a weight of thirty tons ; a bundle of wires one tenth of an inch in diameter, of such size as to have the same quantity of material, will sustain a weight of from thirty-six to forty tons ; and if the wire be drawn more finely, so as to have a diameter of only one 204 CHEMICAL PHYSICS. twentieth or one thirtieth of an inch, a bundle containing the same quantity of material will sustain a weight of from sixty to ninety tons." * Hence cables made of fine iron wire twisted to- gether will sustain a far greater weight than chains containing the same quantity of iron. The cables of suspension bridges are usually made in this way. (112.) Cleavage. — In crystalline bodies, the resistance to rupture is not equally great in all directions. Most crystallized bodies are found to break most readily in certain planes affording a more or less smooth fracture or cleavage, while, if they are broken in any other direction, the fracture is rough and jagged. These planes are called planes of cleavage. They are always parallel either to actual faces on the crystal, or to possible faces. Cleavage can generally be reproduced on the same crystal to an indefinite extent, in planes parallel to each other, thus dividing the crystal into a series of thin laminae. Generally the same crystal may be cleaved in several directions, and the union of the several planes of cleavage forms what is called a solid of cleav- age, which is constant for the same substance, and is always one of the simple forms of the system to which the crystal belongs. Compare (93). Crystals differ very greatly from each other in the facility with which they may be cleaved. In some cases, the laminae can be separated by the fingers. This is the case with mica and several other minerals. At other times, a slight blow of the hammer is required, as, for example, with galena; and calc-spar ; wliile not unfrequently cleavage can be obtained only by using some sharp cutting-tool and a hammer. When other means fail, it can some- times be effected by heating the crystal and immersing it while hot in cold water. When cleavage is easily obtained, it is said to be eminent. In crystals of the Monometric System, cleavage is obtained with equal ease in the direction of any one of the planes of cleav- age ; but in crystals of the other systems, cleavage is obtained with equal ease only in planes which are parallel to the similar planes of the crystal. The cubic crystals of galena, for example, which belong to the Monometric System, may be cleaved with equal readiness in either of the three directions which are parallel to * Carpenter's Mechanical Philosophy. THE THREE STATES OF MATTER. 205 the faces of the cube. On the other hand, the crystals of gjpsnm, ■which belong to the Monoclinic System, may be cleaved with great facility in one direction, less readily in a second, and only with some difficulty in a third ; in thick crystals, the last two cleavages are scarcely attainable. The general laws with respect to cleavage are stated by Pro- fessor Dana* as follows : — 1. Cleavage in crystals of the same species yields the same form and angles. 2. Cleavage is obtained with equal ease or diffi,culty parallel to similar faces, and with unequal ease or difficulty parallel to dissimilar faces . 3. Cleavage parallel to similar planes affords planes of similar lustre and appearance, and the converse. (113.) Ductility and Malleability. — Some substances will not allow a permanent displacement of their molecules, and break whenever the strain exceeds the limit of elasticity. Such substances are called brittle bodies, and to this class belong glass, tempered steel, marble, sulphur, and many others. There are other substances, on the contrary, which, when submitted to various mechanical processes, allow a permanent displacement, more or less considerable, of their molecules, which then assume new positions of equilibrium. This property is possessed in a high degree by the metals, and is called ductility or malleability, according as it is applied in drawing out wire, or in reducing the metal to sheets and leaves in a rolling-mill or under the hammer. The machine for drawing wire consists essentially of a plate of hardened steel pierced with a number of conical holes of dif- ferent sizes. Through one of these holes is passed the end of a metallic rod, which has been reduced in size for the purpose. This end is then seized with a pair of pliers and pulled with con- siderable force. In being thus forced through the hole, the rod becomes lengthened, and diminished in size. It is then passed in like manner through a smaller hole, and thus successively, until the wire is reduced to the requisite fineness. Pig. 208 is a representation of a mill used for drawing iron wire. The coarser wire is unwound from the reel jP, and, after having * System of Mineralogy, Vol. I. p. 103. 18 20G CHEMICAL PHYSICS. Kg. 208. passed the draioing-plate A B, is received on the dram C, to which the force is applied through the cog-wlieels r p, n q (see Mg. 209). In order that a substance should read- ily yield to this mechanical action, it is evidently essential, not only that its par- ticles should have the power of readily changing their position, but also that it should be endowed with great tenacity. Hence those metals whose particles ad- mit most readily of change of position are not necessarily the most ductile. A rolling-mill consists of two steel rollers, arranged as represented in Fig. 210, so that their distance apart can be varied at pleasure, and so that they may be turned together in unison, but in op- posite directions. The plate of metal is applied between the two rollers, and is forced to accommodate its thickness to the distance between them, which is adjusted so as to be a little less than the thickness of the plate. This distance may then be diminished, and the process repeated until the thick- ness of the plate is reduced to the desired amount. Many of the metals can be reduced to leaves of exceeding te- nuity under the hammer. It is in this way that the goldleaf used in gilding is prepared. The gold plate is first reduced in a rolling-mill to the thickness of aboiit one millimetre. Several rig. 209. THE THREE STATES OF MATTER. 207 Fig. 210. of these plates are now piled on each other, and spread out by- beating the pile with a heavy mallet until they are reduced to the thickness of a sheet of paper. The leaves are next separated from each other by sheets of paper, and the pile beaten again. Finally, the sheets of paper are replaced by others made of gold- beaters' skin. In this, as in all similar processes, the metal be- comes brittle, and would infallibly break or tear were it not frequently reannealed. The process of annealing consists in heating the substance to a high temperature, and then allow- ing it to cool very slowly. The relative malleability of the metals is not the same when hammered as when rolled, and the difference appears to arise from the sudden shocks which accompany the blows of the ham- mer. In the following table, the relative malleability of the useful metals by both methods is given side by side, together with the relative tenacity and ductility. A comparison of the columns will illustrate what has been stated above. Tenacity. DnctiUty. Malleability under the Hammer. Malleability under the EoUing-MiU. Iron Platinum Lead Gold Copper Silver Tin Silver Platinum Iron Gold Copper Silver Copper Zinc Tin Zinc Gold Silver Lead Gold Zinc Copper . Zinc Lead Tin Platinum Platinum Tin Lead Iron Iron The action of heat modifies, in a most marked manner, both the ductility and malleability of many bodies. Iron, for example, is 208 CHEMICAL PHYSICS. very malleable at a red heat, and in this condition it can be read- ily forged or rolled into sheets. Glass, again, which is brittle at the ordinary temperature, is both malleable and ductile to the highest degree at a red heat. Copper, on the other hand, is most malleable when cold, and zinc cannot be rolled out with success except between the temperatures of 130° and 150° C. Above this last temperature, it becomes very brittle. The malleable metals are capable of receiving impressions from blows ; a property which is continually made use of in various processes of the arts. The processes of stamping coins and em- bossing figures on surfaces of various kinds are an illustration of the fact. The impression is made by means of a die, in which the design is sunk, just as the raised impression which the wax is to present is sunk in the seal. The die, which is made of the hardest steel, is forced down upon the blank coin by means of a powerful screw or lever, and the metal of the coin, being comparatively soft, is driven with great force into the cavities of the die, and retains the impression. Hardness. (114.) Scale of Hardness. — Hardness is the resistance which bodies oppose to being scratched or worn by other bodies. Of two substances, that one is said to be the hardest which will scratch the other. The hardness of a body is closely related to its ductility and tenacity, all circumstances which increase the ductility or diminish the tenacity rendering the body softer, and the reverse. In order to distinguish a harder body from a softer, we either attempt to scratch the one with the other, or we try each with a file. The last method is generally to be pre- ferred ; but both should be employed when practicable, since some bodies " give a low hardness under the file, owing either to impurities or imperfect aggregation of the particles, while they scratch a harder species, — showing that the particles are hard, although loosely aggregated." * Hardness is, an important character of a substance, and is much used by mineralogists as a means of distinguishing between mineral species. In order to fix a common standard of compari- son, the distinguished German mineralogist, Mohs, introduced a * Dana's System of Mineralogy, Vol. I. p. 130. THE THREE STATES OF MATTER. 209 scale of hardness. This scale consisted of ten minerals, which gradually increase in hardness, marked from 1 to 10. It has been since modified by Breithaupt, who has introduced two ad- ditional degrees of hardness, one between 2 and 3, the other between 5 and 6, as these intervals were larger than the rest. The numbers of Mohs, however, have been retained. The scale is as follows : — 1. Talc ; common laminated, light-green variety. 2. Gypsum ; a crystallized variety. 2.5. Mica ; variety from Zinnwald. 3. Calcite ; transparent variety. 4. Fluor- Spar ; crystalline variety. 5. Apatite ; transparent variety. 5.5. Scapolite ; crystalline variety. 6. Felspar (orthoclase) ; white, cleavable variety. 7. Quartz; transparent. 8. Topaz; transparent. 9. Sapphire ; cleavable varieties. 10. Diamond. In determining the hardness of a mineral, we draw a file over it with considerable pressure. If the file abrades the mineral with the same ease as No. 4, and produces an equal depth of abrasion with the same force, the hardness is said to be 4 ; if less readily than 4, but more readily than 5, it is said to be between 4 and 5 (written 4 - 5) ; or we may determine it with more accu- racy as 4.25 or 4.50. Several successive trials should be made, in order to insure accuracy, and the student should practise him- self in the use of the file with specimens of known hardness, until he can obtain constant results.* (115.) Sclerometer. — In testing the hardness of the dissim- ilar faces of the crystal, very marked differences are frequently observed. Differences may also be perceived on the same face when examined in different directions. For the purpose of measuring with great accuracy the differences in hardness which the faces of a crystal present, an apparatus has been contrived by Grailichf and Pekarek, called a sclerometer. It consists * Boxes containing the twelve minerals of the Mohs scale can be procured from the dealers in philosophical apparatus. t Sitzungsberichte der mathem.-naturw. Classe der kais. Akad. der Wissen., (Wien, 1854,) Band XUI. «. 410. 18* 210 CHEMICAL PHYSICS. essentially of a hard steel point attached to the under side, at one end, of a balance beam, which is carefully poised on its knife-edge. Above the point, and on the upper side of the beam, there is a pan to receive weights, by which the steel point may be pressed down upon the face of a crystal with a regulated force. At the other end of the beam there is fastened a spirit- level, and the whole is so adjusted that the beam — with the point and pan at one end, and with the spirit-level at the other — is just in equilibrium. By means of the sclerometer, it appears, for example, that the rhombohedral faces of crystals of calcite, r (Fig. 211), are softer rig. 211. Fig. 212. than the end faces, a. It has also been found that the hardness is not the same in all directions on the rhombohedral face. From a series of determinations made by Grailich and Pekarek with their sclerometer, it appears that the greatest hardness is in the direction of the shorter diagonal of the face, from C to E (Fig. 212), and the least hardness in the opposite direction, from E to C on the same diagonal. The weights required in the pan above the hard point, in order to scratch the face in various directions, were as follows : — ADgle.* 0° Shorter diagonal from C to E, 39° Perpendicular to edge x, 51° Parallel to edge z, 90° Longer diagonal from U to C, 129° Parallel to edge x, 141° Perpendicular to edge z, 180° Shorter diagonal from JE to C, These numbers are in each case the mean of several observa- tions. Similar differences have been observed on a large number Weight. 285 centigrammes 250 u 213 «fc 152 a 135 it 126 ti 96 it * These angles are those made by the given direction -with the shorter diagonal. THE THREE STATES OP MATTER. 211 of other ciystals, and they lead to the following general con- clusions : — 1. That the hardest planes of a crystal are those which are perpendicular to the plane of most perfect cleavage.* 2. That on a given plane the direction of greatest hardness is that which is most inclined to the direction of most perfect cleavage. (116.) Annealing- and Tempering: — The hardness of many substances may be greatly modified by the action of heat, and by various mechanical processes. The effects of change of tempera- ture in varying the degree of hardness are most important in re- gard to steel, since it is on this influence that the application of steel to so great a variety of useful purposes depends. If steel is heated to a red heat, and then very slowly cooled, it becomes ductile, flexible, soft, and comparatively unelastic* This pro- cess is called annealing; and, when thus annealed, steel can read- ily be drawn into wire, rolled into sheets, or manufactured into its numerous useful forms. If, however, the articles thus manu- factured are heated to a white heat, and then suddenly cooled by plunging them into water or mercury, the steel becomes very hard, brittle, highly elastic, and less dense. In its state of greatest hardness, steel is scarcely fit for any purposes in the arts, since it is so brittle that its points or edges are broken by a very slight resistance. But by reheating it to a lower temperature, and then slowly cooling it, this extreme hardness may be reduced, and the flexibility of the steel propor- tionally increased. The amount of the reduction is greater, the higher the temperature to which the articles are heated, and if heated to a red heat, they again become soft. This process of reheating is termed letting' down or tempering; and the workman is guided to the effects he wishes to produce by the changes of color which the surface of polished steel exhibits at different temperatures. The tints which correspond approxi- matively to the different temperatures are as follows : — Light straw, 220° Violet-yellow, 265° Blue, 293° Golden-yellow, 230° Purple-violet, 277° Deep Blue, 317° Orange-yellow, 240° Feeble blue, 288° Sea-green, 330° * Lehrbuch der Krystallographie von Miller iibersetzt und erweitert durch Dr. J. Grailich, (Wien, 1856,) Seite 229. 212 CHEMICAL PHYSICS. The hardest steel is used for little else than the making of dies for coining. The steel of the hardest files is hnt little let down. The first shade of yellow indicates that the reheating has been carried sufficiently far for lancet and other small surgeons' instru- ments, on wliich the keenest edge is required. Razor and pen- knife blades are heated until they exhibit a light straw-color. Scissors, shears, and chisels, in which a greater tenacity is required, are tempered at the first shade of orange. Table cutlery, in which flexibility is more desirable than the hardness, which would give a fine but brittle edge, are heated to the violet. Watch-springs are heated to a full blue, and coach-springs to a deep blue. In many manufactories the temper is given by immersing tlie hardened steel articles in a bath of mercury or oil, the heat of which can be exactly regulated by a thermometer. The bath is heated up to the required temperature, and then allowed to cool slowly. In this way, any number of articles which are to receive the same temper may be equably heated and gradually cooled. Most other metals are acted upon by heat and cold in some- what the same manner, although to a much less degree. Copper, however, is a remarkable exception to the rule, its properties being exactly the reverse of tliose of steel ; for when cooled slowly it becomes hard and brittle, but when cooled rapidly, soft and malleable. This same property is possessed to a still higher degree by bronze, which is an alloy of copper and tin. Glass undergoes, from the action of heat and cold, the same changes as steel. When heated to a red heat, and suddenly cooled, it becomes more brittle, harder, and less dense than in its annealed condition. When a glass vessel is first blown, it cools rapidly and irregularly, and the varying hardness of its different parts gives to it such a degree of brittleness, that the slightest shock or a small change of temperature would break it. In order to prevent this, it is annealed, by passing it through a long furnace, of which the heat is very great at one end and slowly diminishes towards the other, and it is thus cooled gradually and equably. ^ The properties of unannealed glass are illustrated y^ by Prince Rupert's drops. These are made by drop- /l ping melted glass into water, which of course cools IlI them suddenly, and gives to the glass a high degree of Fig 213. hardness and a proportionate brittleness. They have a THE THREE STATES OF MATTER. 213 long oval form, tapermg to a point at one end (Pig. 213). The body of the drop is so hard that it will bear a smart stroke ; but if a portion be broken off from the small end, the whole imme- diately flies into minute particles with a loud snap. The cause of the changes in hardness produced by the action of heat has not been as yet satisfactorily explained. The expla- nation usually given is this. When a bar of steel highly heated, and hence greatly expanded, is immersed in cold water, the ex- terior layers suddenly contract, and are compelled to adapt them- selves, by a permanent displacement of their molecules, to the core, which is still in an expanded state within. Subsequently, when the interior of the mass cools, its particles cannot approach each other freely, because they are more or less united to the ex- ternal crust, which has been already fixed in position. Hence, these particles remain in a state of tension, and this is supposed to give rise to the peculiar change of properties. Were this explanation correct, the effects of a sudden change of temperature ought to be greatest on thick bars of steel, but in fact the reverse is the case. The change is most probably con- nected with the phenomena of dimorphism (98), but in what way is not yet understood. Most metals are hardened, not only by sudden cooling, but also by such mechanical processes as tend to Condense them perma- nently, and thus increase their density. The processes of stamp- ing coin, of wire-drawing, of rolling out metallic plates, and of hammering, are all evidently of this nature. This change is usually called hammer-hardening, and its effects are the same on almost all ductile bodies. They become denser, more tenacious, harder, more brittle, and more elastic. All these effects can be removed by annealing ; and hence the necessity of continually reannealing the metals, during the processes just mentioned. PROBLEMS. Elasticity of Tension. 91. A rectangular iron bar 2 m. in length, and whose section is equal to 2 c m.'', is suspended by its upper extremity to a firm support, and to its lower extremity is attached a weight of 1,000 kilog. How much is it temporarily elongated by the strain, when the temperature is 15° ? 92. An annealed iron wire 2 m. m. in diameter and 2.25 m. in length is suspended as in the last example. How much weight is required to elon- gate it 0.26 m. m., when the temperature is 15° ? 214 CHEMICAL PHYSIOS. 93. A silver wire 0.75 m. m. in diameter and 5 m. long is elongated by a weight 0.25 m. m. How great is this weight when the temperature is 15°? Tenacity. 94. With how much weight in kilogrammes must a copper wire be loaded, in order to part it, when the diameter of the wire is equal to 1 m. m. ? Calculate both for annealed and unannealed wire. 95. In a pendulum experiment, it is required to suspend a weight of 50 kilog. by a copper wire. What must be the diameter of the wire, allowing -^^ for security beyond the diameter absolutely essential ? Cal- culate both for annealed and unannealed wire. Collision of Perfectly Elastic Bodies. In the following problems marked with a {*),the masses and velocities of the two balls are indicated as described in (109). The motion is from left to right, unless the rei^erse is indi- cated hij a negative sign. In each problem it is required to find the velocities of the two balls after the impact, and also the direction of the motion. *96. i/= 6. D = 3m. M' = 17. t)' = 1 m. *97. 3f = 10. t) = 5 m. M' = 20. b' = 2.5 m. *98. M = 10. t) = 10 m. M' = 100. b' = 0m. *99. M = 20. 6 = 10 m. M' = 10. b' = — 5 m. 100. M = 15. 6 = 16 m. M' = 10. b' = — 32 m. 101. A ball whose mass is M, with a velocity i), meets a second ball moving in the same direction, whose mass is M'. What must be th^ velocity of the second ball, when the first ball remains at rest after the collision ? 102. A ball strikes on a plane making an angle of incidence equal to 60°. What will be the angle of reflection when, in consequence of the imperfection of the elasticity both of the plane and the body, one tliird of the vertical velocity is lost by the impact ? Solve the same problem, sup- posing that one fourth of the velocity is lost. 103. An elastic ball falls from the height of 2 m. How high will it re- bound, supposing that one fifth of the final velocity is lost at the impact, in consequence of imperfect elasticity ? 104. Two perfectly elastic balls, moving in the same plane, meet each other obliquely. The angles made by the two directions of their motions with the line n U(Fig. 206), lying in the same plane and tangent to both balls at the point of contact, are a = 60° and /? = 30°- The masses are Jlf = 10 and M'= 5 ; the velocities are ll = 2.5 and t)' = 5. It is required to find the velocities of the two balls after collision, and the angles which the directions of their motions make with the given line. 105. Solve the same problem for the following values : — „ = 40°. ,? = 30°. M = 5. M' = 10. Ij = 4 m. I)' = 6 m. THE THEEE STATES OF MATTER. 215 II. Characteristic Properties op Liquids. (117.) Mechanical Condition of Liquids. Fluidity. — The liquid has not, like the solid (79), a definite , form ; but it takes the form of the vessel in which it is placed. Its particles are in a condition of equilibrium between t/ie attractive and repulsive forces (78), and instead of being bound together, as in a solid, they possess a perfect freedom of motion ; and under the influ- ence of the slightest force, they move among each other without friction and without disturbing the general equilibrium. This mechanical condition of matter is termed fluidity, and belongs both to liquids and gases. Liquids are not, however, perfect fluids, for there always exists between their particles a certain amount of adhesion,*owing to ah excess oi attractive force which renders them more or less viscous. Between an almost perfect fluid, like water, and a condition like dough, we have every grade of fluidity. Tliis is illustrated by the well-known series of or- ganic acids, commencing with formic acid and ending with me- lissic acid. Tlie series consists of over twenty members, and pre- sents every grade of condition. Formic acid is as fluid as water ; but as we descend in the series, the numbers are found to be more and more viscous, becoming first oily, then soft fats, next hard fats, and finally solids, like wax. (118.) Elasticity of Liquids. — It has already been stated (76), that liquids are compressible, and, moreover, that they re- sume exactly their original volume as soon as the pressure by which this was diminished is removed. It follows from these facts, that liquids are perfectly elastic, and that this elasticity is unlimited in extent. In the early experiments on compressibility made by Oersted, it was assumed that tlie capacity of the hiiVo A, of the appara- tus already described (Fig. 214), remained invariable. This as- sumption was based on the fact, that the walls of this reservoir were equally pressed by the fluid on both sides. It is easy, however, to see that this assumption is incorrect ; for if we suppose the interior of the bulb to be filled with solid glass, it is evident that the volume of the interior core, and hence that of the bulb, would be diminished by the exact amount that this glass core would be compressed by the given pressure. In such a case, the pressure on the exterior surface of the bulb would be 216 CHEMICAL PHYSICS. exactly balanced by the reaction of the glass core. If, now, the place of the glass core is supplied by water, the pressure on the exterior surface remaining the same, it is evident that the reac- tion of the water core must be exactly the same as that exerted by the glass core ; for otherwise the law of action and reaction (41) would not be obeyed. The conditions, then, with respect to the bulb, are not changed, and it is evident that its volume will be just as much reduced when filled with water as when filled with glass ; that is, by the amount to which a glass core just fill- ing it would be compressed by the given force. It follows from this, that the apparent condensation of any fluid under a given pressure, when determined by the apparatus repre- sented in Fig. 214, is not so great as the real condensation,* and that it is neces- sary to correct the determinations thus made by adding to the observed compres- sion an amount eqiial to the compres- sion, under a given pressure, of a glass core which would just fill the interior of the bulb. This amount can in any case be calculated from data furnished by experiments on the elongation of glass rods by tension, since, according to M. Wertheim, the diminution, under a given pressure, of one cubic cen- timetre of glass, in fractions of a cubic centimetre, is just equal to the elonga- tion of a glass rod one centimetre long, in fractions of a centimetre, under an equivalent tension. M. Grassi has carefully redetermined the compressi- bility of several liquids, making use of an improved apparatus contrived by Regnault, and correcting his observa- tions for the compressibility of the reservoir used according to the formulae of Wertheim. He has also studied the inflxience of a variation of temperature on the compressibility, as well as the influence of different pressures. The most important results ob- tained by M. Grassi are given in the following table. In every case, the numbers expressing the compressibility of fi liquid Fix. 211. THE THKEE STATES OP MATTER. 217 indicate the fraction of its volume by wliicli it is condensed -when submitted to a pressure of one atmospliere. Table of the Coefficients of CompressiMlityJ"' Pressure in Atmos- Liquid. Temperature. CompreBsibility. pheres, from which the Compressibility was determined. Mercury, .... o 0.0 0.00000295 Water, .... u 70 IE H 13.1 0.0000991 8.97 Methylic Alcohol, 13.5 0.0000913 , , Chloroform, 8.5 0.0000625 , . *' . . 12.0 0.0000648 1.309 it 12.5 0.0000763 9.2 In tlie case of water, it was found tliat tlie amount of condensa- tion was proportional to the pressure, and that it diminished when the temperature was increased. On the other hand, it appeared that the compressibility of alcohol, ether, and chloro- form increased with the temperatui'e, and, moreover, that the compressibility of these fluids, as well as that of methylic ether, increased with the pressure. M. Grassi. also made experiments on the compressibility of sa- line solution, and found that, for the same solution, it was as constant as that of pure water, and that it diminished when the amount of salt in solution was increased. * Annales de Chimie et de Physique, 3' Serie, Tom. XXXI. p. 437. •19 218 CHEMICAL PHYSICS. Consequences of the Mechanical Condition of Liquids. (119.) We have seen, in the last two sections, that the mole- cules of a liquid are in a condition of equilibrium, and also that all liquids are but slightly compressible and perfectly elastic. Of the characteristic properties of liquids, we shall only consider those which are a necessary consequence of these conditions. These naturally divide themselves into two classes : first, those which are independent of the action of gravity ; and, secondly, those which depend upon it. (120.) Liquids transmit Pressure in all Directions. — This most important quality of liquids was first clearly stated by Blaise Pascal, in the following terms : Liquids transmit equally in all directions a pressure exerted at any point of their mass. We may illustrate what is meant by this statement of Pascal, by means of Fig. 215, which represents the section of a vessel — which may be of any shape — filled with water, on the sides of which are several apertures closed by movable pistons. Let us suppose that the two pistons d and c present the same surface ; and, further, that the piston a presents twice, and the piston h five times, the area of c. If, now, we press in the piston c with the force of " ^ jig, 215. one kilogramme, this force will be trans- mitted in every direction to the sides of the vessel, and every portion of the interior surface whose area equals that of the piston will be pressed upon with a force of one kilogramme ; the piston d will be pressed out with a force of one kilogramme ; the piston a, with a force of two kilogrammes ; the piston b, with a force of five kilogrammes. And so will it be with any other portion of surface, either on the side of the vessel or im- mersed in the fluid ; it will be pressed upon with a force as many times greater than one kilogramme, as it is itself greater than the surface of the piston c. It is easy to see that this is a necessary consequence of the constitution of liquids. Since fluids are compressible and elastic, it follows that, on pressing in the piston d, the liquid is very slightly condensed, and the elasticity of compression developed in its particles. Bach particle at once becomes like a bent spring, THE THEEE STATES OP MATTER. 219 and presses in all directions. If the particle is in the midst of the fluid mass, it presses against the neighboring particles ; if it is on the side of the vessel, it presses in one direction against the vessel, but in all others against similar particles. Since the same is true of every particle, it follows that the pressure ex- erted by the condensed liquid against any two surfaces will be proportional to the number of particles in contact with these sur- faces ; and as the particles have the same size, it will also be proportional to the area of the surface. Hence the pistons d and c will be pressed out each by the same force, the piston a by a force twice as great, and the piston 6 by a force five times as great, as this. From the principle of equality between action and reaction, it follows that the outward pressure on the piston c is exactly equal to the force applied to press it in ; so that, if this piston is pressed in with a force of one kilogramme, the piston d is pressed out with the same force, the piston a with a force of two kilogrammes, etc. ; which was the proposition to be proved. Representing the area of any portion of the interior surface of a vessel by S, and that of any other portion by S ; representing also by £ and £' the pressure exerted against these surfaces by a confined liquid, in consequence of any compression ; we have £ :£'=S: S'. [77.] Moreover, it is evident from the principle involved, that this equation is true, not only for the surface of the vessel itself, but also for that of any solid immersed in the compressed liquid, or for any section of liquid particles whatsoever in the vessel. (121.) The line indicating the direction of the pressure ex- erted by any liquid particle against the surface with which it is in contact, is always a perpendicular to this surface at the point of contact. If the surface is a plane, the line is a perpendicular to this plane ; if the surface is curved, the line is a normal to this curve. The truth of this principle will be seen, if we consider what must be the result if the direction of the pressure were oblique. It is evident that such oblique pressure would be re- solved into two forces (35), one perpendicular to the surface, and the other tangent to it. The second component could of course exert no pressure against the surface ; so that the whole pressure exerted by the liquid particle would be that of the first compo- nent, which is, as the proposition requires, perpendicular to the surface at the point of contact. 220 CHEMICAL PHYSICS. When the surface is plane, the directions of the pressures ex- erted by the particles are all parallel. It is then always possible, by (39), to find a common resultant of all these parallel forces. The point of application of this resultant is called the centre of pressure. When the pressures exerted by the separate particles are all equal, the centre of pressure is always the centre of figure of the surface. In the case of the pistons (Fig. 215), the centre of pressure is in each one the centre of the circular base, and in studying its mechanical effects we may regard all the pressure as concentrated at that point. Were the base of the piston con- cave, then the directions of the pressures exerted by the separate particles would no longer be parallel ; since the lines indicating these directions would diverge from the centres of curvature. Compare (60) . Moreover, as the area of the curved surface would be greater than that of the plane surface, it is evident that the total amount of pressure which it would sustain under the same circumstances would be greater ; but it can be proved that the pressure available in moving the piston would be the same as before. For this purpose, it is only necessary to decompose the pressure exerted by each particle into two forces, one acting in a direction which is parallel to the axis of the cylinder, and the other at right angles to this direction. The forces acting parallel to the axis of the piston are obviously the only ones which are available in moving it ; and the sum of these forces will be found to be the same as the total pressure which would be exerted if the base of the cylinder were a plane. (122.) Hydrostatic Press. — This most beautiful application of the equality of pressure was conceived by Pascal ; but the difficulty of avoiding the escape of water from the joints of pistons prevented him from realizing his conception, and the press was first constructed by Bramah, in 1796, at London. It is perfectly evident that the principle of equality of pressures deduced in the last section is entirely independent of the form of the vessel, and we may therefore give to the vessel the form of Fig. 216, in which the area of the piston 6 c is twenty times as large as that of the piston a. Hence it follows, that, if we press in the pis- rig. 216. THE THREE STATES OP MATTER. 221 ton a with a force of five kilogrammes, the piston b will be forced out with twenty times as much force, or one hundred kilo- grammes ; and, on the other hand, if we press in the piston b c with a force of one hundred kilogrammes, the piston a will be forced out with a force of only five kilogrammes. It is evidently unimportant that the connection between the piston should be so direct as in Fig. 216. If it is efiected by a long and narrow tube, the principle will still hold true, provided only that the joints are tight and the material of the vessel unyielding. The hydrostatic press, which is used in the arts for producing great pressure, is only a modification of the apparatus represented by the diagram. Pig. 216. One of the most usual forms of this machine is represented in perspective by Fig. 217, and in section by Fig. 218. The same parts are lettered alike on the two figures. It consists of two cylindei-s, A and B, connected together by a tube, K. In the larger cylinder moves the large piston P, which is made in the form of a plunger, touching the walls of the cylinder only at the top, where it passes through a water-tight packing. On the top of this piston is a platform, which rises and falls with 19* 222 CHEMICAL PHYSICS. it, and the articles to be submitted to pressiire are.placed between this and a second platform, Q, which Is firmly fastened to the floor by means of four iron columns, which also serve to guide the motion of the lower platform. The small piston p is con- rig. 218. structed exactly like the larger, and is moved up and down in the cylinder by the pump-handle M. The small cylinder acts as a force-pump. It connects with a reservoir of water below by means of a tube terminating with a rose, a. This tube is guarded by a valve, c, which allows the water to flow up into the pump, but not in the reverse direction. It is evident from this de- scription, that, on working the handle M, water will be alternately sucked up from the reservoir and forced into the large cylinder B, through the pipe K, from which it is prevented from returning by a valve at o. The large piston will thus be forced up by a pres- sure which will be as much greater than that exerted on the small piston as the area of its section is greater. If, for example, it is a hundred times as large, it will be pressed up with a force one hundred times greater than that exerted on p. This force can be so much increased by the lever M, that a man can easily exert a downward pressure of 150 kilogrammes on p, and the piston P will then be pressed up with a force equal to 15,000 kilogrammes. It must be noticed, however, that the piston P will rise very slowly, and as much more slowly than the motion of p as the area of its section is greater. This is in accordance with a well-known principle of mechanics, which is true of all machines, that what is gained in force is lost in velocity (or extent of motion). In the present case, in order to raise the piston P one metre under a force THE THREE STATES OP MATTER. 223 of 15,000 kilogrammes, it is necessary to push down the piston p tlirough one hundred metres witli a force of 150 kilogrammes. This is accomplished by repeated motions of the handle M. The tube K is furnished with a safety-valve, i (Fig. 218), kept in place by a weight acting on it through a lever (Fig. 217). There is also a valve-cock at r, by which the water in the cylinder B may be vented into the reservoir H, in order to lower the pis- ton ; and, lastly, a third valve-cock, by which the communication between the cylinders may be closed when it is desirable to keep the articles under pressure for some time. The peculiar form of the packing at n is also deserving of notice. It is made of thick leather saturated with oil, in the form of an inverted U, and the more the water is compressed, the more firmly the leather is pressed against the sides of the cylinder and piston. The hydraulic press is applied in the arts for a great variety of purposes, such as packing dry goods in bales, pressing out printed sheets, extracting oil from grains, and testing steam-boilers. It was also used for raising the iron tubes of the Britannia Bridge over the Menai Strait. (123.) Pressure exerted by Liquids in Consequence of their Weight. — In the first place, let us consider what will be the pressure exerted by a liquid on the bottom of the containing vessel. Let arm, Fig. 219, be a conical vessel, which we will suppose filled with water to the point o. Let us suppose the liquid to be divided into a number of strata by the planes be, e d, ig, pm, which we may take as thin as we wish, and only consider in each stratum the cyhndrical mass , . Fig. 219. enclosed in dotted lines. It as now evi- dent that the pressure exerted by each cylindrical mass on its own base will be equal to its own weight. Then, from the prin- ciple of Pascal, the pressure exerted by the weight of the first mass will be transmitted to the whole section b c, so that this will have to support a pressure as much greater than the weight of the first mass as the area of this section is greater than the area of the base of the first cylinder. Hence it follows, that it will support a pressure equal to the weight of a column of water whose base equals b c, and whose height is that of the first cylinder. This pressure will then be added to the weight of the second cyUnder, 224 CHEMICAL PHYSICS. which, on the same principle, will be transmitted to the whole section e d ; and hence the resulting pressure exerted on the sec- tion e d is equal to the weight of a column of water whose base equals this section, and whose height eq\ials the sum of the heights of the first and second cylinders. The same course of reasoning may be extended to the sections i g, p n, and also to the base, r m. Hence the pressure on the base, r m, is equal to the weight of a column of water wliose base equals this base, and wjiose height equals the sum of the heights of all the cylin- ders, or VI. This demonstration is evidently independent of the number of strata, and must therefore hold when this number is infinite and the vessel conical. It is also evident that it is independent of the form of the vessel. It would hold if the vessel, remaining conical, were placed in an inverted position, or for a vessel of any shape whatsoever. We may therefore conclude, as the general result of this discussion, that the pressure exerted by a liquid on the horizontal base of the containing- vessel is equal to the weight of a column of this liquid whose base equals the base of the vessel, and whose height equals the depth of the liquid in the vessel. The fact, that the pressure exerted by a liquid on the bottom of the vessel containing it is independent of the form of the vessel, may be demonstrated experimentally by means of the apparatus represented in Fig. 220, which was invented by Haldat, and is known by his name. It consists of a bent glass tube, AB C, a.t one end of which, A, is a brass cap, to which may be screwed either of the glass vessels M and P. There is also a cock by which the liquid in the vessel may be drawn off. In order to make the ex- periment, we fill the bent tube with mercury, and then screw into its place the larger of the two vessels, which we fill with water. This presses up the mercury in the branch C, and we mark the level to which it rises by means of the ring a. We also mark the level of the water in the vessel by means of the index-rod c, which we push down until it just touches the surface. We then draw off the water, and, having replaced the vessel M by the smaller ves- sel P, we fill this with water to the same height as marked by the index, when we find that the mercury rises in the branch C to precisely the same level as before. As the effect produced by the pressure of the water in the two cases is the same, we have a right to conclude that the two pressures are equal. This pres- THE THREE STATES OP MATTER. 225 Fig. 220. sure, then, is independent of the form of the vessel or of the quantity of water ; and, since the base of tlie vessel is the same in both cases, (that is, the surface of the mercury in the tiibe A,} and tlie height of the liquid also the same, it is evident that the equality of pressure is a necessary result of the principle before proved. (124.) Upward Pressure. — If we consider any given section of liquid, as p n, Fig. 219, it is evident that the particles on this section are com- pressed by the weight of the liquid above them, and hence must be ex- erting pressure in every direction, and just as much upward pressure as downward pressure. If, then, we immerse in the liquid a cylindrical body, such as c d, Pig. 221, it is plain that the particles of water in contact with the base, d, of the cylinder, be- ing in a compressed condition, must exert an upward pressure on the base , , , rig. 221. of the cylinder equal to the pressure they exert on the section of liquid next below them. This 226 CHEMICAL PHYSICS. pressure, by the last section, is equal to the weight of a column of liquid having the same base as the cylinder, and having a height equal to the depth of the section below the surface of the liquid. (125.) Pressure on the Sides of a Vessel. — This same course of reasoning may also be extended to the pressure exerted by a liquid against the sides of the containing vessel. It is evident, for example, that the particles of the liquid in contact with the piston b, Fig. 221, are in a state of tension caiised by the pressure of the weight of liquid above them. They are therefore exerting pressure in all directions, and hence also against the surface of the piston in directions which are perpendicular to that sur- face. Now the pressure of any one particle is, by the principle of (123), equal to the weight of a column of similar particles whose height is equal to the depth of this particle be- low the surface. And since the total pressure against the piston is equal to the sum of the pressures of the sep- arate particles, it follows that the total pressure is equal to the loeight of a column of liquid, the area of whose base is equal to the area of the surface of the piston, and ivhose height is equal to the mean depth of the various particles below the surface. This mean depth, in the example under consideration, is evidently the depth of the centre of the piston, and hence e g- is a column of liquid whose weight is equal to the pressure. In the same way, the pressure against the piston a is equal to the column represented by h i. It is easy to extend this demonstration to any portion of the sides of a vessel, whether plane or curved. It can also easily be proved that the mean depth of the various particles of liquid in contact with any surface is in every case equal to the depth of the centre of gravity of these particles. Were the pressure exerted by each of the particles of water in contact with the piston (Fig. 221) the same, the centre of pres- sure (121) would, as in Fig. 215, coincide with the centre of Kg. 221. THE THREE STATES OF MATTER. 227 figure. This, however, is not the case ; the particles below the level of the centre of the piston, being at a greater depth, exert a greater pressure than those above this level. Hence the point of application of the parallel forces which they ex- ert, (being nearest to the greater forces [20],) must be below the centre of figure. In any similar case, the position of the centre of pressure is below the centre of gravity of the particles composing the section against which the pressure is exerted, and it can always be found by calculation when the form of the sur- face is known. (126.) Generalization. — The separate results at which we have arrived in the last three sections may be generalized as fol- lows : The pressure exerted by a liquid on any section whatso- ever is equal to the weight of a column of the liquid, the area of whose base is equal to the area of the section, and whose height is equal to the depth of the centre of gravity of the section below the surface of the liquid. (127.) The pressures exerted by two liquids on equal sections at equal depths are proportional to the specific gravities of these liquids. It follows, from the last section, that the two pressures are equal to the weights of equal columns — and hence of equal volumes — of the two liquids. But it follows from (69), that the weights of equal volumes of two liquids are to each other as their specific gravities, and hence the pressures exerted by them on equal sections at equal depths must be in the same pro- portion. If we represent by S the area of any section in square cen- timetres, by Ifthe depth of the centre of gravity in centimetres, we have, by geometry, for the volume of the column of liquid whose weight represents the pressure, V=H. S, in which V stands for a certain number of cubic centimetres. But we know by [56], that W= V. Sp. Gr., and hence, if we represent the pressure exerted on any section by if, we have f=W=H.S.iSp.Gr.') [78.] For any other section, having the same area and at the same depth, we have _ ^ ^„„ ^ ^ £':=H. S.(Sp.Gr.y; [79.] and, comparing, jT : iT' = (-^. Gr.) : (Sp. Gr.y. [80.] 228 CHEMICAL PHYSICS. (128.) Hydrostatic Paradox. — It is evident from (123), that tlie pressure of a liquid on tlie bottom of the containing vessel may be very much greater than the weight of liquid it contains. For example, the pressure of the liquid on the bottom of the vessel D C, Fig. 222, is the same as if its diameter were equal throughout to that of the lower part ; and from this it would seem to follow, that, if the vessel were placed in the pan of a balance, M N, it ought to produce the same effect as a cylindrical vessel of the same weight, containing the same height of water, and having through- Fig. 222. ^^^ ^jjg diameter of the part D. But it has been shown, that the liquid presses on the walls w o as well as on the bottom, and, since this pressure is in an upward direction, it will tend to make the vessel rise, while the pressure on the bot- tom tends to make it fall. The difference of these two pressures is all that is exerted on the pan of the balance, and this in every case is just equal to the weight of the vessel and that of the liquid which it contains. This fact is usually called the Hydrostatic Paradox. It is, however, evidently no paradox, but only a necessary consequence of the mechanical condition of liquid matter. Equilibrium of Liquids. (129.) In order that there should be a condition of equi- librium in a liquid mass, it is essential that each particle of the liquid should be pressed on all sides equally. This principle — the first statement of which is attributed to Archimedes — is a necessary consequence of the mobility of liquid particles. For, suppose that any one particle were not pressed on all sides equal- ly, it is evident that, being free to move, it must move in the direction of the greatest pressure, and there would not be an equilibrium (28). When a liquid mass under the influence of gravity is sup- ported in a vessel, it is essential, in order that each particle may be pressed on all sides equally (in other words, in order that there may be a condition of equilibrium), that two conditions should be fulfilled, which we will now consider. THE THREE STATES OP MATTER. 229 1. The surface of the liquid must be perpendicular at each point to the direction of gravity ; that is to say, it must be hori- zontal. To prove this, let us suppose that the surface of the^ liquid has any other form, as iu Fig. 223. It is then evident, that the force of gravity acting on any particle, m, and represented by the line mp (31), will be decomposed into two others (35). One of these, represented by m q, is nor- mal to the surface at the point m, and, being balanced by the resistance of the rig. 223. fluid particles, would not cause motion. The second compo- nent is tangent to the surface, and, not being balanced, tends to move the particles in the direction mf. Hence, under these circumstances, tliere could not be an equilibrium. If, however, the surface is horizontal, the tendency of the force of gravity is solely to sink the particles under the surface, and since all the particles at the surface are solicited equally by this force, the equilibrium is maintained. It follows from this, that the surface of still water is horizontal when its extent is so limited that we can regard the directions of the forces of gravity as all parallel (44). Such is not, however, the case with the surface of the ocean when at rest, or of a large sea. For since this surface must be perpendicular at every point to the plumb-line, and since all plumb-lines, if extended, pass ap- proximatively through the centre of the earth, it follows that the surface must be sensibly spherical (60). The principle just illustrated is only a particular case of a more extended principle, which may be thus stated : — When a liquid mass is in equilibrium, the resultant of all the forces acting" at any point of its surface is normal to the surface- at that point, 2. The pressure must be equal over the whole surface of any horizontal section. The necessity of this condition is easily shown. For suppose this not to be the case, then there must be somewhere on the same horizontal section — for example, p n, Fig. 219 — two adjacent particles which are not equally pressed by the superincumbent liquid. But two such particles must ex- ert, in consequence of their elasticity, an unequal pressure on each other, a condition which is evidently not consistent with a state of equilibrium. 20 230 CHEMICAL PHYSICS. At the surface of a liquid the pressure must be everywhere zero, and hence, in a state of equilibrium, the surface must be horizontal ; so that the first condition may be regarded as a special case of the last. This condition is also a particular case of a general principle, which may be thus stated : — Any liquid mass in equilibrium may be regarded as consisting of an infinite number of laminw, normal at each point of their surface to the resultant of all the forces tvhich act at this point, and sustaining at every point exactly the same pressure. It is a consequence of this principle, that any liquid mass, which is not acted upon by external forces, will take the form of a sphere in consequence of tlie mutual attraction of its own particles. In this case, the infinitely thin laminae are concentric spherical sur- faces, and the i-esultant of all the forces acting on any particle in every case passes through the centre of the sphere, and is nor- mal to the spherical surface on which the point is situated. By no other form than the sphere would the conditions of eqmlibrium be satisfied. Observation confirms this result of theory. Drops of water or mercury, so small as not to be sensibly deformed by their own weight, take a spherical form when placed on surfaces they do not wet. The rain-drop also is spherical, and in like manner the drops of melted lead become spherical while falling in the shot- towers. But the theory is still more beautifully illustrated by an experiment devised by Plateau. By mixing alcohol and water, a liquid can be obtained having the same density as oil. If, now, we add drops of oil to the liquid, these drops, as we shall soon see, are in the same condition as if they had no weight, and in conformity with the theory take a spherical form. By carefully introducing the oil, a sphere of considerable size can be formed, suspended in the alcoholic fluid. Plateau succeeded in giving to this liquid sphere a rotation by means of very simple machinery, and found that, by regulating the velocity, he could caiise it to become flattened at the poles, to throw off rings and satellites, and thus in various ways illustrate the nebular hypothesis of Laplace. (130.) A liquid when in equilibrium always maintains the same level in vessels communicating with each other. — This fa- miliar fact is illustrated by Fig. 224, which represents four ves- THE THREE STATES OP MATTER. 231 Fig. 224. sels, A, B, C, D, communicating tlirongli the tiibe mn, in all of which the liquid stands at the same level. That this must neces- sarily be the case, is easily shown. Consider any vertical section in the tube m n, separating the liquid in D from that in C, and let us denote the area of its surface by S. Now it is evident that this section can be in equilibrium only when the pressures on its two faces are equal. The pressure on the face towards D is, by [78], f=S.H.(^Sp. Gr.^, in which If is the depth of the centre of gravity of the section below the level of the liquid in D. The pressure on the face towards G is, in like manner, f = S . H' . (^Sp.Gr.'), in which H' equals the depth of the centre of gravity below the level of the liquid in G. Since these two pressures are equal when there is an equilibrium, it follows that H= H', which demonstrates the prin- ciple in question. , (131.) When two vessels communicating together are filled with different liquids, which will not mix or combine chemically with each other, the heights of the two liquid columns when in equi- librium are inversely proportional to the specific gravities of the liquids. This principle may be il- lustrated by means of the apparatus represented in Fig. 225. It consists of two tubes, m and w, connected together by a smaller tube below. The lower portion of both tubes is filled with mercury, and on the surface of the mercury in the tube n rests a column of water, A B. If now we conceive a horizontal line, B G, drawn across the apparatus from the surface of the mercury at B, it is evident, from the rig. 225. 232 CHEMICAL PHYSICS. last section, that the liquid below this line is in equilibrium ; and hence it follows, that the column of water B A is just bal- anced by the column of mercury D C. On measuring these two heights, it will be found that D C is thirteen and a half times smaller than A B ; and by referring to the table of specific grav- ities, it will be found that the specific gravity of mercury is thir- teen and a half times greater than that of water ; or, in other words, the heights are inversely proportional to the specific gravities. The truth of this principle can easily be proved. If we represent the surface of the mercury at B by S,^ and the height of the column of water B Ahy H, the specific gravity of water by Sp.Gr., then by [78] the pressure on the surface is f = S . H . {Sp.Gr.). In the same way, the pressure of the column of mercury, C D, is f = S' . H' . { Sp. Gr.y, where -S' is the area of the section at C, H' the height of the column C D, and {Sp.Gr.y the specific gravity of the mercury. Now, it fol- lows from (120), that there can be an equilibrium only when the pressures exerted on the two surfaces at B and C are proportional to the area of these surfaces, or when £ : f = S : S'. Substi- tuting the value of f and f, we find that when this is the case, H. (Sp.Gr.-) = H' . (Sp.Gr.y, or [81.J H: H>= (Sp.Gr.y : (Sp.Gr.). Hence, there can be an equilibrium only where the heights of the two columns are inversely as the specific gravities of the liquids. (182.) Spirit-Level. — We have seen that the surface of a liquid at rest is always horizontal, that is to say, perpendicular to the direction of gravity. We have, therefore, in this fact a ready means of determining the hor- izontal plane. The spir- it-level, which is used for this purpose, con- sists of a tube of glass (Fig. 226) very slightly curved, and filled with Fig 227. alcohol,* leaving only a B <^^ ":^— tc~:^^ D Fig. 226. 4fr-^= — \- I )/"""-^— \ HiVHiB^BHHMiilliaMIHll j^^^Wr__ j- * Alcohol does not freeze even at the lowest temperatures. THE THREE STATES OF MATTER. 233 small bulb of air, which always tends to occupy the highest part. The tube is hermetically sealed, and mounted on a brass or wooden stand, D C, Pig. 227, the base of which is carefully ad- justed, so that when it rests on a horizontal plane, P, the air- bubble, M, shall rest just at the middle of the tube. (133.) Artesian Wells. — The tendency of water to seek its own level is illustrated by all seas, lakes, springs, and rivers, which are so many vessels connecting with each other. One of the most remarkable of this class of illustrations is the Artesian well, named from the old province of Artois, in France, where these wells were first made. They are narrow tubes sunk in the earth to various depths, in which the water frequently rises many feet above the surface of the ground. The principle of the Artesian well is illustrated by Fig. 228. The crust of our globe is formed of numerous strata, some of which are permeable to water, like sand and gravel, while others, such as clay, are impermeable. Let us suppose, then, that in a geological basin we have an alternation of such strata, for example, two beds of clay-rock, A and B, enclosing a bed of some permeable material, M, as sand ; and let us also suppose that the sand bed comes to the surface at some higher level (Fig. 229), where it will receive the rain-water. This water will filter through the sand and collect under the geographical basin, without being able to rise to the surface, on account of the clay bed A. But if we sink a tube through this bed, it is evid«nt 20* Fig. 229. 234 CHEMICAL PHYSICS. that the water will rise to a height as much above the soil as is the level at which it stands in the peculiar reservoir formed by the clay beds. These wells are sunk with a peculiar form of auger, which is worked within an iron tube, the tube be- ing driven down as fast as the auger de- scends. One of the most remarkable of these wells is that of Grenelle, on the out- skirts of Paris. It is 548 metres deep, and yields 3,000 litres of water each min- ute. The water has a constant tempera- of 27° C. (134.) Salt Wells. — An illustration of the principles of section (131) is fur- nished by the mode in which salt wells are worked in some parts of Germany. It not unfrequcntly happens, that beds of rock-salt occur in the midst of impermeable strata (see Fig. 230). It can then be extracted '';■; Fig. 230. in the following way. An Artesian well (Pig. 231) is first sunk to about the mid- dle of the bed. Within this well is en- closed a smaller tube of copper, descend- ing to the bottom of the bed of salt, and therefore considerably lower than the iron tube forming the sides of the well. The lower end of the copper tube is closed, but it is perforated with little holes to. the height of a few metres, which allow the water, but not dirt, to enter. From some convenient source fresh water is made to flow into the well, and descends outside of the copper tube to the salt bed. It Fig. 231. THE THREE STATES OP MATTER. - 235 dissolves the salt, and the heavy brine sinks to the bottom of the bed, where it finds the lower end of the copper tube. Tliis tube then fills with salt water ; but the brine does not rise to the sur- face of the soil, but only to such a level that the column of brine in the interior copper tube shall be in equilibrium with that of water in the annular space outside. The specific gravity of sat- urated brine is about 1.20, that of water being 1 ; hence, if we represent tlie heights of the two columns by H and H', we shall have H: H' = 1.20 : 1. If, then, the depth of the well is 200 metres, the brine will rise i^ . 200 = 166, and consequently to a level 34 m. below the surface of the soil. Through this dis- tance it is raised by a pump. Buoyancy of Liquids, (135.) Principle of Archimedes. — All liquids buoy up solids immersed in them with a force equal to the weight of the liquid displaced. This very important fact was discovered by Archime- des, and is generally known under the name of tlie Principle of Archimedes. It is generally stated that the discovery was made by this renowned philosopher of antiquity while reflecting on the buoyancy of the water on his own body when he was batlaing ; and he is said to have been so much elated by the discovery, that he rushed from the bath through the streets of Syracuse, exclaiming, EvprjKa ! evprjKa ! Tlie principle of Archimedes may be illustrated by means of the apparatus represented in Fig. 232. The brass cylinder B is made so as to fit accurately the brass ciip A. In experi- menting witli the apparatus, the cylinder and cup, having been suspended to one pan of a balance arranged for the purpose, are carefully poised, by placing weights in the opposite pan ; the cylinder is then immersed in water, as represented in the figure. In consequence of the buoyancy of the liquid, the pan containing the weights will preponderate. According to the prin- ciple, this buoyancy is equal to the weight of the water which the cylinder has displaced. But from the construction of the apparatus, the cup A will hold exactly this amount of water ; and hence, if the principle is correct, the equilibrium will be re- stored on filling the cup A with water, — and this we find to be the case. The same result would also be obtained with alcohol, or with any other liquid. 236 CHEMICAL PHYSICS. Eig 232. It appears, then, that the cylinder is buoyed up by a force equal to the weight of the liquid which it displaces. But this statement expresses only one half of the truth ; for it is a necessary result of the equality of action and reaction, that the upward pressure of the water on the cylinder must be accompa- nied by an equivalent down- ward pressure of the cylin- der on the water ; or, in other words, not only that the cylinder loses in weight, but also that the water gains . the weight which the cyl- inder loses. In order to il- Fig. 233. lustrate this fact, we caa THE THREE STATES OP MATTER. 237 arrange the experiment as represented in Fig. 233. "We first balance the vessel of water, and then immerse in the liquid the brass cylinder, supported as represented in the figure. The ■water will be found to have gained in weight, and in order to restore the equilibrium it will be necessary to remove from the vessel sufficient water to just fill the cylinder A. (136.) Demonstration. — The principle of Archimedes is a necessary consequence of the law enunciated in (126), as can easily be proved. Let us, in the first place, suppose that the body im- mersed in the liquid is a right cyl- inder, as c d, Pig. 234, suspended so that its bases shall be horizontal. Consider now the pressure exerted by the liquid at any one point on the side of this cylinder. By (121) the direction of this pressure is normal to the surface at this point. But, as is well known, this normal, if pro- duced, will coincide with the diam- eter of tlie circular section of the cylinder which would be made by a horizontal plane cutting the cylin- der at the point in question. Now, as the other end of this diameter is in contact with the liquid, and at the same depth below its surface, it is evident that this point will sustain a pressure equal in amount and opposite in direction to that sustained by the first point. These two pressures will consequently balance each other, and, since the same holds true of every other similar point, it follows that the whole pressure of the liquid on the convex surface of the cylinder is in equilibrium. It is different, however, with the pressure on the two horizon- tal bases. The pressure exerted on the base d is, by (126), equal to the weight of the liquid cylinder represented by e g, and the pressure on the base c to the weight of the liquid cylinder h i. There is, therefore, an excess of upward pressure equal to the weight of the liquid cylinder fg, which is equal in size to the cylinder c d. The cylinder, then, is buoyed up with a force equal to the weight of liqiiid displaced. Fig. 231. 238 CHEMICAL PHYSICS. (137.) This demonstration may readily be extended to a body of any form whatsoever. Let s s' s" be the body, and ox,oy, o z three co-ordinate axes perpendicular with each other, to which we can refer position. The pressure exerted by a liquid on any infinitely small element of surface, s, is by [78] £ = s.H. {Sp.Gr.). This pressure, which by (121) is nor- mal to the surface, may be resolved into three forces, at right angles to each other and parallel to the co-or- dinate axes. Representing the nor- mal by p, and the angles which it makes with :c as P , y, ~i <^° xi y 2 » we have, for the three components, iF' = JT cos -^ , £" ^ J" cos -^ , and JF"' = £ cos ■? . Substituting for £ its value given above, the three components become Fig. 235. £' = H.(Sp.Gr.) .scos P . £" = H. (Sp.Gr.). s cos' £" H .(Sp.G.-) .s cos^. [82.J [83.J [84.] But s cos -^ is the projection of the surface s on the plane oiy z, and this projection is equal to the right section of an infinitely small cylinder parallel to the axis of x. Representing the area of this section by r", we have, for the value of the first compo- nent, £' =z H . (^ Sp. Gr.) r". But this pressiire will obviously be balanced by the pressure exerted on the element of surface, s", which, decomposed in the same way, will give a component also equal to H . (^Sp. Gr.) r", and parallel to the axis of x, but act- ing in the opposite direction. It can easily be shown that the same is true of the component parallel to the axis of z. This will be balanced by an opposite and equal component of the pressure exerted on the element s'". Let us, lastly, consider what will be the effect of the component parallel to the axis of ij. In the value of £" [83] , the quantity of s cos ^ is the projection of the surface s on the plane of x y. This pro- jection is equal to the right section of the vertical cylinder s s'. THE THREE STATES OF MATTER. 239 Representing the area of this section by r', we have, for the value of the vertical component, £" = H {Sp.Gr.') r', a force which tends to raise the body. This force is in part balanced by the pressure exerted on the element s'. By decomposing this force, it will be found that the vertical component which exerts a down- ward pressure in the direction 5' s, is equal to £i^H'( Sp. Gr.) r'. The vertical cylinder of the body s s' is then buoyed up by a force eqvial to the difference of these two values, that is, f" — fi = (H—H''){Sp:Gr.}r', which is the weight of a column of liquid of the same volume as the cylinder. By extending the same coiirse of reasoning to each of the in- finitely small elements of surface which the body presents, we should decompose the body into an infinite number of vertical cylinders similar to s s', each of which is buoyed up by a force equal to the weight of its own volume of liquid. The whole body is of course buoyed up by a force equal to the sum of the forces acting on the elementary cylinders, that is, by a force equal to the weight of the liquid which it displaces. (138.) The correctness of the principle of Archimedes can be proved in another way, which more directly connects it with the condition of equilibrium which exists among the particles of all liquids when at rest. Consider, for example, any cubic centimetre of the liquid contained in the vessel, Fig. 236, such as A B. Since the liquid is at rest, it is evident that this liquid cube is ex- actly sustained in its position by the pres- sure of the surrounding particles. But the mass of liquid, of which it consists, has weight ; and it is therefore also evident, that the liquid cube is sustained because it is buoyed up by a force which is just equal to its weight. Let us now suppose the liquid cube to be suddenly solidified without changing its volume ; it is evident that it will be buoyed up by the same force as be- fore ; for no change has taken place either in the position or the conditions of the surrounding particles. Whatever, therefore, may be the substance or weight of the solid cube, it will be buoyed up by a force equal to the weight of one cubic centimetre of the liquid in which it is immersed. This demonstration can evident- ly be extended to any other body, of whatsoever size or shape. Fig. 236. 240 CHEMICAL PHYSICS. Fig. 236. (139.) Centre of Pressure. — It lias been proved (45), that the resultant of all the forces which gravity exerts on the parti- cles of a body is a single force — represented by the weight of the body — directed vertically downwards. And it has further been proved (46), that this force may always be regarded as ap- plied at the centre of gravity, whatever position the body may assume. Now, since the supposed liquid cube (Fig. 236) is exactly supported, it fol- lows that the resultant of all the pressures which it receives from the surrounding par- ticles of liquid must also be a single force equal to the weight of the cube, but di- rected vertically upwards. Moreover, if our ideal cube could be turned in the liquid, it would evidently still remain in equilibrium, in whatever position it might be placed. Since in all possible positions the resultant of the forces of gravity may be regarded as applied at the centre of gravity, it follows that in the different positions the resultant of all the pressures may also be regarded as applied at the same point. The same point, then, which is common to all the resultants of the forces of gravity in the different positions which a body may assume, is common, also, to all the resultants of pressure ; in other words, the centre of gravity of our liquid cube is also the centre of pressiire. If, now, we replace the ideal cube of liquid with a cube of brass having the same size and volume, it is evident that the conditions of the particles exerting the pressure have not been changed. Hence the resultant of the pressures exerted by these particles will still be a force acting vertically upwards ; and, further, in any position which the brass cube may assume, the direction of this resultant will pass through what would be the centre of grav- ity of a liquid cube of the same form and volume. This com- mon point, through which the resultant of the pressure passes, in any position of the brass cube, is its centre of pressure. We have made use of a brass cube in this discussion, merely to give distinctness to our conceptions ; but it is evident that the same reasoning would apply to a body of any shape whatsoever. In any case, the centre of pressure is always the same point which THE THREE STATES OP MATTER. 241 was previously the centre of gravity of the liquid which has been displaced by the body. If the body is homogeneous and entirely immersed in water, tlie centre of pressure coincides with the centre of gravity of the body. If, however, tlae body is not homogeneous, — if, for ex- ample, it is loaded on one side, — then the centre of gravity will no longer coincide with the centre of pressure ; because it will not coincide with the centre of gravity of a liquid body of the same shape and volume. (140.) Floating Bodies. — If the weight of a body is less than that of the liquid which it displaces, then, the buoyancy be- ing greater than the weight, the body will rise to the surface of the liquid, and float. On the other hand, if the weight of a body is greater than that of the liquid which it displaces, it will sink. Moreover, since the specific gravities of any two substances are to each other as the weights of equal volumes of these substances, it is also true that a homogeneous solid will float when its spe- cific gravity is less than that of the liquid, and that it will sink when these conditions are reversed. An iron bar sinks in water, but floats in mercury, because a given volume of iron weighs less than the same volume of mer- cury, and more than the same volume of water. For a similar reason, a piece of boxwood will float in water, but sink in alco- hol. The bar of iron, however, can be made into a hollow vessel, which will float on water ; and, in the same manner, boxwood can be made to float on alcohol. The volumes of the bodies will thus be increased without increasing the weight, and since the weight of the liquid they displace is now greater than their own weight, they will float. Steamships are frequently made of iron, and loaded with heavy machinery ; but nevertheless, since their whole weight is less than that of the water which they displace, they float. The specific gravity of the human body is very nearly the same as that of water, and can readily, therefore, by a little effort, be kept at the surface in the act of swimming. By in- creasing slightly the volume of water displaced, without increas- ing sensibly its weight, the body will float without effort. Most persons can expand the chest, by a little effort, sufficiently to make the specific gravity of the body less than that of water, and it is well known that good swimmers can float their bodies by lying back on the surface of the water and expanding the chest. This is 21 242 CHEMICAL PHYSICS. also the theory of life-preservers, which are bags filled with air, or pieces of cork worn under the arms. They so far increase the volume of the body as to make the specific gravity of the life- preserver and the body together, as a whole, less than that of water. The large floating tanks, called camels, which are used to lift large vessels over the sand-bars that obstruct the mouths of many harbors, are an ingenious application of the same principle. These tanks, which are closed on all sides and water-tight, having been filled with water, are fastened under the sides of the vessel. The water is then pumped out, when the tanks rise, and raise the ves- sel with them. A similar contrivance, called a floating dock, is very much used in the United States for raising ships completely out of water, for repairs. It consists of a large platform, on which the ship is to rest, beneath which are hollow and water- tight tanks, so loaded that, when full of water, they will sink. The platform is, in the first place, sunk to the depth of several fathoms, and the ship to be raised is then floated over it. The water is now pumped out of the tanks beneath the platform, which then rises, and raises the vessel with it. (141.) Equilibrium of Floating Bodies. — When a body is at rest, floating on the surface of a liquid, there must be an equi- librium between the weight of the body and the buoyancy of the liquid. Hence it follows, from (135), that the weight of the liquid actually displaced by a floating body is equal to its own weight. We can always determine the weight of a ship by measuring the volume which is below the water-level, and mul- tiplying this by the specific gravity of the liquid. This will, by [56], give the weight of water displaced, which, as we have just seen, is the same as the weight of the ship. We can also deter- mine the weight of the cargo by determining the volume of water displaced by the ship both before and after loading. The differ- ence between these two volumes, multiplied by the specific gravity of the liquid, will give the weight of the cargo. The centre of pressure of a floating body is, by (139), the same point as the centre of gravity of the fluid it displaces. It is obviously, therefore, an entirely different point from the centre of gravity of the body, and must always be below this point when the body is a homogeneous solid. For example, in Pig. 237, the centre of gravity of the homogeneous floating body a b c d is THE THREE STATES OP MATTER. 243 Fig. 237. {he point G. The centre of pressure, P, is the centre of gravity of the liquid displaced, and this is obviously below the centre of gravity of the whole body. When the floating body is not homoge- neous, the centre of gravity may be below the centre of pressure. For example, if we should attach to the bottom of the body abed a piece of lead, this would sink the body still deeper in the water, and thus raise the centre of pres- sure, while at the same time it would lower the centre of gravity, and thus might change the relative position of the two points. In order that a floating body should be in equilibrium, it is not only necessary that it should displace its own weight of liquid, but it is also essential that the centres of gravity and pressure should be situated on the same vertical. If, as in Fig. 238, the two points are not situated on the same vertical, then the resultants of the forces of gravity and pres- sure will be represented by two opposite vertical forces, as P ^ and O r. Since these forces are equal, they will neither tend to raise nor depress the body in the liquid ; but nevertheless, as the two forces form a coiiple (38), they will tend to rotate the body. Hence, although the body will neither rise nor fall, it will turn in the liquid until the centre of pressure falls in the same vertical with the centre of gravity, but in such a way that the amount of water displaced by the body shall be always the same. (142.) Stable and Unstable Equilibrium. — "When the cen- tres of pressure and gravity are in the same vertical, there will be a condition of equilibrium, but this equilibrium may be either stable, unstable, or neutral. The equilibrium is said to be stable when, on turning the floating body slightly in the water, it tends to return to its first position ; it is said to be unstable, when, under these circumstances, it continues to turn until it passes Fig. 238. 244 CHEMICAL PHYSICS. into a new condition of equilibrium ; and it is said to be neutral, when it will remain at rest in any position indifferently. The condition of a floating body is always stable when the centre of gravity is below the centre of pressure. The truth of this statement is an immediate consequence of the princi- ples of the last section. The centre of pressure is a point at which the whole upward pressure of the liquid may be re- garded as concentrated. It may therefore be considered as the point of support of the floating body ; and it has already been shown (48), that the condition of a body is stable when the centre of gravity is below the point of support. It does not fol- low, however, that the condition is necessarily unstable when the centre of gravity is above the point of support. In this case, the stability of the body depends upon the position of a variable point, which is called the metacentre ; and the equilibrium is still stable, when the centre of gravity is below this point. The position of the metacentre depends on the form and position of the body. We shall only be able to point out its position in the case of one of the simplest solids ; but this example will serve to illustrate the general principle. Let us suppose, then, that the floating body is a homogeneous rectangular prism (Fig. 239). The centre of gravity will then tr' -■—■- z.y--- Fig 239. Fig. 240. be the same as the centre of its figure, or G, and the centre of pressure the centre of gravity of the part immersed in the liquid, a variable point, depending on the position of the body. If, now, when it is floating on its broadest side, we turn it through the angle e o c (Fig. 240), the portion represented by the triangle e o c is raised out of the liquid, and that represented by b' of sub- merged ; and since the quantity of water displaced must be the THE THREE STATES OF MATTER. 24S same in every position of the body, it follows that the portion eoc is equal to the portion b' of. But now the form of the submerged portion is entirely changed, and the centre of gravity of the sub- merged portion, which is the centre of pressure, is also changed, and moved to the point P. If in this position we draw through the point P a perpendicular, it will intersect the perpendicular drawn through the point P in the previous position, namely, O q, at a point q, and this point is the metacentre. In the case before us, the metacentre is above the centre of gravity ; and it is evi- dent from the figures, that the couple formed by the resultants of the forces of gravity and of the pressure tends to restore the floating body to its first position (Pig. 239). Let us now suppose that the rectangular prism is floating on its narrow side, as in Fig. 241 ; and that, as before, we turn it to Kg. 241. Fig. 212. the right through a small angle. The centre of pressure will then be shifted to a new position, at the right of the plane of symmetry (Fig. 242). If, now, we erect a perpendicular, it will intersect the perpendicular drawn through the centre of pressxire in the previous position, at a point q, below the centre of gravity ; and it can easily be seen that the couple formed by the force of gravity and the pressure will tend to turn the body still fur- ther, and it will only come to rest when it falls back into the position of stable equilibrium, floating on its broad side, as in Fig. 239. What has now been illustrated in the case of a rectangular prism, is true of all floating bodies. In general, the metacentre may be defined as the point where the vertical passimg through the centre of pressure in the position of equilibrium, meets the vertical drawn through the new centre of pressure after the body 21* 246 CHEMICAL PHYSICS. has been slightly displaced from this position. A floating body is in a stable condition when the metacentre is above the centre of gravity, and unstable when this condition of things is reversed. When the centre of gravity is below the centre of pressure, the metacentre must evidently always be above the centre of gravity, and, as before shown, this condition is always stable. It is also evident, from the above discussion, that the stability of a floating body is the greater the broader the submerged part and the lower the position of the centre of gravity. It is of great importance to pay attention to the conditions of stable equilibrium in the construction and loading of ships. Vessels which are used to transport passengers or light cargoes require to be ballasted, by depositing immediately above the keel a quantity of heavy matter, such as stones or pigs of iron. The centre of gravity may thus be brought so low, as to give the vessel such stability that no lateral force of the wind acting on its sails can capsize it. So, also, the heaviest part of a cargo should always be deposited in the lowest possible position, in or- der that its centre of gravity may be immediately over the keel. When this is the case, any inclination of the vessel causes the centre of gravity to rise ; and to accomplish this requires a force proportional to the weight of the vessel, and to the height through which the centre is elevated. The equilibrium of a boat may be rendered unstable by the passengers standing up in it ; and this is not unfrequently the cause of accidents to light sail-boats. If the centre of gravity of a vessel be not directly over the keel, the vessel will incline to that side at which it is placed ; and if this displacement is considerable, danger may ensue. The rolling of a vessel in a storm may so derange the ballast or cargo, as to throw the vessel on her beam-ends. (143.) Neutral Equilibrium. — In some cases, the position of the centre of pressure is not changed by any change of position of the body which is compatible with displacing its own weight of fliiid. In such a case, the body will float in equilibrium in any position indiflerently, and is said to be in a condition of neu- tral equilibrium. A sphere of uniform density is an example of this ; for in whatever position it floats, the part immersed is always a segment of the sphere of precisely the same magnitude and shape, so that the centre of pressure has always the same posi- THE THREE STATES OP MATTER. 247 tion with reference to the centre of gravity of the sphere. Con- sequently, the sphere will float indifferently in any position in which it may be placed. Methods of determining Specific Gravity. (144.) The specific gravity of a substance has been defined as the ratio of its weight to that of an equal volume of pure wa^er at 4° C, — the temperature at which the volume of the solid is measured being 0° C. As most of the methods iised for determining specific gravity are illustrations of the principles of hydrostatics, we will briefly describe them in this connection, reserving, however, for the chapter on Weighing and Measuring, the practical details of the subject. (145.) First Method. Specific- Gravity Bottle. — The most obvious method of determining the specific gravity of a substance is to weigh equal volumes of the substance and of water, and then divide the first weight by the last. When the substance is a liquid, this method is readily applied. We use for the purpose a small glass bottle, such as is represented in Fig. 243. The bottle is closed by a perforated ground-glass stopper of peculiar construction, terminating in a fine tube, ^ on which is marked, with a file, a point to which | the bottle is to be filled at each experiment. The w^ bottle, whose tare has been previously ascertained, | is first of all filled with pure water, and the stopper i^ inserted, when the water rises in the glass tube. Ifi The excess of water above the mark is now removed /S^^^^ with a piece of bibulous paper, and the bottle care- i == '^jjj fully weighed. By substracting from this weight \^^/ the tare of the bottle, we have the weight of a given rig. 243. volume of water, which is thiis ascertained once for all. If, then, we wish to obtain the specific gravity of any other liquid, we fill the bottle with this liquid in the same way as be- fore, and weigh it ; then, having subtracted the weight of the bottle, we have the weight of a volume of this liquid equal to the volume of the water. Kepresenting these two weights by W'&udi TT, we have, by definition, iSp.Gr.-) = ^,. [85.] 248 CHEMICAL PHYSICS. If we repeat this process at different temperatures, we obtain different results, owing to the expansion both of the liquids and of the glass. It is, therefore, essential to observe carefully the tem- perature of the liquids at the time of filling the bottle, and then to calculate, by means of tables prepared for the purpose, what would have been the result had the temperature of the water been at 4° C. and that of the substance at 0° C. This is called reducing- the results to the standard temperature, and the method of making the reduction will be described in the chapter just re- ferred to. The specific-gravity bottle may also be applied to determin- ing the specific gravity of solids, when they can be broken into small pieces. For this purpose, we take a specific-gravity bottle and determine the weight of the bottle when filled with water, as before described. Call this weight W^. We then in- troduce into the bottle a known weight of the solid, W, and fill up the remainder of the bottle with water. The weight of the bottle, solid and water, which we then ascertain, we will repre- sent by Wi. It is then evident that the weight of water dis- placed by the solid is W' := Wi -{- W — W^, and hence we have (Sp.Gh:') = W W, + W— Wi [86.] rig. 241. Here, as before, it is necessary to reduce the results obtained to the standard tem- perature. (146.) Second Method. The Hydro- static Balance. — We suspend the body by a fine thread to the pan of a balance (Fig. 244), and, having equipoised it by means of a tare in the other pan, immerse it in water, as represented in the figure. The weight which it loses, being exactly equal to that of the water which it dis- places, is the weight of a volume of water equal to that of the body which we wish to find. Hence, in order to de- termine this weight, we have only to add weights to the pan from which the body is suspended, until the equilibrium is es- THE THREE STATES OP MATTER, 249 tablished. It is evidently essential to the accuracy of this meth- od, that the water used should be pure, and the thread so fine that we can, without sensible error, neglect the weight of water which it itself displaces. Representing by W the weight of the body, and by W the weight required to restore the equilibrium, we have, by defini- tion, ^Sp.Gr.) = ^,. [87.] The value thus obtained must be reduced to the standard tem- perature. This method may also be applied to liquids as well as to solids. For this purpose we prepare a closed glass tube, and enclose in it sufficient mercury to sink the tube beneath any liquid, with the exception of the two heaviest, mer- cury and bromine. To this tube we attach a fine platinum wire, as in Pig. 245, which represents the apparatus of its full size. We commence by deter- mining once for all, by the method just described, the weight of the volume of water at 4° C. which the glass tube displaces. This we may call C, as it is a con- stant quantity for each apparatus. In order, now, to determine the specific gravity of a liquid, we suspend the tube to the pan of a balance, and, having equi- poised it by placing a weight, prepared for the pur- pose, in the other pan, immerse it in the liquid. The amount of weight required to restore the equilibrium is the weight of the volume of this liquid which the tube displaces, and the weight of the same volume of water at 4° C. is known to be C. Hence the specific W" Jiff, 245, gravity of the liquid is -p . This value must be cor- rected for the temperature at which the experiment is made. (147.) Third Method. Hydrometers. — In this method, the balance is not used, but its place is supplied by floating bodies of peculiar construction, called hydrometers. A few of these we will now describe. They may, for convenience, be divided into two classes, — Hydrometers with a Constant Volume, and Hy- drometers with a Constant Weight. 250 CHEMICAL PHYSICS. HYDROMETERS WITff A CONSTANT VOLTIME. 1. Nicholson's Hydrometer. — This instrument is represent- ed in Fig. 246. It consists of a hollow, cylindrical vessel, B, made usually of sheet brass or tinned iron. To the lover end of this vessel is fastened a cone filled with lead, C, the base of which forms a pan on which the body whose specific gravity is to be determined is placed. The object of the lead is to load the apparatus so that the centre of gravity may be below the centre of pressure, which, as we have seen (142), is a condition of stable equilibrium. To the top of the vessel is fastened a wire, which supports the pan A, and on this wire is marked a fixed point, o. In using this apparatus, we commence by determining the weight which, placed in the pan A, will sink the hydrometer to the fixed point o. This is a constant quantity for the same apparatus, and may be represented by C. Let us suppose that in any given case it is 125 grammes, and that it is required to determine the spe- cific gravity of sulphur. We take a piece of sulphur, weighing less than 125 grammes, and place it on the pan A, and then add weights until the hydrometer sinks again to the fixed point o. If it requires 55 grammes to sink it to the fixed point, it is evident that the weight of the sul- phur is 125 — 55 ^ 70 grammes. Having determined the weight of the sulphur in the air, it only remains to determine the weight of an equal volume of water. For this purpose, we raise the hydrometer, and, without disturbing the weights, shift the piece of sulphur to the pan C, and replace the instrument in the water. It will not, of course, sink to the fixed point ; be- cause the piece of sulphur, which is now submerged, is buoyed up by a force equal to the weight of its volume of water. If, now, we add weights to the pan A, until the hydrometer again sinks to the point o, we shall find that 34.4 grammes are re- quired. This is then the weight of its volume of water, and the specific gravity is ^^ == 2.03. Eepresenting the successive Fig. 246. THE THREE STATES OF MATTER, 251 weights described above by C, W, and W', we have in every case (^Sp. Gr.~) = — = — . If the instrument is to be used for sub- stances lighter than -water, a perforated cover is adapted to the pan (7, to prevent them from rising to the surface of the liquid. 2. FahrenheW s Hydrometer. — This instrument (Fig. 247) is used for determining the specific gravity of liquid, and differs from the one just described only in being made of glass, and in having no lower pan. In using this instrument, we commence by weighing it in a balance. Let us call its weight G. Then, having placed it in water, we determine the amount of weight required to sink it to a fixed point, marlced on the stem, which we will rep- resent by c. The siim of these constant weights, or C -\- c, is, by (141), equal to the weight of the water displaced. We then float the hy- drometer in the liquid whose specific gravity we wish to find, and determine the weight re- quired to sink it in this liquid to the fixed point. Call this weight W. Then C-\-W is equal to the weight of the liquid displaced, and since C -\- c and C -\-W are the weights of the same volumes of water and the liquid, the specific gravity of the liquid is easily found; since rig. 247. (-S/j.GV.) ~ G-\-c • [88.J HYDROMETERS WITH A CONSTANT WEIGHT. In the two hydrometers just described, the volume of the instrument, which is submerged, remains constant during the experiment, and the specific gravity is determined from the amount of weight required to keep the volume constant under different circumstances. The hydrometers in most general use are constructed on a different principle. In these the weight is constant, and the specific gravity of a liquid is determined by measuring the volume of this liquid which the instrument dis- places when floating in it. The weight of this volume is, by (141), the same as the weight of the instrument. If, then, we represent by V the volume of water which the instrument dis- places when floating in this liquid, and by V the volume of any 252 CHEMICAL PHYSICS. A other liquid -whicli it displaces, it is evident that the volumes V and V of the two liquids have the same weight, namely, that of the hydrometer. But it follows from [56] , that when the weights of different volumes of two liquids are equal, V . (^Sp.Gr.^ = V' . (Sjo. Gr.}'. When one of the liquids is water, ((Sp. Gr.y = l, and we obtain, for the specific gravity of the other liquid, (:Sp.Gr.) = ^-. [89.] From this it appears, that, when we know the volumes of equal weights of water and any given liquid, we can find the specific gravity of the liquid by dividing the volume of the water by the volume of the liquid. 3. Gay-Lussac's Volumeter. — This is the best instrument of its class. In its simplest form (Fig. 248), it consists of a glass tube closed at both ends, which is graduated into parts of equal capacity. The size of the parts is unimportant, it being only neces- sary that they should all be equal. The di- visions are numbered from 1 to 100, or to 150, as the case may require, commencing at the lower end of the tube. Before the tube is finally closed, it is loaded with mercury, so that, when floating on water, it will sink to the 100 til division on the scale ; or, in other words, so that it will displace 100 measures of water. If, now, we float it on sulphuric acid, it will only sink to the 54th division. Hence 100 measures of water and 54 measures of sulphuric acid have the same weight, and the specific gravity of sulphuric acid is, there- fore, -Vt" = 1.85. If we float the hydrome- ter on alcohol, it will sink to the 125th divis- ion. Hence the specific gravity of alcohol is Igf = 0.80. Since a definite specific grav- ity corresponds to each of the divisions of the scale, if is usual to calculate these, and inscribe them on the scale in place of the simple nimibers denoting the vohime. The instrument, when so prepared, is generally called a densimeter. As there are no liquids which have a less specific gravity than 0.60, and only two (mercury and bromine) which have a greater specific I Fig 248 Fig. 249 THE THREE STATES OP MATTER. 253 gravity than 2, it is evident that the divisions on the scale need only extend from 50 to 166. It is not usual, however, to have the whole scale on a single instrument, and, as a general rule, the scale is divided over three separate hydrometers. The first one, for liquids lighter than water, is graduated from 100 (cor- responding to the specific gravity 1.00), near the middle of the tube, to 166 (corresponding to 0.60), at the top of the tube ; the second, for saline solutions, is graduated from 100 (corresponding to 1.00), at the top of the tube, to 75 (corresponding to 1.33), near the middle ; finally, the third instrument is graduated from 75 (corresponding to 1.33), at the top of the tube, to 50 (cor- responding to 2.00), near the middle of the tube. In graduating each instrument, it is so loaded that it shall sink in water to the 100th division of the centesimal scale, and in all cases the spe- cific gravities are subsequently calculated, and inscribed on the scale against each division. It is more usual to give to the hydrometer the form rep- resented in Pig. 249. This shortens the instrument very great- ly, since the volume of the long tube in Fig. 248 is here re- placed by a short bulb. The principle of the two forms of the instrument is precisely the same, but it is more difficult to grad- uate the second pattern. The easiest method is the following. If the instrument is to be used for liquids heavier than water, we first load it with mercury until it sinks to a point A, near the top of the tube, which we mark 100. We next float it in a liquid of known specific gravity, for example, 1.333, and it will sink to a point B. Now, by [85], 1.333 = J^, and a; = 75. This division is, therefore, the 75th, and we divide the space between the two into 25 equal parts, and continue the divisions of the same size to the base of the stem. Bach of these divisions will then be j^;y of the whole volume of the apparatus below the 100th division first marked at A. If the instrument is to be used for liquids heavier than water, we adjust it so that the 100th division shall be at the base of the stem, and then, by floating the instrument in alcohol of known specific gravity, determine a higher point, and then divide the stem as before. 4. Baume's Hydrometer. — This hydrometer belongs to the same class with that of Gay-Lussac, but it is graduated in a man- ner which is entirely arbitrary, and does not indicate the specific gravity of the liquid. There are two methods used in graduat- 22 254 CHEMICAL PHYSICS. ing it, according as it is to be used for liquids heavier or lighter than water. In the first case, it is loaded so that it will sink in water to a point A, near the top of the stem, which we mark 0°. A second point is now obtained by floating the instrument in a solution of fifteen parts of common salt in eighty-fiye parts of water. This solution having a greater specific gravity than pure water, the instrument rises until the level of the liquid stands at a point B, which we mark 15°. Lastly, we divide the distance between A and B into fifteen equal parts, and continue the divis- ions to the bottom of the stem of the same size as one of these parts. It is essential that the diameter of the stem should be the same throughout. This instrument is called Pese-Sels. To prepare a hydrometer for liquids lighter than water, Baume floated the hydrometer in a solution of ninety parts of water and ten parts of common salt, and marked the point to which it sank as 0°. He next floated the instrument in water, and marked this point 10°. The interval between these points he divided into ten equal parts, and continued the divisions of the same size to the top of the tube. This instrument is called Pese- Liqueurs. Althoiigh the graduation of Baume is entirely arbitrary, yet this hydrometer is in more general use than any other. It is principally used for determining when a sohition or an acid has reached the proper degree of con- centration. For example, it has been found by experiment, that in a well-manufactured syrup the pese-sels of Baume stands at 35° when the liquid is cold, and also that in the strongest sul- phuric acid it stands at 66° ; so that the instrument enables the manufacturer to tell when his syrup or acid has reached the proper strength. The instrument, therefore, serves as a useful indicator in the arts, but it has no scientific value. Correspond- ing to each degree of the Baume scale is a definite specific grav- ity, which can be found by referring to appropriate tables, as can also those corresponding to the degrees of the scales of Car- tier and Beck, which, like that of Baume, are purely arbitrary. 5. Gay-Lussac's Alcoometer. — This is a kind of hydrometer, which is used for measuring the strength of alcoholic liquids. rig. 260. THE THEEE STATES OF MATTER. 255 The form of the instrument is precisely the same as that of Baume ; but the graduation, which is made at 15°, is different. The scale on the stem is divided into one hundred degrees, each of which represents one per cent of pure alcohol in volume. The hydrometer sinks to 0° in pure water, and to 100° in pure alcohol. If in any given alcoholic liq\iid it sinks to 15°, the liquid contains 15 per cent by volume of pure alcohol. The in- strument is graduated by floating it in liquids of known strength, and marking the points on the stem to which it sinks. It is only accurate at the temperature of 15°. If the temperature is dif- ferent from this, the indications of the instrument must be cor- rected by means of tables, which have been prepared for the purpose. There are a great variety of other hydrometers, which are graduated so as to give the strength of milk, beer, vinegar, and other liquids. They are all similar in principle to the alco- ometer, and do not require description. 6. Rousseau's Hydrometer. — All the hydrometers which have been described require a sufficient amount of liquid to fill a glass of some size ; but there are many cases in which it is desirable to ascertain promptly the specific gravity of a liquid, when only a few grammes of it can be obtained. The form of hydrometer represented in Fig. 251 has been contrived by Rousseau for this purpose. The general form of the instrument is similar to the others which have been described ; but it differs in having on the top of the stem a small cup. A, which holds the liquids to be experimented upon. On the side of this cup is a mark which indicates a capacity of one cubic centimetre. In order to graduate the instrument, it is floated in pure water at 4°, and loaded with mercury until it sinks to a point, B, marked at the base of the stem, which is the zero of the scale. The cup A is next filled up to the mark with distilled water at 4°, or, what amounts to the same thing, a weight of one gramme is placed in the cup. The instru- ment is so constructed that it will then sink to a point near the middle of the stem, which is marked 20°. The interval be- JPig. 251. 256 CHEMICAL PHYSICS. tween these- divisions is now divided into twenty equal parts, and the divisions are continued to the top of the stem. Since this has exactly the same size throughout, each division corresponds to one twentieth of a gramme, or 0.05 gram. According to this graduation, if we wish to obtain the density of any liquid, — bile, for example, — we fill the cup with the liquid to the point marked on the side. The instrument will now sink, perhaps, to the 20.5 division on the stem. The weight of one cubic centimetre of bile is, then, 0.05 X 20.5 = 1.025 gram. Since the weight of the same volume of water at 4° is one gramme, the specific gravity of bile is 1.025 -r- 1 = 1.025. In general, then, the specific gravity of a liquid is found with this instrument by multiplying 0.05 by the number of the division to which it sinks in water, when loaded with one cubic centimetre of the liquid. The indications of all hy- drometers are very much influenced by capillary at- traction, and the more so the more delicately they are constructed. They are not, therefore, instruments of precision ; but they are use- ful, since they give rapidly approximate results. (148.) Fourth Method. — A fourth method of find- ing the specific gravity of a liquid, which may be ad- vantageously used under certain circumstances, is il- lustrated by Fig. 252. It depends on the principle of the equilibrium of liquids in connected vessels (131). Fig. 262. The apparatus consists of THE THREE STATES OP MATTER. 257 two tubes connected above with each other and with the chambei* of an air-syringe. The lower ends of these tubes dip, the one into a glass of water, and the other into a glass containing the liquid whose specific gravity is required. On partially exhausting the air from the top of the tubes by means of the syringe, the liquids will rise in the two tubes. If, now, we close the stopcock con- necting with the syringe, the liquids will stand permanently at a certain height in either tube. Moreover, it is evident, from the construction of the apparatus, that the two columns of liquid are in equilibrium with each other. Using, then, the notation of (131), we have, from [81], H : H' = 1 : (Sp. Gr.), or (Sp. Gr.-) = ~ ; [90.] that is, the specific gravity of the liquid is found by dividing the height of the column of water by that of the liquid. The heights of the columns may be measured either by means of a scale on the tube, or by a cathetometer (see Pig. 196). If the liquid were alcohol, for example, and the height of the water column meas- ured 60 cm., the height of the alcohol column would be found to measure 75 cm. Hence, the specific gravity of alcohol is f% = 0.80. PROBLEMS. Buoyancy of Liquids. 106. A man, exerting all his force, can raise a weight of 50 kilog. What would be the weight of a stone (i^. Gr. = 2.5) which he could just raise under water ? 107. How much force in kilogrammes would he required to raise under water a mass of asphaltum (Sp.Gr. = 1.10) weighing 500 kilogrammes? 108. How many kilogrammes wiU 100 kilogrammes of cast-iron (Sp. Gr. = 7.25) weigh under water ? 109. How much wiU the same amount of iron weigh under alcohol {Sp. Gr. = 0.798) ? 110. If a given piece of gold be balanced by its weight of brass in a vacuum, what addition must be made to the brass so that they may be in equilibrium when immersed in water ? 111. How much force in kilogrammes would be required to sustain under mercury at 0° a cubic decimetre of platinum ? The specific grav- ity of platinum is 21.5 ; that of mercury, 13.598. 22* 258 CHEMICAL PHYSICS. Floating Bodies. 112. How much bulk must a hollow vessel of copper fill, weighing one kilogramme, which will just float in water ? 113. How much bulk must a hollow vessel of iron occupy, weighing 10 kilogrammes, which sinks one half in water ? 114. A boat displaces lOiia;^ of water. What is the weight of the boat ? 115. A cube of wood, weighing 100 kilogrammes, sinks three quarters in water. "What is the specific gravity of the wood, and what is the size of the cube ? 116. What portion of a cube of solid iron {Sp. Gr. = 7.7) will sink in mercury {Sp. Gr. = 13. G) ? 117. A life-boat contains 100 iiT'.^ of wood, whose specific gravity is equal to 0.8, and 50 inT^ of air, whose specific gravity is 0.0012. When filled with fresh water, what weight of iron ballast, whose specific gravity is 7.C4.J, must be thrown into it before it will begin to sink ? 118. If the specific gravities of a man, of water, and of cork be 1,120, 1,000, and 240 respectively, find what quantity of cork must be connected to a man, weighing 75 kilogrammes, that he may just float in the water. 119. Determine the weight of a hydrometer, which sinks as deep in rectified spirits, whose specific gravity is 0.866, as it sinks in water when loaded with 4 gram. 120. A ship, sailing into a river, sinks 2 c. m., and, after discharging 12,000 kilogrammes of her cargo, rises 1 c. m. ; determine the weight of the ship and cargo, the specific gravity of sea-water being to that of fresh as 1.02G is to 1. 121. If a solid, whose specific gravity = 6, float in a liquid, whose spe- cific gravity = 15, determine the proportion of the parts immersed. 122. If a globe of wood, when placed in a vessel of water, rise 5 cm. above the surface, but, when placed in a liquid whose specific gravity is 0.80, rise only 3 c. m. above the surface of the liquid, determine the di- ameter of the globe. 123. Having given the specific gravities of iron and water, determine what proportion the thickness of a hollow iron globe must bear to its diameter, that it may just float in water. 124. A parallelepiped of ice, whose three dimensions are 10.5 m., 15.75 m., and 20.45 m., is floating in sea-water on its broadest face ; the specific gravity of sea-water is 1.026, and that of ice 0.930. Required the height of the parallelepiped above the surface of the water. 125. A cone, 1.5 m. high and 1.2 m. in diameter at the base, is floating on its base in a liquid in a vertical position, and sinks in it 20 c. m. How much of the liquid is displaced by the cone ? If the cone is inverted, and made to float on its apex, how deep will it then sink ? THE THREE STATES OP MATTER. 259 126. A hollow cylinder of iron plate is 2.5 m. in diameter and 1.75 m. high. The plate is 1 c. m. thick, and its specific gravity 7.79. Will it float on water, and if so, how deep will it sink when its axis is vertical ? 127. A cube of lead measures 4 cm. on each side. It is required to sustain it under water by suspending it to a cube of cork. What must be the size of a cube of cork which just sustains it, assuming that the specific gravity of cork equals 0.24, and that of lead 11.35 ? Elasticity of Liquids. 128. A cubic metre of water is submitted to a pressure of 15 atmos- pheres. How great is the condensation ? and what is the specific gravity of the condensed liquid ? 129. At a depth in the ocean of a little over 5 kilometres, the pressure amounts to 500 atmospheres. What is the specific gravity of the water at that depth, assuming that the specific gravity of sea-water is 1.026, and the compressibility 0.0000436 ? Hydrostatic Press. 130. In the hydrostatic press are given the diameters of the two cylin- ders d and d', and the force applied to the pump F. Determine the pressure produced. 131. In the hydrostatic press, suppose the diameters to be 4 cm. and 80 c. m. respectively, the length of the pump-handle to be 1 m., and the distance of the pump from the fulcrum of the handle 1 c. m. Deter- mine in what proportion the power is increased. Pressure exerted hy Liquids in Consequence of their Weight. It is assumed, in the following problems, that liquids are incompressible, and hence that their specijic gravity is not increased, however great may be the pressure to which they are exposed. 132. The whole pressure on the bottom of a pail of water, the radius of which is 30 c. m., is 50 kilogrammes. What is the depth of the water in the pail ? 133. What is the pressure exerted by the water on every square cen- timetre of the base of a cylindrical vessel, in which the liquid stands at the height of 10.336 m. above the base ? If the water in the vessel were replaced by mercury, how high must the liquid stand, so that the pressure should be the same as before ? 134. The horizontal and circular bottom of a flask, 15 c. m. in diame- ter, is filled with mercury to the depth of 20 c. m. How great is the pressm'e on the bottom ? 135. What height must a column of water have, which will exert a pressure of 1,000 kilogrammes on every square decimetre ? 136. A cubical vessel is filled with water, and into its side a bent tube 260 CHEMICAL PHYSICS. is inserted, filled with water, and communicating with the water in the vessel. Determine the pressure on the top of the vessel, the vertical height of the extremity of the tube above the vessel being (m) times the height of the vessel. 137. A sphere, 10 c. m. in diameter, is sunk to the depth of 100 m. in a fresh-water lake. Determine the total pressure exerted on its surface. 138. A cylinder, 15 cm. in diameter, is sunk fo that its centre is at the depth of 1 m. below the surface of the water. Determine the total pressure exerted on its surface. 139. A hollow cone, 10 c. m. in diameter at the base and 5 cm. high, is filled with water. Determine the pressure on the base and on the con- vex surface. 140. A cylindrical vessel, 10 cm. in diameter and 10c. m. high, is filled with water. Determine the pressure on the base and on the convex surface. 141. A hollow cone, without a bottom, stands on a horizontal plane, and water is poured in at the vertex. The weight of the cone being given, how far may it be filled so as not to run out below ? 142. A hemispherical vessel, 10 c. m. in diameter, without a bottom, stands on a horizontal plane. When just filled with water, the liquid be- gins to run out at the bottom. Determine the weight of the vessel. 143. A straight line is immersed vertically in a liquid. Required to divide it into three portions, which shall be equally pressed. 144. Compare the pressures on the three sides of an equilateral tri- angle, just immersed in a liquid in such a manner that one side may be perpendicular to its surface. Specific Gravity. 145. Determine the specific gravity of absolute alcohol from the fol- lowing data : — "Weight of bottle empty, ..... 4.326 gram. " " filled with water at 4°, . 19.654 " " " filled with alcohol at 0°, . . 16.741 " 146. Determine the specific gravity of sulphuric acid from the follow- ing data : — Weight of bottle empty, 4.326 gram. " " filled with water at 4°, . 19.654 " " " filled with sulphuric acid at 0°, 28.219 " 147. Determine the specific gravity of lead shot from the foUovring data : — Weight of bottle filled with water at 4°, . 19.654 gram. " shot, 15.456 " " bottle, shot, and water, . . 33.766 " THE THREE STATES OP MATTER. 261 148. Determine the specific gravity of gold from the following data : — Weight of gold in air, . . . . 4.213 gram. Loss of weight in water, .... 0.2205 " 149. Determine the specific gravity of hammered copper from the fol- lowing data : — Weight of copper in air, .... 1.809 gram. " " under water, . . 1.608 " 150. Determine the specific gravity of saltpetre from the following data : — Weight of saltpetre in air, .... 1.216 gram. " " under alcohol, . . 0.7345 " Specific gravity of alcohol, .... 0.792 " 151. Determine the specific gravity of asln wood from the following data : — Weight of wood in air, . . . 25.350 gram. " " a copper sinker, . . 11.000 " • " " wood and sinker under water, 5.100 " Specific gravity of copper, . . . 8.950 " 152. A sphere of platinum weighs in air 84 gram., and in mercury 22.6 gram. What is the density of platinum ? 153. A piece of metal weighs 5.219 gram, in air, 4.132 gram, in water, and 5.009 gram, in a given liquid. What is the specific gravity of the metal and of the liquid ? 154. A body. A, weighs in air 7.55 gram., in water 5.17 gram., in an- other liquid 6.35 gram. What is the specific gravity of the body and of the liquid ? 155. A body weighs 14 gram, in a vacuum and 9 gram, in water ; an- other weighs 8 gram, in a vacuum and 7 gram-, in water. Compare their specific gravities. 156. A glass ball, weighing 10 gram., loses 3.636 gram, in water, and 2.88 gram, in alcohol. What is the specific gravity of alcohol ? 157. A glass ball, weighing 10 gram, and whose Sp. Gr. = 2.75, weighs, under rape-seed oil, 6.658 gram. What is the specific gravity of this oil ? 158. A glass ball, as above, weighs under water 6.364 gram., and under another liquid 7.12 gram. What is the specific gravity of this liquid .-* 159. A volumetre, whose stem is exactly cylindrical, sinks in a liquid whose (SJB. Gr. = 1.1 to a point b, and in pure water at 4° C. to a point a. The distance from a to J is 4 c. m. How far from a must the divisions be placed to which the hydrometer will sink in liquids whose Sp. Gr. = 1.01, 1.02, 1.03, 1.04, 1.05. 160. A similar volumeter sinks in a liquid whose Sp. Gr. = y to a point b, and in a liquid whose Sp. Gr. = y' to a point a, higher on the stem. What is the specific gravity of a liquid in which it sinks to an in- termediate point, d, when bd ^ X, and ab =1. 262 CHEMICAL PHYSICS. 161. A column of water 1.55 m. high is in equilibrium with a column of liquid 3.17 m. high. "What is the specific gravity of the liquid ? Miscellaneous. 162. An alloy of gold and silver weighs 10 kilogrammes in air, and 9.375 kilogrammes in water. What are the proportions of gold and silver ? The specific gravity of gold = 19.2, of silver = 10.5. 163. An alloy of copper and silver weighs 37 kilogrammes in the air, and loses 3.666 kilogrammes when weighed in water. What are the pro- portions of silver and copper ? 164. The specific gravity of zinc is 7, and that of copper 9, nearly-. What amounts of zinc and copper must be taken to form an alloy weigh- ing 50 gram., and having a specific gravity equal to 8.2, assuming that the volume of the alloy is exactly the sum of the volumes of the two metals ? 165. Required the specific gravity of a mixture of 18 kilogrammes of sulphuric acid and 8 kilogrammes of water, assuming that the specific gravity of the acid is equal to 1.84, and that the volume of the mixture is condensed ^'j. 166. Into a cylindrical vessel with a horizontal base 10 cm. in diame- ter, there are poured 12 kilogrammes of mercury. At what height will the liquid rise in the cylinder? The specific gravity of mercury is 13.596. 167. How much mercury will a conical vessel hold which is 87 cm. high and 46 c. m. in diameter at the base ? 168. A cylinder of oak wood is 30 cm. in diameter and 2.5 m. long; the specific gravity of the wood is 1.17. Wliat is the volume and the weight of the cylinder ? 169. A cylindrical vessel is 36.9 cm. high, and 24.6 cm. in diameter, interior measure. How much alcohol of specific gravity 0.863 will the cylinder contain ? 170. Leaves of gold are made only 0.001 m.m. in thickness ; the spe- cific gravity of gold equals 19.632. How much surface can be covered with 10 gram, of gold ? 171. A cast-iron ball weighs 12 kilogrammes ; the specific gravity of cast-iron is 7 35. AVhat is the radius of the ball ? 172. What is the diameter of a platinum wire which weighs 28 gram, for each metre of length ? The specific gravity of platinum is 22.06. 173. A silver wire 125 m. long weighs 6 gram.; the specific gravity of silver is 10.474. What is the diameter of the wire ? 174. In a capillary tube is contained a column of mercury which meas- ures 13.7 c. m. at 0° C. What is the diameter of the tube ? 175. A wire 0.785 m. long, and weighing 0.364 gram., loses 0.017 gram, when weighed under water. What is the diameter of the wire ? THE THREE STATES OP MATTER. 263 III. Characteristic Properties of Gases. (149.) Mechanical Condition of Gases. — The peculiar prop- erties of a gas seem to depend on the fact, that the repulsive forces existing between its particles are greater than the attract tive forces (78). Consequently, the particles of a gas tend to recede from each other, and were it not for extraneous causes the gas would expand — so far as is known — indefinitely into space. This natural tendency of gases is restrained on the surface of our globe by the pressure which the atmosphere exerts in consequence of its weight ; but when this pres- sure is removed, the expansive ten- dency becomes at once manifest. The air which is contained in the India-rubber bag (Pig. 253), for example, is prevented from expand- ing by the pressure of the atmos- phere on its exterior surface. If, however, we place the bag under the receiver of an air-pump, and remove the pressure by exhausting the air, the bag will at once ex- pand ; and this expansion will con- tinue until the expansive tendency of the air is balanced by the elas- rsg. 253. ticity of the bag. The force with which a gas tends to expand is called its ten- sion ; and it is evident that, when in a state of rest, the tension of a gas must be exactly equal to the pressure to which it is ex- posed ;. for were this not the case, the force which was in excess would cause a motion in the particles, which is inconsistent with the supposition. It appears, therefore, that in a gas, as in a liquid, the particles are in a condition of equilibrium ; the only difference being, that in a liquid the equilibrium exists between the attractive and repulsive forces in the liquid itself, but in the gas, between the excess of repulsive forces in the body and an ex- ternal pressure. In consequence of this condition of equilibrium, the particles of gases are endowed with perfect freedom of motion, and gases are therefore /wirfs (117). Moreover, since they are both elastic (77) and ponderable (7), it follows that all those 264 CHEMICAL PHYSICS. properties which are the necessary consequence of these mechan- ical conditions must belong to gases as well as to_ liquids. These, as before (119), naturally divide themselves into two classes: first, those which are independent of the action of gravity ; and, secondly, those which depend upon it. As these properties have been so fully discussed in the case of liquids, it will only be necessary to extend the principles already established to the case of gases. Properties Common to Gases and Liquids. (150.) Pressure which is independent of the Action of Grav- ity. — Let us now suppose that the vessel (Fig. 254) already described (120) is filled with air, instead of water. As this air is in a permanent state of tension, it will, in consequence of its elasticity, exert pres- sure in all directions ; and it is evident, from the same course of reasoning used in the case of water (120), that the pres- sures it exerts against the pistons a, b, c, d will be proportional to their areas. In jj 254 like manner, the same will be true of any portion of the interior surface of the ves- sel, and also of any ideal section in the interior of the vessel. If two sections are equal, they will receive equal pressures ; if un- equal, the pressures will be proportional to their areas. If the air in the interior of the vessel is in the same condition as the external atmosphere, it is evident, from what has been said, that the pressure of the air on the interior surface of the vessel will be exactly balanced by the pressure of the atmosphere on the outside. The piston, therefore, being pressed eqvially on their inner and outer surfaces, will have no tendency to move. This being the condition of the air in the vessel, let us suppose that we condense the air still further, by pressing in one of the pistons ; it is evident that we shall thus develop a greater elas- ticity in the particles, and each particle will in consequence exert a greater pressure. The increased pressures now exerted against the inner surfaces of the pistons will be proportional to the num- ber of gaseous particles in contact with them, or, in other words, proportional to their areas. The pressures on the inner siir- faces being also greater than those on the outer surfaces, the THE THREE STATES OP MATTER. 265 pistons will tend to move out with forces varying In the same proportion. From these considerations, it appears that gases, like liquids, transmit pressure equally in all directions ; the only difference being this, that in our experiments on gases we start with a cer- tain initial pressure due to their permanent elasticity. Gases, like liquids, will transmit pressure through long tubes and through any passages, however circuitous, provided only that there is a line of gaseous particles. A good example of this is furnished by the gas-pipes of large cities. Any pressure applied at the gasometer is transmitted almost instantaneously through hundreds of miles of pipe distributed in a most circuitous man- ner over several square miles of area. The close resemblance which gases bear to liquids is also shown by the fact that they transmit pressure from one to the other indifferently. We shall have occasion to notice several examples of this farther on. Since the proof used in (121) applies to gases as well as to liquids, it follows that the line indicating the direction of the pressure exerted by any gaseous particle against the section with which it is in contact, is always a perpendicular to this section at the point of contact. (161.) Pressure depending on the Action of Gravity. — The facts in regard to the pressure exerted by liquids in consequence of their weight are, as we found in sections (123) to (129), all necessary consequences of the one fundamental property, that they transmit pressure equally in all directions ; and it therefore follows, that each of these facts must be true of gases. Let us commence with an ideal case. Suppose a closed cylindrical ves- sel, several kilometres high, filled with air of the same density through its whole extent, and rising vertically from the surface of the globe. It would be true of such a vessel, that the pres- sure exerted by the air on the base of the cylinder, or on any por- tion of its side, or, in fine, on any section whatsoever, would be equal to the weight of a column of air, the area of whose base is equal to the area of the section, and whose height is equal to the vertical distance of the centre of gravity of the section from the top of the cylinder. Moreover, the pressure on any given sec- tion would be entirely independent of the form or size of the vessel, provided only that the height remained the same. This last circumstance is one of great importance, because it 23 266 CHEMICAL PHYSICS. enables us to extend our conclusions at once to the case of the atmosphere. The atmosphere is a mass of air retained upon the surface of the globe by the force of gravitation, and rising to a height which is estimated approximately at forty-seven kilometres. It is supposed to have, like the ocean, a definite surface, which, when at rest, is perpendicular at each point to the direction of gravity. It partakes of the rotation of the globe on its axis, and would remain at rest relatively to terrestrial objects were it not for local causes, which produce winds and disturb at each mo- ment its equilibrium. Neglecting these disturbances, we may regard the atmosphere as a gaseous ocean in equilibrium covering the earth to a certain level, and exerting the same effects of pres- sure as if it were a liquid having a very small density. It fol- lows, therefore, that each particle of the air exerts a pressure equal to the weight of a vertical line of superincumbent particles rising to the surface of the atmosphere. This pressure will be constant on surfaces at the same level ; it will increase as we de- scend in the atmosphere, and diminish as we rise in it. At any one position, it will be equal on surfaces of the same area, what- ever may be their direction ; and on surfaces of uneqiial area it will be in proportion to the extent of the areas. It will be the same in the interior of any vessel or room as in the outer air, provided only there is a connection with the exterior atmosphere by some aperture, however small. Finally, the air will buoy up all bodies immersed in it with a force which will be equal to the weight of the volume of air displaced. As the validity of these conclusions has already been established in regard to liquids, it will only be necessary, in the case of gases, to illustrate the gen- eral facts by a few experiments. (152.) Pressure of the Atmosphere. — The pressure exerted by the atmosphere on all bodies near the surface of the globe is exceedingly great, amounting, as we shall soon prove, to over one kilogramme on every square centimetre of surface, and to about 16,000 kilogrammes on the surface of the body of a man of or- dinary stature. But since this pressure is exerted equally in all directions, and since the cavities of the body are filled either by air or other gases, which exert a pressure on the one surface of its delicate membranes exactly equal to that exerted on the other, this great pressure is not perceptible, and indeed was not known to exist until it was discovered by Torricelli in 1643. If, how- THE THBKE STATES OP MATTER. 26T L J Fig. 255. ever, by any means, we can remove the pressure from one side only of a membrane, then the pressure on the other side vill be- come evident. We can readily remove the pressure from the interior surface of a vessel, by removing the air by means of an air-pump (175), and thus remov- ing the fluid medium through which the pressure is transmitted. For exam- ple, if we remove the air from the cylin- drical glass vessel which is represent- ed in Fig. 255, resting on the plate of an air-pump, we shall also remove the pressure from the lower surface of the thin animal membrane which covers and closes the cylinder from above. Then the great pressure on the upper surface, being no longer balanced, will exert its full effect, first, by depressing the membrane, and afterwards by bursting it, if it be not too strong. That the pressure of the atmosphere is exerted upwards as well as downwards, may be further illustrated by means of the apparatus represented in Fig. 256. It consists of a glass vessel supported on a tripod stand, having a large opening below, and a small tubulature above. The lower opening is closed by a bag of India-rubber cloth, as represented in the figure, and the tu- bulature is connected with an air- pump by means of a flexible hose. On exhausting the air, the bag is pressed up into the glass vessel with sufiicient force to raise the heavy weight which is attached to it by means of a leather strap. By modi- fying the apparatus, it is easy to show that the pressure is exerted, not only upwards and downwards, but also in all direc- tions. These various forms of apparatus, however, only demon- strate the existence of pressure. They do not enable us to measure it. Fig. 256. 268 CHEMICAL PHYSICS. Fig. 257. (153.) Buoyancy of the Air. — The general fact, that air, like liquids, buoys up all bodies immersed in it, may be illus- trated by means of the apparatus represented in Fig. 257. It con- sists of a closed globe suspended to one arm of a delicate balance, equipoised by a weight suspend- ed to the other. The two are in equilibrium in tlie air, but only because the globe, being larger than the weight, is buoyed up by a greater force. If, now, the apparatus is placed upon the plate of an air-pump and covered with a glass bell, we shall find, on removing the air, that the globe will preponderate, as is shown in the figure. By remov- ing tliG air, we increase the ai> parent weight both of the globe and of the counterpoise by just the weight of the air displaced by each ; but as the globe is much the largest, we increase its weight more than that of the smaller brass counterpoise, and hence the result. If we allow the air to re-enter the bell, it will buoy iip the globe, as before, so much more than the counterpoise, as to restore tlie equilibrium. (154.) Weight of a Body in Air. — An important consequence of the principle just illustrated is evident. The balance does not give us the true relative weight, W, of a body, but a slightly dif- ferent weight, depending on the weight of air displaced by the body compared with the weight of air displaced by the brass or platinum weights used in weighing. As the volume of these weights is generally less than that of the body, the weight indi- cated by the balance is almost always too small ; but when the volume of the weights is greater than that of the body, the weight indicated by the balance is too large. When the two volumes are equal, the balance will indicate the same weight in air as in a vacuum. It is easy to ascertain the correction which it is necessary to add to or siibtract from the weight of a body in air, in order to obtain its true weight. It must be remembered that the brass and platinum weights THE THREE STATES OP MATTER. 269 which are used in delicate determinations of weight are only standard when in a vacuum (64). Let us, then, represent the various values as follows : — W = weight of the body in air as estimated by standard weights, and also the weight of the standard weights themselves in a vacuum. V = volume of the standard weights in cubic centimetres. V = volume of the body in cubic centimetres. ■w = weight of one cubic centimetre of air at the time of the weighing. W = weight of the body in a vacuum, — which we wish to find. We can now easily deduce the following values : — F' w = buoyancy of air on the weights. Vw = buoyancy of air on the body. W — V w = actual weight of standard weights in air. W — Vw r= actual weight of body in air. Since these Weights just balanced each other, we have W—Vio=W' — r'iv, or W=W'-\-w{ V— V). [91.] The correction w (F — F'), which must be made to the weight determined by a balance in air in order to obtain the weight in a vacuum, is evidently additive when the volume of the body is greater than that of the weights, and subtractive when these con- ditions are reversed. When the volumes are equal, the correc- tion becomes 0. In all ordinary cases of weighing, the correction is so small that it may be neglected without sensible error ; but it becomes of the greatest importance in determining the weight of a gas. In such cases, we have to determine the weight of a large glass globe when completely vacuous and when filled with gas ; and it not unfrequently happens that the buoyancy of the air is greater than the weight of the gas itself, and it is always a considerable part of it. If the buoyancy of the air is the same when the globe is weighed in its vacuous condition and when filled with gas, it would not affect the weight of the gas, which would be obtained by subtracting the fi'rst weight from the last. But, unfortunately, the buoyancy is constantly changing; and it is therefore necessary to determine the amoimt carefully at each weighing, and reduce the weights of the globe in the two condi- tions to what they would be if the experiments had been made in a vacuum. 23* 270 CHEMICAL PHYSICS. ^ When the temperature is 0° C. and the barometer stands at 76 cm., and when the air contains neither vapor of water nor carbonic acid, iv is equal to 0.001293 gram. Were tlie atmos- phere always in this condition, nothing would be easier than to calculate the actual weight of a body from the weight found by weighing in this normal atmosphere. But this is far from being the case ; for the temperature, the pressure, and the composition of the atmosphere are changing at each moment, and the value of w varies with all these atmospheric changes. We shall here- after show in what way the value of iv may be ascertained, at any given time, when the condition of the atmosphere is known. It is frequently possible to conduct the process of weighing in such a way that the correction for the buoyancy of the atmos- phere, always some- « ^wtfw/,'wffw , -,'.rrWr-,-^^wrr^r~.w^,-^ , -„-,-r-rtfw a^;^ what unccrtain , may 1 ^^"^K^^^^^^T^P^^^^^^ / be avoided. For ex- ample, in weighing a gas, instead of equipoising the glass globe when empty, by means of ordina- ry weights, we may equipoise it by means of a second globe, hermetically closed, and having the same volume as the first, in the manner repre- sented in Fig. 258. It is evident that in this case, whatever VyW7/''.'.y,-/--^M I I- <-/, ■/^^MMarffi'''''"'''''^''''''''"''-^'''"''''"'^'!''^' Fig. 258. may be the buoyancy of the atmosphere, it will equally affect both globes, and we shall only have to consider the buoyancy of the air on the small weights necessary to restore the equilibrium after the globe is filled with the gas to be weighed ; but this is so small that it may always be neglected. (165.) Balloons. — If the weight of a body is less than that of the gas which it displaces, it is evident that the body will rise in the gas ; and hence the phenomena of floating bodies, which we have THE THREE STATES OP MATTER. 271 already studied in the case of liquids (140), must be repeated in the case of gases. It is not difficult to construct a body which shall be, taken as a whole, specifically lighter than air, and which will therefore rise in the atmosphere as wood rises in water. Hy- drogen gas is 14^ times lighter than air, and by enclosing a large Tolume of this gas in a light bag made of oiled silk, called a balloon, we shall have a body which will displace a weight of air much greater than its own weight. For example, let us suppose that the balloon, when fully inflated, forms a sphere two me- tres in diameter. It is easy to calculate that it will contain 4.1887902 m.' of hydrogen, which will weigh 374.436 gram. Neglecting the volume occupied by the material of the balloon, it will displace an equal volume of air, weighing 5,418.75 gram. The difference between these weights, or 5,044.31 gram., will repres.ent the excess of the buoyancy of the air over the weight of the hydrogen ; and hence, if the balloon and its attachments weigh less than this, it will, when inflated with hydrogen, rise in tiie atmosphere. The difference between the weight of the bal- loon inflated with hydrogen and that of the air displaced by it is termed the ascensional force of the balloon. If the balloon is ten metres in diameter, and weighs 100 kilogrammes, it would have an ascensional force of 580.5 kilogrammes, and therefore sufficient to raise a car with several passengers into the atmos- phere. In practice, a balloon is never at first more than two thirds filled with hydrogen ; because, as it rises in the atmosphere, the gas rapidly expands, and it is necessary to allow for this expansion. Moreover, the hydrogen used is mixed, to a greater or less extent, with air and vapor, which greatly increase its weight. These causes diminish the ascensional force to such an extent, that in practice the ascensional force of a balloon ten metres in diameter would not be more than one half of what it is estimated above. Since the introduction of coal-gas as an illuminating material, this is almost exclusively used for inflating large balloons. The specific gravity of this gas is on an average about 0.5, and it is only, therefore, about twice as light as air. Hence, in order to obtain the same ascensional force with coal-gas as with hydrogen, it is necessary to use very much larger balloons. When the spe- cific gravity of a gas is given, it is easy to calculate the ascensional force which in any given case may be obtained with it. 272 CHEMICAL PHYSICS, Let xis represent by d and d' the specific gravities of air and the gas to be iised, referred to water [58] ; by W, the weight of the material of the balloon and its attachments; and by F, its volume when inflated. Then, by [56], we have for the weight of the gas in grammes Vd', and for the weight of the air it displaces Vd. Neglecting, for the moment, the weight of the balloon itself, we should haA^e for the ascensional force V (d — d'^. Subtracting the weight of the balloon and its attachments, we have, for the total ascensional force F, F=r(d — d')—W. [92. J If the balloon is a sphere of which, ii is the radius, then we should have for the value of V, when the balloon was fully in- flated, f Tt R', and for the value of F, F=iTtR'(d—d')—W. [93.] When the gas used is pure hydrogen, d = 0.00129363, and d'^ 0.00008939. Substituting these values, and also for vt its well- known value, the expression becomes F = 0.00504431 R= — W, [94.] in which R stands for a certain number of centimetres, and W for a certain number of grammes. As we live at the bottom of the ocean of air which surrounds the globe, we cannot, from the nature of the case, imitate with it the condition of a vessel floating on the surface of the water j but with other gases this condition of things may be, at least in a small way, very nearly approached. The large fermenting-vats of breweries and distilleries are al- most constantly filled with carbonic acid gas, which, being heav- ier than the air, remains in the tank, and has a surface like that of water, although it is not quite so definite. By exploding a little gunpowder in the gas, and thus filling it with smoke, the surface becomes distinctly visible. Avery illustrative experiment can be made at such vats, by allowing soap-bubbles, blown with a common tobacco-pipe, to fall on the gas thus clouded. They will for a few moments float on the surface, and illustrate in a most striking manner the analogy between gases and liquids. THE THREE STATES OP MATTEB. 273 Differences between Liquids and Gases. (156.)^ We shall fail to give an accurate idea of the nature of a gas, if, after having dwelt upon the analogies between liquids and gases, we do not point out those qualities which distinguish these two conditions of matter. 1. Difference of Specific Gravity. — The most obvious differ- ence between gases and liquids is to be found in their relative weight. A litre of water weighs 1,000 grammes, and the weight of the same volume of other liquids varies from 600 to 3,000 grammes, leaving out of account mercury and other metals, when in a melted state, which are much heavier. Between these limits we find almost every possible gradation. One litre of air weighs 1.294 gram., and the weight of one litre of other gases varies between 0.089 gram, and 20 gram. There is, therefore, a wide gap between the lightest liquid and the heaviest gas, but yet this difference is one entirely of degree ; and although this gap is not filled by any known substance in its normal condition on the globe, yet Natterer, in his experiments on the condensation of gases,* must have had atmospheric gas in every degree of density between its ordinary density and that of water. 2. Compressibility. — Gases are also distinguished from liquids by being far more compressible. When by means of a piston we attempt to condense a liquid, we find that we can only reduce its volume very slightly. But this almost insensible diminution of volume develops a very great elasticity ; for it is only necessary to reduce the volume one forty-five-millionth to produce a resist- ance equal to the pressure of our atmosphere. It is different with gases. When, for example, we press down a piston into a cylinder containing air (Fig. 51), it is necessary to reduce the volume to one half in order to double the resistance, and to one third in order to treble it. As the pressure is increased, the volume of a gas is diminished almost in the same proportion ; as the pressure is diminished, on the other hand, the volume of the gas is proportionally increased. For this reason, gases are frequently called compressible, and liquids incompressible fluids ; but here again the difference is one of degree rather than of kind. This difference of compressibility gives rise to an important dif- * Poggendorff, Annalen, XCIV. 436. 274 CHEMICAL PHYSICS. ference of condition between the atmosphere, regarded as an ocean of gas, and the liquid oceans of our globe. As we de- scend in the ocean, although the pressure increases with great rapidity, yet the density of the water is not materially increased. It is very different with the atmosphere. As we rise in this ocean of gas, the air becomes less dense in proportion as the pressure is diminished, and when at a height of about 5,520 m. the pressure is reduced one half, the density is also reduced one half. On the other hand, when we descend into mines, and the pressure from above is increased, the density of the air increases in the same proportion. The atmosphere does not, therefore, like the sea, consist of a fluid of nearly uniform density throughout, but its density very rapidly diminishes as we rise above the surface of the globe. It would not, then, be possible to have a cylin- drical vessel filled with air of uniform density throughout its whole height, as we supposed in (151). Such a condition of things is wholly ideal, and was introduced merely for the sake of illustration. Were the atmosphere, like the sea, of nearly uniform density, its height would be only about eight kilome- tres, instead of forty-seven, as already stated. The pressure exerted by such an ideal fluid would be precisely the same as that exerted by the atmosphere ; so that, while merely studying the pressure on the surface of the earth, we may conceive of the pressure as exerted by a fluid of uniform density, without com- mitting any material error ; but it must be remembered that the real state of the case is very different. We shall return to this subject in a future section. 3. Permanent Elasticity. — We have already dwelt at some length on this property of gases, which distinguishes them pre- eminently from liquids (149) ; but even here the difference is not so strongly marked as it would at first sight seem. A simple experiment will illustrate this point, and at the same time make the distinction between the two fluid conditions of matter clearer. Let us take, then, a volume, F, of water, contained in a vessel of much greater capacity, and let tis suppose that its temperature is 100°, and that it is exposed to a given pressure, for example of ten atmospheres. If, now, we diminish the pressure succes- sively by one atmosphere each time, the volume Fwill increase by a very small amount, represented by Vfi, at each operation. As THE THREE STATES OP MATTER. 275 soon, however, as the pressure is reduced to one atmosphere, this law of expansion ceases abruptly, and the water, without any intermediate transition, takes a volume 1,200 times greater than before, changing into a gas having all the properties of air, and preserving these properties at any pressure less than one at- mosphere. We may now reverse this experiment. Let us, then, increase the pressure upon this gas formed by water ; we shall find that, when the pressure is doubled, the volume of the gas will be re- duced one half, but as soon as the pressure exceeds one atmos- phere it will suddenly take a volume 1,200 times smaller than be- fore, and a density 1,200 times greater, collecting in the lower part of the vessel in a liquid form. After this, it can be compressed but very slightly by increasing pressures. We have taken, as an example, water at 100°, because the change of state which it undergoes at this temperature is a familiar fact to every one. We might have cited sulphurous acid gas, which liquefies at — 10", or carbonic acid gas, which liquefies at — 78° ; but what- ever might be the body examined, the result would be the same. What has now been stated in regard to gases may be summed up in a few words. They are bodies constituted, like liquids, of molecules which repel each other, bodies which transmit pressure equally in all directions, which arrange themselves under the influ- ence of gravity in strata whose density and elasticity increase as we descend, which buoy up all bodies immersed in them with a force equal to the weight of the fluid displaced, and in which the laws of the equilibrium of floating bodies are reproduced. These are the analogies. On the other hand, they are bodies having a very small density, obeying a special law of compressibility, and which, when submitted to a suf&cient pressure, change into liquids.* Such, then, are the characteristic properties of gases ; but before studying these more in detail, we must consider the mode by which the pressure of a gas may be accurately measured. THE BAROMETER. (157.) Experiment of Torricelli. — Before the middle of the seventeenth century, the phenomena which we now refer to the pressure of the air were explained by a principle invented * We shall hereafter learn that there are some gases which hare not been liquefied. 276 CHEMICAL PHYSICS. bj the Aristoteleans, namely, that " Nature abhors a vacuum." These ancient philosophers noticed that space was always filled with some material substance, and that, the moment a solid body was removed, air or water always rushed in to fill the space thus deserted. Hence they concluded that it was a universal law of nature that space could not exist unoccupied by matter, and the phrase just quoted was merely their figurative expression of this idea. When, for example, the piston of a common pump was drawn up, the rise of the water was explained by declaring that, as from the nature of things a vacuum could not exist, the water necessarily filled the space deserted by the piston. This physical dogma served the purposes of natural philosophy for two thousand years, and it was not until the seventeenth cen- tury that men discovered any limit to Nature's horror of a vacuum. Even as late as 1644, Mersenne speaks of a siphon which shall go over a mountain, being then ignorant that the effect of such an instrument was limited to a height of ten metres. This limit appears to have been first discovered by Galileo. Some Floren- tine engineers, being employed to sink a pump to an unusual depth, found that they could not raise water higher than ten me- tres in the barrel. Galileo was consulted, and he is said to have replied, that Nature did not abhor a vacuum above ten metres. However this may be, it appears that Galileo did not understand the cause of the phenomenon, although he had previously taught that air has weight ; and it was left for his pupil, Torricelli, to discover the true explanation. Torricelli reasoned that the force, whatever it is, which sustains a column of water ten metres high in a cylindrical tube, must be equivalent to the weight of the mass of water sustained ; and consequently, if another liquid were used, heavier than water, the same force could only sustain a column of proportionally less height. The weight of mercury being 13^ times greater than that of water, Torricelli argued that, if the force imputed to the abhorrence of a vacuum could sustain a column of water 10 metres high, it could only sustain a column of mercury 13J times lower, or about 76 c. m. high. This led to the following experiment, which has since become so celebrated in the history of science. Torricelli took a long glass tube, open at one end, such as d c, Pig. 259, and, having filled it with mercury, closed the open end with his thumb, and, inverting the tube, plunged this end into THE THREE STATES OP MATTER. 277 a basin of mercury. On removing his thumb, the mercury, in- stead of remaining in the tube, fell, as he expected, and after a few oscillations came to rest at a height of about 76 c. m. above the level of the mercury in the basin. The correctness of his induction having been thus completely veriiied, Torricelli soon discovered the real nature of the force •which sustained both the water in the pump and the mercury in his tube. This experiment excited a great sensation among the sci- entific men of Europe'; but, as might have been expected, the explanation given of it by Torri- celli was very generally rejected. It was opposed to a long-estab- lished dogma, and Nature's hor- ror of a vacuum could not be so easily overcome. The cele- brated Blaise Pascal, however, had the sagacity to perceive the force of Torricelli' s reasoning, and devised an experimentum crucis which put an end to all controversy on the subject. " If," said Pascal, " it be really the weight of the atmosphere, under which we live, that supports the column of mercury in Torricelli's tube, we shall find, by trans- porting this tube upwards in the atmosphere, that in proportion as it leaves below it more and more of the air, and has conse- quently less and less above it, there will be a less column sus- tained in the tube, inasmuch as the weight of the air above the tube, which is declared by Torricelli to be the force which sus- tains it, will be diminished by the increased elevation of the tube." * Accordingly, Pascal carried the tube to the top of a church-steeple in Paris, and observed that the height of the mercury in the tube fell slightly ; but, not satisfied with this Kg. 259. * Lardner's Hand-Book of Natural Philosophy. 24 278 CHEMICAL PHYSICS. result, he wrote to his brother-in-law, who lived near the high mountain of Puy de D8me, in Auvergne, to make the experiment there, where the result would be more decisive. " You see," he writes, " that if it happens that the height of the mercury at the top of the hill be less than at the bottom, (which I have many reasons to believe, though all those who have thought about it are of a different opinion,) it will follow that the weight and pressure of the air are the sole cause of this suspension, and not the horror of a vacuum : since it is very certain that there is more air to weigli on it at the bottom than at the top ; while we cannot say that Nature abhors a vacuum at the foot of a moun- tain more than on its summit." M. Perrier, Pascal's cor- respondent, made the observation as he desired, and found a difference of nearly eight centimetres of mercury, " which," he replies, " ravished us with admiration and astonishment." * Pascal still further varied and extended the original experi- ment of Torricelli, and deduced the theory of the equilibrium of liquids and gases, which he left almost perfect. (158.) Theory of the Barometer. — It is hardly necessary to state that the tube of Torricelli is tlie instrument which is now so well known as the Barometer. This name, indeed, is de- rived from two Greek words, ^apv -Ho — h'o. There will, therefore, be an excess of pressure in the direction of the vessel c equal to h'o — ho, which will cause a constant flow of liquid in the direction of the greatest pressure. This flow will continue until ho = h'o, or until the level is the same in both vessels. If the vessel c is removed, then h'o represents the height of a column of mercury equivalent to a column of the liquid used whose height equals the vertical distance between the mouth of the tube and b. If this mouth is below the level of the bottom of the vessel a, it is evident that ho Can never equal /t'„ ; and hence the flow in this case will continue until the surface of the liquid in the vessel falls below the mouth of the tube at a. It is evi- dent, that, other things being equal, the velocity of the flow will 322 CHEMICAL PHYSICS. depend on the difference between h\ and //„. In the ordinary method of using a siphon, as represented in Pig. 294, this differ- ence is constantly diminishing; and hence the velocity of the flow is constantly diminishing. The siphon is frequently employed in the laboratory for de- canting liquids. Before using the instrument, it is necessary to fill it with the liquid to be decanted. If this liquid is water, the siphon is easily filled by closing the end of the short leg with the finger, and, after inverting the instrument, by pouring in water at the other end, the air being allowed to escape from the short leg by lifting for a moment the finger. When the tube is filled, it can easily be reversed, and the end, still closed with the finger, plunged under the liquid in the vessel ; when, on removing the Fig. 295. finger, the water will begin to flow. The siphon can also be filled by dipping the end of the short leg in the liquid, and sucking out the air from the other leg with the mouth. In the labora- tory, the siphon is frequently used for decanting corrosive liquid; and it is then necessaiy to resort to various contrivances for fill- ing it. The one represented in Fig. 295, which can easily be made of glass tubes and cork, is one of the best. The short leg is plunged, as usual, into the liquid. The end of the long leg is then closed by the finger, which can be protected by a piece of India-rubber, and the air is sucked out by the mouth applied at THE THREE STATES OP MATTER. 323 the end of the side tube. As soon as the liquid descends into the enlargement at the end of the long leg, the finger is with- drawn. (173.) Mariotte's Flask. — It is sometimes important to ob- tain with the siphon a uniform flow of liquid. This can be easily secured by means of the apparatus represented in Fig. 296, called Mariotte's flask. It consists of a bottle with two necks, into one of which a straight tube, and into the other a bent tube, have been adjusted air-tight, both reaching nearly to the bottom of the bot- tle. The siphon-tube is filled by blowing in air through the straight tube, when the Aov^ contin- ues of uniform velocity until the surface of the liquid in the bottle has fallen to the level bed, the air constantly entering the bottle by the straight tube at b. It can easily be shown that the flow in this case must be uniform in velocity. Consider, as before, a section through the siphon-tube at the highest point. The pressure on the surface of this section towards o is evi- dently f" = sCHo — h',-); [114.] where h'o is the height of a column of mercury equivalent to a column of the liquid used whose height equals the vertical dis- tance from o to the centre of gravity of the section. The surface of the section towards c is evidently exposed to the pressure exerted by the confined air on the surface of the liquid in the bottle, less the pressure of a column of the liquid whose height equals the vertical distance between this surface and the centre of gravity of the section. If we represent the tension of the confined air by ^, and the height of a column of mercury equivalent to the column of liquid by k"„, we easily obtain for the pressure on the surface of the section, if' = s(i5 — /t"o). When the apparatus is in use, and air is freely entering through b, it is evident that the pressure of the atmosphere at b is bal- anced by the pressure of the confined air on the surface of the liquid, and by the pressure of the column of liquid above b. 824 CHEMICAL PHYSICS. Representing the equivalent of this column in centimetres of mercury by /i"'o, and the height of the barometer by H^, we ob- tain iZo = ^ + /i"'o ; and by substitution, j = 5[ir„-(A"„+n)]. [115.J Subtracting this value from [114] , we obtain £ — £' = s IK— (n+ h%~)-\ . [116.] The value A"o+ /j"'o represents the height of a column of mer- cury equivalent to a column of the liquid used whose height equals the vertical distance between c and the centre of gravity of the section. As this height regains constant, and is indepen- dent of the height of the liquid in the bottle, it is evident that the difference of pressure [116] which determines the velocity of the flow will also be constant. It is also evident that the dif- ference of pressure is always equal to a column of the liquid used whose height equals the difference of level between b and o. A very useful application of Mariotte's bottle is represented in Fig. 297. It is frequently necessary, in the laboratory, to wash for several hovirs, or even days, a precipitate which has been collected on a filter. This is done by keeping the filter constantly full of wa- ter, which slowly percolates through the porous mass on the filter, and washes out everything which is soluble. Mariotte's bottle furnishes an automatic machine, by which the water in the fil- ter can be maintained at a constant level. The disposi- tion of the apparatus is suf- ciently explained by the fig- \ive. The difference of level between b and o is made very small, and the water flows from the bottle to the filter, until the level rises to the lower dotted line in the figure. Then the flow ceases, but recommences as soon as the level falls. 1 1 ill II 1 1 ) 1 If "rv-s>j_ Fig. 297. THE THBEB STATES OP MATTER. 325 Fig. 298. The principle of Mariotte's bottle is also applied to produce a uniform flow of air through the tiibe apparatus which is frequently used in chemical analysis. Fig. 298 represents what is termed an aspirator jar. The tube, which passes air-tight through the cork in the neck, has a free communi- cation with the atmosphere, and the current of air is caused by the flow of water from the cock at r. The veloci- ty of the flow of water from the cock, other things being equal, depends upon the pressure exerted on a sec- tion of the stopcock ; and it can easily be seen that this will be the same until the level of the water in the jar has fallen below the mouth of the tube V. (174.) Wash-Bottle. — This simple in- strument (Fig. 299), which is so much used in the laboratory, is one of the most useful applications of the properties of gas- es. By condensing the air over the water in the bottle, by blowing in at the tube a, the liquid is forced out at o in a fine jet, which can be directed at pleasure. Fig. 299. Machines for Rarefying and Condensing Air. (175.) The Air-Pump. — One of the simplest forms of the air-pump is represented in Fig. 300. It consists of a hollow brass cylinder, in which a piston moves readily up and down by a handle attached to the piston-rod above. The inner surface of the cylinder is perfectly smooth and true, so that the piston, whicli is formed of yielding materials, moves air-tight through its whole course. Moreover, the under surface of the piston fits exactly the bottom of the cylinder, so that, when the piston is in the lowest position, there can be no air between it and the cylin- der bottom. The upper end of the piston is closed by a brass cov- er, through which the piston-rod passes freely, and the atmosphere 326 CHEMICAL PHYSICS. has free access to the upper surface of the piston. The lower end of the cylinder opens into a narrow tube, which connects, at one end, with the glass bell on the plate of the air-pump through the Kg. 300. stopcock M, and at the other, with the atmosphere through the stopcock p. Just below the bottom of the cylinder there is placed a stopcock of peculiar construction. The core of the cock is bored with two holes, one of which has the same position as in ordinary stopcocks, and as is shown in the figure. The po- sition of the second is shown in the small section at the side. When the cock has the position indicated in the main figure, there is a direct connection between the interior of the cylinder and the glass bell. If the cock be now turned through ninety de- grees, till it takes the position shown in the small section, the con- nection with the glass bell will be closed, and direct communica- tion with the atmosphere opened through tlie channel s v. The channel r m opens in the centre of a round plate made of brass, or, still better for chemical uses, of glass. This plate is ground on its upper surface perfectly plane. The lower edges of the glass THE THREE STATES OP MATTER. 327 bell-receivers are also carefully ground, and may be made to adhere air-tight to the plane by interposing a little oil. The principle of the air-pump can now be easily explained. Let us suppose that tlie piston is in its lowest position, and that the stopcock is in the position represented in the figure. If now we draw up tlie piston by the hand, the air contained in the bell- receiver and in the tube connecting it with the cylinder will expand until it fills the cylinder ; and its volume being thus increased, its density will be proportionally diminished. Let us next turn the stopcock q into the position represented in the sec- tion. The bell is thus hermetically closed, but a connection is opened between the cylinder and the atmosphere. Now, on press- ing down the piston, all the air in the cylinder will be forced into the atmosphere. The stopcock may then be turned back to its first position, and the same motion repeated, which will fur- ther rarefy the air in the bell ; and thus the process may be con- tinued until the required degree of exhaustion is obtained. (176.) Degree of Exhaustion. — It is obvious that the effect of the air-pump depends upon tlie expansive force of air, and that each motion of the piston is accompanied with a certain amount of expansion of the air in the bell. This amount is evi- dently determined by the size of the cylinder, as compared with that of the bell and the tube leading to it. With these data, we can easily calculate the degree of exhaustion after each stroke of tlie piston. Let us then represent the volume of the bell-receiver and of the tube connecting it with the cylinder by V; and that of the cylin- der itself, when the piston is at its highest position, by v. Let us suppose that the piston starts from its lowest position, and let us take the quantity of air contained in the receiver and the tube as unity. When now the piston is raised, tlie volume occupied by this quantity of air (taken as unity) becomes V-\-v. When the stopcock is turned and the piston lowered, the volume v is ex- pelled, which is a portion of the original quantity (or unity) represented by „_, . The piston is now in its initial position, and the quantity of air remaining in the receiver and tube, after the first stroke, is 328 CHEMICAL PHYSICS. Eeversing the stopcock, and raising again the piston, this qnan- y tity of air, j^ , , occupying the Tolume V, expands to the vol- ume F-f- V. When the piston descends, the volume v is ex- V V V V pelled, which is -tf-i — of the whole, or of -17^-; — j that is, —r-, — to •^ ' y-\-v V -\-v ( I -\-vy of unity. There remains, therefore, after the second, stroke, V V V T'2 [118.J At the third stroke of the piston, the same proportion of the air now remaining is expelled as before ; and there is consequently left, after the third stroke. Y2 ^ Y2 {V-\-vy (V-\-v)^— {V-{-vy In like manner there will remain, after the 7it\i stroke. [119.] [120.J If, for example, the volume of the receiver is equal to ten litres, and that of the cylinder to one litre, we shall have, for the amount 10™ of air left after the fiftieth stroke, —55 = 0.0085 of the original quantity. Since the value of [120] never can become zero until w = 00 , it is evident that we can never, even theoretically, by means of the air-pump, exhaust the whole of the air. Nevertheless, theo- retically we ought to be able to approach a perfect vacuum in- definitely by continuing the process for a sufficiently long time. Practically, however, the limit is soon reached ; and even with the best pumps, we can never obtain a degree of exhaustion greater than that when ytiVirth of the original quantity of air is left in the receiver. It is not difficult to explain the cause of the discrepancy between the theoretical and the practical results. In any machine, however well made, there must be a number of joints which are never absolutely hermetical. There are fre- quently, even in the metal itself, imperceptible pores which trans- mit air. During the first few strokes of the piston, this minute leakage produces no perceptible effect ; but when we attain a high degree of exhaustion, the air enters by these minute crevices as fast as we can remove it by the pump. THE THREE STATES OF MATTER. 329 But besides this imperfection, the capability of the instrument is limited in still another way. In calculating the degree of ex- haustion, we supposed that at each descent of the piston the whole of the air was expelled from the cylinder ; and this would be the case, if the base of the piston adhered exactly to the base of the cylinder. In practice, however, there is never an absolute adhesion ; and a small amount of air remains between the two, which no force applied to th.e piston is able to expel. When, therefore, after working the pump for some time, this small amount of air, expanded through the whole interior of the cylin- der, exerts a pressure equal to that of the air remaining in tlie receiver, it is evident that the air from the receiver can no longer expand into the cylinder, and the pump will cease to exhaust. But although a perfect vacuum can never be obtained with an air-pump, yet a sufficient degree of exhaustion for all practical purposes is easily attained. Fig. 301. (177.) Air-Pump with Valves. — The form of air-pump de- scribed in (175) is exceedingly simple in its construction, and not liable to get out of order. It is therefore well adapted for use in 28* 330 CHEMICAL PHYSICS. the chemist's laboratory, where it is exposed to vapors which are likely to injure any delicate valves. It is open, however, to two serious objections. In the first place, the stopcock q must be turned by the hand at each stroke of the piston ; and although this motion may be obtained by means of cranks and levers, yet this machinery renders the instrument unnecessarily complicated. In the second place, the piston must be raised tlirough the whole length of each stroke, against a great pressure of air, which rapidly increases as the exhaustion proceeds, an objection which would be very serious in a large pump, rendering a great force necessary to work it. Both of these difficul- ties are overcome in the pump represented in Fig. 301. A section of this pump is represented in Fig. 302, and the details of the upper valve in Fig. 303. In this air-pump there are three valves, all open- ing upwards : one at the bottom of the cylinder, covering the mouth of the tube connecting with the receiver (a in Fig. 302) ; one at the top of the piston, b, covering the holes perforated through it; and, finally, one at the top of the cylinder, c, cov- ering the aperture which opens into the atmosphere. The piston- rod passes through a packing-box, 6, in which it moves air-tight, and the power is applied to the piston-rod by means of a lever, which facilitates the working of the pump. Let us now sup- pose that we start with the piston at the bottom of the cylinder, and proceed to raise it. The air from the receiver expands Kg. 302. THE THREE STATES OF MATTER. 331 into the empty space thus formed in the cylinder, raising the valve a. As now the piston descends, the valve a closes and prevents the air from re- turning to the receiver ; and this air passes up, through the holes in the piston, into the upper part of the cylin- der, raising the valve d. When next the piston rises, this same air, now in the up- ^'s- sos. per part of the cylinder, is forced out into the atmosphere by rais- ing the valve c. At the same time, a fresh amount of air from the receiver expands into the space below the piston, which air is forced out by the next stroke at the valve c, as before, and thus continuously. It is evident from the construction, that, as the piston rises, the air above it is gradually condensed, and the valve c does not open until the density of the air is equal to that of the atmosphere. During the first few strokes, the force required to raise the piston is considerable ; but as the exhaustion proceeds, the effort neces- sary becomes less and less, until at last only sufficient force is required to overcome the friction, and a sudden pressure at the end of the stroke to expel the air condensed at the top of the cylinder. In pumps like the one represented in Fig. 300, the size of the piston and cylinder is necessarily very limited ; be- cause, if the area of the piston exceeds a very limited extent, the pressure of the air on the upper surface becomes so great, as the exhaustion proceeds, as to reqiiire an impracticable amount of force to work the pump. With pumps of the construction just described, this pressure is in great measure removed ; and it is possible to increase very greatly their size advantageously. Fig- ure 304 is a representation of a large air-pump of this descrip- tion, made by Ritchie,* of Boston. The piston is 10 c. m. in diameter, and the length of the stroke 26 c. m. The ground brass plate is 37 c. m. in diameter, and admits of as large a bell- receiver as can be readily made. The efficiency of the pump depends in great measure upon the valves. These are best made * The two representations of air-pumps, Pig. 301 and Fig. 304, are from the cata- logue of Mr. E. S. Eitchie, a very expert philosophical-instrument maker of Boston. 332 CHEMICAL PHYSICS. of delicate oil-silk. The details of the upper valve of the pump, as made by Ritchie, are shown in Fig. 303. The oil-silk disk, a, Fig. 304. is kept in its place by the pin b, and the whole is protected by the dome-shaped covering c d. The tube at the side discharges the air, and the oil which escapes with it is conducted into a reser- voir placed below the basement of the pump. This pump is furnished with a manometer similar in principle to the one repre- sented in Fig. 272, by which the degree of exhaustion can be ascertained. It is represented in the figure on the left-hand side of the pump. Besides those already enumerated, there is obviously another limit to the degree of exhaustion whicli can be obtained with this pump. This arrives when the elasticity of the air left in the receiver is insufficient to raise the lower valve a. Fig. 302. In order to overcome this difficulty, the lower valve in the French form of air-pump* is opened and shut mechanically. Babinet * For a description of the French form of air-pump, see any of the French works on physics. THE THREE STATES OF MATTER. 338 has still further improved the French air-pump, hy so connecting the two barrels that, after a certain- degree of exhaustion has been attained, the second is made to exhaust the first. There can be no doubt that a higher degree of exhaustion can be ob- tained with the French pump, thus arranged, than with the pump just described ; but this gain is hardly compensated by the greater complexity and consequent liability to derangement, more espe- cially since a sufficient degree of exhaustion for all practical purposes can be obtained without these complications. (178.) Condensing-Pump. — This instrument is just the re- verse of the air-pump, and it is used for increasing the density of air in a receiver, while the air- pump is used for diminishing it. Any air-pump may be converted into a condensing-pump by changing the direction of all the valves. For ex- ample, we may use the pump repre- sented in Fig. 300 as a condensing- pump. Starting with the piston at the bottom of the cylinder, we give the stopcock the position represented in the section at the side. Then, on raising the piston, the air enters at v and fills the cylinder. We now turn the cock into the second position, when, on pushing down the piston, this air is forced into the receiv- er. We can then reverse the stop- cock and repeat the process, until the required degree of condensation is obtained. Instead, however, of placing the receiver on the brass plate, as before, we screw it on be- yond the stopcock p, opening this stopcock, and fclosing the stopcock u. The most convenient form of con- ^'e- 305. densing-pump for the laboratory is represented in Fig. 305. It consists of a cylinder, and a piston, which is moved by the handle M. The two valves, which are both at the bottom of the cylinder, are represented in section in 334 CHEMICAL PHYSICS. Pig. 306. They are made to fit exactly the conical openings at, the bottom of the cylinder, and are kept in place by very delicate Fig. 306. spiral springs. When the piston rises, the ralvc A opens and admits the air through the tube c a into the cylinder. On the other hand, when the piston descends, the valve A closes, while B opens, and the air is forced out, through the tube b d, into the receiver placed at d. It is evident, that if two receivers are con- nected with the pump, one at c and the other at d, the air will be exhausted from one and condensed in the other. The pump may, therefore, be used either for condensing or rarefying. In using the pump, it is fastened firmly to a table, or some other solid support, and the handle M is moved up and down alter- nately with the two hands. This simple machine is sufficient for almost all purposes. If, however, a more powerful apparatus is required for condensing gases into large reservoirs, it is best not to increase the size of the pump; but to combine several cylinders, connecting them all with the same receiver. The piston-rods of all these cylinders can be united by cranks to one axis, and a handle connected with a fly-wheel can be used to give this axis a regular and uniform motion. (179.) Water-Pump. — Entirely analogous in its principle to the air-pump is the common water-pump, a glass model of which is represented in Fig. 307. It consists also of a hollow cylinder, in which moves a piston, B. It has two valves, both opening up- wards ; one at the bottom of the cylinder, covering the mouth of the tube leading to the water of the well, and the other at the THE THREE STATES OF MATTER. 335 top of the piston, covering the hole with which it is pierced. If the piston and valves are sufficiently tight, this pump will act as an air-pump, and on moving the piston by the handle P alter- nately up and down, it will ex- haust the air from the tube A. But since the end of the tube dips under water, the pressure of the air will force up the water until it fills both the tube and the cylinder below the piston. Then, on lowering the piston, the water in the cylinder will raise the valve o, and pass above the piston. Afterwards, on rais- ing the piston, this water will be lifted and discharged into the pipe C, while a fresh quantity of water will be forced up by the atmospheric pressure through the valve S. Thus, at each stroke of the piston, a quantity of water is lifted equal to the capacity of the cylinder less the volume occupied by the piston itself. If the piston and valves are not sufficiently tight to pump out the air, they can be made so by pouring a little water into the pump. This is what is called the drawing of water, and the philosophy of this well-known process is evident. It follows from this description, that the pump will not work, if the bottom of the piston, in its highest position, is over ten metres above the level of the water in the well ; and it was an attempt of some Florentine engineers to raise water in the suction-tube of a pump above this height, which led to the discovery of the pressure of the atmosphere. On account of the imperfections of the valves and piston, a pump will seldom work in practice higher than eight metres. The height of the tube C, in which the water is lifted by the piston, may be very considerable, and the whole height through which the water is raised by the pump is fre- quently very much over ten metres ; but the difficulty of working Fig. 307. 336 CHEMICAL PHYSICS. a pump, and keeping it in order, increases very rapidly with the height of the column of water which is lifted. PROBLEMS. Unless otherwise stated, the temperature in all the following problems is to be taken as 0° C., and the height of the barometer at 76 c. m. Weight of a Body in Air. 176. A mass of metal, whose a^. Gr. = 11.35, weighs 0.575 gramme in a vacuum. How many milligrammes will it lose when weighed in air .'' 177. A brass weight {Sp. Gr. = 8.55) weighs in a vacuum one kilo- gramme. How many milligrammes does it lose when weighed in air ? 178. A body loses in carbonic acid gas 1.15 gramme of its weight. What would be the loss of its weight in air and in hydrogen ? 179. A body loses 7 grammes of its weight in air; how much of its weight would it lose in carbonic acid and in hydrogen ? 180. AVhat is the weight of hydrogen contained in a glass globe whose surface is equal to 10 m.° ? 181. A glass globe from which the air has been exhausted weighs 254.735 gram. When full of air, it weighs 5,4-22.737 gram. When full of another gas, 651.175 gram. What is the capacity of the globe, and what is the specific gravity of the gas ? 182. A glass globe 30 c. m. in diameter, filled with air, and hermeti- cally sealed, is balanced in the atmosphere by brass weights amounting to 356.225 gram. How much would it weigh in a vacuum ? How much would the globe weigh in a vacuum, if it were opened so that the air could be exhausted from the interior? Sp. Gr. of brass 8.55, and of glass 3.33. 183. A glass globe hermetically sealed weighs in the air 25.236 gram, and gains in a vacuum, 0.632 gram. What is its diameter ? Buoyancy of Air. 184. What is the ascensional force of a balloon one metre in diameter, three quarters filled with hydrogen, when the balloon itself weighs one kilogramme ? 185. Calculate the ascensional force of a spherical balloon made of prepared silk and filled with impure hydrogen, knowing that the bal- loon itself weighs 63,620 gram., that the prepared silk weighs 250 gram, the square metre, and that a cubic metre of impure hydrogen weighs 100 gram. 186. What would be the ascensional force of a spherical balloon seven metres in diameter, two thirds filled with hydrogen, when the balloon and attachments weigh twenty kilogrammes ? THE THREE STATES OP MATTER. 337 187. The material of a balloon containing 1229 c. m." weighs 1.5 gram. The balloon is filled with hydrogen, whose specific gravity referred to water is 0.00009003. The specific gravity of the surrounding air is 0.0013. Will the balloon rise in the atmosphere ? 188. The material of a spherical balloon and its attachments weighs 400 kilogrammes. This balloon is 15 m. in diameter, and is three fourths fiUed with gas whose specific gravity equals 0.0006. The specific gravity of the surrounding air is 0.0013. "What is the ascensional force of the balloon ? Barometer. 189. When the surface of a column of mercury in a barometer stands at 76 centimetres above the mercury in the basin, with what weight is the atmosphere pressing on every square centimetre of surface ? Sp. Gr. of mercury = 13.596. 190. To what difference of pressure does a difference of one centi- metre in the barometric column correspond ? 191. When the water barometer stands at ten metres, what is the pressure of the air if the temperature is 4° ? 192. How high would an alcohol barometer, and how high a sulphuric- acid barometer, stand under the same circumstances, disregarding in each case the tension of the vapor ? *S^. Gr. of alcohol = 0.8095 ; Sp. Gr. of sulphuric acid = 1.85. 193. When the mercury in a barometer stands 75.2 c. m., with what weight is the atmosphere pressing on every square centimetre of surface ? How high would barometers stand under the same circumstances, filled with Uquids of the following specific gravities, viz. 1.12, 1.45, 2.36, 3 ? 194. When the mercury barometer stands at 76 c. m^, what must be the length of a water barometer inclined to the horizon at an angle of 30° ? 195. If a barometer, having its lower end immersed in a basin of mer- cury, be suspended from the beam of a balance, and weighed, is its weight altered by weighing it again when inverted and containing the same quantity of mercury as before ? Pressure of the Atmosphere. 196. When the barometer stands at 76 c. m., how great is the pres- sure of the air upon a plane surface having an area of one square metre .'' 197. The body of a man of ordinary stature exposes a surface of about one square metre. How great a pressure does the body sustain when the barometer stands at 72 c. m. ? If the barometer rises to 78 c. m., how great is the increase of pressure ? 29 338 CHEMICAL PHYSICS. 198. When the barometer stands at 72 c. m., how great is the pres- sure of the air on a sphere whose radius is equal to 6675 c. m. ? 199. When the barometer stands at 76 c. m., what is the pressure ex- erted in the vertical direction on a sphere 125 c. m. in diameter ? Mariotte's Law. In all these problems the law is to he regarded as invariable. 200. A volume of hydrogen gas was measured and found to be equal to 250 c. m.^ The height of the barometer, observed at the same time, was 74.2 c. m. What would have been the volume if observed when the ba- rometer stood at 76 c. m. ? What would be the volume at an elevation at which the barometer stands at 56 c. m. ? 201. A volume of nitrogen gas measured 756 c. m.^ when the barometer stood at 77.4 c. m. What would it have measured if the barometer had stood at 76 cm.? 202. A volume of air standing in a bell-glass over a mercury pneumatic trough measured 568 c. m.^ Tlie barometer at the time stood at 75.4 centim., and the surface of the mercury in the bell was found, by meas- urement, to be 6.5 c. m. above the surface of the mercury in the trough. What would have been the volume had the air been exposed to the pres- sure of 76 cm.? 203. A volume of air standing in a tall bell-glass over a mercury pneu- matic trough measured 78 c. m.^ The barometer at the time stood at 74.6 (,'. m., and the mercury in the bell at 57.4 c m. above tlie mercury in the trough. What would have been the volume had the pressure been 76 cm.? 204. What would be the answers to the last two problems, had the pneumatic trough been filled with water instead of mercury ? 205. The specific gravity of air at 0° and 76 c m. referred to water is 0.00129363. What is the specific gravity when the barometer stands at the following heights, viz. 72.65 c m., 74.23 c. m., 75.54 c. m., 77.82 c. m. ? 206. The specific gravity of carbonic acid gas at 0° and 76 c m. re- ferred to water is 0.00196663. AMiat is the specific gravity when the barometer stands at the heights given in the last problem ? 207. A glass globe 10 c. m. in diameter hermetically sealed weighs 45.120 gram, when the barometer stands at 74.5 c. m. What would it weigh if tlie barometer stood at 76 c. m. ? 208. A glass globe hermetically sealed, 30 c. m. in diameter, suspended to one pan of a balance, is poised by 325.422 grammes in brass weights when the barometer stands at 76.21 c. m. After several hours it is found to have lost in weight 0.022 gram. What is now the height of the ba- rometer, supposing the temperature not to have changed ? THE THREE STATES OP MATTER. 339 209. A glass globe hermetically closed was found to weigh 354.567 gi-am. when the barometer stood at 73 c. m., and to weigh 353.917 gram, when the barometer stood at 77 c. m. What is the diameter of the globe? 210. A glass globe 25 c. m. in diameter contains how many grammes of hydrogen at the following pressures, viz. 72.2 c. m., 74.6 c. m., 76 c. m., 77.2 cm.? 211. Two glass globes are connected by a tube in which there is a stopcock. In the first globe there are 250 c. m." of air at a tension of 2 c. m. In the second, 340 cTm.'' of air at a tension of 10 c. m. After opening the stopcock, what will be the tension in both globes ? 212. Into an exhausted jar having a capacity of 60 litres there have been poured 30 litres of nitrogen at the pressure of 72 c. m., 15 litres of oxygen at the pressure of 64 c. m., and 5 litres of carbonic acid gas at the pressure of 78 c. m. What is the elastic force of the mixture ? 213. A glass globe contains 8.548 gram, of air. It is afterwards filled with protoxide of nitrogen whose Sp. Gr. = 1.52, that of air being unity. What is the weight of the gas, 1st. when the tension of the two gases is the same, 2d. when the tension of the air is 76 c. m. and that of the pro- toxide of nitrogen 78 c. m. ? 214. A glass globe weighs, when completely empty, 152.475 gram. ; full of air, it weighs 168.386 gram., and fuU of another gas, 157.235 gram. What is the density of the gas, supposing the pressure the same at both weighings ? Also, what correction must be made if the pressure was 77 c. m. during the weighing of the air, and 74 c. m. during the weighing of the gas ? The tension of the air and gas in the })alloon is supposed to be 76 c. m., and the temperature is supposed invariable. Atmos'p'here. The foUomng prdbUms may he solved by Babinets formvla. See note to page 304. 215. Find the difference of level of two stations from the following- data : — Height of barometer at lower station reduced to 0° C, 755 m. m. Temperature of air " " 15° C. Height of barometer at upper station reduced to 0° C, 255 m. m. Temperature of air « " 10° C. 216. Find the difference of level of two stations from the following data : — ■ Height of barometer at lower station reduced to 0° C, 730 m. m. Temperature of air " " 20° C. Height of barometer at upper station reduced to 0° C, 635 m. m. Temperature of air « « 15° C. 217. Find the height of Mount Washington above sea level from the following observations of Prof. Arnold Guyot, Aug. 8, 1851, 4 P. M. : — 340 CHEMICAL PHYSICS. Pleight of barometer at Gorham reduced to 0° C, 740.70 m. m. Temperature of air at Gorham, . . . 22°. 25 Height of barometer one foot below the summit of Mount Washington reduced to 0° C, . . 608.93 m. m. Temperature of air at summit, .... 10°. 30 Barometer at Gorham above sea level, . . 251 m. Air-Pump. 218. The capacity of the cylinder of a pump is one third of the ca- pacity of the receiver. After how many strokes of the piston will the ten- sion of the air in the receiver be reduced to j^jr of its primitive amount ? 219. The capacity of the cylinder of a pump is one tenth of that of the receiver. What will be the tension of the air in the receiver after 1, 2, 3, 4, 5, 10, and 40 strokes of the piston ? 220. If the air in the receiver of an ah'-pump is by two strokes of the piston made four times rarer than it was at first, what is the ratio of the capacity of the receiver to that of the barrel ? 221. If in an air-pump the density before is to the density after three strokes of the piston as 35 is to 8, determine the ratio of the ca- pacity of the receiver to that of the barrel. 222. If, in an air-pump similar in construction to the common water- pump, an interval be left between the piston and the lower valve at the lowest possible position of the piston, determine the density of the air in the receiver after n strokes and after an infinite number. 223. What are the conditions under which the common pump will not work, when the piston does not descend to the fixed valve ? 224. If a body when placed under the receiver of a given air-pump weighs a gram., and after n strokes weighs h gram., determine the weight of the body in a vacuum ; and, supposing the specific gravity of the body known, determine the specific gravity of the air in the receiver at first. Miscellaneous. 225. A bell full of mercury is standing over a mercury pneumatic trough. Its interior diameter is 6 c. m. The extreme height of the col- umn of mercury it contains, from the surface of mercury in the trough, is 18 c. m. The weight of the bell itself is one kilogramme. How much force in grammes is required to sustain the bell in its position, supposing that no portion of the beU dips under the mercury ? 226. A cylinder, the height of which is 6 c. m. and the radius of the base 1 c. m., is filled with atmospheric air. To what depth will a piston sink in the cylinder which weighs 10 kilogrammes ? To what depth would it sink if it weighed 1000 kilogrammes ? 227. In the cylinder described in the last example, a piston is forced THE THREE STATES OP MATTER. 341 down 2 c. m. ; determine the pressure of the confined air. Determine also the pressure of the air when it is forced down 5.64 c. m. 228. Calculate the total weight of the atmosphere in kilogrammes, sup- posing the height of the barometer 76 c. m., and the radius of the earth considered as a sphere equal to 6,366 kilometres. Calculate also the volume of an equivalent mass of gold, knowing that the Sp. Gr. of gold = 19.363, and that of mercury = 13.593. 229. If the altitude of the mercury in a barometer placed in a cylin- drical diving-beU be observed at the beginning and end of a descent, de- termine the depth descended. 230. Determine the tension of the rope by which a cylindrical diving- bell is suspended at any depth below the surface. 231. If a cylindrical tube 152 c. m. long be half flUed with mercury, and then inverted, determine how high the mercury will stand when the barometer stands at 76 c. m. 232. Having given the quantity of air left in a barometer tube be- fore immersion, find the height at which the mercury is supported after immersion. 233. If in an imperfectly filled barometer tube, of which the length is 80 c. m., the mercury stands at 74 c m., when in a well-filled tube it stands at 76 c. m., determine at what height it will stand in the imperfect one when it stands at 70 in the perfect one. 234. Two barometers , of the same given length, I, being imperfectly filled with mercury, are observed to stand at the heights ^and H on one day, and h and h' on another. Determine the quantity of air left in each, supposing the temperature invariable. 235. A cylinder of known density and magnitude floats with its axis vertical in a vessel of water. What will be the effect of removing the atmospheric pressure ? 236. Investigate a formula by which Nicholson's hydrometer may serve as a barometer. 237. A cylinder of known density and magnitude floats with its axis vertical in a vessel of water placed under the receiver of a condenser ; determine after how many strokes of the piston it will be elevated by a given amount. 238. If a balloon of given weight and capacity be so constructed, that as it rises the hydrogen escapes till the elasticities of the gas and the ex- ternal air are equal, compare the greatest height it can attain with that which it could have attained if the air had not been suffered to escape. 239. How high will the balloon of example 238 ascend? When it floats in the air, determine to what additional height it will rise if 50 kilo- grammes of ballast be thrown out. 29* 842 CHEMICAL PHYSICS. MOLECULAR FORCES BETWEEN HETEROGENEOUS MOLECULES. (180.) Adhesion. — Having studied the phenomena caused by the action of molecular forces between homogeneous mole- cules, as manifested in the characteristic properties of solids, liquids, and gases, we come next to consider those phenomena which are caused by the action of molecular forces between hete- rogeneous molecules. As we have already seen, the molecular forces are either attractive or repulsive (78). To the attractive force, when exerted between homogeneous molecules, lilse those of the same body, whether it be solid, liquid, or gaseous, we give the name of cohesion (79). But when the attractive force is exerted between heterogeneous molecules, like those of different bodies, and still does not produce any chemical change, we call it adhesion. It must not, however, be supposed that these attractive forces are essentially different in the two cases. The distinction between cohesion and adhesion is only made for the sake of classification, and it is at least possible that they are merely different manifestations of the one force of universal gravitation already considered. The phenomena of adhesion are quite numerous, and they can be most conveniently classified according to the mechanical con- dition of the masses of matter between which the force acts. "We will, therefore, consider in order the phenomena caused by the action of, — First, solids on solids (cements^ . Secondly, solids on liquids (capillarily , solution^) . Thirdly, solids on gases (^absorption of gases, osmose}. Fourthly, liquids on liquids (liquid diffusion}. Fifthly, liquids on gases (solution of gases'). Sixthly, gases on gases (gaseous diffusion} . Solids on Solids. (181.) Adhesion betioeen Solids. — Many of the most famil- iar phenomena of daily life are owing to the attractive forces which 'Cxist between heterogeneous particles of solids. Thus the particles of dust floating in a room adhere to the ceiling in opposition to the force of gravity. In like manner, the particles of chalk adhere to the vertical surface of a blackboard, and the THE THREE STATES OF MATTER. 343 particles of plumbago abraded from a lead pencil adhere to a sheet of ■writing-paper. So also the adhesion of paint to wood or canvas, that of the tin amalgam to the backs of glass mirrors, and that of gold-leaf to picture-frames, belong to the same class of phenomena. The numerous important applications of india- rubber in the chemical laboratory furnish still further illustra- tions of adhesive force. India-rubber adheres very strongly to glass, and this property renders it invakiable for making stoppers to glass bottles and air- tight joints between glass tubes. The common method of unit- ing together glass tubes in adjusting chemical apparatus consists in stretching over the ends of the tubes a short tube of india- rubber called a connector, e /, (Pig. 308,") so that the ends of the two glass '' -^ tubes shall meet within it. On binding ^ , the india-rubber to the glass by means of t " <• 4 a silk cord or fine copper wire, the adhe- ^'^" ^°^' sion is sufficient to resist the action of most gases, unless the pres- sure is considerably greater than that of the atmosphere. These connectors can easily be made of the required dimensions from sheet india-rubber. We apply a strip of india-rubber previously softened by heat, to the glass tube, as represented in Fig. 309, and then cut the two edges with a pair of scissors, which should have broad, flat blades, and be perfectly clean. The cut edges immediately imite, and the union can be made more solid by pressing them together between the thtmib-nails. The india-rubber connector will ad- here at first firmly to the glass tube, but it can be easily removed after dipping the tube into water. The water is drawn up between the glass and the india-rubber by capillary attraction, and the adhesion is destroyed. (182.) Cements. — The use of cements not only illustrates the existence of an attractive force between the molecules of heterogeneous solids, but also the additional fact, that the strength of this force varies with the nature of the solids. In order to unite two pieces of wood, we first fit together carefully 344 ' CHEMICAL PHYSICS. the surfaces to be joined, and then interpose between these sur- faces, perfectly cleaned, a thin layer of melted glue. When the glue hardens, it firmly cements together the two pieces of wood, — first, by the adhesion between the glue and the wood, and, secondly, by the cohesion between the particles of the glue itself. This same glue, however, would fail to cement together pieces of glass or of stone, because the adhesion of glue to these solids is much feebler than its adhesion to wood ; but fragments of glass and porcelain may be united by some resinous material, such as shellac, and those of stone and brick by mortar or some cal- careous cement.* It is evident that in all these cases the phenomena of adhesion are mixed with those of cohesion. The adhesion only takes place at the surfaces, where the heterogeneous particles are brought in contact, while the particles of the solids, and those of the cement, are alike held together by the force of cohe- sion. The thinner the layer of cement, the more perfectly does it fulfil its office, since, when a thick mass is used, the unequal expansion of the different solids in contact, caused by changes in temperature, tends to destroy the cohesion of the particles of the cement. It not unfrequently happens that the adhesion between the particles of a cement and the bodies which it unites, is greater than the cohesion which holds together the particles of the body itself. On attempting to separate two pieces of wood along a glued seam, we often see a film of wood split off adhering to the surface of the glue ; and the feat of splitting a bank-note is accomplished by cementing it firmly between two flat surfaces, and then forcibly separating them, when, the cohesion of the paper being feebler than the adhesion of the cement, the paper is split through the middle. f Solids and Liquids. (183.) Adhesion of Liquids to Solids. — That the svirfaces of solids are generally wetted when dipped into a liquid is a fact universally known, and it is self-evident that the liquid mole- cules are held to the solid surface by a mutual attraction between * For a description of the various cements used in the laboratory, the student is refen-ed to the works on chemical manipulations by Taraday, Morfit, and others. t Miller, Elements of Chemistry, page 59. THE THREE STATES OP MATTER. 345- the liquid and solid particles. The strength of this attraction, which is much greater than is generally supposed, can be made evident by a simple experiment. If a disk of glass is suspended to the pan of a hydrostatic balance, and, having been exactly counterpoised by weights in the opposite pan, is applied to the surface of a liquid capable of wetting it, it will be found neces- sary to add a very considerable weight to the counterpoise in order to separate the disk. Moreover, when the separation takes place, the disk will be found wet, showing that the separation has been between the particles of liquid, and not between the solid and liquid surfaces, and indicating that the adhesion was greater than the cohesion of the liquid. In experiments made by Gay-Lussac, at a temperature of 8°, with a circular plate 118.366 m. m. in diameter, 69.4 gram, were required to separate it from water, 31.08 to separate it from alco- hol (Sp. Gr. = 0.8196), and 34.1 to separate it from oil of tur- pentine. It was also found that the substance and thickness of the plate had no influence on the result, proving, as before, that the force overcome by the weiglit was the cohesion between the particles of the liquid, and further showing that the distance through which the force acted was less than the thickness of the liquid film which remained adhering to the plate. These num- bers cannot, however, be regarded as a direct measure of the rel- ative cohesion of the three liquids, as could easily be shown by a further examination of the conditions of the experiment. Adhesion also exists between liquids and such solid surfaces as they have not the power of wetting. Gay-Lussac found that a disk of glass adhered to the surface of mercury with a very, con- siderable force. In an experiment made as just described, with a disk of glass 118 m. m. in diameter, resting on the surface of a basin of mercury, it required in one case 296 gram., and in another 158 gram., to effect a separation, the amount of weight required depending on the manner in which the surfaces were applied to each other. In these experiments, when the surfaces were parted, the separation took place between the mercury and the glass, indicating that the weight overcame the adhesion of the heterogeneous particles, and not the cohesion of the liquid, as in the other experiments. Moreover, the force required to effect the ' separation was no longer independent of the material of the disk. 346 CHEMICAL PHYSICS. Fig. 810. (184.) Capillary Attraction. — When a solid body is par- tially immersed in a liquid, the force of adhesion produces im- portant modifications in the laws of liquid equilibrium as already enunciated. Thus, for example, if we dip the end of a fine glass tube, 2 or 3 millimetres in diameter, into water, the liquid will not maintain the same level within and without the tube as required by the principle of (130), but will be elevated in the interior of the tube, and maintained at a height which is very considerably above the exterior level, and which is the greater the smaller the diameter of the tulie. Moreover, the surface of the water does not remain horizontal near the walls of the tube, as required by (129), but on the outside it curves towards the tube, as represented in Fig. 810, and in the interior it assumes a concave form, which, for tubes less than 2 millimetres in diameter, is sensibly hemispherical. If now we dip the end of the same tube into liquid mercury, we shall obtain a result equally opposed to the laws of liquid equilibriiim, but of a reversed order. The column of mercury in the interior of the tube will be depressed below the oiitside level, and its surface will assume a convex shape, which for a small tube is as before sensibly hemispherical, while on the outside the surface of the liquid will curve from the tube, as if repelled by it (Fig. 311). By repeating these experiments with different liquids, and with tubes of various kinds, we shall obtain results like the first when- ever the liqiiid has the power of wetting the walls of the tube, and results like the second when tlio reverse is the case ; while in some few cases (as, for example, when the tube is polished steel, and the liquid is alcohol) the level will not be changed, and the surface of the liquid will remain horizontal both within and without tlie tube. These phenomena are termed in general capillarity, and the curved surfaces which the liquids assume in the proximity of solid bodies are called, respectively, concave and convex meniscuses. In studying this subject, we will first consider what changes the molecular forces must l^e ex- pected to produce a priori in the laws of liquid equilibrium, ^nd afterwards we will examine the phenomena and see liow closely Fig 311. THE THREE STATES OF MATTER. 347 the facts coincide with our theoretical deduction. Let us com- mence with the simplest case possible, and consider how the sur- face of a liquid must be disturbed by the contact of a solid bar. Take, for example, a liquid particle, m (Fig. 312), in contact with a solid bar, dipping under the surface of any liquid. This particle is evidently acted upon by the force of gravity, g, and by three other fox'ces. The first of these, /, is the result- ant of the attractive forces exerted by the liquid particles included in the quarter- sphere mab. The other two,/' and/", are the resultants of the attractive forces exerted by the solid particles inchided in the two quarter-spheres mo c and mob, the radius of the sphere in each case being the insensible distance through which the mole- cular forces can act. We can now decompose each of these three forces into a vertical and a horizontal component. Considering the components which act in the directions m a or m b positive, we shall have for the horizontal components (35), / cos 45°, — /' cos 45°, — /" cos 45° ; and remembering that /" = /', we shall also liave for the single resultant of the three horizontal components (/ — 2 /') cos 45°. In like manner, for the vertical components, including gravity, we shall have, — g, f cos 45°, — /' cos 45°, /" cos 45°, and for the single vertical resultant, g -|-/ cos 45°. Let us next inquire what will be the direction of the final resultant of the horizontal and vertical forces, whose values are (1.) (/— 2/')cos45°; (2.) g- + / cos 45. '[121.J It is evident that the vertical force must always be positive, and hence directed downwards ; but the direction of tlie horizontal force will depend on the relative values of/ and /', that is, on the relative strength of the cohesive and adhesive attractions. There may be three cases, according as / is less than, is greater than, or is equal to 2 /'. We will consider each case separately. 1st. When / <; 2 /'. If the cohesive force is less than twice the adhesive force, tlien the horizontal force [121. 1] is negative, and the resultant of this force with the vertical force [121. 2] will 848 CHEMICAL PHYSICS. Fig. 313. fall within the angle bmo, and take, for example, the direction MR (Pig. 313). Now, since the surface of a liquid must at every point be normal to the resultant of all the forces acting at that point (129), it fol- lows that the liquid surface will be drawn up towards the solid bar, so as to be per- pendicular to the line M R, and tangent to the line M N, making with the bar an angle D M N, which is constant for the same sub- stances, and is called the angle of contact. If next we consider the liquid particles M' M", &c. adjacent to M on the surface of the liquid, it is evident that on account of their greater distance they will be acted upon less strongly by the solid bar, and hence the resultants M' R', M"R", &c. will approach more and more nearly the vertical, with which they will soon coincide. Thus it appears that the liquid surface, which must be at each point perpendicular to these resultants, will be curved up towards the bar, but will become horizontal at a certain small distance from it. It is easy to see that, if a sec- ond bar is dipped into the liquid parallel to the first, the surface of the liquid between the bars will take the form of a concave cylindrical surface, in case the bars are sufficiently near together, and that in a tube it would take the form of a concave meniscus, formed by the revolution of the curve MM' M" round the axis of the tube. 2d. "When / > 2 /'. If the cohesive force is greater than twice the adhesive force, then the horizontal force [121. 1] is positive, and consequently directed towards the liquid. Hence the resultant of this force and the ver- tical force [121. 2] will fall within the angle amb (Fig. 312), taking, for ex- ample, the direction MR (Fig. 314), and the surface of the liquid will be per- pendicular to this resultant, making with the solid bar an angle D M N less than rig 3ii. 9oo_ Moreover, for the particles M', M", &c. adjacent to M on the surface of the liquid, it can be proved that the resultants of the molecular forces and gravity will ap- proach the vertical nearer and nearer the farther we recede from the bar, and will soon coincide with it. Hence it follows that THE THREE STATES OP MATTER. 349 the liquid surface will, in this case, be convex, taking the form of a convex cylinder between two parallel bars, and of a convex meniscus in a fine tube. 3d. When / = 2 /'. When the cohesive force exactly equals twice the adhesive force, then the horizontal force [121. 1 j becomes zero, aind the resultant of all the molecular forces and gravity, acting on the particle vi, coincides with the vertical. In this case alone the surface of the liquid is horizontal, even to the line of contact with the solid bar, and consequently, likewise, hori- zontal between two bars, or in the interior of a tube. (185.) Form of the Meniscus. — It is evident from the last section, that the exact form of the meniscus, and the angle of contact, depend upon the relative values of /and 2/' [121], and hence upon the nature of the solids and liquids used. The con- ditions are changed, however, when,, as is usual in such experi- ments, the solid bar or tube has been previously rinsed with the liquid. In such cases tlie action takes place between the parti- cles of the thin film of liquid covering the solid, and those of the same liquid into which it is dipped, the solid itself serving only to sustain the liqiiid film, and it is then found that the result is entirely independent of the nature of the solid. Moreover, when the solid has not been previously moistened, the phenomena are rendered very irregular by the film of air which covers the sur- face of the bar or tube, and which it is almost impossible to remove without moistening the whole surface. So also, when the liquid has not the power of wetting the solid surface, as in the case of mercury and glass, there may be a film of air between the two of sufficient thickness to keep the liqixid particles beyond the sphere of action of the adhesive force. In such cases the form of the liqviid surface will be determined by the action of the cohesive force alone, and this action will be entirely similar to that which gives to the rain-drop its spherical form (129). Since it has been observed that the surface of a liquid in a tube is concave when it wets the walls of the tube, and convex when it has not the power of tluis wetting them, it follows from the last section that a liquid will wet a solid surface when the force of cohesion between its particles is less than twice the force of adhesion of these particles to the solid. (186.) Pressure exerted by the Molecular Forces. — Having seen how the molecular forces may modify the form of a liquid 30 350 CHEMICAL PHYSICS. surface, and produce either a concave or a convex meniscus, let us further inquire how the form of the surface may modify the law of liquid pressure already enunciated (126). In discussing the subject of liquid pressure, caused by the force of gravity (123 5eg.), we left out of view any action which might be exerted by tlie molecular forces emanating from the liquid particles themselves. This leads us into no error, so long as the surface of the liquid is horizontal ; but when, as in capillary tubes, this surface is curved, tlie action of the molecular forces can no longer be disregarded. In order to investigate the man- ner in which the molecular forces may inflxience the pressure exerted by a liquid mass, terminated by a given surface, ZF (Fig. 315), let us study the action which they would exert on any particle taken on Pig. 315. or near this surface. If this molecule is on the surface, as M, it will evidently be attracted by all the particles of liquid comprised within the hemisphere described round the point M, with a radius eqiial to the distance of sensible attrac- tion, and it is easy to see that the resultant of all these attractive forces will be in the direction M P, normal to the surface. If the molecule is within the surface, as at M', then the active por- tion of the liquid will be the mass enclosed by the sphere of sen- sible attraction, ABC. This may be divided into three parts by an equatorial plane, P Q, and by a surface. A' B', symmetrical with A B, and equidistant from the equator. 'The attraction ex- erted by the portion A B P Q is evidently balanced by the equal and opposite attraction exerted by A' B' P Q, so that the result is the same as if the molecule were only attracted by the portion A' B' C. The resultant of all the attractive forces exerted by the particles contained in this portion of the sphere is evidently much less than before, but still it is normal to the surface. Fi- nally, if we talte a molecule, M", at a distance from the surface eqxial to the radius of sensible attraction, it is evident that the attractive forces acting upon it will balance each other. If then we draw a surface, X'Y', parallel to ZY, and at a distance from it equal to the radius of sensible attraction, we shall have com- THE THREE STATES OP MATTER. 351 prised between these two surfaces a liquid film whose particles are under the influence of forces acting perpendicularly to the surfaces, and exerting an effect similar to that of gravity. There must then result from the action of these molecular forces a pressiire, which will be transmitted in all directions, according to the principle of (120), and whose effect must be added to those of gravity and atmospheric pressure. (187.) Amount and Effect of the Molecular Pressure. — Let us now inquire wheilier the form of the surface exerts any influence on the amount of the molecular pressure. For this purpose let us take a molecule, M' (Fig. 316), at a distance below the surface, M' H, less than M' C, the radius of sensible attraction, and con- sider what will be the relative amount of molecular pressure exerted by this molecule, — 1st, when tlie surface is plane; 2dly, when it is concave; and 3dly, when it is convex. If the surface is plane, as A B, the attraction exerted by the liquid mass A BPQ is balanced by that of A' B' PQ, and the only force which produces pres- sure is the attraction exerted by A'B'C. Lot us represent the value of this force by A. If now the surface is concave, as J) E, it is evident that the only portion of the liquid within the sphere of sensible attraction, whose attractive force is not neutralized, is the portion D' E C, cut off" by a surface D' E, drawn symmetrically to D E. Since this liquid mass is less than A' B' C, the attractive force which it exerts must be less by an amount wo will call B, and it is evi- dent that the value of B will increase as the radius of curvature of the surface diminishes. The value of the force which is ex- erted in molecular pressure may then be represented by ^ — B, when the surface is concave. If, lastly, the surface is convex, as KL, and wo draw K' L' symmetrical with this, if is equally evident that the active por- tion of the liquid is now K' L' C; and since this mass is greater than A' B' C, the value of the molecular pressure may be repre- sented by ^ -|- -B', when the surface is convex. Since what has been sliown to be true of the pressure exerted Fig 316. 352 CHEMICAL PHYSICS. by the molecule M' is true of all the molecules contained in the thin film bounded by the surfaces X Y, and X' Y' (Pig. 315), it follows that, when the surface of a column of liquid is concave, it exerts a less pressure, and conversely, when the surface is convex, it exerts a greater pressure than when it is plane, as- suming always that the radius of curvature of the surface is comparable with the radius of sensible attraction. (188.) Effects of Molecular Pressure. — It is now easy to see in what way the molecular pressure may modify the prin- ciple of (130), when one of the vessels is very small. Let us suppose, then, that wc have a fine tube of glass, dipping into a liquid (Fig. 317). By the principles of hydrostatics, the level of the liquid should be the same within and without the tube, because it is a necessary condition of equilibrium that the pressure on any given section, as MN, should be the same, whether exerted by the column of liquid in tlie tube, or by tlie liquid mass outside, and tills cau only be when S.H. <^Sp. Gr.) = S. IT . (Sp. Gr.) [122.] or when 11= H' (compare 130). This equation, however, only has regard to the pressure exerted by liquids in consequence of their weight, although, as we have just said, the molecular forces exert a pressure themselves whose effect must be added to that of gravity. As the surface of the liquid outside the tube is hori- zontal, tlio molecular pressure transmitted by it to the section M TV may be represented by A, and the whole pressure on the section will be S . //. (Sp.Gr.y -\- A. If, however, the liquid wets the tube, the interior surface will be concave, and the pres- sure transmitted from the interior of the tube to the section will be S.H'. (Sp. Gr.) -\-QA — B}. Evidently there can only be an equilibrium when Fig. 317. or S.Il. (Sp. Gr.) -\-A=S.H'. (Sp.Gr.) -f (A — B), H' = I-I+ h; [123.] that is to say, when the level in the tube is above the level outside. The difference of level, A, measures the difference of THE THREE STATES OP MATTER. 353 pressure, B, caused by tlie concavity of the surface. If the liquid does not wet the tube (Fig. 318), then the interior surface will be con- vex, and the pressure transmitted from the interior of the tube to the section will be S. H' . {Sp.Gr.) + (4 + 5'). We shall then have equilibrium when Fig 318. S.H . (Sp. Gr.) + A= S . II' . (Sp. Gr.) + (4 + 5'), or H' = H — h'; [124.] that is to say, when the level in the tube is below the level oxit- side ; and here, as before, the difference of level measures the difference of pressure, which is caused in this case by the con- vexity of the surface. Between these two conditions there is a third, in which the liquid surface is level within the tube. In this case it is evident that the molecular pressures will balance each other, and there can be equilibrium only when H' = H, or when the level is the same within and withoiit the tube. These results, which we have now deduced theoretically, are fully confirmed by observation ; for we find, as has already been stated (184), that a concave meniscus is always accompanied by an elevation of the liquid column in a capillary tube, and a con- vex meniscus by a corresponding depression. The phenomena of capillarity may be illustrated not only by means of a simple tube, as represented in Figs. 310 and 311, but also by a siphon tube, one of whose branches is very small, while the other is at least 20 millimetres in diameter (Figs. 319 and 320). The depression or elevation of the liquid in the smaller tube becomes then very evi- dent, and can easily be measured. A number of these tubes may be moxuited together for comparison, as represented in Fig. 321. These phenomena are entirely independent of the pressure 30* Fig 319. Fig. 320. 364 CHEMICAL PHYSICS. to which the apparatus is ex- posed. They are the same in compressed air as in a vacuum, and are uot influenced hy the thickness of the walls of the tube. They vary, on the oth- er hand, witli the material of the tube, and with the nature of the liquid. When, how- ever, the tube has previously been wet with the liquid, tlie phenomena arc also entirely independent of tlie material of which it is formed, and at any given temperature vary only with the nature of the liquid and the diameter of the tube. If we take tubes of the same diameter, and dip their ends in different liquids, capable of moistening the walls, we find that the heights to which the liqiiid columns are elevated differ very greatly. If the tube is 1.3 m. m. in diameter, the height is 23.1 m. m. for water, 9.8 m. m. for oil of turpentine, 7.07 m. m. for alcohol, and still less for ether. It is essential in these experiments that the tubes should be pre- viously cleaned, and carefully rinsed out with the liquid to be used. Otherwise the phenomena are also influenced by the ma- terial of the tube, and are rendered very irreg\ilar by the film of air adhering to the siirface. This is especially true when the liquid has not the power of wetting the surface, and the order of the phenomena is reversed. The amount of depression in such cases not only varies with the nature of the tube and of the liquid, biit, moreover, it is not the same for the same tube and liquid \inder different circumstances. For example, in the case of mercury and glass, the form of the meniscus, and the depres- sion of the mercury column, which depends vipon this form, vary so greatly with the impurity of the metal, the presence of tlie air, and the nature of the glass, that it is not possible to calculate the amount from any general measurements, but it is necessary to de- rig. 321. THE THREE STATES OP MATTER. 355 termine it by experiment for eacli particular instrumentj Thus, in the same tube the mercury column will be more depressed iu a vacuum than in the air, especially when the air is moist. So, also, mercury which has been boiled in the air forms a less con- vex meniscus than merciiry which has been boiled in an atmos- phere of hydrogen or carbonic acid. And lastly, a small amount of oxide dissolved in the mercury may even invert the order of the phenomena, causing it to assume a plane, or even a slightly concave surface. In determining the amount of pressure from the height of a mercury column in a barometer tube, or in other forms of tube-apparatus \ised in experiments on gases, it is important to correct the observations for the capillary depression ;, but since, from the causes just stated, the amount is uncertain, it is best either to use tubes so large that it is reiidered insensible, or else so to arrange the apparatus that the effect of capillarity in one arm of a siphon is balanced by an equal eifect in the other. In the barometers of Regnault and Fortin the amount of depres- sion is a constant quantity, and is determined once for each instru- ment (159 and 160) ; but even in a well-made barometer the surface of the mercury is liable to changes, which alter the form of the meniscus, and consequently cause a variation in the amount of depression. The convexity of the meniscus can gen- erally be restored by tapping on the glass ; but when the surface of the mercury is badly soiled, it is necessary to refill the tube. (189.) Numerical Laws. — Although the theory of capillarity, as thus far developed, explains and predicts the general order of the phenomena, it does not yet enable us to calculate the amount of the elevation and depression in different tubes. This, as we have seen, varies with the na- ture of the liquid, and, when the walls of the tube have not been previously moistened with the liquid, also with the nature of the tube. But assuming that all other conditions are equal, let us in- vestigate the relation between the capillary effect and the size of the tube. For this piirpose let us take the simple case of a capillary tube (Fig. 322) dipping in a mass of liquid which is. capable of wetting its surface, and which consequently rises in its bore to a ^^l|^^ 356 CHEMICAL PHYSICS. mean height A B. In the first place, it is evident that the mass of the tube just above tliis level must attract the liquid molecules below, and that there will thus result a vertical force, which will tend to raise the liquid column. Since this force is proportional to the number of solid particles within the sphere of attraction, and hence to the perimeter of the tube, we may represent it by the expression pa, in which a is a constant quantity depending on tlie nature of the tube and the liquid, and p the perimeter of the tube. If now, in the second place, we con- sider the portion of the tube between A B and C D, it is equally evident that the attractive forces exerted by the solid particles will balance each other, and can therefore produce no effect eitlier in elevating or depressing the column. Finally, the molecules of the tube placed just above CD will attract the particles situated just below in the prolongation of the liquid column, and will evi- dently exert a force tending to raise tliis column, which equals, as before, pa, and which added to the first gives us 2pa as the whole value of the upward pressure. But we have thus far left out of view the liquid mass below the end of the tube. If we conceive of the solid tube as pro- longed by a tube of liquid, C D M N, it is evident that the liquid particles forming the walls of this tube will attract those of the liquid column just above C D, and will thus exert a force tending to depress it. Representing. by a' a constant depending on the nature of the liquid, we shall have for this downward force the value p a', and for the whole vertical force the value p (2 a — a'), a force which will raise or depress the column according as (2 a — «') is positive or negative. This force must evidently be equal to the weight of the column of liquid which it elevates or depresses ; and since this weight may be found by multiplying together the area of the section of the tube, s, the height of the column, h, and the specific gravity of the liquid, Sp. Gr., we obtain p(2a—a')=s.h. (Sp. Gr.), or A = -£ 2«ir^=±^«», [125.J s iSp. Gr. s ' 2 a a' in which last a' = -^ — p^-;- , and is constant so long as the liqiiid and substance of the tube are the same. THE THREE STATES OP MATTER. 35T If the tube is cylindrical, 2 = ^^^ = ^ and A = ± i a\ s n D'- D D For another tube of the same material, but different diameter, -D', we obtain h' = ± ^j, «", whence we deduce ± /t : zb A' = D' : D, [126.] or in words. The elevations or depressions of a given liquid in cylindrical tubes of the same material, but of different diameters, are inversely proportional to the diameters of the tubes. If the tube has a rectangular section, the perimeter is equal to 2 (m -\- n'), the lengths m and n being those of the sides of the rectangle, and we have -^= — ^^ — ^^^—^. When the length s m n „ ° of one side is infinite, we have also w = oo , ^ = — , and 2 s m h = ± — a% from which we can deduce m ± A : dz h' =m': m. [127.] The case supposed is evidently that of two plates parallel to each other, and separated by a distance m. Hence the elevation or depression of a given liquid between two parallel plates is inversely proportional to their distance apart. If, lastly, we compare the effect produced by a cylindrical tube 4 2 when h= zi=y.a', and that by parallel plates when A' = ± — a", we obtain the proportion h:h' = 2m:D, [128.] by which we find, that when m = D, then A = 2 A', or in words. The variation of level caused by two plates is one half of that caused by a tube of the same nature, whose diameter is equal to the distance between the plates. (190.) Verification of the Laws. First Law. — It follows from [126], that, if the first of the three mimerical laws, which have thus been deduced theoretically, is correct, the product of the elevation or depression of the liquid column into the diam- eter of the tube must be always a constant quantity for the same liquid. That this is approximatively, at least, the case, is shown by the following table, taken from Jamin's Cours de Physique, 358 CHEMICAL PHYSICS. to which we are indebted also for the general method followed in the discussion of this subject. Diiimeter D. Elevation k. Troduct D h, m. m m. m. (1.20 23.16 29.87 (1.90 15.58 29.60 (1.29 9.18 11.84 1,1.90 6.08 11.55 Parallel Plates and Water, . 1.069 13.57 14.52 Water, Alcohol, This law is not, however, exact, when the diameter of the tube is so large that we can no longer neglect the curvature of the surface which terminates the liquid column (we assume always tliat the height of the column is measured to the lowest point of the concavity, or to the highest point of the con- vexity). When the diameter of the tube is not greater than one or two millimetres, the surface is approximatively hemi- spherical, and we can then easily estimate the amount of devi- ation. If, as above, we represent by h and li' the heights of two columns of the same liquid in tubes of different diameters, measured to the lowest point, n, of a concave meniscus, it is evi- dent that, in order to obtain exactly the weight of these liquid columns, we must add to the weights of the liquid cylinders s . h . QSp. Gr.) and s' . h' . (^Sp. Gr.~) the weight of liquid above the point n. The volume of this liquid is evidently equal to the difference of volume between a hemisphere and a cylin- der of the same diameter and of a height equal to the radius of the hemisphere. Using the notation of the last section, we find for this volume the value ^ D~' n — j\, D' n = j'j D' n, and for the total weights of the liquid columns the values iD' 7t (a + f ) ( Sp. Gr.), and i D" n (h' + ~\ ( Sp. Gr.), and by the same course of reasoning as before [125], we deduce ±(h+^):±[h'+^) = D':D. [129.] Tiie double sign ± is used, because, as can easily be proved, the proportion is equally true when the meniscus is convex. Hence it follows, that, when the tubes are not more than one or two mil- limetres in diameter, the law of inverse proportions is correct, when we add to the observed heights one sixth of, the diameter THE THREE STATES OF MATTER. 359 of the tube, the correction required for the meniscus ; and obser- vation confirms this result of theory. When the tubes are very small, and the elevations or depres- sions correspondingly large, we can neglect the very small value ^, and regard the law as accurate without this correction. When, however, the tubes are extremely small, a new cause of devia- tion from the law is introduced. In experiments on capillarity, as already stated, we can obtain constant results only when the surfaces of the tubes have been previously moistened with the liqxiid to be used, and the results are then the same as if the experiment were made with a liquid tube of less diameter, the solid wall serving only to support the liquid particles. If the tube is one or two millimetres in diameter, the thickness of the liquid film may be neglected ; but when the tube is very small, this thickness sensibly diminishes its effective size, and we should therefore expect that it would raise a liquid column to a greater height than that required by the law, as we find to be the case. Wlien, on the other hand, the tubes are more than three milli- metres in diameter, the surface of the liquid column differs so considerably from that of a hemisphere, that the proportion [129] no longer holds true, and the deviation from the law becomes very large. Even in such cases, however, the heights to which liquids will rise can be calculated when the precise form of the meniscus is given ; but the methods are too complicated for an elementary treatise. Second Law. — The second law of (189) can be verified by a very instructive experiment. If we take two glass plates, iinited by hinges at one side, and, having very slightly opened these hinges, dip the ends of the plates, as repre- sented by Pig. 323, in colored water, we find that the liquid rises between these plates to a variable height, depending on the interval which separates them, its up- per surface taking the form of a curve. Fig. 393. known in geometry under the name of an equilateral hyperbola. Let us inquire whether the form of this curve does not furnish a confirmation of the law under discussion. 360 CHEMICAL PHYSICS. Fig 324 We may evidently regard the two glass plates as consisting of an infinite number of infinitely narrow parallel strips, as shown by Fig. 324. If then the law is ^^^HHH[|HB|| correct, it follows [127] that the heights ^^^^^^^Hm^J to which the liquid is elevated, at any two points, will be proportional to the interval between the plates at these points, so that 2 a^ at every point we must have h = — . If now we take for the axis of y the vertical line of intersection of the two planes, and for the axis of x the line of contact of the water level with one of them, we shall have (Pig. 325), MP=h = y, A P ^ X, and PQ = m=Cx, in which C is a constant quantity depend- ing on the angle between the planes. Substituting we obtain these values 2/= 77::> in h = V X rig. 325. or 2 a X y^ —7^ = a constant. which is the equation of an equilateral hyperbola referred to its asymptotes as co-ordinate axes. Since this is the curve which the liquid surface always assumes, it is evident that the second law is verified by the experiment. Third Law. — When the ends of two parallel glass plates, maintained at a small distance from each other, arc dipped into water, and the difference of level measured, it has been found that the product of the distance between the plates by the elevation of the liquid is one half of that obtained with glass tubes. This fact is shown in the table on page 358, and verifies the third law. (191.) Influence of Temperature on Capillary Phenomena. — The general expression for the elevation or depression of the liquid column in a capillary tube [125] may be written 2 a — a' ± '. = i- {Sp.Gr.)' and it is evident that any cause which changes either the spe- cific gravity of the liquid, or the relative values of the cohesive and adhesive forces, will produce variations in the value h. Hence an increase of temperature, which diminishes the specific THE THREE STATES OP MATTER. 361 gravity by expanding the liquid, would of itself alone increase the elevation or depression of the column ; but since this increase of temperature produces changes in the molecular forces, and hence affects the value of the term 2 a — a', we find that the elevation or depression, instead of increasing witli the tempera- ture, actually diminishes. This decrease is not, however, simply proportional to the temperature, but follows much more compli- cated laws. The following table shows the height at which the dif- ferent liquids enumerated stand at 0° 0. in a tube two millimetres in diameter, together with the coefficient of correction for tempera- ture, which, multiplied by t, the number of degrees above 0°, gives the amount in millimetres to be deducted from the height at 0°, in order to find the height of the capillary column at the temperature required. The last column gives the limits of tem- perature between which the formulae hold true. Water, Sp. Gr. atoo. 1.0000 h IQ.II1> 15.332 —0.0286 1 Limits of Temperature, o o to 82 Ether, 0.7370 5.400 —0.0254 1 —6 to 35 Olive Oil, 0.9150 7.461 —0.0105 t 15 to 150 Oil of Turpentine Alcohol, , 0.8902 0.8208 6.760 6.050 —0.0167* —0.0116 t —0.000051 «= 17 to 137 to* 75 Sulphuric Acid, 1.840 8.400 -0.0153 t —0.000094 1^ 12 to 90 (192.) Spheroidal Condition of Liquids. — When the adhe- sion of a liquid to a solid surface is more than twice as great as the cohesion between its particles, it spreads over the surface of the solid and wets it (185). If, however, the force of adhesion is less than this, the liquid forms in drops, which roll round on the solid surface like drops of mercury on glass, or drops of water on oiled paper. The form of these drops is determined by the action of tliree forces ; first, the cohesion of the particles of the liquid, secondly, the adhesion of the liquid to the solid, and lastly, gravity. When very small, the drops are sensibly spher- ical ; but as they increase, the sphere becomes flattened by the action of gravity, and they assume a spheroidal shape. Hence liquids, under these circumstances, are said to be in a spheroidal condition. Since most solid surfaces are wet by water, alcohol, and similar liquids, the spheroidal condition is their exceptional state ; but it js familiar to us in the cases just mentioned, and in several others. As the effect of heat is to diminish both the 31 362 CHEMICAL PHYSICS. cohesive and adhesive forces, we can easily conceive how it may so far alter their relative values as entirely to change the rela- tions of a liquid to a solid sui'face. This result is readily ob- tained with water, alcohol, and similar liquids, which, at the ordinary temperature, wet metallic surfaces. It will hereafter be shown, that we cannot heat a liquid in the open air above its boiling point, and hence we cannot diminish the cohesive force, except to a limited extent ; while, on the other hand, we can heat the metals to a far higher temperature, and thus di- minish the adhesion, until the force becomes less than twice that of cohesion, when the liquid will assume the spheroidal state. Thus, for example, if water is dropped into a metallic vessel heat- ed above 171° C, it rolls along the surface of the metal like mer- cury on glass, and remains in that state until the temperature falls to 142° ; then it moistens the metallic surface, and evaporates rapidly. Alcohol acts in the same way when the temperature of the vessel is above 134°, and ether when it is above 61°. The temperature of the liquid itself, under these circumstances, is nearly constant, being always several degrees below its boiling point : thus 96.5 is the temperature of water, 75.8 that of absolute alcohol, 34. 2 that of ether, and — 10.5 that of liquid sulphurous acid. The temperature of the liquid may there- fore be several hundred degrees below that of the metallic vessel, as is well illustrated by liquid sulphiirous acid, which in the spheroidal state retains a temperature 10.5 degrees below the freezing point of water, oven when the metallic crucible containing it is visibly red-hot. If water is slowly dropped into this singular liquid under these circumstances, it is at once congealed, thus exhibiting the apparent paradox of freezing water in a red-hot crucible. One of the most instructive illustrations of the spheroidal con- dition of water is the rude method used in laundries for testing the degree of heat of a flat-iron. If a drop of saliva let fall upon it does not boil, but runs along the surface of the metal, the iron is considered sufficiently hot ; but if the drop adheres, and rapidly boils away, the temperature is known to be too low. We shall have occasion to return to this subject in the chapter on Heat. (198.) Examples and Illustrations of Capillarity. — One of the most familiar examples of capillary action is seen in the wicks of lamps and candles. These consist of very fine THE THREE STATES OP MATTER. 363 vegetable tubes, through which the oil or melted combustible is elevated to the flame, and supplied as fast as it is burnt. This same principle also influences the circulation of the liquid juices in the porous tissues of organized beings, and it is the principal means by which water, with the substances it holds in solution, is supplied to the* growing plant. It is the capillary action, which, during the droughts of summer, draws up to the surface of the soil the water necessary for vegetation, which had penetrated into it during the heavy rains of spring. When the water holds salts in solution, these are deposited as it subsequently evaporates, forming those incrustations which are frequently seen on the brick walls of old houses and on the surfaces of saltpetre beds. The laws of capillary action furnish the explanation of many other remarkable phenomena. A platinum wire will float on the surface of mercury, although its specific gravity is very much greater tlian that of the liquid metal. So also a very fine metal- lic wire, which has been slightly greased by passing it between the fingers, can be made to float upon water, and the same is true of many metallic powders. This singular result is explained by the fact, that the floating body is not wet by the liquid, and con- sequently there forms around it a meniscus, which displaces a large volume of liquid in comparison with that of the solid ; and since the volume of water thus displaced weighs as much as the floating body, it cannot sink. There are some insects which walk on the surface of water, but which would almost entirely sink in the liquid were it not that the capillary depres- sion formed by their extended feet (which are kept from being wet by a greasy coating) displaces a weight of water equal to that of the insect. (194.) Absorption. — The power which porous solids, like wood, cloth, paper, or animal membrane, possess of absorbing liquids, is ailso a phase of capillary action. These solid bodies are filled with minute channels, into which the liquid is drawn with great force, as before explained. We may gain, an idea of the intensity of tliis force by reflecting that in a tube 1 millimetre in diameter it is measured by a column of water 30 m.m. high, and hence in a tube -j^^ millimetre in diameter by a column of water 3 metres in height. Now since the minute channels with which these porous solids are filled are as small as this, or even smaller, it is evident that they will absorb water with an almost 364 CHEMICAL PHYSICS. irresistible force ; hence the difficulty of pressing out the liquid when it has once been imbibed. In many cases the absorp- tion of a liquid is attended with an increase of volume, and the intensity of the capillary force is rendered evident by the expansive power which is thus exliibited. A common method of splitting granite rock consists in drilling a number of holes along the line of fracture, and subsequently plugging tliem up with dry wood. Water is then poured over the plugs, which expand and split the stone. The amount of liquid absorbed by a given solid varies with the nature of the liquid used ; thus it has been found that 100 parts by weight of the dried bladder of an ox absorbed in twenty-four hours 2G8 parts of pure water, 133 " water saturated with common salt, 38 " alcohol, 84 per cent. 17 " bone oil. It has also been found, that, if the bladder saturated with oil is soaked in water, the oil is after a while entirely replaced by water, and by as much water as the bladder is capable of absorbing. These facts indicate not only that porous solids exert an unequal attraction for different liquids, but also that they attract most powerfully those of which they absorb the greatest volume. In connection with these facts may be mentioned the singular property which many kinds of charcoal possess, of absorbing color- ing-matters and other organic principles. Thus, if water colored by litmus is shaken up with pulverized charcoal, nearly the whole of the coloring-matter will bo retained by the charcoal, and, on filtering, the liquid will run through colorless. A variety of char- coal called bone-black possesses this power in a high degree, and " is used for removing the color from the brown syrups in the pro- cess of refining sugar. The syrups are filtered through a layer of charcoal twelve or thirteen feet in thickness, contained in a tall iron cylinder, and are thus obtained perfectly colorless. Bone- black is prepared by calcining bones in close vessels, and does not contain more than one tenth or one twelfth of its weight of char- coal ; the remainder consists of earthy matter, chiefly phosphate of lime. Whether the peculiar property under considei-ation is due to the charcoal alone, or whether it is also shared by the earthy salts, is not known. Other animal substances, especially THE THREE STATES OP MATTER. 365 dried blood, furnish -when calcined a charcoal, which, if well washed, is even more efficacious than bone-black, and the addi- tion of carbonate of potash to the mass before calcining still further increases the decolorizing power of the charcoal. The absorbing power of charcoal is not, however, confined to the coloring principles alone. Many inorganic substances when in solution, especially of feeble solubility, are absorbed in the same way. Professor Graham has shown that this is the case with the metallic oxides when dissolved in potash or ammonia, and -with arsenious acid when dissolved in water. It is also true of most organic extractive matters. Thus, if porter is filtered through lampblack, it will be found to have lost the greater part of its bitterness, as well as its color, and in the preparation of oi'ganic extracts much of the active principle is lost, if, as is not unfrequently the case, the liquid is digested with animal char- coal for the purpose of removing the color. (195.) Solution. — When the adhesion of a liquid to a solid is sufficiently strong to overcome the force of cohesion, the solid enters into solution ; that is, it diffuses throughout the mass of the liquid, without destroying its transparency. Thus salt or sugar dissolves in water, resins dissolve in alcohol, fats dissolve in ether, and most of the metals dissolve in mercury. The solvent power of a given liquid for different solids varies almost indefi- nitely. Thus sulphate of baryta is almost insoluble in water ; sulphate of lime dissolves in the proportion of about one part in 400 parts of water, and siigar in one third of its weight of water, while hydrate of potassa may be dissolved in this liquid to almost any extent. If we add a solid body, in successive portions, to a liquid capable of dissolving it, we find that the first portions disap- pear very rapidly, but each succeeding portion dissolves less rapidly, until at length a point is reached when the solid is no longer dissolved. The liquid is then said to be saturated with the particular solid. It would appear that the adhesion of the liquid had the power of overcoming the cohesion of the solid to a limited extent, imtil the. two forces were in a condition of equilibrium. A liquid, however, which is satura,ted with one substance may still continue to dissolve others. The solvent power of a given liquid for the same solid, as a general rvile, varies very greatly with the temperature. Since 31* 366 CHEMICAL PHYSICS. heat tends to weaken the force of cohesion, we should naturally expect that it would increase the solvent power of a liquid, and we iind that in most cases it does. There are, however, many- striking exceptions to this rule. Thus water at the freezing point dissolves nearly twice as much lime as it does when boiling ; and in like manner sulphate of lime, citrate of lime, sulphate of lanthanum, and several other substances, are known to be more soluble in cold than in hot water. The increase of solubility with the temperature is very unequal in different cases. The solubility of common salt scarcely in- creases between 0° and 100°. Thus 100 parts of water dissolve at the ordinary temperature 36 parts of common salt, and at the boiling point a little over 39 parts. With a few salts the increase of solubility is exactly proportional to the temperature, and may be represented by the general formula, S = A -\- Bt, in which A represents the solubility at 0°, and B the increase of solubility for each degree of temperature. This is the case with the fol- lowing three salts. One hundred jDarts of water dissolve at t", Parts. of Sulphate of Potash, S = S.OG + 0.1741 1, " Chloride of Potassium, S = 29.23 -f 0.2738 f, " Chloride of Barium, S = 32.02 -|- 0.2711 f. In most cases, however, the solubility increases more rapidly than the temperature. This is the case with common nitre, as may be seen in the following table, in which the solvibilities both of nitre and chloride of potassium are given side by side for every 20° be- tween the freezing and boiling points of water. Chloride of Potassium. Nitre. Temperature. ^"5^'„f f^tj." '^'I'-^"-''- Temperature. 'j^oO ofllat"" T>\S...^<^o. 20.23 ,._ 13.32 Parts of Salt in 100 of Water. Differenc 20.23 5.47 34.70 5.48 40.18 5.48 45.66 5.48 51.14 5.48 20 34.70 ^ 20 31.70 40 40.18 g'^g 40 63.97 60 45.66 g'^g 60 110.33 80 51.14 .' 80 170.25 18.38 32.27 46.36 59.92 100 56.62 100 Since tlic solubility of a salt is always some function of the tem- perature, it can in every case be expressed by the general formula, into which every algebraic fiuiction may be developed : 8:= A + Bt+ Cf-^ Dt' + &(i. [130.] THE THREE STATES OP MATTER. 367 In this forimila, A is the solubility at 0°, and B, C, D, the amount of crystallized salt which will dissolve at the given temperature in 100 parts of water. THE THREE STATES OF MATTER. 371 Instead of evaporating the solution, it is frequently more con- Yenient to determine the weight of salt dissolved by precipitating one of its constituents, as in the ordinary method of chemical analysis. Thus the amount of sulphate of soda in a solution may be ascertained by precipitating tlie sulphuric acid as sul^ phate of baryta, and afterwards collecting and weighing the pre- cipitate in the usual way ; and the same method may be followed with any sulphate. In like manner, the solubility of any chloride in water may be determined by precipitating the chlorine as chloride of silver. In either case, from the weight of the pre- cipitate we can easily calculate, by the rules of stochiometry, the weight of salt which was in solution, whether in an anhydrous or a crystalline condition. When a salt is easily decomposed by heat, this chemical method of determining its solubility is always to be preferred. (197.) Solution and Chemical Change. — Solution is gener- ally regarded as merely a mechanical separation of the particles of a solid, which are diffused through the liquid solvent. Thus, when sugar dissolves in water, its particles are diffused through- out the liquid ; but they are not supposed to undergo any essen- tial change, for the syrup retains tlie sweetness of the sugar, and on evaporation yields solid sugar, with all its peculiar properties. So also a solution of camphor in alcohol partakes of the proper- ties of both substances, and when evaporated deposits the solid camphor entirely unchanged. Such a change is supposed to be entirely mechanical, and to differ widely from true chemical com- bination, in which the properties of tlie combining substances are entirely merged and lost in those of the compound. Thus, when we add lime to dilute nitric acid, it apparently dissolves, as sugar dissolves in water, and the result is a clear solution ; if, however, we examine the solution, we find that the properties of lime have disappeared, and on evaporating it we obtain, not lime, but a new substance called nitrate of lime. These examples would seem to indicate that there is a very marked distinction . between solution and chemical combination, and this conclusion is apparently confirmed by the fact, that whereas chemical com- bination takes place most easily between those substances which are most iinlike, solution generally occurs most readily when the solvent is more or less closely allied in its properties to the body dissolved ; thus mercury dissolves the metals, alcohol 372 CHEMICAL PHYSICS. the, resins, and oils dissolve the fats. But if, instead of compar- ing these extreme cases, we study the whole range of chemical phenomena, we shall find tliat the distinction between solution and chemical combination is by no means so clearly marked, and that it is impossible to say where the one ends and the other begins. In many cases, what seems to be an example of simple solution can be shown to be a mixed effect, at least, of solution and chem- ical combination ; and between this condition of things, where the evidence of cliemical combination is unmistakable, and a simple solution like that of sugar in water, we have every degree of gradation. To such an extent is this true, that the facts seem to justify the opinion that solution is in every case a chemical com- bination of the substance dissolved with the solvent, and that it differs from other examples of chemical change only in the weakness of the combining force. There are many remarkable phenomena connected with the solution of salts in water, which are probably caused by the intervention of chemical affinity. There are but few anhydrous salts which dissolve in water without entering into chemical combination with it ; in such cases we obtain, not, properly speaking, a solution of the anhy- drous salt, but a solution of a compound of the anhydrous salt and water. Thus, for example, if we dissolve anhydrous sul- phate of soda in water, every 44.2 parts of the salt combine with 65.8 parts of water, and we obtain a solution, not of Na 0, SO3, but of Na 0, S O3 . 10 HO ; and on evaporating the solution at the ordinary temperature, crystals of the hydrated salt are de- posited. The water which is thus combined with the salt is termed water of crystallization. It is combined in definite pro- portions, but is united by so feeble an affinity, that it is entirely driven off when the ci'ystallized salt is heated to 33° in the open air. It is true that it is difficult, and frequently impossible, to ascertain the condition in which a salt exists when in solution, and that the condition in which it is deposited on evaporation is not necessarily the same as that in which it was dissolved. Even in the case just cited, it is impossible to determine with certainty whether the hydrated salt exists as such, in solution, or whether it is first formed at the moment of crystallization. Several facts, however, seem to support the first hypothesis. On examining the curve of solubility of anhydrous sulphate of soda (Pig. 328), it will be noticed that the solubility rapidly THE THREE STATES OP MATTER. 373 increases -with the temperature up to 33°, where it reaches its maximum, and then diminishes' as the temperature rises above this point. Such a sudden break in the continuity of the curve as this is inexplicable, at least with our present knowledge, if we suppose that the water holds in solution one and the same body throughout the whole range of temperature ; while it is easily explained, if we assume that the composition of the salt in solu- tion changes with the temperature ; — for if, as would naturally be the case, the solubility of the salt is different in its hydrated and its anhydrous conditions, the sudden change in its solubility may be caused by a change of composition commencing at a par- ticular point. That this is the case with sulphate of soda is substantiated by the fact, that the sudden change in the law of its solubility takes place at 83°, the temperature at which the hydrated salt loses its water in the air. It is not supposed, how- ever, that the change of composition is completed at that tem- perature, but only that it commences at that point; and becomes more complete as the temperature rises. Below 33°, the change of soUxbility is owing to the natural effect of heat in increasing the solubility of the hydrated salt. Above 33°, the change is a mixed effect of the cause just mentioned and of the change of the hydrated into the less soluble anhydrous salt. It is obvious, from what has been stated, that the curve of solubility of anhydrous sulphate of soda given in Fig. 328 is a 32 374 CHEMICAL PHYSICS. pure fiction, since below 33° it is NaO, SO3 . 10 HO, and not NaO, SO3, whicli is in solution ; and the same is true also of sul- phate of magnesia and chloride of barium, both of which form crystalline compounds in water. Indeed, in order that such a curve should be a representation of actual facts, it is essential to know in what condition the salt exists in solution at each tem- perature, and to calculate the solubility solely for the hydrate which is known to be present. A separate curve should then be constructed for each definite compound, between the limits of temperature at which it is known to exist. This has been done in the case of sulphate of soda, by Loewel,* who has determined separately the solubility of the three compounds Na 0, SO3, Na 0, SO3 . 7 HO, and Na 0, SO3 . 10 HO, between the limits of temperature at which they are capable of existing. His numer- ical results are given in the table on page 375,t and from them the curve may easily be drawn. In the case of the two hydrates, the table gives in each in- stance the amount of anhydrous salt corresponding to the hydrate dissolved, and by comparing the three columns headed " anhy- drous salt," it will be seen that the amount of Na 0, SO3 which 100 parts of water will dissolve at 20°, for example, varies very considerably with the condition of hydration in whicii it exists. It will also be noticed, that the change of solubility for each com- pound follows a uniform law throughout ; the solubility increas- ing with the temperature in the case of the two hydrates, and diminishing with the temperature in that of the anhydrous salt. It is the combination of these two phenomena which causes the seeming irregularity in the curve of anhydrous sulphate of soda, as determined by Gay-Lussac, and represented in the figure above. Similar irregularities, which have been observed in seleniate of soda, carbonate of soda, and many other salts, are probably to be explained in the same way, although the subject has not been as yet sufficiently investigated to furnish the data for a satisfac- tory conclusion in all cases. Loewel, whose memoirs on the solubility of sulphate of soda we have just cited, has investigated with equal care the solubil- ity of a few other salts. $ In the case both of carbonate of soda * Annalcs de Cliimie et do Physique, Tom. XXIX. p. 62 ; Tom. XXXIII. p. 334. t Ibid., Tom. XLIX. p. 32. t Ibid., Tom. XXXIII. p. 334 ; Tom. XLIII. p. 405 ; Tom. XLIV. p. 313. THE THREE STATES OP MATTER. 375 •So lis « CO t- o O CO O b" h4 IN q d •^ m" d Mf ja in CO eo CO PH '^ 1— I s £".-a r-( »-> N (N CO •^ O i>. 3 " » >-t CQ g-t ^ OtJ M S O H ^1^ ■^ O as O) 11 CO p4 ?^ QD Oi i> lO O Tf CO 1 i Ij w CO I-H n c^ d iti r^ w d CO d 1 |i J> CO CO CO o Cl *> CO w CO CO CO eo eo CO CO IN IN (N (N IN M 91 CQ o < |«S 3 ^1 »o CO CO p-( r^ pH CO 00 ^ 99 91 in CO 10 I'-'g o CO in I-H CO CO d d in d b; 00 q 00 d d q q q « (N H g flca lO in in in m TP TT t -* Tjt ■^ TP TP -^ R 1—1 p d < m s , o i« o o o o o o o o © in -f Cl 95 t* CQ o o q q o q q o q q pi -T t- q ■^ F- |l ''o d >o QD d »n d d CO -r d in d d d ■^ CO CO Tf 9) PI pi ;B 3. 5^ l-t IN C4 CO eo IN Cl < 2« S as 3 -91 M N -# eo ,_i in in 1^ in -f 00 Pi (N evi in CO in P <^ o l> i> i-j CO q eo CO q i> CO q "1! CO q CO c 3 in d fH d 00 »> CO i-^ d d 00 t^ d in -T 91 91 c r 3 < 1-1 Pi C4 CO '^ ■^ in in -f -T ■T -T -T tP Tjt il i^i o t* o ^ in CO in -f CO CO m «„ CS pi w t* C o CO CO Oi o b; fr- 00 (7 q q ■^ »^ q -r PI m» |l d fH CO l> in OP d r^ w CO d in d d d -r eo bn i-H « (N CO CO CO CO -T -^ in iQ i> QD g ri U3 376 CHEMICAL PHYSICS. and sulphate of magnesia, lie found, very remarkably, that the solubility not only differed for the different hydrates, but also was different for the different states of the same hydrate. Thus the salt NaO, CO2 . 7 HO can be obtained in two different con- ditions or allotropic modifications, which we may distinguish as a and b, the salt a crystallizing in rhombohedrons, the salt b in tabular prisms. Loewel observed that the solubility of the salt was very different in these two modifications, that of a being nearly twice as great as that of b. The table on page 377, which has been taken from the original memoir,* gives the solubility at dif- ferent temperatures, not only of these two modifications, but also of the ordinary crystallized carbonate of soda, which contains ten equivalents of water of crystallization. In the case of each salt, the corresponding amounts of anhydrous salt are given for the sake of comparison. This table illustrates even in a more marked manner than the last the fact on which we have insisted so strongly in this section, that the solubility of a salt varies not only with the temperature, but also with its state of hydration ; and it illustrates an addition- al fact, that the solubility may also be altered by a mere change of moleciilar condition, without any change in composition. Phe- nomena analogous to those just described were also observed by Loewel in the case of sulphate of magnesia, but for the details in regard to them we must refer to the original memoir. f (198.) Supersaturated Solutions. — "Water is said to be su- persaturated wlien it contains in solution more of a salt than it would dissolve if presented to the salt at the given temperature. That saturated solutions do not at once deposit the excess of salt which they hold in solution, wlien cooled to a lower temperature, is a fact familiar to every one who has experimented on this sub- ject ; but there can be also no doubt that the prominent exam- ples, which arc frequently cited as illustrations of this fact, are to be referred to the intervention of the force of chemical affinity in a manner similar to that explained in the last section. If we prepare a boiling saturated solution of stilphate of soda in a glass flask, and, having corked the flask while the solution is boiling, allow it to cool to the temperature of the air, it may be * Annalcs dc Cliimie et do Physique, Tom. XXXIII. t Ibid., Tom. XLIII. p. 405. . 334. THE THREE STATES OP MATTER. 377 s 3 d EQ In 100 Parts of Water of Salt crystallized with 10 HO. w 188.37 286.13 381.29 556.71 In 100 Parts of Water of Salt crystallized with 7 HO a. d 112.94 150.77 179.90 220.20 In 100 Parts of Water of Anhydrous Salt. !^ 31.93 37.85 41.55 45.79 QQ In 100 Parts of Water of Sajt crystallized with 10 HO. H 84.28 128.57 160.51 210 58 290.91 447.93 In 100 Parts of Water of Salt cjystallized with 7 HO 6. « 58.93 83.94 100.00 122.25 152.36 196.93 In 100 Parts of Water of Anhydrous Salt. d 20.39 26.33 29.58 38.55 38.07 43.45 S » o i ° a- 1 i 1 lid" I' In 100 Parts of Water of Salt crystallized with 10 HO. M 21.33 40.94 63.20 92.82 149.13 273.64 1142.17 539.63 . , , ., In lOO Parts of Water of Anhydrous Salt. < 6.97 12.06 16 20 21.71 28.50 37.24 51.67 45.47 d* "ooinoinooo-* r-i FH (N Cl ^ C2 O, 32' 878 CHEMICAL PHYSICS. kept for months without crystallizing ; but the moment a glass rod or a crystal of Glauber's salt is dipped into it, the whole mass becomes semi-solid from tlie sudden formation of crystals, which ray out from the solid niicleus in every direction. This singular phenomenon was formerly supposed to be similar to what is fre- quently observed during the freezing of water and the solidify- ing of monohydrated acetic acid, melted phosphorus, and many other substances. It is well known that these liquids, if kept perfectly still, may be cooled several degrees below the melting point without losing their liquid condition, but that if disturbed when in this state, they at once become solid. These phenomena have been referred to the momentum of the particles, which tends to retain the substance in a liquid condition below the usual temperature, and the same explanation has been extended to the sudden crystallization of sulphate of soda, as above described. Loewel, in the memoir already referred to,* has investigated this subject with great care. He found that, if a supersatu- rated solution of sulphate of soda is cooled to a low tempera- ture, it deposits crystals containing seven equivalents of water, which are much more soluble than the ordinary crystals of Glauber's saltf (Na 0, SO3 . 10 HO). From this fact he con- cluded that the so-called supersaturated solution is not a super- saturated solution of Glauber's salt, but merely a saturated solu- tion of the more soluble hydrate (Na 0, SO3 . 7 HO). Tliat the solution is not at all changed by the deposition of the crystals Na 0, SO3 . 7 HO, is proved by the fact, that, if it is exposed to the air or touched by a glass rod, it becomes suddenly semi-solid from the deposition of Glauber's salt. These, and a large number of additional facts which Loewel :j: has observed, all tend to sup- * Annales de Chimie et de Physique, Tom. XXIX. p. 62. t See table on page 375. } In a more recent memoir, Loewel inclines to the opinion, that sulphate of soda always dissolves in water as an anhydrous salt, and hence that in a solution made with Na 0, SO3 . 10 HO, or Na 0, SO3 . 7 HO, none of the water is combined chemi- cally with the salt as water of crystallization. Such a change of views does not, how- ever, seem to be a necessary inference from the facts cited, and, as he admits, the new hypothesis leaves the unequal solubilities of the different hydrates entirely unexplained. The author, therefore, , does not think it necessary to change the opinion expressed above in the text, although it is true that these later investigations of Loewel seem to show that at certain temperatures sulphate of soda exists in the so-called supersaturated solutions in an anhydrous condition. Sec Annales de Chimie et de Physique, (3' Se'rie,) Tom. XXIX. p. 32, and compare Jahresbericht der Chimie, &c. fiir 1857, S. 321. See also an article by Dr. Hugo Schiff, Ann. der Chem. und Pharm., Band CXL S. 68. THE THREE STATES OP MATTER. 879 port the conclusion, that in the so-called supersaturated solution of sulphate of soda the salt exists in solution combined with seven equivalents of water, and does not crystallize until some cil-cumstance causes it to combine with three equivalents more of water, and to change into the less soluble compound which we have called Glauber's salt. What the circumstances are which produce this singular change, or in what way they act, we do not yet fully understand. Some very remarkable facts in con- nection with it have been noticed by Loewel and others. Thus a glass rod, if heated and afterwards cooled, loses its power of causing the crystallization. Alcohol, if poured into the flask so as to form a layer over the solution, generally causes it to crys- tallize ; but if previously boiled, it no longer produces this effect. It slowly, however, withdraws the water from the solution, and causes it to deposit crystals of Na 0, SO3 . 7 HO ; and it was in this way that Loewel obtained the largest and purest crystals of this hydrate. The opinion has been advanced by Lieben,* that it is the dust floating in the air, or adhering to the glass rod, which causes the sudden crystallization of supersaturated solu- tion ; and he has endeavored to show that neither the air nor a solid body will produce the effect after they have been freed from dust, by heating, by washing with sulphuric acid, or by any other means. 'Tliis theory, although ingenious, and supported by experiment, does not meet all the facts of the case, and the subject requires further investigation. The phenomena of " supersaturated " solutions, which are so marked in the case of Glauber's salt, have also been noticed in the case of carbonate of soda, of sulphate of magnesia, of acetate of soda, of chloride of calcium, and of many other salts. f In some of these cases, they are to be explained as in the case of Glauber's salts, by the formation of a hydrate more soluble than the one dissolved, while in others tliey may be caused by the formation of a more soluble modification of the same hydrate; but the whole subject is still involved in great obscurity. Solids on Gases. (199.) Absorption of Gases by Porous Solids. — If apiece of well-burnt boxwood charcoal is plunged while red-hot under mercury, and when cold passed up into a jar of gas confined over * Wien. Acad. Ber., XII. 771 and 1087. t See the memoirs of Loewel, just cited. 880 CHEMICAL PHYSICS. the same liquid, it will be found to absorb the gas to a greater or less extent, varyhig with the nature of the gas used. Accord- ing to Saussure's experiments, one cubic centimetre of charcoal will absorb the number of cubic centimetres of the different gases given in the following table : — Absorption of Gases by Charcoal. Ammonia, 90 c . m.^ Olefiant Gas, . . 35 c. m;" Chlorohydric Acid, 85 (. Carbonic Oxide, 9.4 " Sulphurous Acid, . . G5 " Oxygen, . . 9.2 " Sulphide of Hydrogen, 55 a Nitrogen, 7.2 " Protoxide of Nitrogen, . 40 ii Marsh Gas, . 5.0 « Carbonic Acid, . 35 a Hydrogen, 1.7 " In some cases the volume of the gases thus condensed is less than that which they would occupy in a liquid state, and as a general rule, the more readily a gas can be condensed to a liquid, the greater is the volume absorbed by the charcoal. It will also be noticed, that the above results follow very nearly the same order as the solubility of the gases in water. A piece of freshly burnt charcoal, if exposed to the air, con- denses the gases and moisture of the atmosphere to such an extent, that its weight frequently increases one fifth in a few days. The presence of condensed air in common wood charcoal can easily be made evident by plunging it under hot water. The heat of the water expands the confined air, which is thus driven out of the pores of the wood, and bubbles up through the water. Owing to this absorbing power of charcoal, water saturated with many gases may be freed from them by filtering it through ivory- black. Water impregnated with sulphide of hydrogen may be in this way so perfectly purified, that its presence cannot be de- tected cither by the natiseous odor or by the ordinary tests. This power of absorbing gases is not confined to charcoal, but belongs in a greater or less degree to other porous solids. The following table gives the number of cubic centimetres of different gases absorbed respectively by one cubic centimetre of Meer- schaum, plaster of Paris, and silk, when the temperature is 15° and the pressure of the air 73 c. m. By comparing this table with tl>e last, it will be noticed that not only the absolute quan- tities of the gases absorbed are different for different solids, but also that the relative power of absorption of these solids for the different gases is different in every case. THE THREE STATES OF MATTER. 381 Absorption of Gases hy Meerschaum, Plaster of Paris, and Silk. Meerschaum. Plaster of Paris. Silk. Ammonia, 15. cTin.^ 78.1 c.m, Protoxide of Nitrogen , 3.75 " Carbonic AeicI, 5.2G " 0.43 c-m.^" 1.1 " Oxide of Carbon, 1.17 " 0.3 « Oxygen, 1.49 " 0.58 « 0.44 « Nitrogen, 1.60 " 0.53 " 0.13 " Hydrogen, .44 " 0.50 " 0.3 In like manner the metals in the state of fine powder, lead, iron, and platinum, for example, absorb gases in very large amounts. The finely divided platinum called platinum-black, which is obtained by precipitating a solution of chloride of plati- num with alcohol, absorbs, according to Doebereiner, 250 times its own volume of oxygen. The latent heat which is set free by this great condensation is sufficient to ignite the metallic mass. Platinum sponge, and even platinum plate, possess the same power, although to a less degree, and it is probable that all solid surfaces exert a similar influence to a limited extent. . The absorption of gases by solids is very greatly influenced both by the temperature and the pressure to wliich they are exposed. The higher the temperature, the smaller is the amount of gas absorbed, and the most efficient means of expelling the gas from a porous solid is to expose it to a red heat. It is how- ever uncertain whether even in this way we can remove all the gas condensed on the surfaces of solid substances, and at all events to do this requires a considerable time. Charcoal and other porous solids absorb the largest amount of gas only after a prolonged ignition in, a vacuum. In filling a barometer tube the mercury is boiled in the tube in order to remove tlie air and moisture, not only from the mercury, but also from the surface of the glass. The greater the pressiire to which a gas is exposed, the great- er is the quantity which is absorbed by a solid ; but then the quantity does not increase so rapidly as the pressure. On the other hand, under a diminished pressure a solid body absorbs a less quantity of gas, but a greater volume. Hence it is not possible by means of an air-pump to remove all the air from a porous solid. If a porous body, which is saturated with one gas, is put into 382 CHEMICAL PHYSICS. a different gas, it gives up a portion of the gas which it had first absorbed, and takes in its place a quantity of the second. Sometimes tlie presence of one gas increases the power of a solid for absorbing a second. Thus charcoal saturated with oxygen will absorb more hydrogen, and charcoal saturated witli hydrogen will absorb more nitrogen, than it would if the other gas was not present. But as a general rule, the presence of one gas diminishes the power of a solid for absorlnng others. Thus charcoal, which after ignition will absorb thirty-fire times its Tolume of carbonic acid, will only absorb about fifteen times its volume if it has been previously exposed to the atmosphere, and thus saturated Avith air and moisture. From the analogous constitution of liquids and gases, we sliould naturally expect that solids would act on these two forms of fluid matter in an analogous way. The same adhesive force which attracts liquids to the surfaces of solids wo shoiild ex- pect would also attract gases ; and, moreover, since gases are very compressible, we should further expect that the adhesion would condense the gas upon the surface in proportion to the strength of the attraction. Moreover, as in the case of liquids, we should expect that the amount of gas adhering to the siir- face or absorbed into the pores of a solid would vary with the nature both of the solid and of the gas, with the extent of the surface, with the fineness of the pores, and, lastly, with the tem- perature, becoming less as the temperature rose. The phenomena just described, it will be noticed, coincide perfectly, as far as they go, with these natural inferences, thus showing that they are merely phases of adhesion and capillary action. The force of surface attraction, and hence the amount of gas absorbed, varies even more markedly tlian m the case of liquids, both with the nature of the solid and that of the gas. It varies also with the extent of the surface ; and, other things being equal, it is greatest with porous bodies or fine powders, which expose tlie greatest sxirface ; finally heat, which lessens the at- tractive force, diminishes the amount of gas absorbed by a solid, as it does the amount of liquid. There are, it is true, phenomena connected with the adhesion of gases to solids which liquids do not present, but these are such as may be svipposed to arise from the special law of compressibility, which all gases obey. The phenomena described in this section,, like those both of THE THREE STATES OP MATTER. 383 capillarity and solution, are greatly influenced, it will be noticed, by the chemical nature of the bodies concerned, and in fact pass by insensible gradations into those which we should class among purely chemical changes. Like most phenomena which occupy the debatable ground between chemistry and physics, they present great complexity, and are difficult to investigate, so tliat our knowledge in regard to them is exceedingly in- complete.* There are many phenomena besides those of absorption which are coimected with the adhesion of gases to solids. The fact that iron filings, and many otlier fine powders, sifted over the surface of water, will float, tliough very much heavier tlian the liqiiid, has already been mentioned. This was tlien explained by the principles of capillary action. The water is prevented from wetting the solid, and therefore forms around the particles a concave meniscus which buoys them up. But it is solely the thin film of air adhering to these particles which prevents them from becoming wet, when they would at once sink. The same is true also of the platinum wire floating on mercury, and of other seemingly paradoxical phenomena. ly all cases, if the liqiiid is boiled, the film of air is removed and the paradox disappears. Liquids on Liquids. (200.) Liquid Diffusion. — As a general riile, the adhesion between the particles of different liquids is so much greater than the cohesion between their own molecules, that they may bo mixed together in any proportion. This is not, however, always the case ; for after the liquids have been mixed to a limited extent, the cohesion may balance the adhesion, and the liquids will then be mutually saturated. Thus ether and water cannot be mixed indefinitely, and if shaken up together, they will separate in a great measure on being allowed to stand, the water dissolving only about one eighth or one tenth of its bulk of ether, and the ether dissolving about the same amount of water. So also the volatile oils, if shaken up with water, separate from it al- most entirely if the mixture is allowed to stand, although the water retains in solution a sufficient amount to acquire the flavor and odor of the essence. * See a recent paper by Quincke, Pogg. Ann., CVIII. 326. 384 CHEMICAL PHYSICS. The tendency of liquids to mix with each other has been termed liquid diffusion, and can be made evident by a simple experiment. A tall glass jar is about two thirds filled with a solution of blue litmus, and then, by means of a tube funnel reaching to the bottom, oil of vitriol is cautiously poured in, so as to occupy the lower portion of the jar. The plane of separa- tion of the two liquids will be at first distinctly marked. But this will soon disappear : the colored water will sink, and the acid will rise, until the two liquids have become perfectly incor- porated. This will require, however, two or three days, and, if watched at intervals, the progress of the diffusion may be traced by tlie gradual change of color in the water from blue to red, commencing at the bottom and slowly progressing towards the top. A similar experiment can be made with alcohol, or with brine, and water ; also with oil of turpentine and alcohol, and indeed with almost any two liquids which differ considerably in their specific gravities. By coloring one of the liquids, the pro- cess may be readily traced. (201.) Experiments of Professor Graham. — The subject of liquid diffusion has been investigated with care in regard to sa- line solutions, and we are chiefly indebted to Professor Graham of London for our knowledge on the subject. His experiments were made with a very simple apparatus. " It consisted of a set of phials of nearly equal capacity, cast in the same mould, and further adjusted by grinding to a uniform size of aperture. The phials were 3.8 inches high, witli a neck 0.5 inch in depth, and aperture 1.25 inch wide, capacity to base of neck eqiial to 20.80 grains of water, or between 4 and 5 ounces. For each diffusion-phial a plain glass water-jar was also provided, 4 inches in diameter and 7 inches deep." * (Fig. 329.) The diffusion-phial was in the first place filled with the saline solution to the base of the neck, or, more accurately, to a level exactly half an inch below the ground surface of the lip. The neck was then filled with distilled water, and a light float Fig. 329. * Graham's Elements of Chemistry, edited by Watts, Vol. II. p. 604. THE THREE STATES OF MATTER. 385 placed upon the surface. Thus prepared, the phial was trans- ferred to the jar, which was then filled with water to the height of an inch above the mouth of the phial, which was opened by the floating of the cover. This required about 20 ounces of water. The apparatus was then left undisturbed, and kept at a constant temperature for several days. At the end of the re- quired time, the diffusion was interrupted by closing the mouth of the phial with a ground-glass plate, and the amount of salt diffused ascertained, by evaporating the water in the jar to dry- ness, and weighing the residue. From these experiments, and a number of others made in a similar manner, the following important conclusions have been deduced. 1. With solutions of the same substance, but of different strengths, the quantity of salt diffused in equal times is propor- tioned to the quantity in solution. For example, four solutions of common salt were prepared, containing, respectively, 1, 2, 3, and 4 parts of salt to 100 of water. The experiments continued for eight days, and the quantities diffused were respectively 2.78 grains, 5.54 grains, 8.37 grains, and 11.11 grains. These num- bers are almost exactly proportional to the first. 2. With solutions of different substances of the same strength, the quantity diffused varies with the chemical nature of the sub- stance. This is shown by the following table, which gives the weight in grains of the substance diffused in eight days, from solutions containing, in each case, 20 parts of the solid dis- solved in 100 parts of water, and exposed to a temperature of 60°.5 F. Diffusion of Solids in Solution. Substances used. Sp. Qr. at 60o F. Weight in Grains diSused. Sulphate of Magnesia, 1.185 27.42 Chloride of Sodium, 1.126 58.68 Nitrate of Soda, 1.120 51.56 Oil of Vitriol, 1.108 69.32 Sugar-Candy, 1.070 26.74 Barley Sugar, 1.066 26.21 Starch Sugar, 1.061 26.94 Gum Arabic, 1.060 13.24 Albumen, 1.053 3.08 33 386 CHEMICAL PHYSICS. The substances have been arranged in the order of the specific gravities of the solution, and the table also shows that there is no apparent connection between the anaount of diffusion and the specific gravity of the solution. 3. If, instead of comparing together, as in the last table, the amounts of different substances diffused in equal times, we com- pare together the times required for the equal diffusion of these same substances, we discover some remarkable numerical rela- tions. There exist classes of equi-diffusive substances, and, as a general rule, those substances which have an analogous chemical composition, and crystallize in closely allied forms, have equal rates of diffusion. Several such groups have been distinguished, and the rate of diflFasion in each group is connected with the rate of diffusion in the other groups by a simple numerical relation, as is shown in the following table. The first column gives the number of the group, with the name of the most characteristic substance belonging to it. The second gives the relative diffu- sion of these substances in equal times, in other words, the rate of diffusion. The third gives the times of equal diffusion ; and the fourth, the sqtiares of these times, wliich stand to each other very nearly in the simple relation expressed in the last colunm. Groups. 1. Chlorohydric Acid, 2. Hydrate of Potasli, 8. Nitrate of Potash, 4. Nitrate of Soda, 5. Sulphate of Potash, 6. Sulphate of Soda, 7. Sulphate of Magnesia, 4. The rate of diffusion increases with the temperature, but increases in an equal proportion for all substances, so that the ratio between the diffusion of different bodies is the same for all temperatures. 5. If two substances, which do not combine chemically and have different rates of diffusion, are placed in the diffusion-phial, they may be partially separated by the process of diffusion, since the more diffusible passes oixt the most rapidly, although the relative rate of diffusion may be somewhat changed. Chemical decomposition may be even effected in this way, one ingredient of the compound diffusing more rapidly than the other. Eateof DilTusion. Times of Equal Diffusion. Squares of Times. Eati 1.000 8.960 15.682 2 0.800 4.050 24.502 8 0.565 7.000 49.000 6 0.462 8.573 73.496 9 0.400 9.900 98.010 12 0.326 12.125 147.015 18 0.200 19.800 392.040 48 THE THREE STATES OP MATTER. 387 From a solution of bisulphatc of potash saturated at 20° C , there were diffused in fifty days 31.8 parts of bisulphate of potash, and 12.8 parts of hydrated sulpliuric acid. From a solution of 8 parts of anhydrous alum in 100 parts of water there were dif- fused in eight days, at 17°. 9 C, 6.3 parts of alum and 2.2 parts of sulphate of potash ; and other similar examples might be cited.* 6. The diffusion of a salt into the solution of another salt takes place with nearly the same velocity as into pure water, at least when the solutions are dilute. Here, as in all experiments on liquid diffusion, uniformity of action takes place only in dilute solution. As the solution becomes saturated, the cohesion of the particles of the solid appears to introduce irregularities. 7. " The velocity with which a soluble salt diffuses from a stronger into a weaker solution, is proportional to the difference of concentration between two contiguous strata." This law has been experimentally demonstrated by Fick in the case of chlo ride of sodium, but it cannot as yet be regarded as completely established.! (202.) Osmose. — When two liquids are separated by a porous diapliragm, diffusion may still take place, although the phenomena are modified in a remarkable manner by the presence of the septum. This is best illustrated by means of the apparatus called an osmometer. It may be constructed in various ways, but as represented in Fig. 330 it con- sists of a membranous bag or bladder opening into a glass tube, to which it is fastened hermetically. The bladder is filled with a concentrated solution of common salt, ^nd suspended in a jar filled with pure water. Since the animal membrane is readily penetrat- ed by the water, it is evident that the water on the one side, and the salt solution on the other, must be in direct contact, and hence a diffusion of * Graham's Chemistry, Vol. II. p. 614. t Ibid., p. 610. Ui-sM*^.^v^ ff IiJtSMl Uyiff ti-1 (UrijLc^ }ti^t^^!''mii^o . ^' 1 - '^f' 388 CHEMICAL PHYSICS. the salt must take place, following the laws of liquid diffusion enunciated in the last section. "We should, therefore, expect that the salt would pass out into the water of the jar, as we find to be the case ; but the remarkable fact in connection with this experiment is, that a volume of water enters the bladder which is very much greater than could be introduced by simple liquid diffusion, amounting in some cases to several hundred times that of the salt displaced, the liquid slowly rising in the glass tube of the osmometer until it attains a very considerable height. The flow of water through the membrane is termed osmose, and the unknown power which produces it, osmotic force. It is a force of great intensity, capable of supporting a column of water several metres high. The only important phe- nomenon to be studied in this connection is this remarkable flow of water. The movement of the salt in the opposite direction appears to follow the laws of liquid diffusion, and, according to Graham's experiments, is not influenced by the presence of the membrane, unless it is quite thick. We have supposed that the bladder in this experiment con- tained a solution of common salt ; but we may use in its place alcohol, or solutions of cane sugar, of Glauber's salt, and of many other saline bodies, with precisely the same result. The conditions of osmose appear to be, that the liquids are capable of mixing, and that the membrane or septum which separates them has a greater adhesion for one liquid than for the other. When the osmose takes place between water and solutions of salts, the quantity of salt which passes through the membrane into the water is always replaced by a definite qiiantity of water, and the ratio obtained by dividing the last quantity by the first has been termed the osmotic equivalent of the salt. This ratio varies with the nature of the salt, and also, to some extent cer- tainly, with that of the membrane. It moreover increases with the temperature, biit it appears to be independent of the density of the solution. The osmotic equivalent for Glauber's salts, for example, when the pericardium of the calf is used as the septum, was found by Hoffmann * to be 5.1. The action of the septum in osmose has been explained in various ways. The simplest explanation which has been given * Untersuchungen uber das endosmotische Aequivalent des Glaubersalzes. Giessen, 1858. THE THREE STATES OP MATTER. 389 is based on the unequal adhesion of the two liquids to the porous septum. Let us suppose that the septum is a piece of the blad- der of an ox, and that on one side it is in contact with alcohol, and on the other with water. As was stated (194) the mem- brane has a very much greater attraction for water than for alcohol, and would therefore absorb the first to the entire exclu- sion of the second, were it not for the adhesion between the two liquids. In consequence of this, the alcohol is slowly diffused through the water contained in the membrane, which thus be- comes saturated with greatly diluted alcohol. Hence, on the side of the membrane towards the alcohol, nearly pure water is in contact with strong alcohol, and a rapid diffusion of the first into the last necessarily results. The place of the water thus escaping is supplied by fresh water, and a current of water is thus established flowing in towards the alcohol. On the side of the membrane towards the water, we have, on the other hand, very dilute alcohol in contact with water, so that, although dif- fusion tabes place, it is very much less rapid than that in the opposite direction. The flow of the water is then the result of two forces, — first, the excess of the attraction of the bladder for water over its attraction for alcohol, and, secondly, the diffu- sive force between the two liquids ; while the flow of the alcohol is due to the diffusive force alone, and must therefore be less rapid. The foregoing explanation of osmotic action is probably true for the particular case of water and alcohol, but it will not cover all the phenomena of this class. This subject also has been carefully investigated by Professor Graham, who has established several important facts in relation to it. He used as septa in his osmometer, which was constructed in a peculiar way, fresh ox-bladder, or a piece of cotton cloth soaked in white of egg and dipped into boiling water to coagulate it, and also the porous earthen-ware cells of a galvanic battery. He found, first, that solutions of neutral organic substances, such as urea, gum arabic, and sugar of milk, caiised little or no osmotic action ; secondly, that neutral salts, such as sulphate of magnesia, chloride of sodium, and chloride of barium, likewise produced but little effect; thirdly, that alkaline solutions, and especially solutions of the carbonates of potassa and soda, caused a very rapid flow of the water, — for example, when a solution of carbonate of 390 CHEMICAL PHYSICS. potassa was placed in the osmometer containing one part of salt to 1000 of water, 500 grains of water entered the instrument to every 'grain of the salt diffused into the outer cylinder, and it was found generally that osmose was most rapid when the solu- tion did not contain more than two per cent of the salt ; fourthly, that acid solutions, either dilute acids or acid salts, caused a current in the opposite direction to that caused by the alkaline solution ; lastly, that the corrosion of the septum seemed to be a necessary condition of osmose, the water always flowing to the alkaline side. When septa were used which were not chemi- cally acted upon by the saline solution, there appeared to be no osmotic action, although they were not deficient in po- rosity. From the above and many other interesting facts, for which we must refer the student to the original memoir,* Graham advances the hypothesis that osmose is due to a chemical action of the liquids on the septum, which is different on its two surfaces not in degree only, but also in kind, — acid on one side and alkaline on the other ; — and he compares the flow of water to the alka- line side to the similar flow of water in electrolysis towards the negative pole of the galvanic battery. In electrolysis, as in os- mose, the water current always follows the alkalies and hydrogen. The accumulation of water around the negative pole of the gal- vanic battery has been explained by assuming that the liquid molecule of water, which is decomposed by galvanism, consists not simply of HO, but of H„_^iO„ + i, and that this is divided by the current into H„+iO„-j-0. The part H„_,_,0„ being positive, it is drawn to the negative pole, and there splits up into H, which escapes as a gas, and E[„0„, which increases the volume of the liquid in the cell into which the pole dips. This hypothesis may be extended to the phenomena of osmose, since we may suppose a number of molecules of water attached to each particle of the base and the acid of the salt, and we can thus conceive that a chemical decomposition of the salt by the porous septum should be attended with a motion of liquid similar to that which attends the decomposition of the same salt by galvanism, this motion in either case being made perceptible by the presence of the dia- phragm, which prevents the water from recovering its level. * Journal of the Chemical Society of London, Vol. VIII. p. 43. THE THREE STATES OP MATTER. 391 " Osmose," according to Graham, " is the conversion of affin- ity into mechanical effect;" but what is tlie nature of the chem- ical process which in any given case produces such remarkable and great resiilts has not been shown. It is impossible, with our present knowledge, to decide how far the action is chemical and how far purely mechanical, and we must therefore leave the sub- ject in this unsatisfactory condition. It is evident from the porous nature of the walls, both of animal and vegetable ves- sels, that the phenomena of osmose must play an important part in the living organism ; but whether, as some have supposed, it is the efficient agent in causing the ascent of the sap in the plant, or in the processes of secretion in the animal, we cannot deter- mine in the present state of our knowledge. Liquids on Gases. (203.) Adhesion of Liquids to Gases. — The adhesion of liquids to gases is ex- emplified by the familiar fact, that, when liquids are poured from one vessel to an- other, bubbles of air are carried down with the descending stream, which rise and break upon the surface of the liquid. The adhe- sion of water to air is a force of considerable power, and is applied in some places for producing the constant blast which is re- qiiired for working an iron forge. In Pig. 331 is represented the machine which is used for this purpose at some iron forges in Catalonia. Water is discharged from the reservoir A, into which it flows from a higher level, ^J!!R'Wgyr^K into the tube B, through a conical orifice, a a. The op- enings c c ad- mit air to the upper part of the tube B, Fig. 331. 392 CHEMICAL PHYSICS. which is carried down by the stream of water into the reservoir C, and then forced tlirough the tube EF G and the tuyere T TJ into the ci-ucible of the forge. The stream of water is broken on a projecting ledge, and escapes by the opening D. By rais- ing or lowering the stopper g-, the quantity of water whicli falls, and hence also the intensity of the blast, can easily be regulated. An aspirator for establishing a current of gas through various forms of chemical apparatus, founded on the principle of this blast machine, has been described by M. W. Johnson.* It con- sists merely of a tube ten or twelve inches in length, attached by means of an india-rubber connector to a water-cock. Near the top of this tube there is a lateral tubulature, which is connected by an india-rubber hoso with the vessel through which the air is to be drawn. When the water-cock is partially opened, a very uniforni and abundant current of gas is drawn in at the lateral opening, and its velocity can be regulated by varying the length of the tube. (204.) Solution of Gases. — Another effect of adhesion, still more important in its chemical relations than the one just con- sidered, is the absorption of gases by water and other liquids. Water has the power of dissolving all gases, although in very different proportions, varying from one thousand times its own volume, in the case of ammonia, to only about one fiftieth of its volume, in that of nitrogen. The amount of gas dissolved by a liquid on which it exerts no chemical action depends upon, — 1st. The peculiar nature of the gas and the absorbing liquid. 2d. The pressure to which the gas is exposed. 3d. The temperature. The volume of a gas (reduced to 0° and to 76 cm. pressure) which is absorbed by one cubic centimetre of a liquid under the pressure of 76 c. m. is called the coefficient of absorption. This coefficient of absorption varies with the temperature, but for any given temperature it is a constant quantity for the same gas and liquid. The coefficients of absorption at 0° of a few of the best known gases are given in the following table, both for water and for alcohol : — * Journal of the Chemical Society of London, Vol. IV. p. 186. THE THREE STATES OP MATTER. 893 Name of Gas. Nitrogen, Hydrogen, Oxygen, Carbonic Acid, . Sulphide of Hydrogen, Sulphurous Acid, Ammonia, . Volume in c. m." absorbed by one c. m." of "Water. 0.02035 . 0.01930 0.04114 . 1.79670 4.37060 . 68.86100 1049.60000 Alcohol. 0.12634 0.06925 0.28397 4.32950 17.89100 328.62000 (205.) Variation of the Coefficient of Absorption with the Temperature. — In a solid, the force which the solvent power of a liquid has to overcome is that of cohesion ; in a gas, on the other hand, it is that of repulsion ; and we should therefore naturally expect, contrary to what is true of solids, that the sol- ubility of gases would diminish with the increase of the tempera- ture. This we find to be the case, and, with a few exceptions, the solubility of a gas is greater the lower the temperature. As in the case of solids, however, the law of the variation depends upon the nature of the gas, and must therefore be determined for each special case. In Table VII. of the Appendix, the coefficients of solubility of the most familiar gases are given for different tem- peratures within the limits of ordinary observation. By compar- ing together the results of observation at different temperatures, we can obtain, as in the case of the solubility of solids, interpo- lation formulae by means of which the coefficients may be cal- culated for other temperatures within certain restricted limits. Thus in the case of the absorption of nitrogen by water, the results of five experiments were as given in the following table from Bunsen's Gasometry.* No. of the Experiment. Temperature. Degrees Cent. Coefficients found. Coefficient from Formula. Difference. 1 2 3 4 5 4.0 6.2 12.6 17.7 23.7 0.01843 0.01751 0.01520 0.01436 0.01392 0.01837 0.01737 0.01533 0.01430 0.01384 — 0.00006 —0.00014 +0.00013 —0.00006 —0.00008 By combination of the experiments 1, 2, 3 ; 2, 3, 4 ; 3, 4, 6, we obtain the interpolation formula * Gasometry, by Robert Bunsen. Translated by Eoscoe. London. 1857. 394 CHEMICAL PHYSICS. e = 0.020346 — 0.00053887if + 0.000011156 f, [131.] by means of which the numbers of Table VII. may be calcu- lated. For the interpolation formulae by which the coefficients of absorption of other gases may be calculated, as well in alcohol as in water, we must refer the student to the excellent work of Professor Bunsen already cited, from wliich Table VII. has been taken. To the general law that the solubility of a gas diminishes with the increase of the temperature, there are several excep- tions. Thus, the coefficient of absorption of oxygen in alcohol is constant at 0.28397 for temperatures between 0° and 24°, and the same is true also for hydrogen in water. So also one vol- ume of water at 5° absorbs less chlorine gas than at 8° ; but here, as in similar cases, the apparent exception to the law is caused by the intervention of chemical affinity. Chlorine forms at 0° a definite crystalline compound with water, and the solubility of this solid increases with the temperature up to 10°. Above this temperature the crystalline hydrate cannot exist, the chlo- rine dissolves as a gas, and its solubility follows the general law, diminishing with the temperature. Although the solubility of a gas increases as the tempera- ture falls, yet at the moment the liquid freezes, the absorbed gas is almost entirely set free. During the freezing of water the air dissolved separates from it, forming bubbles in the ice. So also the oxygen which is absorbed in large quantity by melted silver is evolved when it solidifies. But when at the freezing point the dissolved gas forms a definite compound with the water, it sometimes happens that no gas is evolved when the water freezes, as is the case with the solution of chlorine just mentioned. (206.) Variation of the Solubiliti/ of a Gas with the Pres- sure. — This variation follows a very simple law. The quarir tity of gas * absorbed by a liquid varies directly as the pressure which the gas exerts upon it. If now, instead of considering the quantity of gas absorbed, we consider the volume absorbed under any given pressure, it follows, from Mariotte's law, that this volume must be the same in all cases. Thus, for example, at 0° one cubic centimetre of water absorbs 1.797 cTm.'' of carbonic * By the term quantity of a gas is always to be understood the number of cubic cen- timetres measured at 0° C. and under a pressure measured by 76 c. m. of mercury. THE THREE STATES OP MATTER. 395 acid gas, whatever may be its pressure. If the pressure is 76 c. m., the quantity of gas absorbed measures, at the standard tempera- ture and pressure, exactly 1.797 c. m.°. If now the pressure is doubled, the volume of gas absorbed is the same as before, but the quantity (measured at 0° C. and 76 c. m.) will be found equal to twice 1.797 or 3.594 cTm.', and the same is true for all pres- sures within the limits at which Mariotte's law holds good. (165.) It is true that the law has not been demonstrated ex- perimentally except in a few cases and within very restricted limits, but it is highly probable that it is as constant as that of Mariotte. Representing by V„ and VJ ihe quantities oi & ^yea gas absorbed by a given volume of liquid corresponding to the pressures H„ and HJ, we have for the mathematical expression of this fundamental law of gasometry the proportion F. : V' = H„ : Hj [132.] The principles of this section are illustrated by the apparatus represented in Figs. 832 and 333, used for saturating water with carbonic acid gas under pressure (soda-water). It is made of earthenware ; and the two chambers A and B, as shown in the section, are connected to- gether by the fine tube a b. Through the neck of the apparatus at u, water is introduced into the upper chamber, B, which is then closed by a screw plug. Through this plug passes a tube, p i, closed by a valve stopcock, by means of which the water may be drawn off when saturated with gas. Through a tubulature at o, which can also be closed by a screw plug, the materials for making carbonic acid gas (bicarbonate of soda, tartaric acid, and water) are in- troduced into the lower chamber, A. The gas, as it is evolved, escapes through the tube b a into the upper part of the chamber B where it comes in contact with the surface of the water, and is in part dissolved, while the rest exerts a pressure upon it rig. 332. Fig. 333. 396 CHEMICAL PHYSICS. amounting to several atmospheres. On opening the stopcock, the water charged with gas is driven out with force, and the amount of gas dissolved is found to be exactly proportional to the pressure which it exerted on the surface of the water. When the water thus surcharged with gas is drawn out into a glass tumbler, the excess of gas escapes with effervescence. If the process is closely examined, it will be noticed that the bubbles of gas rise from the sides and bottom of the tumbler, and if, while the water is still saturated, we drop into it a solid body with a rough surface, a piece of bread, for example, there will ensue a brisk effervescence around the body. The cause of this phenom- enon is thus explained. The gas, as we have assumed, is held in solution by the adhesion of the liquid particles. In the midst of the water the particles of carbonic acid are surrounded on all sides by particles of liquid, but immediately in contact with the solid they are only attracted on one side by the liquid, since on the other they are in contact with the solid surface. It is evident that the adhesive force, and hence also the solvent power, must be less in the last case than in the first, so that the particles of gas in contact with the solid surfaces will be the first to assume the aeriform condition. These particles iiniting together form a small bubble of gas, which, as it rises through the solution, con- stantly enlarges, and acquires a considerable size before it breaks on the surface. The bubble increases in size as it ascends, be- cause, as is evident, it m\ist have the same effect as a solid body on all the particles of the solution with which it comes in contact, diminishing the adhesive force between the water and gas. If water saturated with carbonic acid is placed under a glass bell resting on the plate of an air-pump, the carbonic acid will escape from the solution, and collect in the bell, imtil the quantity remaining in solution corresponds to the pressure exerted by the carbonic acid wliich has escaped. The presence of air in the bell does not in any way affect the final result, and precisely the same quantity of carbonic acid, and no more, would rise into the bell if the air were completely removed. It is true, how- ever, that, if the bell Avere exhausted, this quantity would escape instantaneously, while, if it is filled with air, the equilibrium is only attained after a considerable time. The same is true if the bell is filled with other gases than air. Let us now suppose that, after the equilibrium has been attained, a portion of the mixture THE THREE STATES OP MATTEE. 397 of carbonic acid and air is removed by the piimp. The pressure •which the carbonic acid exerts on the solution will thus be di- minished, and more gas will escape from the solution, until the equilibrium between the gas dissolved and the pressure of gas in the bell is again restored. It is evident that the whole gas can- not be removed from a solution by the air-pump, since we can never remove the whole of the gas from the surface of the liquid, and cannot therefore entirely remove the pressure which the gas escaping from the solution exerts. This object, however, can be readily attained by placing at the side of the glass holding the solution another glass, containing some chemical reagent which has the power of absorbing the gas. Thus, if we place under the same bell containing a solution of carbonic acid a concen- trated solution of caustic potash, this reagent will keep the bell free from carbonic acid, and reduce the pressure it exerts to nothing, so that the gas will continue to escape from the solution until the whole is removed. If at the same time we exhaust the air with the pump, we shall greatly hasten the process, although the final result is not affected by the presence of the air, or any other chemically inactive gas. The amount of carbonic acid present in the atmosphere is so small, that it exerts no appreciable pressure ; so that, if a solu- tion of this gas is exposed to the atmosphere, the whole of the gas should according to the law escape. This we find to be the case, although, on account of the slow diffusion of carbonic acid into air, it requires a long time before the whole has disappeared. The same must, of course, also be true of solutions of all gases with the exception of those composing the atmosphere. The most available means of driving out a gas from a solution is boiling. The high temperature diminishes the coefficient of absorption, and moreover the escaping vapor carries away with it the gas from the siirface of the liquid, so that the pressure which the gas exerts on this surface is constantly diminishing, and with it also the amount of the gas which the liquid can hold in solution. On this same principle, protoxide of nitrogen can be entirely removed from water by passing through it a current of air. There are a few gases, such as chlorohydric acid, which have so strong an affinity for water that they cannot be removed by boiling, since, after the solution is reduced to a certain degree 34 398 CHEMICAL PHYSICS. of concentration, the liquid and gas evaporate together as a whole. (207.) As a general rule, the solubility of a gas is diminished by the presence of other substances in the solution. Thus, for example, water containing sulphuric acid or any salt will absorb, in most cases, less gas than when pure. As a necessary conse- quence, the gas which water holds in solution can in great meas- ure be driven out by the addition of oil of vitriol, or by dissolving in it some salt. So also melted silver, which absorbs from the atmosphere a large volume of oxygen, disengages with efferves- cence the whole of the dissolved gas, on the addition of an equal weight of melted gold. Whenever, on the other hand, as is sometimes the case, the solubility of a gas is increased by the presence of salts or other substances in solution, this exception to the general rule is appar- ently caused by the chemical affinity of the dissolved substance. The presence of phosphate of soda increases greatly the solubility of carbonic acid, and the presence of sulphate of copper and sul- phate of protoxide of iron, the solubility of oxide of carbon and deutoxide of nitrogen, respectively. It is true that in all these cases the gas can be driven out of the solution by boiling, but nevertheless it is probable that unstable compounds are in each case formed ; and this opinion is substantiated in the last case by the very remarkable change of color which the solution of green vitriol undergoes by absorbing deutoxide of nitrogen gas. The principles of this section, it should be noticed, apply only to solid and liquid bodies, since the coefficient of absorption of one gas is not apparently influenced by tlie presence in the solu- tion of ajiother gas on which it is chemically inactive. This last principle will be considered in detail in section (209). (208.) Determination of the Coefficient of Absorption. — As has been already stated, the coefficient of absorption is the volume of gas (measured in cubic centimetres at 0° and 76 c. m.) absorbed by one cubic centimetre of liquid. Since this coefficient varies with the temperature, it must be determined for each temperature, or we may determine it with accuracy for several temperatures at suitable intervals, and then from these results deduce an interpo- lation formula by which we may calculate the coefficient for all intermediate temperatures, and prepare tables like Table VII. of the Appendix. It is only then necessary to inquire how the THE THREE STATES OP MATTER. 399 coefficient is determined for any given temperature, t. There are, in general, two methods which are used for this purpose. First Method. — The first method consists in passing a current of the gas through the liquid under experiment, until the last is Fig. 331. saturated; then, having carefully observed the temperature of the solution, transferring with proper precautions a measured volume to a glass beaker, and determining the weight of the dis- solved gas by some process of chemical analysis. This method will be better understood if illustrated by an example, and we will select for the purpose the determination of the coefficient of absorption of sulphide of hydrogen in alcohol, which was made by Drs. Schonfeld and Carius, with the apparatus represented in Pig. 334.* The flask aa \s closed by a tight cork, through which four holes have been bored. Through the first of these passes a ther- * See Bunsen's Gasometry, page 160. 400 CHEMICAL PHYSICS. mometer, b; through the second, the tube, c, conducting the gas; through the third, a short tube, d, serving as a vent to the gas, and ending in a small india-rixbber tube, which can be easily closed by a glass rod ; lastly, through the fourth hole passes a siphon tube, e. These tubes exactly fit the holes in the cork, so that if the tube d is closed while the current of gas is flowing into the flask through the tube c, the solution will be forced out through this siphon tube, e. In making the determination, the sulphide of hydrogen was generated from sulphide of iron and dilute sulphuric acid, and, having been washed with water, was passed through alcohol in the flask, which had been previously boiled in order to expel all the air it contained in solution. The alcohol in the mean time was kept at a constant temperature by placing the flask in a wa- ter-bath, and this temperature, which was carefully observed by the thermometer b, we will call f. The tube d was also left open, so that the sulphide of hydrogen gas, which filled the upper part of the flask, exerted the same pressure on the surface of the alcohol as that indicated by the barometer at the time of the experiment. We will represent this by H. At the end of two hours, when it was assumed that the liquid was saturated with the gas, the india-rubber connector at d was closed by a glass rod, and the solution, as it was forced out through the siphon e, collected in a measuring-glass. The tube e was so adjusted as to reach to the bottom of the measuring-glass, and after the glass was full, the solution was permitted to overflow the mouth for some time, and until the upper layers of the liquid, which had been exposed to the air, and consequently lost a. portion of their gas, had been replaced by the saturated solution rising from below. The glass was then quickly closed by its stopper, and its contents immediately after transferred to a beaker containing a solution of chloride of copper. The volume of the solution used was, of course, the same as that of the measuring-glass, and we will represent it by V. Lastly, the sulphur of the precipitated sulphide of copper was converted into sulphuric acid by nitric acid, and weighed in the usual way as sulphate of baryta. From the weight of sulphate of baryta the weight of sulphide of hydro- gen contained in the solution was easily calculated. Represent this weight by W, and the known weight of one cubic centimetre of sulphide of hydrogen gas at 0° and 76 cm. by w (Table II.), THE THEEB STATES OP MATTER. 401 and we have all the data for calculating the coefficient of absorp- tion at. the temperature of the experiment. V = volume of solution saturated with H S at f and H c. m. W = -weight of H S in ditto, at t° and Jf c. m. Then by [132], 76 W^rr = weight of H S in ditto at t° and 76 cm. Dividing by w, we get W 76 — . -jTr = volume of H S (measured at 0° and 76 c. m.) dissolved at t and 76 cm. It was assumed in this determination that the volume of alcohol underwent no change by absorbing sulphide of hydrogen, so that V represents not only the volume of the solution, but also the volume of the alcohol it contained. Hence, V cubic centime- ir 76 . . tres of alcohol at f dissolve — . -^ cubic centimetres of sulphide of hydrogen, measured at 0° and 76 c. m. Consequently, the coeflScient of absorption, or As is evident, this formula is not only applicable to the particu- lar case under consideration, but may also be used in all similar cases, in which the volume of the liquid is not sensibly altered by dissolving a gas. If, however, we seek to determine the solubility of sulphurous acid gas in alcohol by the same method, it will be found that the assumption made in the last example is no longer correct, and that it is essential to pay regard to the change of volume. As for the rest, the determination may be conducted in precisely the same manner, only the weight, W, of sulphurous acid gas contained in a measured volume, V, of the solution, must be de- termined by some special method of chemical analysis. As we cannot conveniently measure the volume of alcohol before the ab- sorption corresponding to the measured volume, V, of the solution, we determine carefully the specific gravity of the alcohol and of the solution, and thus obtain all the data for our calculation. 34* w w 402 CHEMICAL PHYSICS. Y = volume of alcohol saturated with S Oj at t" and He. m. {Sp. Gr.) = specific gravity of ditto. V . {Sp. Gr.) = weight of ditto. See [56]. W = weight of S Oa dissolved at t' and ITc. m. in Fc.m.^ of solution. V . {Sp. Gr.) — W= weight of alcohol in Vc. m,^ of solution. (<^. Gr.y = specific gravity of alcohol before absorption. Hence by [56], — '-\^Pl ' ^ — = volume of alcohol in FcTm.^ of saturated solution. {Sp. Gr.y IP = weight of one cubic centimetre of S Oj gas measured at 0° and 76 cm. = volume of S 0' (measured at 0° and 76 c. m.) dissolved in V c. m' of solution at t° and ITc. m. — . . __ = volume of ditto dissolved in Vc. m.° of solution at t° and 76 c. m. w H Hence — ^e'"7> y" — c^° °f alcohol dissolve, at f and 76 W 76 3 pan cm., — • Tr c. m. 01 b Oa gas. Whence r_76_ {S p.Gr.y .^3-. w H V.{Sp.Gr.) — W LJ-^*-J This formula may be used in all similar determinations of the coefficient of absorption, where the volume of the liquid is sensibly changed by the absorption of the gas. When there is no change of volume, V = (^2 -|- C3 V3 If there were but two gases, the values ^3 , Ms , and Cs must evi- dently be cancelled in all the above equations ; and, on the other hand, the formulae may readily be extended to any number of gases by introducing additional terms. The solution of atmospheric air in water furnishes a good illus- tration of the principles of this section. Let it be reqiiired to determine the absolute volumes of oxygen and nitrogen absorbed by Vi volume of water at the temperature of 15°. The air is a mixture of oxygen and nitrogen, exerting on the water a variable pressure, which we will assume, at the time of the determination, is 76 c. m. ; and its mean composition in volume is Oxygen, 0.2096 Nitrogen, 0.7904 [141.] 1.0000 The coefficients of absorption at 15° are, by Table VII., of oxygen 0.02989, and of nitrogen 0.01478. The absolute vol- umes of the two gases absorbed by F, volume of water are, then, of oxygen, 0.02989 F, X 0.2096 = 0.006265 F, ; and of nitrogen, 0.01478 F X 0.7904 = 0.011682 F- The composition of the dissolved gas in one volume is, then, by [140], THE THREE STATES OP MATTER. 407 Oxygen, 0.3491 Nitrogen, 0.6509 [142.] * 1.0000 "We can also, evidently, reverse the above calculation, and from the composition of the dissolved gas calculate the composition of the gaseous mixture to which the liquid has been exposed. Rep- resenting the denominators of the fractions [140] by A, we easily obtain the values, v, = ''^ A, v, = '^A, and v^='"-^A, [143.] which are the volumes of the respective gases composing FcTrn]" of the mixture. Dividing each of these quantities by the sum of the whole, we obtain the composition of one volume of the mixture.* w, = 5^ , w.— Cl Ci f3 CI Cs "*" c7 and «3 [144-J C3 W3 = «l «2 U3 — n 1 — CI C2 C3 FroQi the composition of the mixture of oxygen and nitrogen dissolved in rain-water, we can easily calculate, by these formulae, the composition of the air. Evidently, when there are only two gases, the third value, w, , and the last term of the denominators of Wi and Wi are cancelled. All the above formulae are based upon the supposition, that the volume of the gaseous mixture is so large that the partial pres- sures of its constituent gases are not essentially changed by the absorption. This is true in regard to the atmosphere, as already stated; but when we experiment upon a very limited volume of a gaseous mixture, as in the absorption-tube of appar ratus (Fig. 335), such an assumption is far from being correct, and we must then pay regard to the change of composition and of pressure in the gaseous mixture. In order to make the case as simple as possible, let us take a mixture of only two gases, and consider the changes it will undergo by absorption if in contact * It will afford the student assistance, in following out the course of reasoning in this section, to remember that, in the notation adopted, ri -|- w -[- K3 = VcTm.^ of the mixed gases before solution, ui + m ■{■ us = 1 cTm.' of the mixed gases in solution, and wi -{■ W2 + W3 = I cm.' of the mixed gases before solution. 408 CHEMICAL PHYSICS. with a volume of liquid, adopting for the purpose the following notation, and assuming that the volumes of all the gases entering into the calculation are measured at 0°. . V = volume of mixed gases before absorption, measured at pres- sure If. V = volume of mixed gases after absorption, measured at pressure IT'. Vi = volume of absorbing liquid. «„ v-i = volumes respectively of the two gases in the unit volume of the mixed gases before absorption, so that Vi -[- I'j = 1 c.m.^- Mi, Mj = volumes respectively of the two gases in the unit volume of ^ the mixed gases remaining unabsorbed, so that Mi -j- Mj =: 1 cm.'. Ci, Cj = coefficients of absorption of the two gases respectively. It is now evident that the volume V of the mixed gases con- tains Vi V c. m.' of the first gas measured under the pressure H. Under a pressure of 76 c. m. this same volume would measure, hy [98] , Vi V =- cTS.' By the absorption, this quantity of gas is divided into two parts : first, a quantity, a;, , which remains un- dissolved ; second, a quantity, x^ , which dissolves in the liquid ; SO that we have Xi -\- x^^Vx 1^ ^ • The value of x„ may now readily be determined by the laws of absorption, since we know the coefficient of absorption c,, and can easily calculate the par- tial pressure which the gas exerts on the liquid after the absorp- tion. The quantity x^ of gas, if measured at the pressure H', 76 would equal Xi -^; ; and since the whole volume of mixed gases remaining unabsorbed, or F', exerts a pressure H' , the partial 76 X pressure of the portion of this volume Xi -jj-, must be -p; 76. At the pressure of 76 c. m., we know that F^ c; m.' of liquid ab- sorbs Ci Vi cm.' of the gas. Hence, under the pressure of 7^ 76 c. m., the same volume of liquid will absorb ' „' ' cm.' of gas. This is the value of .'<;, ; and substituting it above, we obtain .. + f^;^.^,,r-^, or •^.= ^-^^. [145.] By a similar course of reasoning, we should obtain, for the vol- ume of the second gas remaining unabsorbed, the value THE THREE STATES OF MATTER. 409 VH ca 2/.= 76(l + ^) If, for the sake of abbreviation, we put Ai = Vi V H and Aft := v^ V H, also B,= (l-j- "-ipji j and J5. = (l + ^j^') , we shall A A have Xi = ' and y^ = ' and from these we can easily calculate the composition of the unit of volume of the unab- sorbed gas, which we shall find to be AB.. and V AB t^*^'^ (210.) Analysis of a Mixture of two Gases by the Absorption Meter. — It is evident, from the computations of the last section, that we can even determine the unknown composition of a gase- ous mixture from the change of volume it undergoes by absorp- tion in a known volume of liquid. This leads us to a method of gas analysis, which, under certain circumstances, admits of great accuracy, and enables us to solve problems which cannot be re- solved by the ordinary methods of chemical investigation. Let us suppose, then, that we have given the following data, all reduced to 0° C, as before. V = the original volume of the gaseous mixture, measured under the pressure IT. V = the volume of the mixture after absorption, measured under the ^ pressure JI'. V[ = the volume of absorbing liquid. Ci, C2 = the coefficients of absorption of the two gases composing the mixture. It is required, from these data, to determine the relative pro- portions of the two gases in the original mixture. Let us repre- sent, then, by the unknown quantities x and y the volumes of the two constituent gases measured under the pressure 1 ; by a;' and y', the volumes of these gases after absorption measured under the same pressure. It follows directly from the law of Mariotte, that the volume x' X', if measured under the pressure H', would be jp ; and since 35 410 CHEMICAL PHYSICS. this volume, after the absorption, is expanded through the whole volume F', it is evident that the partial pressure it then exerts on x' the absorbing liquid is as much less than H' as -v^-, is less than x' V, and must therefore be equal to ^, . The volume of the first gas which would be absorbed by F, c.m.^ of liquid under the pressure of 76 c. m. and at 0° (when measured at 0° and 76 c. m.) is c, F. As after the absorption the pressure exerted x' by the first gas on the liquid is -r?; , the volume which is actu- ally absorbed (measured at 0° and 76 c. m.) is, by [132], 'l ' . If this volume is measured under the pressure 1 c. m., it will become c, F, -^ . Hence we have x' CiYy -jyr ■= the volume of first gas absorbed measured under the pressure 1. Hence, also, x=^' + c,Fp=x'(l + ^-!-iiy or a:'= ^ . j-1471 From this value of d we can easily calculate the partial pres- sure which the unabsorbed portion of the first gas exerts on the absorbing liquid. If measured under the pressure H', the vol- ume [147] becomes H' and the partial pressure it exerts is as much less than H' as this volume is less than F'. A simple proportion gives us, for X the value of this pressure, yi \ — y • lu like manner, by a precisely similar course of reasoning, we shall obtain, for the par- tial pressure exerted by th^ unabsorbed portion of the second gas, yr:r — V • Now, since it is these two pressures which make up the observed total pressure H', we have Returning now to the condition of the gas before absorption, it is evident that the volume of the first gas, which measures x THE THREE STATES OP MATTER. 411 under the pressure 1, would measure -^ under the pressure H. Hence the partial pressure which this gas exerted before the absorption was as much less than H as the volume -^ is less than V, and must therefore have been ^ . In like manner, we find that the partial pressure exerted by the second gas was -X- ; so that we also have ^=f+f- [149.] It will be noticed that equation [149] may be derived directly from [148] , by making c, and c^ equal to zero, which would be the case where there was no absorption. These equations may also be written in the forms •^ C«' _l_ /.. V.\ TJi T^ y («' + c, V,)H' ' (F' + c, FO^" If for the sake of abbreviation we put B = (F' + c, F.) H>, the equations become By combining the two, we easily obtain £ W—B A y A— W ' B' [150.] or, calculating the percentage composition, X W—B A . y A — W B rici t As an example of this method of analysis, we will take the data obtained in an experiment with the absorption-meter on a mixture of carbonic acid gas and hydrogen, as given by Bunsen. 412 CHEMICAL PHYSICS, Volume. Pressure. Temp. Volume at 0°. Gas before absorption, 180.94 sXgS 15!4 171.29 Gas after absorption, 122.01 68.09 5.5 119.61 Volume of water, .... " " . . . . Mean, Hence we obtain H = 53.6800, V = 171.290, H'= 68.0900, V = 119.610, c, = 1.4199, F, = 356.400, C2 = 0.0193, W = 9194.847, A =42591.3250, B =8612.568. And by substituting these values in [151], we get the following percentage composition : — By Absorption. By Eudiometer. Hydrogen, 0.9206 0.9246 Carbonic Acid, .... 0.0794 0.0754 1.0000 1.0000 And it will be noticed how closely these results agree with those obtained by chemical analysis with the eudiometer, which are given at the side for comparison. By substituting the numerical values in [146] , it will be found that the percentage composition of the gas remaining uiiab- sorbed is, Hydrogen, . . . .' . . . 0.9829 Carbonic acid, 0.0171 1.0000 The same method of gas analysis may be extended to mixtures of three or more gases ; but when the number of gases exceeds two, the formulae become quite complex, and the results less accurate. Gases on Gases. (211.) Effusion. — It has been found by Professor Graham,* that the velocities with which different gases, when under pressure, flow through a minute aperture in a metallic plate, are closely * Philosophical Transactions, 1846, p. 574. THE THREE STATES OP MATTER. 413 related to their specific gravities ; and to these phenomena has been given the name of effusion. In his experiments, the gases were made io flow througli an aperture in a very thin metallic plate, not more than one three-hundredth of an inch in diameter, into a bell-glass on the plate of an air-pump, which was kept vacuous by continued exhaustion. The velocity of the flow was found to mcrease with the degree of exhaustion, (that is, with the pres- sure,) until it amounted, to about one third of an atmosphere; but higher degrees of exhaustion were not found to produce a corresponding increase of velocity ; and when the vacuum was nearly perfect, a difference of one inch in the height of the mfer- ciiry column of the pump-gauge scarcely affected the rate at wliich the gas entered the bell. Through an aperture in a thin plate, such as described, sixty cubic inches of dry air were found to enter the vacuous or nearly vacuous receiver in one thousand seconds, and in successive experiments the time of passage did not vary more than one or two seconds. The times required for equal volumes of different gases to flow through this aperture were found to be very nearly proportional to the sqiiare roots of their specific gravities. Thus, the time required for sixty cubic inches of oxygen to flow through the aperture was observed to be 1,051.9, 1,051.9, 1,050.6, 1,050.2 seconds, in four different ex- periments. The mean of these numbers is 1,051.1, which bears almost precisely the same relation to 1,000, the time occupied by the same volume of air, as 1.0515, the square root of the spe- cific gravity of oxygen, bears to 1, the square root of the specific gravity of air. Since the times occupied by equal volumes of different gases in flowing through a fine aperture are proportional to the square roots of their specific gravities, it follows that the velocity of the flow must be inversely proportional to the square roots of the specific gravities, or directly proportional to the reciprocals of these quantities. Eepresenting, then, by T and T', the number of seconds required by equal volumes of two gases in flowing into a vacuum, we have r : 2" = ^{Sp. Gr.) : V(*- Gr.y. [152.] Also representing by t) and Jb' the velocity of the flow, (that is, the volume of gas entering the vacuum in one second,) we have, since T : T' = {)' i b, 35* 414 CHEMICAL PHYSICS. b : b' = V(S,.Gr.y : V(%G.o = ;7^ : ;7|^. [153.J If we assume that the velocity of air is unity, it follows from [153], that the velocity of any other gas, as compared with air, must be the reciprocal of the square root of its specific gravity, if the principle just enunciated is correct. That this is really the case is shown by the following table, taken from Miller's Chemical Physics. In the last column of this table, headed " Rate of Effusion," the velocities of different gases compared with air as imity are given, as deduced from the experiments of Professor Graham ; and it will be noticed that they very closely coincide with the reciprocals of the square roots of the specific gravities given in the fourth column. The coincidence is almost absolute in the case of those gases whose specific gravities vary but slightly from that of the air. With very light or very heavy gases the deviation is much greater ; but this can be shown to be occasioned by the tubularity of the aperture, arising from the unavoidable thickness of the metallic plate. Effusion of Gases. Gaa. Sp. Or. 1 Velocity of Diffusion. Rate of Effusion. v'Sp. Gr. VSp- Or. Hydrogen, 0.06926 0.2632 3.7994 3.8300 3.6130 Marsh Gas, 0.55900 0.7476 1.3375 1.3440 1.3220 Steam, . 0.62350 0.7896 1.2664 Carbonic Oxide, 0.96780 0.9837 1.0165 1.0149 1.0123 Nitrogen, 0.97130 0.9836 1.0147 1.0143 1.0164 Olefiant Gas, . 0.97800 0.98S9 1.0112 1.0191 1.0128 Binoxide of Nitrogen, . 1.03900 1.0196 0.9808 Oxygen, 1.10560 1.0515 0.9510 0.9487 0.9500 Sulphuretted Hydrogen, 1.19120 1.0914 0.9162 0.9500 Protoxide of Nitrogen, 1.52700 1.2357 0.8092 0.8200 0.8340 Carbonic Acid, 1.52901 1.2365 0.8087 0.8120 0.8210 Sulphurous Acid, 2.24700 1.4991 ■ 0.6671 0.6800 (212.) Application of the Law of Effusion. — The law of effu- sion, which was verified experimentally by Graham in the case of gases, is true generally of the flow of all fluids, vinder pres- sure, through an aperture in a very thin plate. It has been applied by Bunsen* in a process of determinmg the specific * Hansen's Gasometry, p. 121. THE THREE STATES OF MATTER. 415 gravity of gases, which is exceedingly simple, and of especial value where only a small quantity of the gas can be obtained. The process consists in observing carefully the times required by the same volumes of any given gas and air in flowing through a fine aperture in a thin plate when under the same pressure. Repre- senting these times by T and T', we have, from [152], (Sp.Gr.y : (_Sp.Gr.y = T' : T'^ ; since air is the standard of specific gravity, (Sjp. Gr.y = 1 ; and we easily obtain iSp.Gr.-)= ^,. The apparat^is used by Bunsen in these deter- minations is represented in Fig. 336. It consists of a glass bell, a a, holding about seventy cubic cen- timetres, and closed above by the glass stopcock c. To the neck of the bell, at d, there is adjusted, by grinding with emery, the short tube e, and to the top of this tube there is cemented a small piece of platinum-foil, in which a very fine hole has been perforated. In order that the plate should be as thin, and the hole as fine, as possible, the platinum- foil is first pierced with a very fine cambric needle, and then hammered out with a polished hammer on a polished anvil, until the hole is no longer perceptible to the naked eye, and can only be seen when the plate is held between the eye and a bright light. The edges of the plate are next cut away, so as to leave a small round disk, having the hole in its centre. The diameter of this disk should be a little less than that of the top of the tube, to which it can easily be cemented with a blowpipe. Within the bell, when in use, is placed the glass float, b b, made of thin glass, in order that it may be as light as possible. At the top of this float there is a small knob of black glass, ^, surmoimted by a thread of white glass ; and at the points ^i and ^2 two black glass threads are melted around the stem of the float, which serve as index-marks. [154.J Fig. 336. 416 CHEMICAL PHYSICS. In using this instrument, the glass bell, filled with the gas whose specific gravity is to be determined, is depressed in a mercury trough until the index-mark y^ on its side, is on a level with the surface of the mercury. This index-mark is so placed that, when the bell, previously filled with gas, is de- pressed as just described, the float will be below the surface of the mercury in the trough. The bell is now fastened sec\irely in this position, and the telescope of a cathetometer so adjusted that its axis shall graze the sxirface of the mercury in the trough, one side of which, being made of glass, enables the observer, looking through the telescope, to see the bell distinctly. The apparatus being thus arranged, the observer opens the stopcock c, and then closely watches the tube through the telescope. After some time, the white thread of the float rises into the field, and forewarns the observer that the black knob will soon appear. The moment this is seen, he commences his observation, and notes the exact number of seconds before the index-mark /Sj appears in the field of his telescope, of the approacla of which he is forewarned by previously seeing the mark ^i. Prom the construction of the instrument, it is evident that the time thus observed is the time required for the flow, through the fine hole in the plate e, of a given volume of gas, under a given, although varying, pressure ; and, moreover, that this volume and pressure must be the same in all experiments with the same instrument. Hence the squares of the times, in the case of dif- ferent gases, must be proportional to their specific gravities ; so that, having once for all determined the time required by air, we can easily, by means of [154], calculate the specific gravity of any given gas from a single observation of the time of its effusion. It is always best, however, to repeat the observation several times, and take the mean of the results. The following table will give an idea of the degree of accuracy which can be attained by this process. Column I. gives the mean specific gravities calculated from several effusion experi- ments on each gas, and Column II. the specific gravities of the same gases calculated from their chemical equivalents. The agreement between the calculated and the observed re- sults is very satisfactory ; so that, although this process is not comparable in accuracy with the direct method of determining specific gravities hereafter to be described, it is nevertheless, on THE THREE STATES OP MATTER. 417 account of its great simplicity, recommended by Bunsen for use iu the arts when only approximate results are required. Gases. I. 11. Differences. Air, Carbonic Acid, .... 1 vol. C + 1 TOI. C O2, . Oxygen, 1 vol. + 2 vol. H, . . . Hydrogen, 1.000 1.535 1.203 1.118 0.414 0.079 1.000 1.520 1.244 1.106 0.415 0.069 +0.015 —0.041 +0.012 —0.001 +0.010 (213.) Transpiration. — The flow of gases under pressure through long capillary tubes presents a class of phenomena en- tirely different from those of effusion, and has been termed by Graham Transpiration. "With a tube of a given diameter, Gra- ham found that the shorter the tube, the more nearly the rate of transpiration approximates to the rate of effusion ; while, on the other hand, as the tube was lengthened, he observed a deviation from the effusion rate, which was very rapid with the first increase of length, but became gradually less, and reached a maximum when a certain length had been attained. It was therefore neces- sary, iu order to eliminate the effects of effusion from experiments on transpiration, to employ a considerable length of tube ; and when this precaution was observed, uniform results were obtained. The length required in any case was found to vary with the diameter of the tube, and also, to a certain extent, with the na- ture of the gas. The most important conclusions which have been deduced from the researches hitherto made on transpira- tion are as follows : — First. The velocity of transpiration of a given gas through a given capillary tube increases directly with the pressure. For example, a litre of air of double the density of the atmosphere, and therefore exerting twice the pressure, will pass through a capillary tube into a vacuum in one half of the time required by the same volume of air of its natural density. This is a very remarkable fact, and it shows that the process of transpiration 'differs very greatly in character from efiusion. Secondly. With tubes of the same diameter, the velocity of transpiration of a given gas is inversely as the length of the tube. For example, if one hundred cubic centimetres of air will pass through a capUlary tube two metres long in ten minutes, a 418 CHEMICAL PHYSICS. tube of the same diameter four metres long would allow the passage of only fifty cubic centimetres in the same time. Thirdly. The velocity of transpiration of equal volumes, cesteris paribus, diminishes as the temperature rises. Fourthly. The velocity of transpiration was found to be the same, whether the tubes were of copper or of glass, or even when a porous mass of stucco was used. Fifthly. The velocity of transpiration varies with different gases, and appears to be a constitutional property of an aeriform substance, like the density or the specific heat, not depending, as is the case with effusion, on the specific gravity. Of all gases which have been tried, oxygen has the slowest rate of transpiration ; and hence it may be conveniently taken as a stand- ard of comparison for the other gases. In the first column of the following table, the times of transpiration of equal volumes of the bes1>known gases are given, as compared with that of oxygen ; and in the second column, the corresponding velocities of trans- piration, which are the reciprocals of the first quantities. In each case the gas was transpired through the same tube, and under ' precisely the same circumstances of temperature and pressure. Transpirahility of Gases. Gases. Oxygen, .... Air, . , . . , r Nitrogen, -j Binoxide of Nitrogen, ( Carbonic Oxide, . C Protoxide of Nitrogen, < Hydrochloric Acid, ( Carbonic Acid, . Chlorine, .... Sulphurous Acid, . Sulphuretted Hydrogen, . Light Carburetted Hydrogen, Ammonia, Cyanogen, . . . . defiant Gas, . Hydrogen, .... Times for Transpiration of equal Volumes. 1.0000 0.9030 0.8768 0.8764 0.8737 0.7493 0.7363 0.7300 0.6664 0.6300 0.6195 0.5510 0.5115 0.3060 0.5051 0.4370 Velocity of Transpiration. 1.0000 1.1074 1.1410 1.1410 1.1440 1.3340 1.3610 1.3690 1.5000 1.5380 1.6140 1.8150 1.9350 1.9760 1.9800 2.2880 Some very simple relations in the transpirahility of different gases may be discovered by examining the above table. Thus, THE THREE STATES OP MATTEK. 419 equal weights of oxygen, nitrogen, air, and carbonic oxide are transpired in equal times ; the velocities of nitrogen, binoxide of nitrogen, and carbonic oxide, are equal ; the Telocity of hydro- gen is double that of the three just mentioned ; the velocities of chlorine and of oxygen are as three to two. Many other similar cases might be cited ; but these relations seem to be merely accidental, and have not as yet been connected with the other properties of the substances. " Professor Graham consid- ers, at present, that it is most probable that the rate of transpi- ration is the resultant of a kind of elasticity depending upon the absolute quantity of heat, latent as well as sensible, which differ- ent gases contain under the same volume, and therefore that it will be found to be connected more immediately with the specific heat than with any other property of gases."* Lastly. The velocity of transpiration of a mixtiire of equal volumes of two gases is not always the mean of the velocities of the two gases when separate. For example, the velocity of a mixture of equal volumes of oxygen and hydrogen is 1.110, in- stead of 1.383, which would be the mean velocity of the two gases. (214.) Diffusion. — The tendency of gases to mix with each other is so strong, that it will overcome the greatest differences of specific gravity ; and, contrary to what a superficial consideration would lead us to expect, the more widely two gases differ in specific gravity, the more rapid, is the process of intermixture. This process is termed diffusion, and may be illustrated by means of the apparatus rep- resented in Fig. 337, consisting simply of two bottles, A and H, connected together by a long glass tube. If we fill the upper bottle with hydrogen and the lower bottle with chlorine, we shall find, in the course of a few hours, that the two gases have been perfectly mixed together, although the dif- ference between their specific gravities is three times as great as the difference be- tween the specific gravity of mercury and Kg. 337. * Miller's Elements of Chemistry, Part I. p. 86. 420 CHEMICAL PHYSICS. that of water. The chlorine, although thirty-six times heavier than hydrogen, will be found to have made its way into the upper bottle, as may be seen by its green color, while the hy- drogen will have passed downwards into the lower one ; and when once mixed, the two gases will never separate, however long they may remain at rest. What has been shown to be true of hydrogen and chlorine is equally true of all other gases and vapors, which do not act chem- ically on each other. The only differences observed with differ- ent substances are the times required to effect a perfect mixture ; but when once made, this mixture, in all cases, continues uni- form and permanent. This subject may be still further illus- trated by filling two tall, narrow glass bells of equal diameters over a pneumatic trough, the one half full of hydrogen, and the other half full of air, so that the water shall stand at the same level in both. If, now, we pass up a few drops of ether into each jar, the same quantity of ether will evaporate in both, and cause, ultimately, the same depression of tlie water-level ; but the ex- pansion of the hydrogen will take place much the soonest, because, being fourteen and a half times lighter than air, the heavy ether vapor will mix with it more rapidly. The law which governs the rapidity of gaseous diffusion was discovered by Graham, by means of the apparatus represented in Fig. 338, and called by him a diffusion tube. It consists of a glass tube thirty or forty cen- timetres in length, one end of which is closed by a plug of plaster of Paris, which should be as thin as is consistent with strength. This tube serves as a bell for holding the gas under experiment over the water con- tained in a tall glass jar; and it may be easily filled without wetting the porous diaphragm, by means of a glass siphon-tube, as represented in the figure. While filling the tube, the top is closed by means of a glass plate, which has previously been care- fully ground with emery on to the upper edge above the plaster Fig. 338. THE THREE STATES OF MATTER. 421 diaphragm. The tube, when filled with gas, should be so sup- ported that the water may be on the same level within and without the tube. If then the glass covering-plate is removed, the gas will be found to mix with the air through the thin plaster diaphragm, the gas passing out into the atmosphere, and the air, on the other hand, entering the tube. The relative ve- locity of the two currents will be found to depend on the relative density of the gas as compared with air. If the gas is lighter than air, the outer current will be the most rapid, and the water column will rise in the tube to supply the vacuum thus formed ; while, on the other hand, if the gas is heavier- than air, the inward current will be the most rapid, and the water column will be depressed. If the gas is hydrogen, which is fourteen and a half times lighter than air, the outer current will be so much the most rapid, that in the course of a few minutes the water column, under favorable circumstances, will rise to over one half the height of the tube. In all cases, after a certain time, varying with the specific gravity of the gas and the thickness of the dia- phragm, the gas in the tube will have been replaced entirely by a volume of air, which will be greater or less than the original volume of gas, according as the velocity of diffusion of the air is greater or less than that of the gas. By comparing, then, the original volume of the gas with the volume of the air remaining in the tube at the close of the experiment, we shall have at once the relative velocity of diffusion of the two gases. In making experiments for the purpose of determining the velocity of diffu- sion, it is evidently essential to maintain the water at the same level, both within and without the tube, since otherwise the effects of diffusion would be modified by the hydrostatic pressure. As an illustration of the method of determining the velocity of difiusion, let us suppose that the tube was filled with 100 c.m.° of hydrogen gas, and that at the end of the experiment, during which the surface of the water within, and without the tube was carefully maintained at the same level, there remained in the tube 26.1 ^Tm.' of air. It is evident, then, that during the time 100 cTni." of hydrogen escaped from the tube through the porous diaphragm, 26.1 67m.^ of air entered. Hence, the velocity of the difiusion of hydrogen is 3.83 times (equal to 100 -j- 26.1) more rapid than that of air. In the same way, all the numbers in the column of the following table headed " Velocity of Diflii- 36 422 CHEMICAL PHYSICS. sion " were found. They in. each case indicate the velocity of diffusion as compared with air ; and it -will be noticed that they very nearly coincide with the velocity of effusion. Diffusion of Gases. 6as. Sp. Gr. 1 Telocity of DiffuBion. Rate of Effusion. VSp. Gr. ^/Sp. Gr. Hydrogen, 0.06926 0.2632 3.7994 3.8300 3.6130 Marsh Gas, 0.55900 0.7476 1.3375 1.3440 1.3220 Steam, .... 0.62350 0.7896 1.2664 Carbonic Oxide, 0.96780 0.9837 1.0165 1.0149 1.0123 Nitrogen, 0.97130 0.9856 1.0147 1.0143 1.0164 Oleflant Gas, 0.97800 0.9889 1.0112 1.0191 1.0128 Binoxide of Nitrogen, . 1.03900 1.0196 0.9808 Oxygen, . 1.10560 1.0515 0.9510 0.9487 0.9500 Sulphuretted Hydrogen, 1.19120 1.0914 0.9162 0.9500 Protoxide of Nitrogen, 1.52700 1.2357 0.8092 0.8200 0.8340 Carbonic Acid, 1.52901 1.2365 0.8087 0.8120 0.8210 Sulphurous Acid, 2.24700 1.4991 0.6671 0.6800 It appears, then, that the velocity of diffiision of a gas is the same as the velocity of effusion, and hence, like the latter, is inversely proportional to the square root of its specific gravity. In other words, gases expand into each other according to the same law which they obey in expanding freely into a vacuum. This fact has been thought to support the theory of Dr. Dalton, that gases are inelastic towards each other, one gas offering no more per- manent resistance to the expansion of another gas than would be presented by a vacuum. Thus, in the experiment with the two bottles (Fig. 337), Dalton supposed that the hydrogen ex- panded through the space occupied by the chlorine just as if the space were entirely empty ; and he explained why the expan- sion was not instantaneous by the supposition that the particles, of chlorine offer the same sort of resistance to the motion of hydrogen as is offered by the stones on the bed of a brook to the running of water. There can be no question that the ulti- mate result of diffusion is always in conformity with Dalton's theory ; and although we may hesitate to assume that gases are in all respects vacua to each other, yet this theory is at pres- ent the most convenient mode of expressing the phenomena of diffusion. If, instead of using a homogeneous gas, we introduce a mixture THE THEEE STATES OP MATTER. 423 of two or more gases into the difiusion-tube, each gas ■will be found to preserve its own rate of diffusion. Thus, if the mixture consists of hydrogen and carbonic acid, the hydrogen will escape from the tube much more rapidly than the carbonic acid, and a partial mechanical separation of the two gases may tiius be effected. It is not essential that the top of the diffusion-tube should be closed with plaster of Paris. Any dry porous substance, such as charcoal, wood, unglazed earthen-ware, or dried bladder, may be substituted for the stucco ; but few of them answer so well. The diaphragm is best prepared by casting a very thin disk of plaster on a glass plate, and, after it is thoroughly dried, cutting it to the required size with a sharp knife, and cementing the edges with sealing-wax to the inner rim of the tube. The ascent of a column of water in the tube, when hydrogen is diffused, forms a very striking experiment. This may read- ily be shown to an audience with a Gra- ham's diffusion-tube about a metre in height and four or five centimetres in diameter, resting the bottom in a pan of colored, water. The tube can easily be filled with hydrogen by displacement, and the gas re- tained in its place by covering the top with a ground-glass plate, which should be re- moved at the time of the experiment. The same principle can be even more strikingly illustrated by means of an apparatus de- scribed by Professor Silliman, Jr.,* and represented in Pig. 339. It is made by cementing the open mouth of a porous earthen-ware cell (such as are used in a galvanic battery) to the mouth of a glass funnel, and then lengthening the spout by attaching to it a long glass tube of the same diameter. When in use, the appa- ratus is supported as represented in the Kg. 839. figure, so that the end of the tube shall dip into a glass filled with colored water. If, now, we hold over the * Silliman's Principles of Philosophy, p. 222. 424 CHEMICAL PHYSICS. porous cell a bell-glass filled with hydrogen, there will be an immediate rush of air from the tube through the water, because the hydrogen diffuses into the cell nearly four times as rapidly as the air passes out ; but upon removing the bell of hydrogen the conditions are reversed, — the hydrogen, which the cell now con- tains, diffuses into the atmosphere, and the colored water imme- diately rises into the tube. As all gases are expanded by heat, and therefore rendered specifically lighter, it follows that the absolute velocity of diffu- sion of any gas (measured by volume) increases with an increase of temperature ; but since an elevation of temperature does not increase the rate of diffusion as rapidly as it does the volume of a gas, it is also true that the same weight of any gas will be dif- fused more rapidly at a low than at a high temperature. It will hereafter be shown that heat expands all gases equally, so that their relative densities are preserved, however great the change of temperature. Hence the relative velocities of diffusion, which are given in the table on p. 422, are the same for all tempera- tures, provided, of course, the gases be heated equally. This diffusive power of gases is of the greatest importance in preserving the purity of our atmosphere. As it is, the noxious carbonic acid from our lungs, the deleterious fumes from our factories, and the miasmatic emanations from the marshes, are rapidly spread through the atmosphere and rendered harmless by extreme dilution, until they can be removed by the beneficent means appointed for this end. Moreover, the more they differ in density from the air, and the more, therefore, they would tend to separate from it, the stronger is the force by which they are compelled to mix. Were it not for this provision in the consti- tution of gases, these injurious substances would remain where they were formed, and might produce the most disastrous conse- quences. If we consider, also, the oxygen and nitrogen of which the atmosphere essentially consists, they differ in density in the proportions of 1105 to 971 ; but yet they are so perfectly mixed, that the most accurate chemical analysis has been able to detect no difference between the air brought from the top of Mont Blanc and that from the deepest mine of Cornwall. Were the force of diffusion much less than it is, these two gases would sep- arate partially, and the atmosphere be unfitted for many of its important functions. THE THREE STATES OF MATTER. 425 Bunsen,* who has more recently studied the phenomena of gaseous diffusion, has obtained results which do not coincide with the simple law discovered by Graham, and enunciated above. The discrepancy between the results of these two eminent observ- ers probably arises from the great thickness of the plaster dia- phragm in the apparatus used by Bunsen ; in consequence of which the phenomena of diffusion were modified by those of transpiration. Compare (213). The same must be true, to a certain extent, of the diffusion-tube of Graham ; and the experi- mental results will probably approach the law in proportion as the thickness of the diaphragm is diminished, actually coinciding with it only when the diaphragm is entirely removed and the gases expand freely into each other. (215.) Passage of Gases through Membranes. — If a bladder half filled with air, and having its mouth tied, is passed up into a bell-glass of carbonic acid standing over water, it will become, in the course of twenty-four hours, fully distended, and may even burst, owing to the passage of carbonic acid gas through the pores of the bladder. This is not, however, a simple phenom- enon of diffusion, since the carbonic acid enters the bladder as a liquid dissolved in the water permeating the substance of the membrane, and evaporates from the ipner surface of the bladder like any other volatile liquid. A similar transfer takes place with a jar of gas standing on the shelf of a pneumatic trough. The water dissolves, to a slight extent, the gases of the atmos- phere, which subsequently evaporate into the jar, while at the same time the gas in the jar slowly passes out, in a similar way, into the atmosphere. For this reason, gases confined over water cannot be kept pure for any length of time. Analogous phenom- ena have been observed with membranes of india-rubber, a sub- stance which has the power of absorbing many gases to a remark- able extent, especially those which are more easily liquefied. It is probable that the gases are always liquefied in the india-rubber, and pass through it in this condition, evaporating subsequently on the interior surface of the membrane. A similar absorption must take place, to a greater or less extent, with any diaphragm ; even with plaster of Paris it is appreciable, and slightly modifies the experimental results of diffusion. * Bunsen's Gasometry, p. 198. 36* 426 CHEMICAL PHYSICS. PROBLEMS. Capillarity. In solving these problems, the student will use the data given in the table on page 361 ; if the diameter of the tube is less than half a millimetre, [126] may be em- ployed, but if greater than this, [129] should be used. 240. Eequired the height to which water will rise in tubes of the fol- lowing diameters, when the temperature is 15° :. 1 m. m. ; 0.562 m. m. ; 0.012 m. m.; 2.56 m. m. ; and 0.001 m. m. Calculate, also, the heights for 10°, 50°, and 80°. 241. Eequired the height to which olive-oil will rise in a tube 0.25 m. m. in diameter, at the temperature of 75°. Calculate the heights to which oil of turpentine, alcohol, and sulphuric acid will rise under the same circumstances. 242. Required the height to which water will rise between two glass plates which are maintained parallel to each other at a distance of 0.25 m. m. How high would ether and alcohol rise under the same circum- stances ? The temperature is assumed to be 0°. 243. Two glass plates, 15 c. m. broad, united by hinges at one side, and opened at the opposite side so as to admit a wire 1.5 m. m. in diameter, are placed upright in a dish of water ; required the height to which the water will rise at the following distances from the line of intersection of the two planes measured on the line of contact of the water level with one of them: l.c.m.; 3 cm.; 5c.m.; andlOc.m. (See Figs. 323 and 325.) The temperature is assumed to be 0°. 244. A small glass bell, provided at the top with a capillary tubulature 0.2 m. m. in diameter, is immersed in water with its mouth downwards. How high can the top of the bell be raised above the surface of the water before air wiU begin to enter the beU through the capillary tube, measuring the distance from the base of the tube ? 245. If the bell of the last example is pressed under mercury with its top downwards, when will the mercury begin to enter the bell ? Soluhility. 246. How much sulphate of potash do 100 parts of water dissolve at 100° ? at 50° ? and at 10° ? How much chloride of potassium and how much chloride of barium do 100 parts of water dissolve af the same temperature ? 247. Calculate how much nitre and how much nitrate of baryta 100 parts of water dissolve at the following temperatures : 5° ; 10° ; 50° ; and 100°. 248. Determine from the data given on page 366 the empirical formula which expresses the solubility of nitre in water, and also construct its curve of solubility. THE THREE STATES OP MATTER. 427 249. Determine from the data given on page 375, in column C, the empirical formula for anhydrous sulphate of soda, and also construct its curve of solubility. 250. Determine the formula and curve of Na 0, SO3 . 10 HO, and also of Na O, SO3 . 7 HO, from the data given in columns F and H of page 375. 251. Determine the formula and curve of Na O, COj . 10 HO ; of Na 0, COj . 7 HOb ; and of NaO, COj . 7 HOa, from the data given in columns B, D, and G on page 377. 252. A saturated solution of crystallized carbonate of soda was pre- pared at 25°; of this solution, 52.364 grammes were evaporated to dryness in a glass flask, and the residue was found to weigh 11.614 grammes. What is the solubility of the salt, assuming, first, that the solution con- tained Na O, COj ; and secondly, that it contained Na 0, CO2 . 10 HO ? 253. A saturated solution of Glauber's salts was prepared at 50°.4 ; of this solution, 45.232 grammes were evaporated to dryness, and the residue found to weigh 14.424 grammes. What is the solubility on the assump- tions : first, that the solution contains Na O, CO^ ; secondly, that it con- tains Na O, COj . 10 HO ? Solution of Gases. 254. Determine the quantity of carbonic acid gas absorbed by 500 c.in.* of water at the temperature of 15°, when the pressure of the gas on the surface of the liquid is 76 c. m. .Calculate also the quantity, when the pressure of the gas is 72 c. m. 255. In the following table are given for each gas, first, the volume of water, secondly, the temperature, and, thirdly, the pressure exerted by the gas. Determine the quantity of gas absorbed in each case. r. Nitrogen \,UO'^~S? Oxygen 680 " Sulphide of Hydrogen, ... 560 " Sulphurous Acid, .... 240 " Ammonia, 1,500 " 256. Determine the quantities of the different gases which would dis- solve in alcohol under the conditions given in the last problem. 257. Prepare a table of the solubility of sulphide of hydrogen in water for every five degrees between 0° C. and 45° C. from the following inter- polation formula : — (7 = 4.3706 — 0.083687 < -f 0.0005213*2. 258. Prepare a table of the solubility of ammonia in water for every five degrees between 0° and 30°, from the following formula : — 0= 1049.63 — 29.496-« -f 0.67687^2 _ 0.0095621 <». t. H. 10° 75 c. m. 20 78 " 5 56 " 15 24 " 24 10 " 428 CHEMICAL PHYSICS. 259. Determine an interpolation formula for the solubility of the fol- lowing three gases from the data given : — Carbonic Oxide in Water. Hydrogen in Alcohol. Sulphide of Hydrogen in Alcohol. No. i° C, Coefficient found. NO ,o p Coefficient ' ^- found. No- '°C. Coefficient 1. 5.8 0.028636 1. 1.0 0.06916 1. 1.0 17.367 2. 8.6 0.027125 2. 5.0 0.06847 2. 4.0 15.198 3. 9.0 0.026855 3. 11.4 0.06765 3. 7.5 13.246 4. 17.4 0.023854 4. 14.4 0.06726 4. 10.6 11.446 5. 18.4 0.023147 5. 19.9 0.06668 5. 17.6 8.225 6. 22.0 0.022907 6. 23.7 0.06633 6. 22.0 6.624 Combine the three equations obtained by taking the mean of 1, 2, 3 ; 2, 3, 4, 5 ; and 4, 5, 6. 260. An experiment made by Dr. Pauli with a gas prepared by heating the acetate with hydrate of potash, and carefully freed from elayl and carbonic acid with fuming sulphuric acid and potash, gave, with the absorption-meter, the following elements for calculating the coefficient of absorption : — Original volume of gas reduced to 0°, .... 116.42 c. m.' The pressure on this volume, ,50.65 c.m. Volume of gas reduced to 0° after absorption, . . . 75.18 cTm^' CoiTCsponding pressure, 66.15 c.m. Volume of absorbing water, 318.11 ^m.^ Temperature of absorption-meter, 12°.8 Eequired the coefficient of absorption at -|-12°.8 C. 261. Given the percentage composition of the following gaseous mix- tures, and it is required to determine the composition of the gas absorbed by a limited quantity of water or alcohol ; the amount of the mixture is assumed to be indefinite. I. n. in. Hydrogen, 92.07 Carbonic Oxide, 50.48 Carbonic Acid, 50.06 Carbonic Acid, 7.93 Marsh Gas, 49.52 Carbonic Oxide, 49.94 262. Assuming that the percentage compositions given in the last prob- lem are those of the dissolved gas, whether in water or alcohol, required the percentage composition of the gaseous mixture. 263. It is required to determine the absolute volumes of carbonic acid, carbonic oxide, and nitrogen absorbed by 500 c. m.^ of water from a mix- ture of the three gases having the following composition, and also the per- centage composition of the gas dissolved. It is assumed that the amount of the mixture is indefinitely great, and that it exerts a pressure on the water equal to 76 c. m. Carbonic Acid, 25.03 Carbonic Oxide, 29.97 Nitrogen, 45.00 264. Solve the last problem for alcohol, instead of water. THE THEEE STATES OP MATTER. , 429 265. Determine the composition of a mixture of hydrogen and carbonic acid from the following data, obtained with an absorption-meter. Calcu- late, also, the composition of the gas remaining unabsorbed. Tolume Pressure. Temp. at 0°- c. m. Gas before absorption, .... 119.03 49.51 6.8 Gas after absorption, .... 75.71 60.20 23.3 266. Determine the composition of a mixture of carbonic acid and car- bonic oxide from the following data, and calculate the composition of the gas remaining unabsorbed. Tolume Pressure. Temp, at 0°. cm. o Gas before absorption, .... 500.8 57.60 19.0 Gas after absorption, .... 283.3 74,15 19.0 267. Determine the coefficient of absorption of nitrogen in water at 19° C. from the following data, obtained with an absorption-meter. 1. Observations before the Absorption. Lower surface of mercury in outer cylinder, .... 42.36 c. m.* Upper surface of mercury in absorption-tube, . . . 12.41 " Barometer, 74.69 " Temperature of the absorption-meter, 19°. 2 " " barometer, 19°.0 Volume of gas corresponding to division of tube 12.41, . 34.90 s:ia.' 2. Observations after tlie Absorption. Lower surface of mercury in the outer cylinder, . . . 35.22 c. m. Upper surface of mercury in absorption-tube, . . . 35.07 " " " " water in absorption-tube, .... 6.55 " " " " " in outer cylinder, .... 0.80 " Barometer, 74.63 " Temperature of the absorption-meter, .... 19°.0 " " barometer, 18° .9 Volume of gas corresponding to division of tube 6.55, . 17.67 c. m. " " " " " 35.07, . . 200.04 " Effusion. 268. Determine the specific gravity of hydrogen from the following data : time of effusion of air, 105".o ; that of the same volume of hy- drogen, 29".7. 269. Determine the specific gravity of oxygen from the data, time of effusion of air, 102".5 ; time of effusion of oxygen, 108".5. 270. Determine the specific gravity of carbonic acid from the data, time of effusion of air, 102".7; that of carbonic acid, 127"- 271. Determine the specific gravity of a mixture of hydrogen and oxy- gen from the data, time of effusion of air, 117.9 ; that of the mixed gases, 75.4. * These heights are measured on the scale of the absorption-tube, counting from the top. CHAPTER IV. HEAT. All natural substances are, in certain conditions, capable of producing on our bodies peculiar sensations, ■which we designate by the words heat and cold. These sensations may result from direct contact with the substance, as when we touch a heated stove ; or they may be produced at a great distance from it, as when we are warmed by the radiation from burning fuel or by the rays of the sun. The agent which produces these effects, and which is evidently distinct from the substance, we term heat. In regard to the nature of heat we have no absolute knowledge. Two different theories are current among philosophers in regard to it. According to one theory, it is an imponderable agent, filling all space, for which substances have different affinities, and which may be transferred from one to another, either by contact, or by an actual emission of material particles through space. The effects of heat are supposed to result from an excess or a deficiency of this agent. The second theory admits, like the first, the existence of an imponderable fluid, which is supposed to pervade all space, penetrating through even the densest solids ; but it refers the effects of heat to vibrations in this medium, those substances being the warmest in which these vibrations are most rapid, or have the greatest amplitude. Some of the phenomena of heat are best explained by the first, and some by the second of these theories. Those witli which we shall have chiefly to deal in this work will be the most clearly understood by using the language of the first theory, according to which heat is a material, although an imponderable agent, capable of being transferred from one substance to another and of being measiired with accuracy, and therefore an agent to which all the terms relating to quantity are strictly applicable. (216.) The Action of Heat on Matter. — The mechanical effects of heat on matter may be all explained by assuming that heat acts as a repulsive force between the particles, and therefore HEAT. 431 opposes the attractive force of cohesion. The first effect of heat on matter, in either of its three states, is to expand it. This may be illustrated by a great variety of familiar facts and experi- ments. A ball of metal, which exactly fits a ring when cold, will not pass through it when heated. The parts of a wheel are bound together by the contraction of the tire, which is put on while hot. Clocks go slower in summer than in winter, because the pendulum is lengthened by the heat. Different substances expand unequally for the same increase of temperature. We estimate the expansion either by measuring the increase of length or the increase of bulk. The first is called the linear expansion, the second the cubic expa/nsion. In the case of solids we generally measure solely the linear expansion, while in the case of liquids and gases we as generally measure solely the cubic expansion. The one, however, can easily be calculated from the other, since the cubic expansion is about three times as great as the linear expansion. The following table will give an idea of the amount of expansion in difierent substances, and will show that gases expand very much more than liquids, and liquids very much more than solids. Between the Freezing and Boiling Points of Water : A rod of zinc increases in length -^^-g, that is, 323 c. m. become 324. learl (( u rs\> « 351 ii ii 352. tin « K 5TTT' ft 516 6C a 517. sUver ti (( ■52-S) " 624 it ii 525. glass (crown) ti TiV^J a 1142 ii ii 1143. Qcreases In volume J, that is, 9 c: :^.= become 10. (t cc 2^1 it 23 Cl tt 24. ti (I ^, ^t 65 ii ki 56. Water Mercury Air and the permanent gases expand ^, that is, 80 cm.' become 41. Before, however, we study the phenomena of expansion in detail, it is important to examine the various means by which the effects of expansion are used as a measure of temperature. 432 CHEMICAL PHYSICS. THEEMOMETERS. (217.) Mercurial The)-mometer. — It is obvious that we might use, as the measui-e of temperature, the effect caused by heat in expanding either solids, liquids, or gases, and thermometers have been constructed of each of these three forms of matter. The expansion of solids, however, is so small, and that of gases so difficult to measure, that their indications are not available for the ordinary purposes for which a thermometer is required ; while liquids, on the other hand, having an intermediate degree of expansibility, and their changes of volume being readily meas- ured, are well suited for thermometrical uses. Of the various liquids which might be employed, mercury is much the best, not only on account of the great range of temperature between its freezing and boiling points, but also because its increase of vol- ume is very nearly proportional to the inci-ease of temperature. In order to make a mercury thermometer, a capillary glass tube is first selected, whose bore is of the same calibre throughout, so that equal lengths of the tube will contain equal volumes of mercury. The uniformity of the bore is readily tested by intro- ducing into the tube a small amount of mercury, and moving this short column gradually from one end to the other, measuring its length in each successive position. This should, of course, be the same in every case ; and if not, the tube must be rejected. The glass tube having been selected, and cut off to the required length, a bulb is blown upon the end by the usual method of glass-blowing, using, however, an india-rubber bag instead of the mouth, in order to avoid moisture. The size of the bulb is varJfed according to the degree of sensibility required in the instrument ; but it is always made large in comparison with the tube, so that a slight expansion of the enclosed liquid will caiise it to fill a considerable length of the bore. The form of the bulb may be either spherical or cylindrical. The first is most easily made ; but the last, from exposing a greater surface, is more readily affected by changes of temperature. To facilitate the introduc- tion of the mercury, a cup is sometimes cemented to the open end of the tube, although a paper funnel fastened with twine will answer every purpose. The tube thus prepared is now easily filled with mercury. Holding the tube in a vertical position, we pour mercury into the HEAT. 433 cup, and heat the bulb with a lamp in order to expel a portion of the air. On removing the lamp the glass soon cools, and the mercury is forced in by the pressure of the atmosphere, partially filling the bulb. We now again apply the lamp, as represented in Pig. 340, until the mercury boils ; and continue the boil- ing for several minutes, in order that the mercury vapor may drive out all the air and moisture. The lamp is then again removed, when the mercury, pressed in by the atmosphere, descends and fills completely the whole appara- tus. The cup is then emptied of the excess of mercury, and the tube just below it drawn out to a narrow neck in the flame of a blowpipe, when the cup may be broken off. As the tube is now filled with mer- cury, a greater or less portion of it must be removed, depending on the range to be given to the instrument. This is accomplished by heating the bulb to the highest temperature which the thermometer is expected to measure, when the excess of mercury is expelled through the minute aperture left in the neck of the tube. The source of heat is now withdrawn ; and the moment the column of mercury begins to descend, the flame of a blowpipe directed against the end of the stem hermetically seals the tube. It remains then only to graduate the instrument. (218.) Graduation of the Thermometer. — If the bore is uni- form, it is evident that the rise of the mercury in the tube will be proportional to the expansion, so that we have in the ther- mometer an instrument with which we can measure any change of volume of the included liquid ; and if we assume that the expansion is proportional to the increase of temperature, it is evident that it will also serve as a very delicate measure of tem- perature. The thermometer is always graduated by means of two fixed temperatures, — those of melting ice and of boiling water. The 3T Fig. 340. 434 CHEMICAL PHYSICS. bulb and the portion of the tube filled with mercury are first sur- rounded by pulverized ice, and the point to which the mercury falls is marked with a file on the stem (Fig. 341). The thermometer is next immersed in steam escaping freely into the atmos- phere, and the point to which the mercury rises marked as before. The temperature of free steam is always approximatively the same as that of boiling water, and even more constant, not being affected by many circumstances, such as the nature of the vessel and the presence of impurities, which may change slightly the boiling-point. The apparatus represented in Figs. 342 and 343, invented by Regnault, is admi- rably adapted for fixing the boiling-point. Its construction is sufiiciently evident from the drawing, and does not, there- fore, require description. The steam ris- ing from the boiling water circulates in the direction of the arrows, escaping by the tube D ; and the object of the double envelope is merely to prevent the steam from condensing in the inner cylinder A. Fig. 341. Fig 342. Fi?- 843. HEAT. 435 Since the temperature of boiling water and of the steam escap- ing from it varies with the atmospheric pressure, it is evidently essential to pay regard to this circumstance in graduating the thermometer. The fixed point adopted for the graduation is the temperature at which water boils under a pressure of 76 c. m. ; and if the barometer, at the time of graduation, indicates a dif- ferent pressure, it is necessary to make a correction accordingly. This correction is easily calculated, since Wollaston determined that the boiling-point of water increases one Centigrade degree for every increase of pressure measured by 2.7 cm. of mercury column. In determining the boiling-point with Regnault's ap- paratus, it is necessary to guard against any accidental variation of pressure in the interior ; and for this reason, it is furnished with the manomfeter-tube »?.. The two fixed points having been marked on the tube, the distance between them is next divided into equal parts, called degrees. Two different scales are used in this country. In the Centigrade scale, which is the one most generally used for scien- tific purposes, the distance is divided into one hundred degrees, which are numbered from the freezing-point of water. These divisions are continued of the same size both above .100° and below 0°, the last being distinguished by a minus sign ; thus, — 10° stands for ten degrees below zero. In the Fahrenheit scale, which is used almost exclusively in common life, the distance is divided into one hundred and eighty degrees, which are num- bered from a point thirty-two degrees below the freezing-point of water ; so that on this scale the freezing-point of water is at 32°, and the boiling-point at 32° + 180° = 212°. The Fahrenheit scale originated with an instrument-maker of Dantzic, from whom it is named, and appears to have been based on some theoretical views in regard to the expansion of mercury which have long since been forgotten. It is supposed that the zero was chosen as marking the greatest cold which had been observed at Dantzic, and which Fahrenheit regarded as the great- est possible. We are now, however, able to reduce the tempera- ture of bodies at least one hundred and fifty degrees below the zero of Fahrenheit, so that this zero is far from marking the greatest possible cold ; moreover, since cold is merely the absence of heat, and since we cannot remove all the heat from matter, we can never expect to reach the absolute zero. Indeed, the 436 CHEMICAL PHYSICS. ■whole thermometric scale is to be regarded as purely arbitrary, and may be compared to a chain, extending indefinitely both up- wards and downwards. We select some point on the chain, and begin to count the degrees from that. We fix the length of our degrees by selecting a second point, at a convenient distance above the first, and dividing the intervening length into an arbi- trary number of equal parts. Thus all is arbitrary ; and there is no peculiar virtue in the two points which have been chosen, other than that they can be easily determined with accuracy, and include between them the range of temperature with which we are usiially most concerned. The Centigrade scale has been adopted in this work, not only because it has a decimal subdivision, but also because it is the one most generally adopted in the scientific works both of tliis coun- try and of Europe. At the end of the book there will be found a table by which the degrees of the Centigrade scale may be con- verted into those of the Fahrenheit. This reduction can easily be made mentally, since 100° C. = 180° F., or 5° C. = 9°F.; hence F.° = | C.° -f 32. The 32 is added, because the zero of Fahrenheit is 32 Fahrenheit degrees below the zero of the Centi- grade. An easy rule for mental calculation is. Double the number of Centigrade degrees, subtract one tenth of the whole, and add thirty-two. When the Centigrade degrees are below zero, they are marked with a minus sign ; and this sign must be regarded in using the above rule. Besides the two just mentioned, the scale of Reaumur is also used in some countries of Europe. On this scale the distance between the freezing and boiling points of water is divided into eighty equal parts, but the zero is the same as on the Centigrade. It is, however, never used in this country, and is seldom referred to in scientific works. In all thermometers, after the length of a degree has been ascertained by dividing the distance between the freezing and boiling points of water into equal parts, the divisions are con- tinued of the same size beyond the two fixed points on either side. This method of graduation occasions a defect in the instrument which must now be noticed. (219.) Defects of the Mercury Thermometer. — It will be obvious, from a moment's reflection, that we do not observe in a thermometer-tube the absolute expansion of mercury, but only HEAT. 437 the relative expansion as compared with that of the glass bulb. Did the glass expand as much as the mercury, the cohimn of liquid would evidently remain stationary at all temperatures. If it expanded more than the mercury, an increase of tempera- ture would cause the column to fall. In fact, the expansion of mercury is seven times greater than that of glass f so that its apparent expansion, when enclosed in a glasg vessel, is about one seventh less than the absolute expansion. Th® rise of the column of mercury in a thermometer-tube is, then, a mixed effect of the expansion of the enclosed mercury and of the glass envelope. It is further evident, that the whole value of the thermometer, as a measure of temperature, i*ests xtpon the assumption that the expansion of a given quantity of mercury is exactly proportional to the amount of heat which enters it. If, for example, a given amount of heat, entering the mercury of a thermometer, causes it to expand 0.001 of its volume, and consequently to rise in the stem one centimetre, it is assumed that twice, three times, etc. as much heat will cause it to expand 0.002, 0.003, etc. of its volume, and to rise in the stem 2, 3, etc. centimetres. This assumption is not, however, absolutely correct, for the rate of ' expansion of mercury gradually increases with the tempera- ture ; so that, in the example just cited, twice as much heat will j cause the mercury to expand a little more than 0.002, and three times as much heat a little more than 0.003 of its original vol- ume. Or, to take another illustration, let us suppose that a certain amount of heat, entering the mercury of a thermometer, causes the column to rise in the stem one centimetre, which we may suppose, in a given case, to be the length of one Centigrade degree ; and let us also suppose that exactly equal amounts of heat enter the same thermometer during successive intervals of time. If the rate of expansion of mercury were uniform, each addition of heat would cause the mercury to rise exactly one centimetre ; so that, if the stem were divided into centimetres, each of these would indicate the same accession of heat. As it is, however, the addition of the second quantity of heat causes the mercury to rise a little more than a centimetre, the addition of the third quantity causes a rise still greater than before, and so on. Heuce, in order that the degrees of the thermometer may indicate equal accessions of heat, they shoiild slowly in- crease in length from zero up. In the case of mercury, the rate 37* 438 CHEMICAL PHYSICS. filW ; ■ f t a mm' rig. S44. of expansion changes so slowly, that the increase in the length of the degrees would not be per- ceptible to the eye within the usual range of the scale ; but if the thermometer is filled with water, whose rate of expansion increases very rapidly, the effect becomes very evident. The water thermometer, represented in Fig. 344, is so, graduated that each division on the scale corresponds to an equal amount of heat ; and it will be notie^ed that the degrees near the top of the scale are' several times longer than those near the zero poiat. This, then, is an exagger- ated representation of the way in which a mer- cury thermometer should be graduated, in order to be perfectly accurate ; the length of the de- grees should slowly increase from the zero point xvp. In practice, however, as has been described, they are made of the same length. The error, thus caused, is not important between the two fixed points ; since, by dividing the given dis- tance into equal parts, we obtain a mean length for the degree, which, although too long for the degrees near the freezing-point, and too short for the degrees near the boiling-point, is exact for the intermediate degrees, and very nearly correct for all. But above the boiling-point the same is not the case ; for while the degrees marked on the scale have the same length as those below, the true length of the degree is constantly increasing, until the difference be- comes very considerable. Hence a thermometer above the boiling-point always indicates too high a temperature ; and, for the same reason, below the freezing-point indicates too low a temperature. The value of the mercury thermometer as an accurate instrument would not be materially im- paired by the facts stated above, since it would always be possible to estimate the amount of deviation in any case, and apply the correction to the observed results. Unfortunately, however, HEAT. 439 its indications are also affected by the unequal expansion of the glass envelope. It so Happens that the rate of expansion of glass increases quite as rapidly as that of mercury ; so that the error induced by the increased rate of expansion of mercury is in part corrected, indeed sometimes over-corrected, by the' increasing capacity of the glass bulb. Unfortunately, the rate »f expansion differs very considerably in different kinds of glass, and even in the same glass under different circumstanfc'^; so much so, that two thermometers, even when constnic^ell with the greatest care, seldont agree for temperatures verj.'much above or below the fixed points. It is thus evident, 'that, while the expansion of the glass tends to correct th^ error which would be caused by the unequal expansion of pfercury, it nevertheless renders the indications of the thermometer uncertain to a slight extent, and sufficiently to deprive the instrument of that accuracy which is desirable in a scientific investigation. The facts stated in this section are illustrated by the following table, from the well-known memoir of Regnault * on this subject. Comparison of Different Thermometers. Air Thermometer. True Tempera^ ture. Thermometer without Gtla£8, Thermometer, riint-glaes. Thermometer, Crown-glass. Coefficient of Expan- sion of MercuiT-. o o o 0.000 1790 50.00 49.65 50.20 0.000 1815 100.00 100.00 100.00 100.00 0.000 1830 120.00 120.33 120.12 119.95 0.000 1850 140.00 140.78 140.29 1.S9.85 0.000 1861 160.00 161.33 160.52 159.74 0.000 1871 180.00 182.00 180.80 179.63 0.000 1881 200.00 202.78 201.25 199.70 0.000 1891 220.00 223.67 221.82 219.80 0.000 1901 240.00 244.67 242.55 239.90 0.000 1911 246.30 246.30 260.00 265.78 263.44 260.20 0.000 1921 280.00 287.00 284.48 280.52 0.000 1931 300.00 308.34 305.72 301.08 0.000 1941 320.00 329.79 327.25 321.80 0.000 1951 340.00 851.34 349.30 343.00 0.000 1962 Column 1 gives the temperatures of the air thermometer taken as the standard, which may be regarded as very close approxima- * Memoires de I'lnstitut, Tom. XXI. pp. 239, 328. 440 CHEMICAL PHYSICS. tions to the true temperature. Column 2 gives the corresponding temperatures which would be indicated by a mercury tliermome- ter, graduated in the usual way, if the glass did not expand at all ; showing the error which would be caused by the varying rate of expansion of the mercury alone. Column 3 gives the correspond- ing temperatures indicated by a mercury thermometer made of flint-glass (cristal de Choissy-le-Roi), showing that this error is in part corrected by the unequal expansion of the glass bulb. Column 4 gives the corresponding temperatures indicated by a thermometer of crown-glass (verre ordinaire de Paris), shftwing that the indications of thermometers made with different varieties of glass do not necessarily accord. . Finally, column 5, giving the coefficients of expansion of mercury at each temperature (250), is added, in order to show how rapidly the rate of expansion in- creases with the temperature. It will be noticed that the thermometers agree perfectly at the two fixed points to which they are graduated. Moreover, be- tween these two points the differences are comparatively small, since from the very method of graduation the errors are distrib- uted ; but above 100° the differences between the indications of the mercury thermometers and the true temperatures are contin- ually increasing. The variations from the true temperature in the case of the theoretical thermometer without glass are very large. In the flint-glass thermometer the differences are less, because the varying rate of expansion of merciiry is partially corrected by that of the glass. In the case of the crown-glass thermometer, there is a singular anomaly. This, on account of the remarkable law of expansion which crown-glass obeys, keeps nearly in accord with the air thermometer up to 246°. 30, at which point it coincides with it ; but above this point, at which they separate, the differences between the two rapidly increase. It will also be noticed, that the differences between the temper- atures indicated by the thermometers of flint and crown glass are quite large ; and it is evident that the last are greatly to be preferred in all scientific investigations. Smaller differences have been observed between thermometers made of varieties of crown-glass ; but they are not of practical importance when neither of the varieties contains lead. The facts just stated will be rendered clearer by Fig. 345, which is a geometrical construction of the results given in the HEAT. 441 table on page 439. The figures on the horizontal line, or axis of abscissas, stand for the temperatures of an air thermometer; those on the vertical line, or axis of ordinates, for the differences Fig 345. between the indications of this thermometer and of different mercury thermometers. The curve On am shows the varia- tions from the true temperature of the theoretical thermometer without glass ; and the curves Onac, Onav, On as, Onao, the variations of thermometers made with flint-glass of Choissy- le-Roi, green glass, Swedish glass, and "verre ordinaire de Paris," respectively. The anomaly in the case of the thermom- eter made with the common Paris glass is beautifully illustrated by the last curve. (220.) Change of the Zero Point. — Mercury thermometers, even when constructed with the greatest care, are liable to error from another cause, which cannot be so easily explained as the one just considered. The zero-point of the thermometer fre- quently rises on the scale, the displacement amounting at times even to two degrees. By this is meant, that when the thermom- eter is surrounded by melting ice, as in Fig. 341, the mercury will not sink to the original zero, but only to a point possibly even two degrees above it. According to Despretz, this change may continue for an indefinite period ; and it is therefore impor- tant to verify the position of the zero-point of a thermometer before using it in an observation where great accuracy is required. If the point has been displaced, the amount of the displacement must be subtracted from the observed temperatures. Besides this slow rising of the zero-point, sudden variations in its position have been noticed after the thermometer has been ex- posed to a higher temperature. These variations are sometimes permanent, and at other times merely transient, the zero-point 442 CHEMICAL PHYSICS. returning to its original position after the instrument has been cooled for some time. All these facts tend to show, that determi- nations of temperature with a mercury thermometer are liable to sources of error which cannot always be guarded against ; and it is tlierefore best, when great accuracy is required, to substitute for the mercury tliermometor the air thermometer of Eegnault, which will be described in a future section. (221.) Standard Thermometers. — The causes of error in the mercurial thermometer alreq,dy noticed arise from the very na- ture of the materials, and are inseparably connected even with such instruments as have been constructed with all the refine- ments of modern science. Ordinary thermometers are liable to errors of construction of a far greater magnitude. It is evident, from the theory of the instrument, that unless the bore of the tube has the same calibre throughout, equal increments in the volume of the mercury will not cause an equal rise of the column in all its parts ; and the indications of the instrument, graduated in the usual way, will be more or less erroneous. Now it is seldom, and probably never, the case, that a thermometer-tube has an absolutely uniform bore. Hence, in making a standard instrument, it is essential that _ the tube should be calibrated throughout, and the size of the degrees proportioned to the vary- ing diameter of the tube. This is done by introducing a short column of mercury into the tube, gradually moving it from one end to the other by moans of a small elastic bag tied to the open mouth, and dividing the tube into lengths equal to the lengths of the mercury-column. This length is taken so short that the diameter of the tube may be assumed, without appreciable error, not to vary throughout the short distance; and when the tube is graduated, each of these lengths is divided into the same number of equal parts. Regnault, who has very greatly improved the methods of grad- uating standard thermometers, uses for the purpose a dividing engine, similar to the one represented in Fig. 346, which is con- structed by M. Duboscq, of Paris. It consists of the iron frame A Q, in which is mounted the long, steel screw H. This screw is confined at its two ends by brass collars, in which it turns freely. On the top of the iron frame moves the carriage B, to which the tube to be divided is fastened. Motion is communi- cated to this carriage by the screw H, which plays through a HEAT. 443 socket fastened to the under side, and therefore invisible in the drawing. By turning the screw, tlie carriage b, and the tube fastened iijoon it, are moved forward under the graver, a, which Kg. 346. is attaclied to a very ingenious apparatus for regulating the lengths of the division-lines, making every fifth and tenth line longer than the rest. This dividing apparatus is supported on the upright piece of iron, P, which is itself firmly fastened to the frame of the engine. The whole value of the apparatus depends on the long screw, which is made with great care, and its threads so adjusted that one revolution moves forward the carriage exactly one milli- metre. Motion is communicated to the screw by the handle M, acting through the cogs m and n on the broad wheel op r, and this, in its turn, on a ratchet-wheel fastened to tlie head of the screw, and moving within the first. The wheel opr can revolve in one direction independently of the ratchet-wheel and the screw ; but when turned in the opposite direction, a small detent, fastened to the inner surface of its rim, catches in the teeth, and moves the ratchet-wheel and screw with it. The rim of the wheel opr \s divided on both sides into degrees, and by means of a set of stops its motion can be limited to any number of rev- 444 CHEMICAL PHYSICS. olutions, or to any fraction of a revolution. Let us suppose that the stops are so adjusted that the wheel opr can turn through two revolutions and /^V- Starting, then, from the first stop, and turning the handle M until the motion is arrested by the second stop, the screw Hw'Al be revolved twice and x^o*cr- Consequently, the carriage B will be moved forward 2.54 millimetres. On now turning the handle M in the opposite direction, the wheel opr will be turned back to its first position, without moving the screw, and then, on reversing the motion, the carriage will be moved forward 2. .54 m. m., as before, and so on indefinitely. If at each advance we make a mark with the graver, o, it is evident that our tube will be divided into lengths of 2.54 m. m., or into any other lengths for which we may choose to adjust the stops. This engine may also be used for measuring the length of di- visions already made ; only for this purpose a small microscope, furnished with cross-wires, should be attached to the upright, P, at the side of tlie graver. The microscope having been adjusted so that the cross-wire is just over the first mark on the tube, and the stops which limit the motion of the wheel op r having been removed, the handle M is turned until the cross-wire is exactly over the second mark, the observer carefully noting the number of revolutions and fraction of a revolution required, by means of an index provided for the purpose. Let us suppose 10.75 revo- lutions are required ; then, evidently, the length of the division is 10.75 millimetres. In using the dividing engine for calibrating a thermometer, the tube is adjusted on the carriage B so that its axis shall be per- fectly parallel to the axis of the long screw H. A short column of mercury having been previously introduced into one end, the length of this column is carefully measured as just described, and the position of its two extremities marked with a fine hair- pencil on tlie tube. Adjusting the cross- wire of the microscope to the head of the mercury-column, tliis is next pushed forward in the tube through exactly its own length. The length is again measured, and the position of the head of the mercury- column having been marked as before, the same process is re- peated until the tube is divided into lengths of equal capacity, and their value known. Each of these lengths is next to be divided into the same number of equal parts, and any convenient number is selected, which shall give to the degrees as nearly as HEAT. 445 possible the size required. In order to illustrate the method, let us suppose that the lengths between the pencil-marks are respect- ively as follows : — 18.45 m.m., 18.39 m.m., 18.32 m.m., 18.24 m.m., 18.15 m.m., and that it is decided to divide each length into thirty degrees. The lengths of the degrees in the different divisions will then be, respectively, 0.615 m.m., 0.613 m.m., 0.611 m.m., 0.608 m.m., 0.605 m.m. This calculation having been made, the tube is covered with a varnish such as is used in etching, and the stops on the wheel opr (Pig. 346) so adjusted as to limit its motion to 0.615 of one revolution. The point of the graver is also adjusted to the first pencil-mark, and a cut made through the varnish, exposing the glass. The handle M is now tiirned until its motion is arrested by the stop, and another cut made. The motion of the handle having been reversed, the same process is repeated thirty times, when the point of the graver will have reached the second pencil- mark, and thirty degrees, each 0.615 m. m. in length, are marked on the tube. The adjustment of the stop must now be changed, so as to limit the- motion of the wheel to 0.613 of a revolution, and thirty more divisions made ; and so on until the graduation is completed, when the tube is removed from the engine, and the figures which serve to number the divisions are marked in with the hand. It only remains, now, to expose the tube to the vapor of fluohydric acid, which corrodes the glass wherever the graver has exposed its surface, and subsequently to verify the work by passing another column of mercury through the tube. This should cover the same number of divisions in any position, and will do so if the graduation has been carefully performed. The stem of the thermometer thus adjusted, a bulb is blown upon the end, or, what is better, a cylindrical reservoir previously prepared is cemented to it with a blowpipe. The capacity of this reservoir must be proportional to the size of the tube, and to the range of temperature which the thermometer is intended to cover. Let us suppose that it is required that N divisions of the thermometer should correspond to 100° C, and we wish to know what must be the size of the reservoir for a given graduated tube. We first weigh the tube, both when empty and when con- 38 446 CHEMICAL PHYSICS. taining a column of mercury which covers an observed number of divisions. This gives us the weight of mercury, w, occupying n divisions of the tube. From this we obtain N — , the weight of mercury which will fill N divisions, and by [56] iV ^^ ^^. , the corresponding volume. Biit this volume represents the ex- pansion which the mercury in the reservoir of our proposed ther- mometer must undergo when heated from 0° to 100°. Now we know that the apparent expansion of mercury, under these cir- cumstances, is ^'j of its volume at 0°. Representing, then, by Y the unknown volume of the reservoir, we shall have If the reservoir is spherical, F^ ^ tt 2)°, from which we can calculate the required diameter ; and if it is cylindrical, Y =^ It D^ h, from which we can approximatively determine the required length, /i, when the diameter is known. The tube and bulb are now filled with perfectly pure mercury, and the fixed points marked upon it in the usual way, when the thermometer is finished and ready for use. The divisions marked upon a thermometer so constructed are not, of course, degrees of either of the three scales mentioned in (218) ; but it is always easy to calculate from the indications of this arbitrary scale the corresponding degrees of the Centigrade scale. We ascertain, by observation, the number of divisions on the thermometer between the freezing and boiling points, which we may represent by N, and also the number of the divisions on the arbitrary scale corre- sponding to the freezing-point (the zero of the Centigrade scale). Represent this number by m, the degrees of the Centigrade scale by C, and those of the arbitrary scale by A°. "We have, then, N= 100° C, and C° = ~ {A" — n). Suppose, for example, that there are 354 divisions on the arbitrary scale between the fixed points, and that the freezing-point is at the 132d division from the bottom of the scale ; and let it be required to determine to what temperature the 230th division corresponds in Centi- grade degrees. We shall have, C° = |ff (230 — 132) = 27.68. It is usual to prepare a table for each thermometer thus con- structed, giving the temperature in Centigrade degrees corre- sponding to every division of the tube. HEAT. 447 The scale of a standard thermometer should always be en- graved on the glass stem, as in Fig. 347 ; since, if it is engraved on a strip of metal or ivory fastened to the tube, the expansion of the scale introduces new ^ sources of error into the instrument. It is also essential for a good standard, that it should in- b m elude the boUing and freezing points upon its scale. Where a large range is required, the great length which this involves may be best avoided by making several thermometers with contiauous scales, and enlarging the tube of each instrument at those parts which are covered by the scales of the other thermometers of the set. A thermometer so constructed is represented in Fig. 348, although the enlargement is very greatly exaggerated. It is possible in this way to di- vide each Centigrade degree into twenty parts, and yet include both of the fixed points on the scale. The length of the degrees of a thermometer, and hence its sensibility to small differences of temperature, depends upon the size of the reser- voir as compared with that of the tube, and can be increased by the maker at pleasure. No advantage, however, is gained by increasing the length of the degrees on the stem beyond a lim- ited extent ; since, on account of the imperfec- tions of the instruments noticed in the last section, it is useless, to subdivide the Centigrade degree into more than twenty parts, and only the most carefully constructed standards will bear as great a subdivision as this. Even when the scale is graduated to twentieths, it is possible for a practised eye to estimate the hun- dredth of a Centigrade degree. It is evident that the smaller the absolute size of the bulb, the more rapidly a thermometer will be affected by changes of tem- perature ; and hence it is always best to make the bulb as small as circumstances will permit, and also to give to it a long cylin- drical shape, which, for the same volume, exposes a much greater surface for ihe entrance of heat than a sphere. The size of the column of mercury in the stem of a thermom- Fig. 347. rig. 348. 448 CHEMICAL PHYSICS. eter is so small, as compared with that of the stem itself, that it is essential, in order to avoid th& parallax caused by the thick- ness of the glass, to place the eye in reading on a level with the surface of the column. The scale of a delicate thermometer is always best read through the telescope of a cathetometer (Fig. 260), placed at a sufficient distance to prevent the heat of the body from affecting the instrument. (222.) In using a standard thermometer, it is important to immerse both the bulb and the stem in the medium whose tem- perature is to be measured ; for if the stem of the thermometer is exposed to a lower temperature than the bulb, the whole of the mercury will not be equally expanded, and the thermometer will indicate too low a temperature. Since in testing the tempera- ture of a small quantity of liquid this complete immersion of the thermometer is impossible, it is necessary in such cases to add to the observed temperature a small correction, which becomes very important when the temperature of the medium greatly exceeds that of the air. In order to illustrate the method of calculating the correction, let us suppose that the thermometer is used for testing the tem- perature of an oil-bath ; and that, while the bulb and a portion of the stem are immersed, the greater part of the mercury- column is above the surface of the liquid, as represented in Fig. 401. It is now required to determine how much higher the ther- mometer would stand if the whole column were exposed to the same temperature as the bulb. For this purpose, we will repre- sent the different quantities entering into the calculations as follows : — X = the unknown temperature of the bath. f = the temperature indicated by the thermometer. ^1° == the mean temperature of the mercury in the stem, ascertained by placing in contact with it the bulb of a small thermome- ter at about mid-height of the column. 6 := the number of degrees which the portion of the mercury-column above the surface of the bath occupies in the thermometer- tube. i° — ti° = the difference of temperature between the bulb and the stem ap proximatively . It is evident that, if the temperature of the mercury above the surface of the bath were increased t° — ti", the thermometer HEAT. 449 would indicate the true temperature ; so that, to find the cor- rection required, we have only to calculate how much a column of mercury measuring 6 degrees on the scale will increase in length when its. temperature is raised f — 1°. The apparent expansion in glass of a given volume of mercury, amounting for each degree of temperature to ^^iVtrj ^iU amount for t° — t° to -.qg^' of the whole. Hence, a quantity of mercury which fills one degree of a thermometer-tube will fill 1 -| — pooTf- degrees of the same tube after its temperature has risen f — 1° ; and in like manner a quantity of mercury which fills Q degrees of a thermometer-tube will fill, after the same rise of temperatvire, G -\ — cqqa' degrees. In other words, the column of mer- cury above the surface of the bath would rise „ ' ' de- grees, if its temperature were raised to that of the bath. This, then, is the correction required, and we have, in any case, Since the mean temperature of the mercury-column can never be accurately determined, there is always an uncertainty in re- gard to the value of the correction ; and it is therefore best, when practicable, to avoid the necessity of any by immersing the whole stem in the bath. (223.) A thermometer indicates temperature by either receiv- ing or imparting heat until its own temperature is the same as that of the body tested. It is therefore evident that, unless the temperature of the body is maintained constant by accessions of heat from some external source, a thermometer will give correct indications only when its own mass bears a very inconsiderable proportion to that of the body. This very obvious fact must be carefully borne in mind while using the instrument ; and when the quantity of heat which the thermometer receives or imparts is appreciable, the change of temperature which is thus caused in the body must be calculated, and the observations corrected accordingly. The student will be able to devise methods by which the correction can in any given case be estimated, after studying the sections on Specific Heat. For further information in regard to the construction and use of 450 CHEMICAL PHYSICS. standard thermometers, we would refer the student to the vol- ume of memoirs of Regnault already noticed, and to a note by J. I. Pierre, published in the Annates de Chimie et de Physique, 3° Serie, Tom. I. p. 428. (224.) House Thermometers. — The scales of ordinary ther- mometers are graduated on strips of wood, metal, or ivory, to which the tube is subsequently attached (Fig. 349). Such thermometers are less fragile and more easily read than those graduated on the stem, and at the same time are sufficiently accurate for determining the temperature of a bath or of a room, and for most meteorological observations. They are not, however, usually graduated from the two fixed points, as de- scribed in (218), but by comparison with a standard thermometer. For this purpose, the instrument to be graduated and the standard are dipped together into a bath of water. Care being taken to maintain the water at the same temperature for some time, the number of degrees indicated by the standard is then marked on the stem of the new instrument at the level of the mercury-column. In the same way, by changing the temperature of the bath, several other points are determined. These are subsequently transferred to the strip on which the scale is to be engraved, and the distance between them divided into the number of degrees reqxiired. It has been found almost impossible to maintain a liquid bath at the same temperature in all its parts for any length of time, when this temperature con- siderably exceeds that of the air ; so that we cannot be certain that two thermometers, dipped into the bath side by side, have been exposed to exactly the same degree of heat. The method of graduation just described ought, therefore, never to be used for an instru- ment of precision ; but it is sufficiently accurate for common house thermometers. These instruments, when well made, may be relied upon to within a Fahrenheit degree between the two fixed points ; but beyond these points, and especially below the freezing-point, they are frequently very erroneous. Two ther- mometers hanging side by side, which have been made by the best Fig. 849. HEAT. 451 makers with their usual care, will not unfrequently differ Several degrees -when the temperature is below 0° F., — a fact which accounts for the great discrepancies in the observations of low temperatures. (225.) Thermometers filled with other Liquids. — Mercury boils at 360° C. and freezes at — 40°, and the range of a mer- cury thermometer is necessarily confined within these limits of temperature. Moreover, near its freezing-point the rate of ex- pansion of mercury becomes very irregular, and its indications cannot be relied upon below — 36°, or even — 35° C. Degrees of temperature above 360° are measured by means of a class of instruments called pyrometers, which will be described in con- nection with the laws of expansion of solids and gases ; while for temperatures below — 35°, we use thermometers filled with alcohol, or other liquids which do not freeze even at these great degrees of cold. There is no other liquid which can be compared with mercury in its fitness for filling thermometers. The great range of tem- perature between its freezing and boiling points, the fact that it does not adhere to the surface of glass, and that it can readily be obtained perfectly pure, are all circumstances which pecu- liarly adapt it to thermometric purposes. It is true, as we have seen, that the rate of its expansion increases with the tempera- ture ; still, between the two fixed points the change is so slight that the indications of the thermometer are not perceptibly af-' fected by it. This is not true of thermometers filled with any other liquid. Such thermometers, when graduated on the same principle as the mercury thermometer, give results which are entirely at variance both with it and with themselves. For ex- ample, Deluc obtained the following comparative results with thermometers filled with mercury, oil, alcohol, and water. The numbers in the same vertical column of the table are the tem- peratures indicated by these several thermometers when immersed in the same bath. Mercury, —12.5 —6.25 25.0 •50.0 75.0 100 Oil, 24.1 49.0 74.1 100 Alcohol, —9.6 —4.90 20.6 43.9 70.2 100 Water, 5.1 25.6 57.2 100 452 CHEMICAL PHYSICS. Similar results were also obtained by M. Pierre, in liis very extended investigation of the expansion of liquids, during which he compared thermometers containing twelve different liquids with the mercury thermometer. As is shown by the above ta- ble, he found the water thermometer the most defective. Ther- mometers filled with alcohol or with sulphide of carbon gave less erroneous results ; but of all the liquids he examined, com- mon ether, chloride of ethyle, and bromide of ethyle, were least irregular in their rate of expansion, and are therefore best adapted, after mercury, for filling thermometers. Nevertheless, alcohol thermometers are generally used for measuring very low temperatures. They are graduated by com- parison with standard mercury thermometers, in the way described in the last section, taking care to have a large number of points of comparison, which should be as near together as possible. But even when graduated with the greatest care, such thermometers do not give indications which accord with each other, or with a mercury thermometer. Captain Parry, in his Arctic voyages, ob- served differences of 10° C. between alcohol thermometers of the best makers ; and similar facts were noticed both by Franklin and by Kane. These discrepancies unquestionably originated in part from the impurity of the alcohol, or from other errors of con- struction ; but they are also, to a certain degree, inherent in the thermometer itself. An accurate instrument for measuring low temperatures is still one of the great desiderata of science. (226.) Maximum and Minimum Thermometers. — It is fre- quently desirable to have the means of determining, without the aid of an observer, the highest or lowest temperature which has occurred during the night, or any other interval of time ; and for this purpose a great variety of self-registering thermometers have been invented. One of the simplest is that of Rutherford (Fig. 350). This consists of two thermometers, fastened to a plate of wood, or some other material. The tubes of the ther- mometers are bent at right angles just above the bulbs, as rep- resented in the figure, and the instrument when in use is suspended by a cord, so that the two stems shall be in a horizontal position. The upper thermometer is filled with mercury, and in front of the mercury-column a short piece of iron wire is placed in the tube (seen at A}, which is pushed forward by the mercury and left at the highest point which the column reaches, thus indi- HEAT. 453 eating the maximiim temperature. The lower thermometer is filled with alcohol, and the tube contains a small enamel cylinder (seen at jB), surrounded by the liquid. As the alcohol expands, it readily passes by the enamel cylinder ; but when it contracts, 1 B ' y i lllUllllmiiilllilllllilMilllhLMIUIMMtiaiilliMiJmilliillimiJHlllilllliai l .i^ Pig. 350. the cylinder is drawn back with the receding column, and left at the lowest point, indicating the minimum temperature during the same period. After each observation, the enamel cylinder is brought to the end of the alcohol-column by inclining the instru- ment ; and in like manner the iron wire is restored to the end of the mercury-column by means of a magnet. The iron wire in the tube of Eutherford's maximum thermom- eter is liable to become immersed in the mercury, if the instru- ment is not carefully handled ; and when this accident occurs, it is very difficult to remedy the evil without refilling the tube. Negretti and Zambra have invented a maximum thermometer which is not open to the same objections. Between the bend d rig. 351. and the bulb (Fig. 351) they insert into the tube of the ther- mometer a small rod of glass, a b, which nearly fills the bore. When the mercury expands, it pushes by this obstruction ; but when it contracts, the column breaks, leaving the head of the 454 CHEMICAL PHYSICS. column at the highest point it had attained. On turning the thermometer, so that its stem shall have a vertical position, the mercury readily passes back to the bulb, in virtue of its weight. Walferdin's maximum thermometer is represented in Fig. 352. It is made like an ordinary mercury thermometer, only the upper part of its stem is surrounded by a reservoir containing mercury, which is so arranged that, when the instrument is inverted, the end of its tube dips under the mercury in the reservoir. No graduation on the stem is neces- sary ; but before the instrument is to be used, the bulb must be heated until the mercury overflows the end of the tube. It is then inverted ; when, on cooling, the mercury rises from the reservoir by mechanical adhesion, com- pletely filling the stem. If the thermometer is now replaced in position, its bulb and tube being full of mercury, it is evident that, as the temperature rises, the mercury will gradually flow over from the tube into the reservoir ; and when the temperature subsequently falls, the mercury, contracting, will leave an empty space at the top of the tube. The highest temperature to which the instrument has been exposed is, then, that at which the mercury remaining in the bulb and stem just fills them both completely ; and this can be ascertained by comparison with a standard thermometer, placing both in a water-bath, gradually heating it, and observing the temperature indicated by the standard when the mercu- rial column reaches the top of the stem. The same principle has been applied by Walferdin for Fig!^52. measuring very small differences of temperature. The thermometer for this purpose may be constructed in pre- cisely the same way, only it is made extremely sensitive, so that an expansion corresponding to four Centigrade degrees would raise the mercury-column through the whole length of the stem. The stem is, moreover, very carefully graduated into parts of equal capacity, each division corresponding to a very small fraction of a degree. To show how this thermometer is used, let us suppose that we wish to observe the temperature at which water boils under diiferent atmospheric pressures, where the whole possible variation is between 101° and 98°. We should, in the first place, expose the instrument to a temperature of 101°, ^ HEAT. 455 as indicated By a standard thermometer, and wait until the ex- cess of mercury had overflowed into the upper reservoir. On now allowing the temperature to fall, the mercury-column will rapidly sink in the tube, and at 97° will already have receded into the bulb. The thermometer is now in con- dition to measure with great accuracy differences of tem- perature between 98° and 101° ; and in like manner it may be adjusted to any other range of four degrees. If, for example, the division on the stem correspond to thousandths of a Centigrade degree, and we observ6 a difference in the boiling-point of water under two differ- ent pressures equal to fifteen of these divisions, we con- clude that the temperature is 0.015 of a degree higher in one case than in the other. Since the quantity of mercury which forms the thermometer differs with the range of the instrument, it is evidently necessary to de- termine the value, in fractions of a Centigrade degree, of one of its divisions after each adjustment. The form of reservoir represented in Fig. 352 is difficult to make, and there is generally substituted for it a simple enlargement of the upper end of the tube, as represented in Pig. 353. The neck of the bulb B is strangled at C, so that a slight tap given to the tube while the instrument is cool- ing causes the column to break at that point, leaving the Fig. 353. excess of mercury in the bulb. THERMOSCOPES. (227.) Air Thermometers. — The name -thennoscope (^depfirj, o-zEOTTew) is a convenient designation for a class of instruments which are used chiefly for detecting slight changes of temper- ature, and not, like the thermometer {Oep/Mt), fiiTpov}, for de- terminmg its value in degrees. In a large number of thermo- scopes, these variations are indicated by the change in volume of confined air, which not only expands very regularly and quickly, but also to a very much greater degree than liquids, for the same increase of temperature. Such instruments are fre- quently called air thermometers ; but they must not be eon- founded with the air thermometer of Regnault, which gives the most accurate measures of temperature that we can attain. 456 CHEMICAL PHYSICS. The air thermometer represented in Fig. 354 is ascribed to Sanctorius, an Italian philosopher of the seventeenth century, and is supposed by some to have been the first instrument used for measuring temperature. It consists of a bulbed tube, whose ex- tremity rests in an open vessel containing colored water, which also partially fills the tube. When the bulb is heated, the liquid falls in the tube, and rises when the bulb is cooled. The tube is generally fastened to an upright piece of wood, on which a scale of equal parts is painted. In another form of the same instrument (Pig. 365), the expansion of the air is indicated by the motion of a drop of colored liquid in the stem at A. These instruments are evidently affected by the varying pressure of the atmosphere, and are necessarily imperfect. The same objection does not apply to the dif- ferential thermometer of Leslie, used by him in his experiments on the radiation of heat. This consists (Fig. 356) of two bulbs con- nected together by a glass tube bent twice at right angles. The bulbs contain air, and the connecting tube is half filled with col- ored liquid, which, when the thermometer is at rest, stands at the Fig. 354. Kg. 355. Hg. 356. Fig. 357. same height in the two limbs of the sipnon, and remains in this position so long as the two bulbs are equally heated. Any dif- ference in the temperature of the two bulbs, however, is at once indicated, as represented in the figure, by a difference of level in HEAT. 457 the two liquid columns, and can be measured by means of the scales painted on the 'wooden frame which supports the tube. This is the only thermoscope, of its class, of any scientific value. In a limited number of cases it furnishes an instrument of great utility and delicacy, and its indications are comparable with each other. Rumford's differential thermometer (Fig. 357) is merely a slight variation of Leslie's, the difference in the temperature of the two bulbs being indicated by the motion of a drop of sul- phuric acid along the horizontal tube, which is made somewhat longer than in Leslie's instrument, and surmounted by a scale of equal parts. There are several other forms of air thermometers, but they are not of sufficient importance to require notice. (228.) Thermo-multiplier. — But of all instruments for detect- ing and measuring slight differences of temperature, by far the most delicate and accurate is the thermo-multiplier of Nobili and Melloni. The principle on which this instrument is based was discovered by Seebeck, of Berlin, in 1822, and may be briefly stated thus. If two metallic bars, of different crystalline texture and unequal conducting powers, are united at one end by solder, and the point of junction heated, a current of electricity is ex- cited, which flows from the point of junction to- wards the poorer conductor. Thus, if the junction of two bars of bismuth and antimony (Fig. 358) is heated, and their free ends are connected by wires, the current flows from the antimony to the bismuth at the junction, and from the bismuth to the antimony on the conducting-wire connecting p,g ^^ the free ends of the bars. If cold, instead of heat, is applied to the junction, a current is also established, but in the opposite direction. Similar results can be obtained with other metals, which may be arranged in a thermo-electric series in the following order : bismuth, platinum, lead, tin, copper or silver, zinc, iron, antimony. The most powerful combination is formed of those metals which are most distant from each other in the list, and in every case, when the junction is heated, the current flows through the conducting-wire from those which stand first to those which stand last. The most powerful current is produced, as the above reries 39 458 CHEMICAL PHYSICS. shows, by the combination of bismuth and antimony ; but a single pair of bars, even of these metals, produces only a very feeble effect. The force of the electric current can, however, be very greatly increased by uniting together several pairs of these bars, as represented at a b, Pig. 359, and connecting together the free end of the first bismuth bar with that of the last antimony bar. Such an arrangement is called a thermo-electric pile. Since the Fig. 359. Fig. 360. force of the current is not found to depend on the size of the bars, they may be made very small ; in Melloni's thermo-multiplier thirty pairs of bismuth and antimony bars are packed away in the small brass case, c d. Pig. 359, not more than two or three centime- tres long. The soldered ends of these pairs, called the faces of the pile, are seen at c and d; and the two cups, o, o', called the poles of the pile, are directly connected with the free ends of the two terminal bars. Pinally, the faces of the pile are protected from any latei-al action by a brass cap, t, blackened inside, and having a movable screen, e, in front, or by a brass cone polished on its interior surface, which serves to concentrate the rays of heat. When the two faces of the thermo-electric pile are equally heated, no electrical disturbance results ; but the slightest differ- ence of temperature causes a flow of electricity through the wire connecting the two poles. The direction of the cxirrent is deter- mined by the relative positions of the bars, always following the rule stated above. The force of this current, although much greater than that of the current from a single pair of bars, is still feeble, and can only be detected by a very delicate galva- nometer. This instrument will be described in detail hereafter. HEAT. 459 rig. 361. It is sufficient, for tlie present, to state tlaat it is an application of tlae remarkable facts discovered by Oersted in 1820. This eminent physicist observed, that, if a conducting-wire through which an electric current is passing is placed directly over and parallel to a magnetic needle (Fig. 361), the north pole of the needle is deflected to the right or to the left, according to the direction of the current. If the conducting-wire is placed under the needle, it is also deflected, but in the opposite direction. Hence, if the con- ducting-wire is formed into a loop, and placed around the needle, and at the same time parallel to it, in such a manner that the current may flow from north to south above the needle, and from south to north below it, the two portions of the wire will conspire to deflect the needle, and the effect of one and the same current will be doubled. By turning the wire again round the needle, the effect of the same current will be quadrupled, and by repeating the turns, as in Pig. 362, the deflecting force may be multiplied to a very great extent ; and thus the deflections of a magnetic needle may become the means of detecting a very feeble electric current. The galvanometer represented in Fig. 360 is a direct application of this principle. The conducting-wire, which is covered with silk, is wound round the ivory frame aba great number of times, and terminates at the two ends, n, n'. The magnetic needle is sus- pended, so as to oscillate freely within the ivory frame, by means of a single strand of raw silk,/; and when at rest, its axis is parallel to the turns of the conducting-wire. Parallel to the first needle, and immovably connected with it, is a second needle, Z, which oscillates just above a graduated arc, and thus indicates the amount of deflection. This needle also serves another purpose. Its north pole is placed directly over the south pole of the first needle, and, both being of equal force, the action of the earth's magnetism on one is bal- anced by its action on the other. A needle so arranged is termed 460 CHKMICAL PHYSICS. astatic, and will remain in any position in which it may be placed. Moreover, the action of an electric current Tipon it is not influ- enced by the magnetism of the earth. The graduated disk just referred to rests on the ivory frame, and is made of copper, which has the effect of deadening the oscillations of the needle. When in use, the two poles of the thermo-electric pile (o, o'. Pig. 359) are connected with the ends (w, n', Fig. 360) of the conducting- wire, which is wound round the frame of the galvanometer. Fig. 363. The apparatus is so delicate, that the heat of the hand, placed several feet in front of the conical cap G, will be at once percep- tible, by deflecting the needle. Moreover, when the deflection is not greater than twenty degrees, the angle of deviation is propor- tional to the difference of temperature between the faces of the pile, and may therefore be used as a measure of the intensity of the calorific effect produced on one face when the other is exposed to a constant temperature. Beyond twenty degrees, the angle of deviation is no longer proportional to the temperature ; but a table can be easily constructed for each instrument, in which, for each degree of deviation, are given the corresponding differ- ences of temperature of the two faces. Melloni does not extend these tables beyond thirty-five degrees, because the slightest change in the position of the axis of suspension of the needle would cause a great error in its indications. A deflection of thirty-five degrees corresponds to a difference of from six to eight degrees in the temperature of the two faces of the pile. The instrument, as mounted for use, with its various screens and appendages, is represented in Fig. 363. HEAT. 461 PROBLEMS. Thermometers. 272. It is required to change into Fahrenheit and Reaumur degrees the following temperatures in Centigrade degrees : — Temperature of maximum density of water, . . . . + 3°.87 C. Boiling-point of liquid ammonia, — 10 " " sulphurous acid, — 10 alcohol, +75 " " phosphorus, 290 " " mercury, 360 273. It is required to change into Centigrade and Eeaumur degrees the following temperatures in Fahrenheit. degrees : — Melting-point of mercury, —40° F. " " bromine — 4 " " white wax, ^ . . +158 " " sodium, 194 " "tin, 442.4 " " antimony, 771.8 Incipient red heat, ,...,.... 977 Clear cherry-red heat, 1,832 Dazzling white heat, 9,732 274. How many degrees Centigrade and Reaumur are n° Fahrenheit ? 275. How many degrees Fahrenheit and Reaumur are n° Centigrade ? 276. At what temperatures do — x° C. equal — x° F. ? — x° R. equal —x" F. ? —x" C. equal -\-x° F. ? and —x° R. equal -\-x° F. ? 277. The boiling-point was marked on the stem of a mercurial ther- mometer when the barometer stood at 74.65 c. m. ; the distance between this point and the freezing-point, previously determined, was found to be 21.54 c. m. It is required to determine the position of the true boiling- point on the stem with reference to the first 278. Solve the same problem, representing the height of the barometer by H, and the distance between the freezing-point and the boiling-point hyl. 279. In order that a mercurial thermometer may measure temperatures between — iO° and -(-300°, how many times must the capacity of the bulb be greater than that of the tube ? 280. A thermometer-tube was divided into 1,500 parts of equal ca- pacity, as described in (221). It was then weighed, first when empty, and afterwards when containing a quantity of mercury occupying 45 di- visions. The difference of these weights was 0.032 grammes. It is desired that the distance between the fixed points should be divided into about 1,000 parts, and it is required to find the volume of the reservoir 39* 462 CHEMICAL PHYSICS. necessary to effect this object. If the reservoir is spherical, what must be its diameter ? If it is cylindrical, what must be its length, assuming that its diameter is 0.52 c. m. ? 281. After the thermometer of the last problem was made, it was found that the zero-point corresponded to the 230th division from the bottom of the scale, and the boiling-point to the 1,223d. To what temperature does the 765th division correspond ? Prepare a table giving the temperature in Centigrade degrees corresponding to every tenth division on the tube. 282. A thermometer was graduated with an arbitrary scale, as above ; the zero-point was subsequently found to coincide with the 56th division, and the boiling-point with the 245th division of this scale, when the barometer stood at 74.25. It is required to prepare a table, giving the temperature in Centigrade degrees corresponding to each division of the scale. 283. The temperature of an oil-bath was observed with a mercury- thermometer graduated to Centigrade degrees to be 260° ; the portion of the mercury-column in the stem not immersed occupied 190°, and the mean temperature of this column was 94°. Required the true tempera- ture of the bath. 284. When the thermometer of problem 281 was immersed in an oil- bath, the mercury rose to the 500th division of the scale ; the portion of the mercury-column in the stem not immersed occupied 390 divisions, and its mean temperature was 84°. Required the true temperature of the bath. 285. Reduce the following temperatures, observed with a mercury- thermometer made of crown-glass, to degrees of the air-thermometer : 260°, 180°, 230°, 200°, 300°, and 320°. 286. The coeflBcient of expansion of glass for one Centigrade degree is 0.0000088482. How great is it for one Fahrenheit degree ? How great for one Reaumur degree ? 287. The French unit of heat is the amount of heat required to raise the temperature of one kilogramme of water from 0° C. to 1° C. ; the English unit is the amount of heat required to raise the temperature of one Troy pound of water from 59° F. to 60° F. "What is the relation between the two ? (See table, p. 472.) 288. Convert into French units of heat 7.843 ; 234.62 ; and 52.796 English units. 289. Reduce to English units 52.34; 1,964.72; 0.6845; and 324.7 French units of heat. 290. Two thermometers are made of the same glass ; the spherical bulb of the first has an interior diameter of 7.5 m. m., and its tube a diam- eter of 0.25 m. m. ; the bulb of the second has a diameter of 6.2 m. m., and its tube a diameter of 0.15 m. m. Required the relative size of a degree on each. HEAT. ,. 463 SPECIFIC HEAT. (229.) Temperature. — The amount of expansion which a hot body is capable of producing in the air or mercury of a ther- mometer measures what we term its temperature. This effect is only indirectly connected with the amount of heat which the body contains. If different masses of water, of mercury, of iron, or of wood produce each the same expansion in the air or mer- cury of the thermometer, we say that they all have the same temperature, although, as we shall hereafter see, they may con- tain very different amounts of heat. The thermometer, there- fore, is an instrument for measuring the temperature of a body, and not the amount of heat which it contains. It gives us, though more accurately, the same kind of information as the sense of touch, indicating that condition of a body which pro- duces the sensation of heat and cold. It gives that information which is alone wanted in the practical affairs of life ; for it does not concern us generally, how much heat a body contains, but only what effect its heat will produce on our bodies. The temperature of a body depends on two conditions : first, on the amount of heat which the body contains ; secondly, on the affinity of the body for heat, or, in other words, on the power with which it holds the heat. In illustration of these principles, several well-known facts may be adduced. Two thermometers in- troduced, the one into a wine-glass and the other into a pail, each of which is filled with water just drawn from a well, will indicate the same temperature in both ; simply because, although the water in the pail contains several hundred times as much heat as the water in the wine-glass, it also holds the heat with a pro- portionally greater force, and therefore gives up no more to the bulb of the thermometer than the smaller amount of water in the wine-glass. Again, two thermometers, introduced, the one into a glass containing a kilogramme of water, and the other into a glass containing a kilogramme of mercury, the glasses having been standing together for some time, will, in like manner, indi- cate the same temperature in both ; for although, as will soon be shown, the water contains thirty times as much heat as the mer- cury, it holds it with thirty times as much power. (230.) Thermal Equilibrium. — If, as is sometimes the case in a room, the heat is distributed through the different articles 464 CHEMICAL PHYSICS. of furniture in proportion to their affinity for the imponderable agent, it is evident tliat we shall have a condition of thermal equilibrium ; for there will be no tendency for the heat to pass from one body to another. If we now bring a thermometer in contact with the various articles of furniture, we shall find that they all have the same temperature. Let us next suppose that the stove suddenly receives an accession of heat ; we shall then find that it will indicate a higher temperature than before, be- cause it is in a condition to impart more heat to the mercury of the tliermometer. In the course of a short time, however, this accession of heat will be distributed in various ways through the different bodies in the room, in proportion to their relative affini- ties, when it will be found that all again have the same tempera- ture, although a little higher than before. It therefore appears, first, that when bodies are at the same temperature tliey are in a state of thermal equilibrium ; secondly, that when they are at different temperatures, the warmer will impart heat to the colder until an equilibrium of temperature has been established ; that is, until the heat has been distributed through all in proportion to their relative affinities. (231.) Unit of Heat. — In one condition only the thermom- eter becomes a direct measure of the amount of heat ; and that is in the case of the same weight of the same substance. Thus, if we take one kilogramme of water, it is true that, if a given amount of heat will raise its temperature one degree, twice the amount of heat will raise its temperature two degrees, etc. Here, then, we have a unit for measuring amounts of heat ; and it has been generally agreed to assume, as the unit of heat, the amount of heat required to raise the temperature of one kilogramme of water one Centigrade degree, in the same way that a metre has been taken as a unit of length, and a minute as a unit of time. (232.) Specific Heat. — Assuming, then, this unit of heat, we shall be able to ascertain the relative amounts of heat which differ- ent substances contain at the same temperature, or, what amounts to the same thing, their relative affinities for heat. For this pur- pose, let us in the first place take two vessels, one containing one kilogramme and the other ten kilogrammes of water, and let us expose them both to such a source of heat that equal quan- tities of heat must enter each vessel during the same time. We HEAT. 465 shall find that, when a thermometer in the first vessel indicates that the temperature of the one kilogramme of water has risen ten degrees, a thermometer in the second vessel will have risen only one degree. Since ten units of heat have, by our assump- tion, entered the water in each vessel, it follows that it requires ten times as much heat to raise the temperature of ten kilo- grammes of water one degree as is required to raise the temper- ature of one kilogramme of water to the same extent. Sim- ilar results would be obtained with any other siibstance, and hence we may conclude that the amounts of heat required to raise the temperature of unequal weights of the same substance one degree, are proportional to these weights. As a second experiment, we will take five vessels, containing respectively one kilogramme of water, one kilogramme of sul- phur, one kilogramme of iron, one kilogramme of silver, one kilogramme of mercury, and we will expose them all to such a source of heat that equal amounts must enter each vessel during the same interval. If, now, we observe thermometers placed in these vessels, we shall find, when the temperature of the watej: has risen one degree and consequently when one unit of heat has entered each vessel, that the temperatures of the other substances have increased by the number of degrees given in the second column of the following table. By the principle just established, it follows that, if one unit of heat will raise the temperature of one kilogramme of mercury thirty degrees, it will only require one thirtieth as much, or 0.033 of a unit of heat, to raise the temperature of the same weight one degree. In like manner, the fractional parts of a unit of heat required to raise the temperatures of one kilogramme of each of the other substances one degree can be easily calculated, and are given in the third column of the table. This fraction is commonly called the specific heat of the substance. Water, Sulphur, .... Iron, . . Silver, .... Mercury, .... Water, then, at the same temperature, contains 4.9 times as Temperature. Unit of Heat. o . 1.0 1.000 4.9 0.203 . 8.8 0.114 17.5 0.057 . 30.0 0.033 466 CHEMICAL PHYSICS. much heat as the same weight of sulphur, 8.8 times as much as the same weight of iron, 17.5 times as much as the same weight of silver, and 30 times as much as the same weight of mercury ; and in like manner we should find that, at the same temperature and for equal weights, water contains more heat than any solid or liquid known. Hence, the specific heat of solid or liquid substances is always expressed by fractions. These fractions, as determined by Regnault for the chemical ele- ments, are given in the following table. The numbers in each case denote the fractional part of a unit of heat required to raise the temperature of one kilogramme of the substance one degree. They also represent the relative proportions in which heat is dis- tributed among equal weights of these substances when in the state of thermal equilibrium, and therefore indicate their relative affinities for the imponderable agent. Specific Heat of the Elements. Names of Substances. Specific Heat. Names of Substances. Specific Heat. Preliminc ry Data. Brass, . 0.093910 "Water, 1.008000 Glass, 0.197680 Elem Oil of Turpentine, . ents. 0.425930 Iron, . 0.113790 Platinum plate. 0.0324.'!0 Zinc, 0.095550 " sponge, . 0.032930 Copper, 0.095150 Palladium, 0.059270 Mercury, . 0.033320 Gold, . 0.032440 Solid Mercury, 0.032410 Sulphur, . 0.202590 Cadmium, 0.056690 Selenium, 0.083700 Silver, .... 0.057010 Tellurium, . 0.051650 Arsenic, . 0.081400 Potassium, 0.169560 Lead, . 0.031400 Bromine, liquid. 0.110940 Bismuth, . 0.030840 solid (—28°), 0.084320 Antimony, . 0.050770 Iodine, 0.054120 Tin, 0.056230 Carbon, . 0.024111 Nickel, 0.108630 Phosphorus, 0.188700 Cobalt, . 0.106960 (233.) Determination of the Specific Heat of Solids and Liquids. — There are two methods usually employed for this purpose. The first method is called the method of cooling, HEAT. 467 and is based upon the axiom, that the time required for equal weights of dififerent substances to cool through the same num- ber of degrees, under exactly the same conditions, will be pro- portional to the quantity of heat which they respectively contain, or, in other words, to their specific heat. The only difficulty in applying this principle to practice consists in securing precisely the same conditions for all substances. In order to attain this object, Regnault contrived a very ingenious apparatus, which is described at length in the Annates de Chimie et de Physique, 3* Sdrie, Tom. IX. ; but notwithstanding the utmost precautions and most persevering efforts, this very skilful experimenter could not obtain satisfactory results by this method. We shall not, therefore, enlarge upon it here. The second method, which is called the method of mixture, consists in heating a siibstanco to a known temperature, and then throwing it into a vessel containing a known weight of cold water. The amount of heat communicated to the water will be proportional to the specific heat of the given substance, and gives us the data for calculating it. This last method, which is by far the most accurate of all the methods yet devised, re- quires further illustration. Example 1. If we mix one kilogramme of mercury at 20° with one kilogramme of water at 0°, we shall find that the temperature of the mixture will be 0°.639. The water, there- fore, has gained 0.639 of a unit of heat. This amount of heat, also, is evidently sufBcient to raise the temperature of one kilo- gramme of mercury from 0°.639 to 20°, that is, through 19°. 361. Hence, the amount of heat required to raise the temperature of one kilogramme of mercury one degree must be equal to §^ = 0.033 of one unit. Example 2. If we mix 0.685 of a kilogramme of sulphur at 60° with 4.573 kilogrammes of water at 12°, we shall find that the temperature of the mixture will be 13°.42. The temperature of 4.573 kilogrammes of water has risen 1°.42, and hence the water has acquired 4.573 X 1-42 = 6.493 units of heat. These 6.493 units of heat were sufficient to raise the temperature of 0.685 of a kilogramme of sulphur from 13°.42 to 60°, or through 46° .58. They would, therefore, raise the temperature of one kilo- gramme of sulphur through 46°.58 X 0.685 = 31°.9. Hence, it would require g^^ = 0.203 of a unit of heat to raise the tfempera- 468 CHEMICAL PHYSICS. ture of one kilogramme of sulphur one degree. In like manner all similar problems may be solved. These solutions may easily be made general, and reduced to an algebraic form, in the following way. Let W = weight of water. w = weight of substance, x" = temperature of water. T" = temperature of substance. gP =z temperature of mixture. x = specific heat required. Then we shall have, W = units of heat required to raise temperature of water used one degree. wx = units of heat required to raise temperature of sub- stance used one degree. (6 — t)° ::= number of degrees through which temperature of water has been raised. (T — 6)° =^ number of degrees through which temperature of sub- stance has fallen. (0 — t)" W =. units of heat water has gained. (r — 6)° 10 x^ units of heat substance has lost. Since the gain and the loss must be equal, it follows that (r— eywx = {6 — t)° W; whence ^ — {T—eyw- LJ-o'-J The results obtained from this formula would be accurate, were it not for the fact, that the vessel which holds the water changes its temperature with that of the water, so that the heat lost by the substance not only raises the temperature of the water (^ — t)°, but also the temperature of the vessel, by the same amount. If we know the weight of the vessel and the specific heat of the substance of which it is made, we can easily estimate the amount of heat required for this purpose. The vessel used is generally made of brass or silver, very light and brightly pol- ished, so that these data can be readily obtained. Let iv' = weight of the vessel, and c = specific heat of the vessel; then w' c = amount of heat required to raise its temperature one de- gree. {6 — r)°w'c = amount of heat required to raise its temperature {0 — t)°. HEAT. 469 Since the heat lost by the substance is equal to that gained by the water plus the amount gained by the vessel, it follows that {T—6ywx={6—Ty r+(e— t)°w'c = (5— i)°(r+M>'c); .= <^X^+^«). [158.] If, as is usually the case, the substance is enclosed in a glass tube on a small basket of wire-work, it is also necessary to pay regard to the weight and specific heat of these envelopes in the calculation. Representing, then, by w" and c' the weight and specific heat of the envelope respectively, we shall have, evi- dently, {T — 6)° w"c' = units of heat the envelope has lost. Hence we obtain, {T—6)°w"c' + (.T—eywx = {6 — zy (r-f w'c), and also __ (e-zy{W^w>c)-{T-6Yw"c' — {T—eyw • L^^^-J The above method of determining the specific heat of solids and liquids admits of great accuracy, but its practical appli- cation requires many precautions and great delicacy of ma- nipulation. Regnault, who adopted this method in his very extended investigations on specific heat, used, in making the determinations, the apparatus represented in Fig. 364.* This apparatus consists, first, of the vessel m, in which the heated substance is mixed with water ; secondly, of a peculiarly con- structed steam-bath, VP V, by which the substance is previously heated to a known temperature of about 100°. The substance to be examined is placed in a small basket of brass wire, P. If it is solid, it is broken into small lumps ; but if liquid, it is enclosed in tubes of glass, whose weight and spe- cific heat are known. In the axis of the basket there is fastened a small cylinder of wire-netting, which receives the bulb of a delicate thermometer for determining the temperature of the basket and its contents. During the process of heating, the basket is suspended by means of silk cords in the interior of a * Annales de Chimie et de Physique, 2« S&ie, Tom. LXXIII. p. 20. 40 470 CHEMICAL PHYSICS. steam-bath, formed of three concentric cylinders of tin plate. The space P, in which the basket is suspended, is filled with air, and opens below into the chamber M by means of the slide r r, which can be withdrawn at pleasure. The space V is filled with Fig 364 steam, which is constantly supplied from the boiler C, and after^ wards condensed in the worm s ; and, lastly, the space between the steam-chamber and the outer cylinder is filled with air, which, being a non-conductor, diminishes the loss of heat by the bath, and thus tends to keep its temperature constant. A cylindrical vessel, m, made of very thin sheet-brass, contains the water with which the substance is to be mixed. It is sus- pended, by means of silk cords, to a movable support, which slides in a groove, so that the vessel may be readily moved into the chamber M, under the steam-bath. A delicate thermometer, t, gives very accurately the temperature of the water, and a second thermometer, T, that of the air. These thermometers are observed by means of a telescope placed several feet distant, and every precaution is taken to protect them from extraneous influences. In making a determination of the specific heat of a substance, we wait until the thermometer P indicates a constant tempera- ture, which requires about two hours. Then, in order to be sure that the substance has the same temperature throughout, we wait at least an hour longer, and carefully observe the thermom- eters t and T. Having removed the screen e, we now push the vessel m into the chamber M, and, withdrawing the slide r r, HEAT. 471 quickly drop the basket containing the substance into the water. The vessel is then at once returned to its former position, and, while an assistant stirs up the water, we observe the elevation of temperature indicated by the thermometer t, which reaches its maximum in one or two minutes. In calculating the specific heat of a substance from these results by means of [159], it is necessary to take into the ac- count the quantity of heat received by the vessel m from the air or neighboring bodies during the course of the experiment, as well as that which it loses during the same time. The variation of temperature arising from this cause is ascertained by means of a series of preliminary experiments, made under the same conditions as the final determination, and the observed tempera- ture of t corrected accordingly ; but as the value of this correc- tion is necessarily somewhat uncertain, it is made very small by reducing as much as possible the duration of the experiments, and also by so regulating the temperature of the water that it may be for an equal length of time above and below the temper- ature of the air. Moreover, during the few seconds that the vessel of water is in the chamber M, it is protected from the heat of the steam-bath by the cold water wliich fills the space within the hollow walls D D ; and when outside of the chamber, it is also protected by the screen e. In order to test the accuracy of this process, Regnault deter- mined the specific heat of water with the apparatus just described. In two experiments, in which the liquid was heated to 97°, he obtained the values 1.00709 and 1.00890, thus showing that the specific heat of water increases with the temperature, and also confirming the accuracy of the method. (234.) General Results. — From the numerous investigations which have been made on the specific heat of solid and liquid substances, several important general truths have been deduced. First. The specific heat of substances is a distinguishing prop- erty, closely connected with their chemical eqiiivalents. The relation which exists between these two qualities of matter will be discussed at length in the chapter on Stoichiometry, and need not, therefore, be considered here. Secondly. The specific heat of the same substance increases with the temperature. This is true even in the case of water, which has been selected as the standard to which the specific 472 CHEMICAL PHYSICS. heat of other substances is referred. The unit of heat, it will be remembered, is the quantity of heat required to raise the temperature of one kilogramme of water one Centigrade degree. Now it might be supposed that the same quantity of heat would raise the temperature of a kilogramme of water one degree at all parts of the thermometric scale ; but this is not the case : to raise the temperature of one kilogramme of water from 100° to 101° requires, for example, 1.0130 units of heat, and, as a general rule, the amount required is greater the higher the temperature. This is shown by the following table. In the second column, headed c, opposite to each temperature, is given the specific heat of water at that temperature ; in other words, the number of units of heat required to raise the temperature of one kilo- gramme of water from f to (^ + 1)°. In the third column, headed C, are given the mean specific heats for the interval of temperature between 0° and f. t. C. C. t. c. C. 1.0000 1.0000 100 1.0130 1.0050 20 1.0012 1.0005 120 1.0177 1.0067 40 1.0030 1.0013 140 1.0232 1.0087 60 1.0056 1.0023 160 1.0294 1.0109 80 1.0089 1.0035 180 1.0364 1.0133 It will be noticed that, within the ordinary range of atmos- pheric temperatures, the specific heat of water increases only very slightly ; so that, in determinations of the specific heat of other substances by the method of mixtures, that of water may be regarded as constant between 0° and 20°. But above this temperature the increase of the specific heat of water can no longer be disregarded, and we must therefore modify slightly our definition of the unit of heat. Accurately speaking, the unit of heat is the quantity of heat required to raise the temperature of a kilogramme of toater from 0° to 1°. What is shown by the above table to be true of water, is also true of all other solids and liquids. Dulong and Petit made experiments on a number of metals up to 300°, employing the method of mixtures, and obtained the results given in the follow- ing table : — HEAT. 473 Name of Metal. Mean Specific Heat. r. Name of Metal. Mean Specific Heat T. Between 0° & 100° Between 0° & 300°. Between 0° & 100°. Between 0° & 300°. Iron, Mercury, Zinc, Antimony, 0.1098 0.0330 0.0927 0.0507 0.1218 0.0350 0.1015 0.0549 332!2 318.2 328.5 324.8 Silver, Copper, Platinum, Glass, 0.0557 0.0949 0.0355 0.1770 0.0611 0.1013 0.03^5 0.1990 329!3 320.0 317.9 322.2 In equation [159] , the temperature T is supposed to be given, and from it we can calculate the specific heat of the substance ; but we may evidently reverse this calculation, and, when the specific heat of the substance is known, use the method of mix- tures for determining its temperature. Thus this method fur- nishes a very simple means of measuring high temperatures. If, for example, we wish to measure the temperature of a furnace, we expose to it a mass of platinum of known weight ; and when the mass has acquired the temperature of the furnace, we transfer it to the brass vessel m (Fig. 364), containing a known weight of water, and observe the elevation, taking all the precautions men- tioned in the previous section. If the specific heat of the plati- num is known, we then have all the elements for calculating the temperature. If it is not known, we can make two determina- tions with unequal quantities both of platinum and water, and thus obtain two equations, from which we can eliminate the specific heat. Or, since the mean specific heat of platinum is known between 0° and different high temperatures, we can also calculate the temperature of the furnace from an estimate of the value of the specific heat for the unknown temperature, and afterwards use the specific heat corresponding to the tempera- ture thus obtained for calculating a new value of the temperature, which will be more exact. In order to furnish the data for such calculation, M. Pouillet has determined by experiment the mean specific heat of platinum between 0° and different high tempera- tures, measured by the air thermometer. His results, which are given in the following table, were obtained by the method of mixtures. Mean Specific Heat of Platinum. to 100 0.03350 to 1000 0.03728 " 300 0.03434 « 1200 0.03818 « 500 0.03518 " 1500 0.039-38 « 700 0.03602 40* 474 CHEMICAL PHYSICS. The change of the specific heat with 'the temperature becomes very marked as the solid approaclies its melting point ; and this is especially the case with those solids which soften before they melt. Hence, in stating the specific heat of a substance, it is important to name the temperatures between which the deter- mination was made. The specific heat of liquids varies with the temperature to a much greater extent than that of solids. Thus bromine, according to Regnault, has the specific heats 0.10513, 0.11094, 0.11294, between the temperatures — 6° and +10°, 11° and 48°, 13° and 58°, respectively. So, also, oil of turpentine has the specific heat of 0.426 between 15° and 20°, and 0.4672 between 15° and 100°. Eegnault* has also determined the specific heat of a large number of other liquids by the method of cooling-, which, as he found, gives more accurate results with liquid than with solid substances. Some of the most important of his results are given in the following table. As a general rule, they show that the specific heat increases with the temperature. But the difference between the extreme temperatures is so small, that the slight increase of the specific heat is, in some cases, more than over- balanced by variations arising from other and accidental causes. Mean Specific Heat Names of Liquids. 6° to 10°. 10° to 15°. 15° to 20°. Mercury, .... 0.0282 0.0283 0.0290 Alcohol at 36°, 0.6588 0.6651 0.6725 Mcthylic Alcohol, 0.5901 0.586S 0.6009 Oxulo of Ethylo, . 0.5207 0.5158 0.5157 Bromide of Ethylo, . 0.2161 0.2133 0.2153 Iodide of Ethylo, . 0.1587 0.1584 0.1584 Sulphide of Etliyle, . 0.4715 0.4653 0.4772 Terebene, 0.4154 0.4156 0.4267 Oil of Citron, .... 0.4489 0.4424 0.4501 Bichloride of Tin, . 0.1421 0.1402 0.1416 Chloride of Silicon, . 0.1914 0.1904 0.1904 Chloride of Phosphorus, 0.2017 0.1987 0.1991 Sulphide of Carbon, . 0.2179 0.2183 0.2206 It will be noticed that the increase of the specific heat with the temperature corresponds to the increase of the rate of expan- sion, and it is probable that the two classes of phenomena are * Annalcs de Chimie et de Physique, 3= Se'rie, Tom. IX. p. 336. HEAT. 475 closely connected together. The best explanation which we can give of the facts is this. If the volume of a solid or liquid mass of matter remained the same at all temperatures, it is probable that it would require exactly the same quantity of heat to raise its temperature one degree at all parts of the thermometric scale. As, however, both solid and liqiiid matter are expanded by heat with an irresistible force, a portion of the quantity of heat re- quired to raise the temperature of a given mass one degree is rendered latent in producing this mechanical effect ; and since the rate of expansion increases with the temperature, the quan- tity of heat thus rendered latent, and hence also the specific heat, must be greater at high than at low temperatures. Thirdly. All substances have a greater specific heat in the liquid than in the solid state. This truth, which is rendered evident by the following table, is probably connected with the fact that the rate of expansion of liqiiids is greater than that of solids, and hence the quantity of heat absorbed in producing this mechanical effect is also greater. Solid Liquic . Interval of Temperature. Specific Heat. Interval of Temperature. Specific Heat. Lead, to 100 0.0314 350° to 450° 0.0402 Bromine, .... -78 « -20 0.08432 10 « 48 0.1109 Iodine, .... u 100 0.05412 0.10822 Mercury, . -78 « -40 0.0247 « 100 0.0333 Sulphur, « 100 0.2026 120 11 150 0.234 Bismuth, . « 100 0.030S4 280 S — S', is, then, the quantity of heat absorbed by one cubic metre of each gas, measured as above described, in expanding ^}^ of its initial volume. * By using the more recently determined constants, we should obtain, for the value of S', 0.1678, and for 1 -f- « the value 1.417. 484 CHEMIQAL PHYSICS. By comparing the quantity of heat thus rendered latent in the case of air with that which remains free, and consequently raises the temperature of the gas, it will be found that they stand to each other very nearly in the proportion of 2 to 6. Hence, of seven units of heat imparted to a mass of free air for the pur- pose of increasing its temperature, — as, for example, in warming the air of a room, — two units are absorbed in expanding the air, so that the elevation of temperature results entirely from the remaining five. By comparing the values of /S — S', it will be noticed that the quantity of heat absorbed by equal volumes of these different gases, in expanding to an equal extent, is very nearly the same in all cases. Dulong has verified this principle in the case of a large number of gases not included in the above table, and has stated the law in the following simple terms : — 1. Equal volumes of all gases, measured at the same tempera- ture and pressure, set free or absorb the same quantity of heat when they are compressed or expanded the same fractional part of their volume. If the specific heat of the gases were all eqiial, the same change of volume, and consequently the same absorption or liberation of heat, would cause the same change of temperature. This, however, is not the case, except with oxygen, hydrogen, and nitrogen. The specific heats of the compound gases differ very considerably from each other, and the change of temperature caused by the same change of volume is smaller in proportion as the specific heat of the gas is greater. Hence the second law of Dulong, which should be read in connection with the first. 2. The variations of temperature which result are in the in- verse ratio of the specific heats under constant volume. Whether these empirical laws of Dulong are the exact expres- sions of the truth, or whether they are merely close approxima- tions, remains yet to be ascertained by further investigation. (238.) Mechanical Equivalent of Heat. — The doctrine of the conservation of the physical forces has furnished, through the investigations of Joule on the mechanical equivalent of heat, a ipost remarkable confirmation of the results of the last section. According to this doctrine, there is an exact equivalency of cause and effect between all the forces of nature. Thus, in the case of heat, it would assume that a given mechanical effect would, HEAT. 485 ■under all circumstances, be accompanied by tlie absorption of the same amount of heat ; and conversely, that the same quantity of heat should, imder all conditions, do the same amount of mechanical work — for example, should raise a given ■weight through the same height — in whatever way it may be applied. It is a well-known fact, that friction is, under all circum^ stances, attended with evolution of heat. Now, since friction represents the expenditure of force, it follows that the quantity of heat evolved by friction is the equivalent of the mechanical force expended in overcoming it. Joule was therefore able to fix the mechanical equivalent of heat, by measuring the quantity of heat generated by friction, and comparing this with the power (42) expended in over- coming the friction. The heat was generated by the friction of water, and the apparatus he used for the purpose is represented in Pig. 365. It consisted of a brass paddle-wheel, furnished with eight sets of revolving arms, working between four sets of stationary vanes affixed to a framework, also of sheet-brass. This frame fitted firmly into a copper vessel containing from six to seven kilogrammes of water. In the lid of the vessel there were two necks, the first for the axis to revolve in without touching, the second for the inser- tion of the thermometer. The paddle-wheel was set in motion Hg. 365. rig. 366. by means of two weights connected with its axis by a system of cords and pulleys, as represented in Fig. 366. In making the experiments, the weights were wound iip by means of the handle V, attached to the wooden cylinder v s, and after observing the 41* 486 CHEMICAL PHYSICS. temperature of the water in the vessel, the cylinder was fixed to the axis of the paddle, which was then made to revolve by the fall of the weights to the floor of the laboratory, causing a friction against the water in the vessel. The cylinder was then removed from the axis, the weights wound up again, and the friction re- newed. After this had been repeated twenty times, the experi- ment was concluded with another observation of the temperature of the water. The mean temperature of the laboratory was determined by observations made at the beginning, middle, and end of the experiment, and the quantity of heat which the vessel lost by radiation and otlier causes was determined in every case by means of a second experiment, made under precisely the same circumstances as the first, with the apparatus at rest. It was then easy to calculate, by means of [159], the number of units of heat developed by the friction of the water, since the weights ■ of the copper vessel, of the brass paddle and frame, and of the water, as well as their several capacities for heat, and the increase of temperature caused by the friction of the particles of water, were known. This quantity of heat was, then, evidently the equivalent of the mechanical force expended in moving the paddles and overcoming the friction. In order to estimate the mechanical force thus expended, the value of the weights, the height through which they fell, and the velocity of the fall, were accurately measured. In one series of experiments, the value of the weights was 406,152 grains, the total fall in inches 1,260.248, and the ve- locity 2.42 inches per second. The weight, starting from the state of rest, soon acquired the velocity of 2.42 inches, and afterwards moved with a uniform motion until it reached the ground, where the velocity was destroyed. Dui-ing the uniform motion, it is evident tliat the intensity of the force of gravity acting on the weights was entirely expended in overcoming the friction of tlie water (42) ; but before the motion became uniform, a portion of the force was expended in imparting velocity to the weights. The whole mechanical power expended in overcoming the fric- tion of the water, and thus generating heat, is then the power gen- erated by the force of gravity acting on the mass of the weights through the whole distance fallen, less the power generated by the same force acting through the distance required to impart a velocity of 2.42 inches. By [6], we find that a fall through HEAT. 487 0.0076 of an inch would impart a velocity of 2.42 ; and since the weights were wound up twenty times in each experiment, a fall through twenty times 0.0076, or 0.152 inch, would represent the entire loss due to the increase of velocity. Hence the me- chanical power expended in overcoming the friction of the water was a force having the intensity of 406,152 grains, acting through 1,260.096 inches. Compare (63). We have assumed, in this estimate, that the intensity of the force of gravity was entirely expended in overcoming the friction of the whole ; but this was not the case, for a portion of the force was used in overcoming the friction of the pulleys and the rigid- ity of the cord. This was ascertained by a separate experiment, in which the pulleys and cord were disconnected from the paddle- wheel, to be equal to 2,837 grains acting during the whole time, which, deducted from the value of the weights, gives 403,315 grains for the actual force overcome by the friction. This . force, acting through ^,260.096 inches, is equivalent to a force of 6,050.186 pounds acting through one foot, or, using the technical expression, to 6,050.186 foot-pounds. But in order to obtain the whole power overcome by the friction, we must add to this amount 16.928 foot-pounds for the force developed by the elasticity of the string after the weights touched the ground, making the whole mechanical force expended in overcoming friction, and thus developing heat, equal to 6,067.114 foot-pounds, as the mean of all the experiments of the series. The same series of experi- ments gave, for the mean value of the quantity of heat evolved, 7.842299 English units ; * and hence, |^^ = 773.64 foot- pounds will be the force which is equivalent to one English unit of heat. In these experiments a portion of the force is used in overr coming the resistance of the air, and, making the correction necessary to reduce the results to a vacuum, and omitting the fraction, we get 772 foot-pounds as the mechanical equivalent, which Joule regards as the most probable value. Similar experi' ments, in which the friction was produced by an iron paddle- wheel revolving in mercury, and others, in which it was prodiiced by two cast-iron wheels, gave for the mechanical equivalent of heat 774 foot-pounds, — a number which is surprisingly near the first. * The English unit of heat is the quantity of heat required to raise one pound of water one Fahrenheit degree between 55° and 60°. 488 CHEMICAL PHYSICS. We have given the above calculation in English ■weights and measures, because it is so given in the original memoir,* to which we would refer for further details. In the French system, these results correspond to 430 and 432 kilogramme-metres, or, in other words, the unit of heat is equivalent to a force of 430 kilogrammes acting through one metre. Let us now see in what way these results of Joule confirm those stated in tlie last section. It will be remembered that the value of the specific heat of air under constant volume was de- duced from the velocity of sound. This value furnishes us with all the data required for calculating the mechanical equivalent of heat ; and if the doctrine of the conservation of forces is cor- rect, the equivalent calculated from the velocity of sound ought to agree with that determined by Joule from his experiments on friction. Siich an agreement would not only confirm the value which has been assigned to the specific heat of air, but it would also tend to confirm the doctrine in question. Let \is suppose that we have a cylinder, the area of whose base equals 1 c7m.', filled to the height of 273 c. m. with air at 0° and under a pressure of 76 c. m. By Table II. the weight of this mass of air would be equal to 0.3531 gramme. If we raise the temperature of this air from 0° to 1°, it will expand ^^^ of its volume, and will rise in the cylinder one centimetre, tlius lift- ing the weight of the atmosphere on the base of the cylinder — 1,083.3 grammes — through this distance. The quantity of heat reqiiired to raise the temperature of 0.3527 gramme of air from 0" to 1° is, by (236), equal to 0.3527 X 0.000237, or 0.0000836 unit. Of this amount, a part only is consumed in expanding the air, the rest remaining free and increasing the temperature of the mass of gas. By (237), the part which does the mechan- ical work is equal to the difference between the specific heat under constant pressure and the specific heat under constant volume. Hence, in the present case, it is equal to [160] 0.0000836 — (0.0000836 -r- 1.417) =0.0000246 unit of heat It follows, then, that in the expansion of air 0.0000246 unit of heat Avill raise 1,033.3 grammes one centimetre, or, what is equiv- alent to this, one unit of heat will raise 419 kilogrammes one * Philosophical Transactions, London, 1850, Parti, p. 61. HEAT. 489 tnetre. The difference between this value of the mechanical equivalent of heat and that obtained by Joule (430 kilogramme- metres) is very small, considering the entirely heterogeneous data vrhich enter into the calculation. Assuming, then, that the doctrine of the mechanical equivar lency of heat is established, it follows that the law of Dulong (237) holds in all cases where the same mechanical power, act- ing on equal volumes of different gases, causes the same amount of condensation. But, as we have seen, this is not always the case ; hence the law of Dulong must be subject to the same limi- tation as that of Mariotte (165). Indeed, the law of Dulong is probably only an imperfect expression of the mechanical equiva- lency of heat, and is true so far as the same expansion or com- pression represents the same amount of mechanical work. PROBLEMS. Specific Heat. 291. How much heat is required to raise the temperature of 500 kilogrammes of water from 4° C. to 94° ? 235 sulphur " 20° (( 100°? 336 charcoal " 5° tt 500° 1 9.467 grammes of alcohol " 3° il 20°? 10.234 " " ether " —20° (t 13° 1 292. Calculate the quantity of heat which is required to raise the tem- perature of the weight of the different elements represented by their chem- ical equivalents one degree. 293. The following quantities of water were mixed together : — 2 kilogrammes of water at 10° C., 5 " " " 30° 6 " " " 20° 7 " " " 12°. What was the temperature of the mixture ? 294. The quantities of water Wi, Wj, w^, Wi, at the respective tempera- tures of t°, ti, t°, t°, were mixed together. "What was the tempera- ture of the mixture ? 295. How much water at 99° and how much water at 11° must be mixed together, in order to obtain 20 kilogrammes of water at 30° ? 296. Determine the temperature of a mixture of one kilogramme of water at 100° and one kilogramme of mercury at 0° ; also of one kilo- gramme of mercury at 100° and one kilogramme of water at 0°, 297. How many kilogrammes of mercury at 100° must be added to one 490 CHEMICAL PHYSICS. kilogramme of water at 0° in order that the temperature of the mixture may be 60° ? Also, how much water at 100° must be added to one kilo- gramme of mercury at 0° to raise its temperature to 60° ? 298. Equal volumes of mercury at 100°" and water at 0° are mixed together. Required the temperature of the mixture. 299. A mass of matter weighing 6.17 kilogrammes at the temperature of 80° is mixed with 25.45 kilogrammes of water at the temperature of 12°.5. The mixture is found to have the temperature of 14°. 17. What is the specific heat of the body ? 300. How many kilogrammes of gold at 45° would be required to raise the temperature of 1,000.58 grammes of water from 12°.3 to 15°.7 ? 301. The specific heat of an alloy containing one equivalent of lead (103.6 parts) and one equivalent of tin (58.8 parts) was found by experi- ment to be 0.0407. How does this value correspond with that which may be calculated on the assumption that the alloy is a mechanical mixture of the two metals ? 302. The specific heat of sulphide of mercury (Hg S) was found by experiment to be 0.0512. How does this value agree with that calculated on the assumption made in the last problem ? 303. A piece of iron weighing 20 grammes at the temperature of 98° is dropped into a glass vessel weighing 12 grammes, and containing 150 gi-ammes of water at 10°. The temperature of the water is thus raised to 10°.29. Required the specific heat of iron, knowing that the specific heat of glass is 0.19768. 304. The weights of different substances, iv,, w^, W3, w^, at the re- spective temperatures <,°, 1^°, ^3°, ^4°, and having the respective specific heats c,, Cj, C3, C4, are supposed to be mixed together. Required the spe- cific heat, G, of the mixture in terms of the other values. 305. Calculate the specific heat of oil of turpentine from the follow- ing data : 42.57 grammes of the oil at 33°.7 were mixed with 470.3 grammes of water at 12°.23 ; the temperature of the mixture was found to be 16°.57 ; the oil was enclosed in a glass tube weighing 5.25 grammes and having a specific heat equal to 0.177 ; lastly, the water was contained in a copper vessel weighing 45.25 grammes, and having a specific heat equal to 0.035. 306. A platinum ball weighing 150 grammes is heated to 1,000°, and then plunged into one kilogramme of water at 10°. After an equilibrium is established, how high is the temperature of the water, assuming that the water receives all the heat which the platinum ball loses ? If the water is contained in a brass vessel weighing 200 grammes, how high would be the temperature of the water ? 307. A platinum ball weighing 100 grammes, after having been ex- posed for some time to the heat of a furnace, is thrown into a brass vessel HEAT. 491 containing 750 grammes of water at 6°. The Weight of the brass amounted to 150 grammes, and the temperature of the water after the equilibrium was established to 15°. What was the temperature of the furnace, assuming that no heat was lost from the vessel and water during the experiment ? 308. How much heat is required to raise the temperature of one cubic metre each of air, oxygen, carbonic acid, and hydrogen from 0° to 15°, as- suming that the gas is allowed to expand freely, and that the pressure is constant at 76 c. m. 309. A room measures 7 metres by 6 on the floor, and is 4 metres high. How much heat is required to raise the temperature of the air in that room from 5° to 18° when the barometer stands at 76 c. m. ? How much heat is lost in expanding the air of the room ? 310. How much heat would be required to raise 1,000 kilogrammes of water 100 metres, if the full effect of the heat were realized ? EXPANSION. (239.) Coefficient of Expansion. — It has already been stated (216) that the first effect of heat on matter, in either of its three states, is to expand, it ; and we have also examined the most important means by which the effects of expansion are used as a measure of temperature. We will now study the phenomena of expansion more in detail ; but, first, we will establish a few for- mulae by which the amount of expansion can be, in any case, readily calculated. Linear Expansion. — The small fraction of its length by ■vrhich a rod of iron, or of any other solid, one metre long, expands, when heated from 0° to 1°, is called the Coefficient of Linear Expansion of the solid. A bar of iron one metre long at 0° becomes 1.0000122 at 1°, and the small fraction 0.0000122 is the coefficient of linear expansion of iron. If we assume that the expansion is proportional to the temperature, then a bar of iron one metre long at 0° becomes 1.00122 metres long at 100°, 1.00244 at 200°, 1.0061 at 500°, etc. Hence a bar of iron 26.354 metres long at 0° would become 1.0061 X 26.354 = 26.515 at 500°. To make the solution general, let A; = co- efficient of expansion ; then 1 -j- A; = increased length of a rod which is one metre long at 0°, when heated to 1°, and (1 -}-^ A) = increased length at f. Hence l(l-\-tk') = increased length of 492 CHEMICAL PHYSICS. a rod at f which is I metres long at 0". Representing, then, by t, this increased length, we have Z' = / (1 + ; A-) ; [164.] by which we can easily calculate the length of a rod of any metal at f, when its length at 0" and its coefficient of expansion are given. The coefficients of expansion of the solids most fre- quently used in the arts are given in Table XV. It is frequently the case that we do not know the length of the rod at 0°, but only at some other temperature, t, and it is required to determine the length at a second temperature, V, which may be either higher or lower than t. To obtain a formula for the purpose, denote by I the unknown length of the rod at 0°, by /' the known length at f, and by I" the required length at t'°. "We have then, as above, Z' = / (1 -)- i K), and /" = 1 (\-\-t' k). By combining these equations, we obtain I" = I' (r+^) = ^' [1 + k (f — + Ac] [165.J All the terms of the quotient after the first may be neglected, because they contain powers of the already very small fraction k. We have assumed that the expansion of solids is proportional to the temperature, but this is not strictly true ; for the rate of expansion of solids, like that of mercury (219), increases, although but very slightly, as the temperature rises. The co- efficient of expansion is not, therefore, absolutely the same at all parts of the thermometer-scale ; but the difference is so small that we can neglect it, except in the most refined investiga- tions, more especially if we use, not the coefficient observed at any particular temperature, but a mean coefficient obtained by dividing by 100 the total amount of expansion between 0° and 100°, by which means we average the error. Cubic Expansion. — The small fraction of its volume by which one cubic centimetre of a solid, liquid, or gas increases when heated from 0" to 1°, is called the Coefficient of Cubic Expansion of that substance. The coefficient of expansion of mercury, for example, is 0.00018 ; that is, one cubic centimetre of mercury at 0° becomes 1.00018 ^:^» at 1°, Assuming then HEAT. 493 that the expansion is proportional to the temperature, we obtain, by the same course of reasoning as above, the formula r'=r(l + tK); [166.] by which the increased volume ( F') of any mass of matter may be calculated, when the volume at 0° (F), the temperature (i), and the coefficient of cubic expansion (^), are known. In like manner we easily obtain the formula F" = F' [1 + K Q' — 03, [167.] which will enable us to calculate the volume of a body at t'° from the volume at t° and the coefficient of expansion. (240.) The Coefficient of Cubic Expansion is three times as great as the Coefficient of Linear Expansion. — The truth of this simple principle, which enables us to calculate one coefficient when the other is given, can easily be proved. For this purpose, let us suppose that we have a cube of glass measuring one cen- timetre on each edge at 0° ; and let us inquire what will be its increased volume at 1°, assuming that the coefficient of linear expansion is known. At 1° each edge of this glass cube will be (1 -\- li) c. m. long. Hence the increased volume of the cube will be equal to (1 + A;)' = 1 + 3 A + 3 A;^ -f A:' ; but as A; is an exceedingly small fraction, ¥ and k' may be neglected in comparison without any sensible error, so that the volume of a cube of glass which is one cubic centimetre at 0° becomes (1 _j_ 3 Ic) ^715:' at 1°. Since by [166] the volume of this same cube at 1° would also be expressed by (1 -j- K^ c. m.% it follows that K= 3 k, which was to be proved. (241.) The increased capacity of a hollow vessel, in conse- quence of the expansion of its wall, may be found by calculat- ing the increased volume of a solid mass of the same substance which would just fill the interior of the vessel. — A moment's reflection will show the truth of this statement. Let the hollow vessel be a glass globe, and let us conceive of it as filled with a solid globe of glass. If this mass be heated, it is evident that the glass vessel will expand just as if it formed the outside shell of a solid globe ; the same must be true when the interior core is not present. 42 494 CHEMICAL PHYSICS. Expansion of Solids, (242.) Measurement of Linear Expansion. — The earliest accurate determinations of the coefficients of linear expansion of solids were made by Lavoisier and Laplace "with the apparatus represented in perspective by Fig. 367, and in section by Pig. 368. This apparatus consisted of two parts : first, of a copper tank, in which a bar made of the solid whose coefficient was to be determined was heated to a uniform temperature by immersing it in heated oil or water ; and, secondly, of four stone posts sup- porting an ingenious contrivance for measuring the increase of ^ s \.^ a ,'.' ' ,'^> Fig. 367. length. The solid bar, about two metres in length, rested in the tank on rollers, with one end bearing against an upright immov- able glass bar, i^(see Fig. 368), firmly fastened by cross-pieces to the two stone posts on the left-hand side of Fig. 367, and with the other end bearing against the lever, D. The upper end of Fig. 368. this lever was attached to a horizontal axis turning in sockets inserted into the two stone pillars on the right of Fig. 367, and having at one end the telescope, G, adjusted with its axis perpen- dicular to the lever D. The telescope was furnished with a micrometer eye-piece, and as it was turned by the expansion of the bar, the cross-wires moved over the divisions of a scale, A B, placed in a vertical position at the distance of fifty metres or more from the instrument. HEAT. 495 The apparatus -was used in. the following manner. The bar having been placed in position, the tank was filled with ice-cold water, and the observer noted the division of the scale on which the cross-wire of the telescope was projected. The cold water was then, withdrawn by a stopcock, and its place supplied with boiling water. The temperature soon became stationary and was ascertained by thermometers placed at the side of the bar, when the observer again noted the division on the scale with which the cross-wire of the telescope coincided. Knowing, now, the distance A B on the scale over which the cross-wire had moved, also the distance A G oi the scale from the axis of ro- tation of the telescope, and, lastly, the length of the lever G H, it was easy to determine the value of H C, the elongation of the bar. The two triangles A B G and H C G are similar by construction, and we have H C : H G = A B : A G, or H C = AB -j-p- The value of -jy^ depends, evidently, on the dimensions of the apparatus. In that used by Lavoisier A B and Laplace it was about i^-^, so that IIC= =2j, and hence any error in the measurement oi AB was divided 744 times in the result. The length of the bar at 0° being known, and the elongation corresponding to an observed number of degrees having been measured as just described, it was easy to determine the coeffi- cient of expansion by dividing the elongation in fractions of a metre by the length of the bar in metres and by the number of degrees. For example, let us suppose that the length of the bar at 0° was 1.786 m., and that the elongation corresponding to 80° was 0.004 ; the coefficient of expansion would then be 0.004 — (1.786 X 80) = 0.000028. Since the experiments of Lavoisier and Laplace, the linear coefficient of expansion of glass and of the metals most used in the arts has been redetermined by a number of physicists, and with various methods ; but as these methods do not involve the application of any new principle, it is not important to describe them. (243.) Determination of Coefficient of Cubic Expansion. — We have already seen that the coefficient of cubic expansion is three times that of linear expansion, so that the cubic expansion of a homogeneous solid can always be easily calculated from, the 496 CHEMICAL PHYSICS. linear expansion. In many cases, however, tlie coefficient of cubic expansion can be measured with more accuracy tlian the other, and it is then best to reverse tlie calculation. The coeffi- cient of cubic expansion of several solids can be determined with great accuracy, by means of a process based on the apparent expansion of mercury, which will be described in (254) . It can also be determined in the following manner from the specific gravity of the solid taken at different temperatures : — Let (aS^. 6rr.) and {Sp. Gr.)' represent the specific gravity of the solid at the temperatures t and f respectively. Also let W represent the weight of the solid mass used in the experiment, V the volume at 0°, and K the unknown coefficient which we wish to determine. We have then, hy [166], for the volume of the solid body at f and t'°, the values V(l -\-t K) and V{\-\-t' K) ; by substituting these values in [55] we obtain, for the value of the specific gravity at the two temperatures, Combining these two equations, and reducing, we get for the value of the coefficient of cubic expansion, _ { Sjp.Gr:) - {Sp.Gr:)' ~ (Sp. Gr.y t' — {Sp. Gr.) t ■ L-l°°--l Kopp has determined, by the above method, the coefficient of cubic expansion of a number of solids, and his results are included in Table XV. (244.) General Results. — By examining Table XV. it will be seen that the increase of length which a solid bar undergoes when heated from 0° to 100° is at most very small, amounting in the case of zinc, tlie most expansible of all solids hitherto ob- served, to only si^ of the length at zero. The difference, how- ever, between diffijrent solids is very great, zinc expanding over three times as much as glass for the same increase of temper- ature. The relative expansibility of solids seems to be more nearly related to their relative compressibility than to any other physical quality ; for we find, as a general rule, that those metals are the most expansible which have the smallest coefficients of elas- ticity (101) and are therefore most easily compressed. This fact is shown by the two following series, in which the HEAT. 497 metals are arranged in the order of expansibility and compres- sibility : — Zinc, Lead, Tin, Silver, Gold, Palladium, Copper, Platinum, Steel, Iron, Glass. Lead, Tin, Gold, Silver, Zinc, Palladium, Platinum, Copper, Steel, Iron, Glass. Although these two series are not perfectly parallel, they are sufficiently so to indicate a close connection between the two properties. This connection is also seen in the fact, that the diminution of the coefficient of elasticity with the increase of temperature, already noticed (101), is accompanied with a cor- responding increase of the rate of expansion. The increase of the coefficient of expansion between 0° and 100° is hardly perceptible in solids ; but when tlie change of temperature amounts to several hundred degrees, it is necessary to take account of it in delicate physical measurements. This is especially the case with the glass vessels which are used for air thermometers or in determining the specific gravity of va- pors ; and in order to furnish the necessary data for such experi- ments, Eegnault has determined the mean coefficients of cubic expansion of the common Paris glass, when blown into hollow ware, between zero and different temperatures. His results are as follows : — . ^=0.0000 276. « 0.0000 284. . « 0.0000 291. « 0.0000 298. . « 0.0000 306. « 0.0000 313. From the fact that the rate of expansion of a solid increases with the temperature, we should naturally infer that the rate for any given solid would be greatest just below its melting-point ; and of several solids taken at the temperature of the air, we should expect, other things being equal, that those would be the most expansible which are nearest their melting-points at this temperature, or, in other words, which are the most fusible. This we find, as a general rule, to be true ; the easily fusible solids, like zinc and lead, being more expansible than the 42* Between 0° and 100' a t( « 150 it 'l "^ Turpentine. —21 0.312 20 0.334 6.92 16 * . . • • • 5.88 —10 0.650 11.32 7.90 1.273 18.23 12.73 0.21 +10 2.408 28.65 19.93 13.04 0.23 20 4.40 43.48 29.82 19.02 0.43 30 7.84 63.70 43.46 27.61 0.70 40 13.41 91.36 61.75 36.4C 1.12 60 22.03 126.80 85.27 52.4S 1.72 60 35.00 173.03 116.26 73.8C 2.69 70 53.92 230.95 154.90. 97.62 4.19 80 81.28 294.72 203.05 136.7S 6.12 90 ] 19.04 389.90 262.31 181.1E 9.10 100 ] 68.50 492.04 332.13 235.46 13.49 110 5 !35.1S 624.90 413.63 302.0-1 I 18.73 116 . . ' r07.62 > • • , , . . • 120 : !20.78 612.16 381.8( ) 25.70 130 i 133.12 626.06 472.1C ) 34.70 136 . . 702.92 , . • • • 140 J >63.77 . . . 46.23 150 r25.78 60.45 152 l'61.73 • . 160 . . 77.72 170 98.90 180 122.50 190 . 151.47 200 , 186.56 210 . 225.12 220 , 269.03 222 • 277.85 above its boiling-point. According to the above principle, this tension is the same as that of the vapor of water at 115°, or 126.9 c. m., a number which dififers but very slightly from that deter- mined by actual experiment, and given in the foregoing table. It has been shown, however, by the investigations of Regnault, that Dalton's law is not absolutely rigorous, and at large distances from the boiling-point is so far from coinciding with the facts, that it cannot be relied upon except for furnishing the first rough approximation to the actual tension of a volatile liquid. It follows at once from the law of Dalton, that at any given temperature different liquids may have very unequal tensions, 584 CHEMICAL PHYSICS. Pig. 413. and, moreover, that in any One case the tension must be the greater the lower the boiling-point and hence the more volatile the liquid. These facts may be illustrated by means of the apparatus represented in Fig. 413. It" consists of four barometer-tubes, all dipping into the same basin of mercury. The first at the left is a perfect barometer, and therefore in- dicates the pressure of the air ; but the others contain a few drops of some volatile liquid above the mer- cury-column. The tension of the va- por of these liquids is measured, of course, by the depression of the mer- cury ; this will be found to be greater in proportion as the boiling-point is lower. (291.) Maximum Tension of Vapors. — The vapor of any liquid which forms in a confined space and in the presence of an excess of the liquid, has always the greatest tension which the vapor can have at the given temperature. To recur, for ex- ample, to our previous illustration : at the temperature of 20°, there would form in the vessel described in (284) a cubic metre of vapor weighing 17.155, and having a tension equal to 1.739 c. m., provided only an excess of water were present. Now this is the greatest tension which the vapor of water can have at 20°. If by mechanical means, as by sinking a piston in a cylinder, we attempt to increase the elasticity of the vapor without changing the temperature, we find that it is at once condensed to liquid water, and that its tension remains constant at 1.739 c. m. until all the vapor has disappeared. On now raising the piston, the space will be filled again with vapor ; but so long as a drop of water remains in the cylinder, the tension of this vapor will still be equal to 1.739 c. m. If, however, after all the water has evaporated, we still continue to enlarge the capacity of the cylin- der, then the vapor will act like a gas, and its tension will dimin- ish, in accordance with the law of Mariotte ; compare (156.3) and (163). In the above illustration we have assumed that the tem- perature of the vessel was constant at 20° ; but the same principle HEAT. 685 is equally true at all temperatures and for all liquids, and all the tensions given in the tables on pages 571 and 583 are the maxi- mum tensions possible at the respective temperatures. This principle may be illustrated experimentally by means of the apparatus represented in Fig. 414. It consists of a barom- eter-tube and a deep mercury cistern, in which the tube can be entirely immersed. In order s to mount the apparatus, the tube is, in the first place, nearly filled with mercury, which is boiled to expel the air, and then the rest of the tube filled with ether. On inverting the tube and plunging the open end xmder the mercury of the cistern in the usual way, the ether rises to the top of the tube, and a part remains liquid, while the rest forms a va- por which, at the ordinary temperature of the air, depresses the mercury-column about 36 c. m. ; so that the mercury stands in the tube at 40 c. m., instead of 76 c. m., above the level of the mercury in the cistern. The tension of ether vapor at the ordinary temper- ature is consequently 36 c. m. If now we attempt to increase the tension of this vapor, and consequently diminish its volume, by sink- ing the tube in the cistern (Fig. 414), we shall find that a portion of the vapor will con- dense ; but the mercury-column will remain at the same height in the tube, proving that the vapor which is still uncondensed has the same elasticity as before. On continuing to depress the tube, it vrill be found that the height of the mercury-column, and conse- quently the tension of the vapor, will remain absolutely the same until the last bubble has been condensed. This proves that 36 c, m. is the maximum tension wliich the vapor of ether can be made to assume at the ordinary temperature of the air. (292.) Gases and Vapors. — The principles of the last section furnish a convenient ground of distinction between gases and vapors. It is usual to apply the term vapor to such aeriform Kg. 414. 586 CHEMICAL PHYSICS. substances as are easily condensed, either by pressure or by cold, into liquids, and which, under the ordinary conditions of atmos- pheric temperature and pressure, exist in the liquid state. This definition, however, is purely artificial, and makes no essential distinction between a gas and a vapor ; and we therefore prefer to distinguish by the word vapor the peculiar condition of aeri- form matter when it is at the point of maximum tension. Ac- cording to this definition, a vapor is a condition of aeriform mat- ter which obeys the law of Mariotte when its volume is increased, but which, if the volume be diminished, is in part changed into a liquid ; a gas, on the other hand, is a condition of aeriform matter which obeys the law, whether its volume be increased or diminished. We may also define a vapor as that condition in which a gas exists the moment before its change of state. This distinction between a gas and a vapor will be made clearer by pursuing still further the illustration of the last section. Let lis suppose that we have a cylindrical vessel exposed to the tem- perature of 130°, and filled with steam having a tension equal to 98.956 c. m. By referring to Table IX. of the Appendix, it will be seen that the maximum tension of the vapor of water at 130° is 203.028. Now, if there were in the vessel a supply of water, the liquid would continue to give off vapor tintil this tension was attained. But we will assume that there is no liquid water pres- ent, and that the cylinder is filled with expanded steam. Under these circumstances, the steam must retain the tension of 98.956 cm. so long as both the temperature and the volume remain im changed. If now, keeping the temperature constant, we increase the ca- pacity of the cylinder by raising the piston, the steam will expand, and its tension will diminish in accordance with Mariotte's law. When the volume is doubled, the tension will be found to be 49.478 c. m. ; when quadrupled, the tension will be reduced to 24.739 c. m. ; and in any case we can find the tension corre- sponding to the increased volume by the proportion * V : V = §' : §. [200.] * This equation is merely [98], substituting ^ and i^' lor Hani H'. The stu- dent must be careful to bear in mind that the tension of a gas is always equal to the pressure to which it is exposed (149). We here leave out of the account any deviation from Mariotte's law, which, nevertheless, may be very considerable as the point of con- densation is approached (165 and 166). HEAT. 687 Moreover, when the volume has been only so far increased that the tension of the steam has been reduced to 76 c. m., it is then in the same condition as that in which a gas (like sulphurous acid, for example) exists at the ordinary temperature. It will sustain the pressure of the atmosphere, and, were the tempera- ture of the laboratory as high as 130°, it might be collected over a mercury trough and transferred from one jar to another, like any other gas. Again, if, still keeping the temperature constant at 130°, we now lessen the capacity of the cylinder by sinking the piston, the tension of the confined steam will be increased up to a cer- tain point in accordance with Mariotte's law ; in other words, it will manifest all the characters of a gas, and its tension at any degree of condensation may be calculated by the same for- mula as before. If, however, we continue to sink the piston until the volume of the steam is reduced to a little less than one half of its original volume, and the tension increased to 203.028 c. m., we shall reach a point at which the steam suddenly ceases altogether to obey the law of Mariotte ; and if we sink the piston still further, the tension will not increase in the slightest, but a portion of the steam wiU be changed into water, and this change will proceed until the piston reaches the bottom of the cylinder, the tension all the time remaining constant at 203.028 c. m. It is to this peculiar condition of aeriform matter that we give the name of vapor. Returning now to the initial condition of the cylinder, when it is filled with steam at the tension of 98.956 c. m., let us vary the temperature, while we keep the volume absolutely constant. If we increase the temperature, we shall increase the tension of the confined steam, according to the same law by which the tension of a confined mass of air would be increased under the same circumstances. If, on the other hand, we lessen the tempera- ture, we shall diminish the tension of the confined steam, accord- ing to the same law as before, until we reach a temperature at which the tension of the steam is the maximum tension for that temperature. Then, on still further cooling the cylinder, a por- tion of the steam will change into water, and the tension of the remaining vapor will be found to be the maximum tension corre- sponding to the reduced temperature. If we know the tension of a confined mass of gas at any given 588 CHEMICAL PHYSICS. temperature, we can always readily calculate its tension for any other temperature, assuming, as we have above, that the volume does not change. Let V represent the volume of a gas which has a tension ^ at <°. The volume of this mass of gas at t'", if allowed to expand freely, the tension remaining constant, would be, by [184], V(l + 0.00366 [t' — t]). If now this increased volume is reduced by pressure again to F, the tension (which was before ^) will of course be increased, and we shall evidently have the same condition as if the gas had not been allowed to expand. But we have, by [200] , F (1 + 0.00366 [f — f]'): V= ^' : § , and hence we obtain for the value of the increased tension, f = i^ (1 + 0.00366 [<' — <]). [201.J Applying now this formula in the example under discussion, we should find that the steam, whose tension was equal to 98.956 c. m. at 130°, would have at 105° a tension of ^ = 98.956 -^ (1 + 0.00366 X 25) = 90.641 c. m. ; and on referring to the table, it will be seen that this is the maximum tension which steam can have at 105°. Hence at this point the steam assumes the condition of vapor. Ey the same formula, it will appear that at 104° the tension of the steam would be 90.334 c. m., but by the table 87.541 c. m. is the maximum tension possible at 104° ; as much vapor will, therefore, be con- densed to water as is necessary to reduce the tension to this amount. The same will be true, to a still greater degree, at any lower temperature. (298.) Distillation. — It has now been shown, first, that the tension of the vapor which rises from a boiling liquid is always equal to the pressure of the atmosphere ; secondly, that this ten- sion is the maximum tension possible for the temperature, so that if the volume is reduced by mechanical means the tension is not increased, but a portion of the vapor is condensed to the liquid state. From these two facts it follows, as a necessary conse- quence, that a vapor will be condensed to a liquid by the pres- sure of the atmosphere, if its temperature falls below the boiling- point of this liquid (except under the conditions hereafter to be considered, when the vapor is diffused through the atmosphere itself). HEAT. The process of distillation, whick is used in the arts for the piiTpose of separating a volatile substance from one that is fixed or less volatile, is a direct illustration of this principle. The simplest apparatus for the purpose is represented in Fig. 415. Pig. 415. The liquid is boiled in a glass retort, and the vapor which is thus formed is conducted into a receiver, where it is cooled below the boiling-point, and again rediiced to the liquid state. Since glass vessels when exposed to a naked fire are liable to break, the body of the retort is usually protected by placing it within an iron pot and siirrounding it with sand. Such an arrangement is termed Fig. 416. a scmd-bath, or, when water is used in the place of sand, a toater- bath. Another form of distillatory apparatus is represented in Pig 416. Here the neck of the retort is connected with what is 50 &90 CHEMICAL PHYSICS. usually termed a Liebig's condenser. It consists of a tube of glass, which is kept cold by a current of water circulating through a copper cylinder, which surrounds it. In the corn- Fig. 417. mon still, Pig. 417, a large copper boiler supplies the place of the retort, and the vapor is condensed in a spiral tube of cop- per, called a worm, which is kept immersed in a tank of cold water. Since the boiling-point of a liquid is reduced in proportion as the atmospheric pressure is removed, it is sometimes advantageous to conduct the process of distillation in a par- tial vacuum. This is especially the case with some organic substances which have a high boil- ing-point and are de- composed by heat. The apparatus represented Pig, 41S. '^'^ ^ in Fig. 418 is adapted for this purpose. The retort A is connected by an hermetically sealed joint with the receiver B, and this again, throiigh the tube hbXt. S91 r, with an air-pump, by which the pressure on the surface of the liquid in the retort may be very greatly reduced. The same principle is applied in the sugar refineries in order to concen- trate syrups at a low temperature (vacuum-pans). (294.) Steam-Bath. — The fact, that the temperature of boil- ing water and of the steam rising from it is constant at 100°, is frequently applied in the laboratory when it is important to maintain a moderate and constant degree of heat for a length of time. The arrangement which is usually adopted for evapo- rating liquids at 100° is represented in Fig. 419. The porcelain evaporating-dish rests on the rim of a hemispherical vessel of copper, in which water is kept constantly boiling by means of a spirit-lamp. Fig. 419. Fig. 420. For drying precipitates, or for expelling the water of crystalli- zation from a salt, the chemist frequently uses a steam-bath like the one represented in Fig. 420. This is simply a copper oven with double sides, which is maintained at 100° by boiling the water which partially fills the cavity between the inner and outer lining of the oven. (295.) Papin^s Digester. — Water, when enclosed in a strong vessel, can be heated, as we have seen, to a temperature very much above 100° ; and this fact is advantageously applied in Papin's Digester, which is very useful in the laboratory when it is required to expose substances to the action of water at a tem- perature between 100° and 200° for a length of time. It consists 592 CHEMICAL PHYSICS. generally of a thick cylindrical vessel of brass, D, Fig. 421, closed by a thick cover of the same material, which is kept in its place by the screw B S. A safety-valve, o p A, serves to regulate the pressure, and thus the temperature of the water, as well as to insure the safety of the apparatus. The details of the construction of the safety- valve are given in Fig. 440, This digester can also be used with great advantage to produce chem- ical reactions which could not be readily obtained under the pres- sure of the air. For this pur- pose, the substances are sealed up together in glass tubes, and exposed to the temperature of the overheated water, and any inte- rior pressure resulting from the evolution of gas in the tube is more or less balanced by the ex- terior pressure of the confined steam. (296.) Condensation of Gases. — There are many substances which boil at so low a temperature that they retain, at the ordi- nary temperature of the atmosphere and under the usual pressure, the condition of a gas. The boiling-points of a number of such substances are given in the following table : — Fig. 421. Sulphurous Acid, . . — 10 Cyanogen, . . . — 20 Ammonia, . . . — 36 Arsenide of Hydrogen, . — 58 Sulphide of Hydrogen, . — 73 Hydrochloric Acid, . — 80 Carbonic Acid, . . — 80 Protoxide of Nitrogen, — 87.2 All these substances manifest, at the ordinary temperature of the air, the same physical properties which steam would manifest at 130°, as described in (292) ; and if in either case the temper- ature of the gas is reduced below the boiling-point, then the tension of the vapor will be reduced to less than 76 c. m., and the gas will be condensed to a liquid by the pressure of the air, exactly as in the process of distillation. HEAT. 693 This fact is illustrated by the common method of preparing liquid sulphurous acid. This gas, which is generated by heating together metallic mercury and strong sulphuric acid in a glass retort (Pig. 422), is passed into a U tube surrounded by a mixture of ice and salt, where it collects as a liquid. Had we the means of pro- ducing readily a sufficient J' degree of cold, we might ' easily condense to liquids the other gases in the same way. For any given temperature, the vapor of each of the substances included in the above table has, like the vapor of water, a definite maximum tension, which it cannot exceed ; and if we had the requisite data, we could make out for each one a table of maxi- mum tensions at different temperatures similar to the tables on pages 671 and 683. Bunsen has furnished us with such a table for the first three substances. Fig. 422. Temperature. Sulphurous Acid. Tension in c. m. Cyanogen. Tension in c. m. Ammonia. Tension in c. m —37 . . . . . . 74.9 20 . . . 80 . . . 15 . . . 110 . ■ ■ 10 78 141 ■ • • —5 111 173 304 148 207 361 +5 191 244 426 10 239 283 498 15 293 833 578 20 354 380 667.4 25 420 Moreover, what was shown in (292) to be true in regard to steam at 180° is equally true of these gases at the ordinary tem- perature of the air. If, for example, we suppose the cylinder, so often referred to, to be filled with sulphurous acid gas, and maintained at a constant temperature of 16°, we should find, on pressing down the piston, that the tension would increase as the 50* 594 CHEMICAL PHYSICS. volume diminished, until it became equal to 293 c. m. ; but ou still further reducing the volume, the gas would liquefy. The same would be true of cyanogen when the tension became equal to 333 c. m., and of ammonia when it became equal to 578 c. m., assuming, of course, that the temperature of the cylinder is maintained constant at 15°. If the temperature is diminished, the gases cannot acquire so great a tension ; if it is raised, the tension may be greatly increased. These facts may be very elegantly illustrated by means of the apparatus represented in Fig. 423. It consists of an iron cistern, A, filled with mercury, and closed on all sides with the exception of five circular apertures through the top. Into four of these may be screwed the iron tubes a, h, c, and d, which reach to the bottom of the cistern. These tubes are pro- vided with a broad shoulder, and are screwed down upon lead wash- ers with a wrench, so as to enable the joint to resist a pressure of ten or twelve atmospheres with- out yielding. Into the open ends of these iron tubes the glass tubes 1, 2, 3, and 4 are cemented. They are about one centimetre in diam- eter and closed at the top. When the apparatus is in use, one of the tubes may be filled with air, and the other three with ammonia, cyanogen, and sulphurous acid, respectively. By the fifth aper- ture, e, the interior of the mercury-cistern connects with the force-pump P, through the tube g ; and by this water may be forced in upon the surface of the mercury. The pressure thus exerted will cause the mercury to rise in the several tubes, and as the volumes of the confined gases are diminished, it will be noticed that their tension rapidly increases. This tension, which is evidently the same in all four tubes, is measured by the tube containing air, which serves as a manometer (168. 3). If the temperature of the apparatus is kept constant at 15°, the tension will increase until it is equal to 293 c. m. ; then the sulphurous Kg. 423. HEAT. 695 acid will begin to liquefy, and the tension will remain equal to 293 c. m. until all this gas has disappeared. It will then again increase until it reaches 333 c. m., when the cyanogen will liquefy ; and, finally, after this gas has also been reduced to a liquid, the tension will increase again until it becomes equal to 578 c. m., when, last of all, the ammonia will liquefy. If now we remove the pressure by opening the stopcock, which vents the water from the cistern, the liquids will be seen, one after the other, to boil violently, and return to the condition of gas. Since the tension of a gas is always equal to the pressure to which it is exposed, it follows that any gas will be condensed to a liquid if it is exposed to a pressure which is greater than its maximum tension at the given temperature. The maximum tensions of a number of gases at 0° are approximatively as fol- lows : — Maximum Tension at 0° C. Atmosplieres. Atmospheres Sulphurous Acid, . 1.53 Chlorine, . . 8.95 Cyanogen, 2.37 Sulphide of Hydrogen, . 10 lodohydric Acid, . 3.97 Chlorohydric Acid, . . 26.2 Ammonia, 4.40 Protoxide of Nitrogen, . 32 Arsenide of Hydrogen, . 8.80? Carbonic Acid, . . 38.5 And if, in either case, the temperature being at 0°, the ga^ is exposed to a greater pressure than the tension indicated in the table, it will be condensed to a liquid. If the temperature is higher, the pressure required in each case will be greater. If the temperature is lower, the pressure required will be less ; and if in either case the temperature is reduced below the boiling-point of the substance, the gas will be condensed, as we have seen, by the pressure of the air alone. It is evident that, in condensing gases to liquids, a great advantage is gained by reducing the temperature as low as the circumstances will permit, and hence it is usual to employ both pressure and cold for the purpose. Several of the processes in use are as follows. The simplest method of condensing gases consists in generatr ing a large volume of the gas from the proper chemical materials in a confined space. This method was used by Faraday in his original experiments on this subject. He generated the gas in 596 CHEMICAL PHYSICS. Fig. 424. one end of a strong glass tube, bent at the middle, as represented in Pig. 424, and hermetically sealed. The gas accumulating in the confined space exerted a great pressure against the sides of the tube,- and when this pressure became equal to the maximum ten- sion, a portion of the gas was condensed to a liquid. This collected in the other end of the tube, which was immersed in a freezing-mixture to facilitate the process. With this simple apparatus Faraday succeeded in liquefying sulphurous acid, cyanogen, chlorine, ammonia, sul- phide of hydrogen, carbonic acid, muriatic acid, and nitrous oxide gases. The principle of Faraday's condensing tubes was afterwards applied by Thilorier to condensing carbonic acid gas on a large Fig. 425. scale. The apparatus which he devised for the purpose is repre- sented in Fig. 425. It consists of two cylindrical vessels of iron, made exceedingly strong, and of the capacity of about eight litres each. They are closed by valve stopcocks of peculiar construc- tion, which screw into the necks of the two vessels and can be re- moved at pleasure. By means of the copper connecting-tube F, which can be attached by couplers to the discharging orifice of the valves D and iV, the two cylinders may be united when necessary. HEAT. 597 In order to use the apparatus, the valve G is removed from the cylinder A, called the generator, and a charge is introduced, consisting of one kilogramme of pulverized bicarbonate of soda mixed with a litre of lukewarm water. After this has been poured into the cylinder, a long cylindrical vessel (^), contain- ing about 650 grammes of common oil of vitriol, is carefully let down by a hook without spilling. The valve-cock, having been first carefully closed, is now screwed down tightly to the mouth of the generator, which is then turned upon its supporting-pivots so as completely to invert it, and thus mix the acid with the car- bonate of soda. The carbonic acid of the salt, which amounts to more than half of its weight, is now rapidly disengaged, and accumulates in the vacant part of the generator, exerting great elastic force. The generator is next connected, as represented in the figure, with the second large cylinder (-B), which serves as a receiver, and which is surrounded by a mixture of ice and salt. On opening the two valves, the condensed gas rapidly passes over and collects in the cold receiver. The cylinders are then dis- connected, after first closing the valves, and, the generator having been carefully emptied, the same process is repeated. After two or three charges have been in this way conveyed into the receiver, the pressure becomes sufficient to liquefy the gas ; and after ten or twelve charges the receiver may contain several litres of liquid carbonic acid. The receiver is then finally detached, and the liquid which it contains preserved for use. If this liquid is al- lowed to flow out into the air, a portion of it evaporates, and, as we should expect, with great rapidity ; but, what is more won- derful, the cold caused by the evaporation is so great, that the larger part of the liquid freezes, changing into a white flocculent solid resembling snow. This very remarkable phenomenon will be best studied, however, in connection with the latent heat of vapors. In order to show the substance in its liquid condition, a small quantity may be drawn off from the receiver into the thick glass tube P, which is then closed by a valve-cock like that of the receiver itself. It is always dangerous, however, to con- fine liquid carbonic acid in glass. Although the apparatus of Thilorier is exceedingly conven- ient, and jrields, with little labor, a large supply of liquid carbonic acid, yet its use is not unattended with danger ; and a fatal acci- dent, caused by the bursting of one of the iron generators, at the 598 CHEMICAL PHYSICS. School of Pharmacy in Paris, has brought it into general dis- favor. The danger arises from the circumstance that the chem- ical action of the sulphuric acid on the carbonate of soda is Fig. 427. rig. 426. attended with the evolution of heat, which raises the tempera- ture of the generator, and very greatly increases the maximum tension of the gas. In the receiver, when surrounded by ice and salt, the tension is comparatively feeble, and all danger may be avoided by condensing the gas with a force-pump directly into the cold receiver. An apparatus for this purpose is constructed both by Natterer, in Vienna, and by Bianchi, in Paris. It con- sists of a condensing-pump (178), represented at I in Pig. 426, which draws the gas from a gasometer through the flexible hose s, and forces it into an iron receiver, which is represented in Pig. 427, of one fifth of its usual size. This receiver screws HEAT. 599 upon the upper end of the pump-barrel, and it is closed belo'w' by a self-acting valve, and above by the valve-cock g-, as shown in Fig. 427. A crank and fly-wheel facilitate the working of the pump ; but it requires several hours of hard work to liquefy only 600 grammes of gas. After the receiver is about two thirds filled with liquid, it is unscrewed from the pump- barrel, and the liquid can then be drawn out by inverting it and opening the valve g. This apparatus has been especially used for liquefjdng nitrous oxide gas. Professor Faraday succeeded in liquefying several gases which had not been condensed before, by combining the action of intense cold and great pressure, the last obtained with a very powerful condensing apparatus. This apparatus consisted of two condens- ing syringes. The first had a piston of an inch in diameter, the second of only half an inch ; these syringes were connected by a pipe, so that the first syringe forced the gas through the valves of the second, and the second syringe was then used to compress still more highly the gas which had already been condensed by the action of the first, with a pressure varying from ten to twenty atmospheres. The gases were condensed by this apparatus into tubes of green bottle-glass bent at the middle into the form of a U, and closed at the ends with brass caps and stopcocks, securely fastened by means of a resinous cement. The curved portion of the tube was immersed in a bath of solid carbonic acid and ether, and at times a still greater degreeof cold, estimated at — ^110°, was obtained by placing the bath under the receiver of an air- pump and exhausting the air. When exposed to this very low- temperature, most of the liquefied gases froze, as is shown by the following table, which contains the results of Faraday : — Oases not yet tic[uefled Air. Oxygen. Nitrogen. Hydrogen. Oxide of Carton. Marsh Gas. Deutoxide of Nitrogen s Liquefied, but not Frozen. Gases Liquefied , and also Trozen. Olefiant Gas. Chloroliydric Acid. Fluohydric Acid. Fluosilicic Acid. Phosphide of Hydrogen. Arsenide of Hydrogen. Chlorine. Protoxide of Nitrogen, — 100 More recently, Natterer of Vienna, has constructed a vastly inore powerful condensing apparatus than that of Faraday, al- Bromohydric Acid, Cyanogen, lodohydric Acid, Carbonic Acid, Ammonia, Sulphurous Acid, Sulphide of Hydrogen, Meltiiig- Point. —6° S5 51 75 76 86 600 CHEMICAL PHYSICS. though on a similar principle, by which he has been able to ex- exert a pressure of nearly three thousand atmospheres ; but the gases enumerated in the first column of the above table did not yield even to this immense pressure, and indeed were not con- densed so mtich as we should be led to expect from the law of Mario tte. For a description of this apparatus, the student may consult the memoir already referred to (page 299). The facts of this section all tend to show how completely the mechanical condition of matter depends on the temperature of the globe. If the mean temperature were 100° below the present point, by far the larger number of known gases would be either solids or liquids. To the inhabitants of such a climate (whom we may suppose to use a Centigrade thermometer on which — 100° of our scale would be the zero-point), protoxide of nitro- gen would be a very volatile liquid, freezing at 0° and boiling at 13° ; cyanogen would be a crystalline solid, melting at 65° and boiling at 80° ; and sulphurous acid would be a solid, melting at 24° and boiling at 90°. On the other hand, were the mean tem- perature of the globe 100° above the present point, many of our most familiar liquids would be known chiefly as gases. Ether, alcohol, and water would stand very nearly in the same relation in such a climate that sulphide of hydrogen, cyanogen, and sul- phurous acid do in ours. There is every reason to believe that all gases might be con- densed to liquids, if a sufficient degree of cold and pressure could be attained ; and we ought not to be surprised at the difficulty experienced in liquefying the gases above enumerated, when we remember how very rapidly the maximum tension of vapors in- creases with the temperature, and how very limited our means of reducing the temperature are, as .compared with our means of elevating it. We can easily attain a temperature of 1,000° C, while we can scarcely reduce the temperature of bodies to — 150°. At 1,000° the maximum tension of the vapor of water would be, unquestionably, equal to many thousand atmospheres, and it would undoubtedly be found as difficult to condense to a liquid the vapor of water in the highly rareiied condition which it would have at that temperature under the mere pressure of the air, as it is now found to condense the so-called permanent gases. (297.) Greatest Density of Vapor. — By referring to the table on page 571, it will be seen that the weiglit of one cubic metres HEAT. 601 of the vapor of water — and hence, also, its density (68) — in- creases very rapidly with the temperature. This is also shown by the curve a bfg of Fig. 412. The ordinates of this curve represent the weight of one cubic metre of vapor at the corrcr spending temperatures indicated by the abscissas, and the dis- tance between any two horizontal lines of the figure corresponds to a difference of weight equal to 588.73 grammes. At 230''.9 the weight of one cubic metre of vapor is already -gV of thef weight of a cubic metre of water at 4°, and at the same rate of' increase the weight of the vapor at no great elevation of temper- \ ature would be equal to that of its own volume of water. At such a temperature water would change into vapor without inr creasing its volume, provided that a vessel could be made suffi- ciently strong to bear the immense pressure which it would then exert. The same must also be true of the vapors of other liquids, so that at a temperature' more or less elevated the density of the vapor will become equal to the original density of the liquid, which will then change into vapor without increasing its volume. An approach to these phenomena has been observed by M. €agniard de la Tour.* He sealed up in a strong glass tube a volume of water equal to about one fourth of the capacity of the tube, and exposed it to a gradually increasing temperature. At a fixed temperature the water entirely volatilized, and the tube appeared empty. TJiis temperature, at which water thus evapo- rates into a space of about four times its own bulk, is near the melting-point of zinc (360°) . So great was the solvent power of water on glass at this high temperature, that it soon destroyed the integrity of the tubes, and a small amount of carbonate of soda was added to the water to diminish this action. As the vapor cooled, a point was observed at which a sort of cloud filled the tube, and in a few moments after, the liquid reappeared almost instantaneously. M. de la Tour made similar experi' ments with alcohol, ether, and sulphide of carbon, with the fol- lowing results : — Temperature Volume of Vapor Tension of of Disappear- as compared -witli Vapor In ance. Volume of Liquid. Atmoaptieres, Alcohol (36° Baum^), . . 259° 3 119 Ether, 200 2 37 Sulphide of Carbon, ... 275 2 78 * Annales de Chimie et de Physique, 2« S^rie, Tom. XXL, XXII. 61 602 CHEMICAL PHYSICS. The tension of the vapors, as given in the above table, is far less than we should have expected ; for, if Mariotte's law held good in these cases, ether should have exerted a pressure equal to about 209 atmospheres, and alcohol of at least 242. Here, then, we have a very marked example of the principle previously enunciated (166), that as the point of liquefaction is approached, the compressibility of a gas deviates more and more widely from the law of Mariotte. The experiments of De la Tour also show, that under these enormous pressures, even before the whole of the liquid has evaporated, the tension of the vapor varies with the proportion which the liquid bears to the space in which it is confined. (298.) Smallest Density of Vapor. — Having seen that the highest limit of the density of vapor is probably at least as great as the density of the liquid from which it is formed, we naturally next inquire, Is there any lowest limit ? Do substances continue to evaporate at all temperatures, however low, or is there some limit of temperature at which they cease all at once to emit vapors ? By again referring to the table of maximum tensions (page 571), it will be seen that even at 10° below the freezing- point water forms a vapor weighing 2.284 grammes to the cubic metre, and having a tension of 0.2078 c. m. ; and even at 20° below the freezing-point it forms a vapor with a tension of 0.1383 c. m. It was formerly supposed that substances which were de- cidedly volatile at the ordinary temperature continued to emit vapor, however far the temperature might be depressed, although the quantity became less and less, until it was inappreciable to our senses. It was even thought by some, that fixed solids, such as the metals and the rocks, gave out a sensible amount of vapor, so that traces of these substances were always to be found float- ing in the atmosphere. Some researches of Faraday, however, appear to establish an opposite conclusion. He found that mer- cury gave out a perceptible vapor during the summer, but none during the winter ; and also that some chemical agents which may be volatilized at temperatures above 160° did not undergo the slightest evaporation during four years at the ordinary tem- perature of the air. The best opinion, therefore, appears to be, that there is for every body a temperature at which it ceases all at once to give out vapor. With mercury, this temperature lies between 4° and 15°. HEAT. 603 HEAT OP VAPORIZATION. (299.) Latent Heat of Vapor. — The change of state from liquid to vapor is accompanied with a very great amount of ex- pansion ; thus, IcTSr'of Water at 100° forms about 1700 c.c. of steam at lOo! 1 " « Alcohol " 78.4 " « 485 « « vapor " 78.4. 1 " " " " 35.6 " " 357 « « " " 35.6. And, indeed, the heaviest known vapor, that of iodide of ar- senic (^Sp.Gr. = \Q.\ as compared with air, or 0.021 as com- pared with water), is thirty times hghter than the Hghtest known liquid, eupion (>Sjo.Gr. = 0.633). We should naturally expect that such great expansion would be attended with a large absorp- tion of heat. A single experiment will enable us to illustrate this fact, and also roughly to estimate the amount absorbed in the case of water. Take a glass flask, and having placed in it one kilogramme of ice-cold water, expose it to such a source of heat that equal amounts of heat shall enter it during equal times. Observe carefully the time which elapses before the water boils. We will assume that it is twenty minutes. Observe also the temperature of the water and of the steam which fills the upper part of the flask. It will be found to be 100°, and both will remain at this temperature until the whole of the water has boiled away. Continue the boiling for fifty-four minutes, and at the end of this time weigh the water remaining in the flask, when it will be found that exactly one half has been converted into steam and escaped. We assumed that it required twenty minutes to boil the water, that is, to raise the temperature of one kilogramme of water from 0° to 100°. During this time, then, one hundred units of heat must have entered the liquid. Hence it follows, that, during the succeeding fifty-four minutes, two hundred and sixty-three units of heat entered the water ; but this amount of heat has not raised the temperature in the slightest degree, for both the water and the steam have retained, during the whole inter- val, the constant temperature of 100°. What, then, has become of the heat ? The answer is, that it has been absorbed in con- verting 500 grammes of water at 100° into 500 grammes of steam at the same temperature. It follows, then, that one kilogramme 604 CHEMICAL PHYSICS. of water at 100° absorbs, in changing into steam of the same temperature, 540 units of heat. The latent heat of steam, as well as that of other vapors, can be ascertained with great accu- racy by means of the apparatus represented in Fig. 428, contrived by Brix,* of Berlin. It consists of a small glass retort, R, con- necting with a small metallic cylindrical condenser, B. This condenser has an opening into the atmosphere by the tube L, and is supported in the centre of a larger cylindrical box, A, which is filled with water. A thermometer passing through a tubulature in the cover enables the experimenter to observe the temperature of the water, while by agitating the water with the metallic disk C, its temperar ture can be rendered uni- form throughout. In con- ducting the experiment, the water around the condenser is first cooled a few degrees below the temperature of the atmosphere ; then the vapor is distilled over from the retort until the tem- perature of the water has risen an equal number of degrees above that of the atmosphere. In this way any loss of heat from the water is avoided, since the apparatus is for an equal length of time warmer and cooler than the air. The weight of vapor condensed is then ascertained by the loss of weight of the I'etort, and the amount of heat evolved by its condensation is readily calculated from the weight of the water around the condenser, and the number of degrees through which it has been heated. This amount of heat corresponds to the latent heat of the vapor plus the amount of heat given out by the condensed steam in Fig. 428. * Poggendorff's Annalen, Band LV. HEAT. 605 cooling from the boiling-point to the temperature of the con- denser. To illustrate this by an example, we will suppose that we know The weight of water around the condenser, . . . 500 grammes. The temperature at the beginning of the experiment, . 12°. The temperature at the end of the experiment, . . . 18°. The weight of the water distilled over, . . . 4.82 grammes. Hence it follows (231), that The amount of heat which entered the water equals . 3 units. By (233) the amount of heat required to raise the temper- ature of 4.82 grammes of water from 18° to 100° is equal to 0.395 « And hence the quantity of heat given out by 4.82 grammes of steam in liquefying equals 2.605 " One kilogramme of steam would then set free, in liquefying, 540 " It is evident that, in these experiments, as in the determination of the specific heat by the method of mixtv/res, it is necessary to take into account the amount of heat absorbed by the metals and glass of which the apparatus is made. This can easily be calcU' lated, since the specific heat of these substances is known, and their weight can be easily determined. The formulae for similar calculations have already been given [158] and [159] , and they can readily be modified by the student for any special case. By means of the apparatus described above, Brix obtained for the latent heat of the vapors of several well-known liquids the following values.* These values are, in each case, the number of units of heat required to convert one kilogramme of the liquid at its boiling-point into one kilogramme of vapor at the same temperature. latent Heat of cquai Weights. Latent Heat of equ»l Volumes. at BoilinB-Ppint. Air = l. "Water, . . 540 units. 815.05 0.451 Alcohol, 214 « 348.26 1.258 Ether, . 90 " 265.45 2.280 Oil of Turpentine, 74 " 307.00 3.207 Oil of Lemons, . 80 « * Determinations of the latent heat of rapor's have also been made by Andrews (Quarterly Journal of the Chemical Society, Vol; I. p. 27), by Despretz, and by Favre and Silbennann (Comptes Rendus, Tom; XXIII. p. 524). 51* 606 CHEMICAL PHYSICS. Since the ntimber which expresses the specific gravity of a substance is the same as the weight of one litre in kilogrammes, it follows, that, if we multiply the specific gravity of a vapor at the boiling-point (referred to water) by 1,000, we shall obtain the weight in kilogrammes of one cubic metre of this vapor at this temperature ; and, furthermore, it follows from what has been said, that, if we miiltiply this weight by the latent heat of tlie vapor, wo shall have the number of units of heat required to generate from these liquids at their boiling-points one cubic metre of vapor. Making these calculations, we should obtain the num- bers given in the above table as the latent heats of equal volumes; and it will be noticed that, with the exception of that of ether, these numbers are approximatively equal. The same is also true of other liquids not included in the table ; hence we may say, roughly, that the same volume of vapor will be produced from all liquids by the same expenditure of heat. No important advantage, therefore, could be gained by substituting any other liquid for water in the steam-engine. (300.) Latent Heat of Steam at Different Temperatures. — The latent heat of steam has the value given in the above table only when its tension is 76 cm. and its temperature 100°, which is the case when the steam is formed by boiling water under the normal pressure of the atmosphere. If the tension and temper- ature of the vapor have greater values than the above, then the latent heat is less than 540 units ; and, on the other hand, if these values arc less than 76 c. m. and 100°, then the latent heat of the vapor is more than 540 units. Watt concluded, from his experiments, that the same weight of vapor always contained the same quantity of heat, or, in other words, he supposed that the same quantity of heat would convert one kilogramme of water at 0° into one kilogramme of vapor, whatever the tension or tem- perature of the vapor might be. If this were the case, the sum of the latent and sensible heat of steam would be the same at all temperatures, and we should have for the latent heat the follow- ing values : — Sum. 640 a a « Temperature. Latent Heat of Vapor. 640 units 50 590 " 100 540 " 200 440 « HEAT. 607 Among the other numerical data connected with the steam- engine, Regnault has carefully determined the latent heat of steam at different temperatures, between 5° and 196°. These experiments were made with an apparatus constructed with every possible refinement, and were conducted with the usual skill of this eminent experimentalist ; but for a description both of the apparatus and of the metliods, we must refer the student to the original memoir.* It was proved by this investigation, that the law of Watt, as the principle above stated is frequently called, is far from being an exact expression of the facts, and, like so many other phenomenal laws of nature, can only be regarded as ap- proximatively true (compare page 300). The sum of the latent and sensible heat of steam actually increases, although only very slowly, with the temperature ; and Regnault found that the results of his experiments were very nearly satisfied by the em- pirical formula ' A = 606.5 -f 0.305 t , [202.] in which X represents the sum of the latent and sensible heat, while 606.5 is the latent heat of the vapor at 0°, and t the given temperature. By means of this formula, we can very easily cal- culate the latent heat of the vapor at any temperature. Thus, at 100° we have A = 637, and consequently the latent heat is 637 units less the number of units required to raise the temperature of one kilogramme of water from 0° to 100°. By the table on page 470, we find that this amount is equal to 1.005 X 100 = 100.5, and, subtracting this quantity from 637, we find the latent heat of steam at 100° to be 636.6 units. In like manner, the other values in the following table have been calculated. The second column of the table gives the tension of the vapor of water in centimetres. The third column gives the number of units of heat required to change one kilogramme of . water at 0° into one kilogramme of vapor at f. The fourth col- umn gives the number of units of heat required to change one kilogramme of water at f into one kilogramme of vapor at the same temperature. * Memoires de I'Acad^mie des Sciences, Tom. XXI. 608 CHEMICAL PHYSICS. Tem- pera- ture. Tension. Latent Heat. Sum of Latent and Sensible Heat. Tem- pera- ture. Tension. Latent Heat. Sum of Latent and Sensible Heat. 0° 0.460 606.5 606.5 120° 149.128 522.3 6J3.1 10 0.916 599.5 609.5 1.S0 203.028 515.1 646.1 20 1.739 592.6 612.6 140 271.763 508.0 649.2 30 3.155 585.7 615.7 150 358.123 500.7 652.2 40 5.491 578.7 618.7 160 465.162 493.6 655.3 50 9.198 571.6 621.7 170 596.166 486.2 658.3 60 14.879 664.7 624.8 180 754.639 479.0 661.4 70 23.309 557.6 627.8 190 944.270 471.6 664.4 80 35.464 550.6 630.9 200 1168.896 464.3 667.5 90 52.545 543.5 633.9 210 1432.480 456.8 670.5 100 76.000 536.5 637.0 220 1739.036 449.4 673.6 110 107.537 529.4 640.0 230 2092.640 441.9 676.6 (301.) Illustrations. — The fact that heat is absorbed during evaporation is illustrated by many familiar phenomena. The chill which is felt on leaving a bath is caused by the rapid evap- oration of water from the surface of the skin, whereby heat is withdrawn from the body. In a similar way, the air of a heated room is cooled by sprinkling water on the floor. This principle also explains how man is enabled to bear the scorching heat of the hottest climates, and even, if properly protected, to enter an oven heated above 100°, his blood not exceeding 40° ; a copious perspiration is excited, which removes heat from the body as rapidly as it is received from without. The porous water-jars, which are used in Spain and in Eastern countries to keep liquids cool, also owe their efficacy to the latent heat of vapors. They are made of biscuit earthen-ware, and the water which slowly percolates through the walls and evaporates from the surface withdraws so much heat from the vessel as to retain the tem- perature of the water considerably below the temperature of the surrounding air. The effect is enhanced by placing the jar in a current of air, which accelerates evaporation. In like manner, the evaporation from the surface of the body is increased in a current of air, and hence the sensation of coolness which a draught produces ; while, on the other hand, the oppression which we feel in an atmosphere saturated with moisture arises from the fact that the evaporation is in great measure arrested. The same principles may also be illustrated by a great variety HEAT. 609 Pig. 429. of ©xperiments. One of the most striking of these is that of Leslie, in which water is frozen by its own evaporation. A small and shallow pan of water is supported over a dish of sulphuric acid, and under a bell-glass standing on the plate of an air-pump (Fig. 429). On exhausting the air from the bell, the heat absorbed by the very rapid evapora- tion of the water which ensues is so great, that the larger por- tion of the liquid is converted into ice. The sulphuric acid absorbs the vapor as fast as it forms, and thus accelerates the evaporation. A similar experiment can be made with the instrument rep^ resented in Fig. 430, called the cryophorus (frost-bearer). It consists of two glass bulbs, connected together by a long tube, one of which is partially filled with water. In making the in- strument, it is hermet- ically sealed while filled with steam, so that on cooling a vacuum is left above the water, except in so far as the space is filled with vapor. If now the empty bulb is surrounded by a freezing-mixture, this vapor is condensed as fast as it is formed, and a very rapid evaporation ensues from the surface of the water in the first bulb, which soon reduces the temperature of the liquid to the freezing-point. Even more marked effects than these can be obtained by the evaporation of very volatile liquids, like ether or sulphide of carbon. The rapid evaporation of ether poured upon the hand occasions a very distinct sensation of cold, and water can be frozen by the evaporation of ether from the surface of a glass bulb covered with muslin and kept moistened with the liquid. If the evaporation is accelerated by placing the apparatus under the receiver of an air-pump, even mercury can be frozen in this way. Indeed, an apparatus has been invented for making ice in warm countries, by the evaporation of ether in a partial vacuum. The principles of latent heat can in no way, however, be more strikingly illustrated than with liquid carbonic acid. When this highly volatile liquid is allowed to escape into the air, it evap- Fig. 430. 610 CHEMICAL PHYSICS. orates with siicli rapidity, as has been stated, that the larger por- tion of it almost instantaneously freezes. This frozen carbonic acid can easily be obtained in large quantities by means of the apparatus of Thilorier. From the valve of the receiver B, Fig. 425, a tube descends to near the bottom of the vessel, so that, on opening the valve, the liquid is forced out by the tension of the gas in the interior. A cylindrical brass box, O, connected with the valve of the receiver by the coupler L (which fits in the socket M^, and so constructed as to break the force of the jet, receives the liquid as it issues from the receiver, and soon be- comes filled with solid carbonic acid, which resembles, in its general appearance, freshly fallen snow. This experiment, it will be noticed, is analogous in principle to that of Leslie, in which water was frozen by its own evaporation. , A further illustration of the principles of latent heat is afforded by the fact, that the solid carbonic acid — if in considerable quan- tity and surrounded by poor conductors — may be kept exposed to the air for hours before it entirely disappears. Although exceed- ingly volatile, it evaporates only slowly, for the same reason that a bank of snow melts gradually during a warm spring day. The non-conducting nature of the vessel, and of the atmosphere of gas which surrounds it, prevents the absorption of the heat which is necessary for the change of state. If, however, it is brought into close contact with a good^conductor, like metallic mercury, the ra- pidity of its evaporation is greatly accelerated, and the temperature of the substance reduced to that of the solid gas, which has been estimated as low as 90° C. In this way large masses of mercury can easily be frozen. A greater degree of cold can be obtained by mixing the solid gas with a little ether, which forms with it a semi- fluid mass capable of being brought in closer contact with sub- stances, and thus removing their heat more rapidly. A still greater degree of cold was produced by Faraday, by placing this mixture under the receiver of an air-pump from which the air and gaseous carbonic acid were rapidly removed. An alcohol-thermometer placed in this mixture sinks to the temperature of — 110° ; at this low temperature the mixture of solid carbonic acid and ether is not more volatile than alcohol at the ordinary temperature ' Similar experiments can be made with the liquid protoxide of nitrogen, which is obtained in Bianchi's apparatus. As this does not freeze so readily as liquid carbonic acid, it can be drawn HEAT. 611 out from the condenser in a liquid state, and retains its condition wlien exposed to tlie air longer than solid carbonic acid. It can readily be frozen by its own evaporation, and it furnishes the means of producing the lowest temperature yet attained. When mixed with solid carbonic acid and ether, it produces a cold so in- tense, that absolute alcohol exposed to it assumes the consistency of a thick oil, and a thermometer immersed in a bath formed by mixing tliis liquid with sulphide of carbon was observed by Natterer to fall to — 140° when the bath was placed in vacuo. (302.) Applications of the Latent Heat of Steam. — The great amount of heat which steam contains renders it exceedingly val- uable in the arts as a heating agent. Water may be heated, and even boiled, in wooden tanks, by blowing' steam into it, or by causing the steam to circulate through a coil of copper pipe at the bottom of the tank. Buildings, also, are very frequently warmed by the heat of steam. The steam generated in a boiler placed in the basement is conveyed by iron pipes to the differ- ent apartments. There it is condensed to water in a coil of iron pipes, or in a condenser of some other form, and the heat thus set free is radiated from the iron surface of the condenser. Steam is likewise used as a source of heat in the process of distil- lation, especially when the substance to be heated is liable to al- teration from too high a temperature. For this purpose, the walls of the still are frequently made double, and the steam admitted between the two. It is sometimes found advantageous to blow the steam through the mass of liquid in the still, in which case the volatile product passes over in vapor mixed with the steam, and the two are condensed together in the -worm or receiver. This method is constantly used in the distillation of volatile oils from organic materials. Sometimes the steam is highly heated by passing it through red-hot tubes before it is introduced into the still. In this way the fat acids and many other substances can be distilled, which could not be distilled in the ordinary way. This method is in fact the basis of an important process used in the arts for decomposing tallow and other fats, and extracting from them the fat acids and glycerine, substances which are used in the manufacture of candles and of soap. (303.) Spheroidal Condition of Liquids. — It has already been tetated, that when a liquid is dropped upon a heated surface, the temperature being made to vary with the nature of the liquid, it 612 CHEMICAL PHYSICS. assumes the spheroidal condition, and rolls round on the surface like globules of mercury on a porce- lain plate (Pig. 431). It was also stated, that the temperature of the liquid in this condition is constant, and always below its boiling-point. This fact can be proved by testing the tempera- ture with a thermometer, as shown in Fig. 432. The following table shows in each case, first, the temperature at which the liquid assumes the spheroidal condition in a heated silver capsule ; and, secondly, the temperature of the liquid while in this condition : — Fig. 431. Fig. 432. I, n. Boiling-Point. Water, . 171 96.5 100 Alcohol, . 134 75.8 78 Ether^ . . . . . 61 34.2 35 Sulphurous Acid, ► • • —10.5 —10 When in the spheroidal condition, the globules of liquid have a gyratory motion on the bottom of the capsule, and not only does the liquid not boil, but it evaporates vastly more slowly than when it is in actual ebullition. If the source of heat is removed, the temperature of the capsule will fall until a point is reached at which the liquid wets the metallic surface, and then the liquid will boil violently, and be thrown in all directions with almost ex- plosive violence (Fig. 433). This singular phe- nomenon can also be shown by pouring a small quantity of water into a thick copper flask intensely heated, and corking the flask while the liquid is in the spheroidal condition. For a time, all remains quiet ; but when the flask has cooled sufficiently, the water will be sud- denly converted into steam, and the cork thrown out with great violence (Fig. 434). Fig. 433. It has also been proved that a liquid, when Fig. 434. HEAT. 613 in a spheroidal condition, is not in contact ynth a heated sur- face. Boutigny was able to see the flame of a candle between a globule of water rendered opaque by lampblack and -^ the heated surface on which :^\ ■rj-y.—j. it rested (Pig. 435) ; and, \ ^^^3 moreover, Wartmann and n"^ ^^glP Poggendorff found that a T l^^^i current of electricity would fe^^^a| not pass between the liquid " ^^^^ ^ ^^^m i^Hm spheroid and the metallic rig. 435. disk. The explanation of these singular phenomena has already been in part given. "We have seen that, whenever by the action of heat the adhesion of a liquid to the surface on which it rests becomes less than twice as great as the cohesion between the liquid particles themselves, the liquid will no longer moisten the surface, and we can readily conceive that it may be even re- pelled by it, and with a force sufficiently great to overcome the weight of the liquid mass. That such a repulsion really exists Boutigny proved by two curious experiments. He poured water into a basket made of platinum wire-netting and heated to redness, and found that the liquid did not drop through the interstices. He also whirled round, in a sling, a heated capsule containing a liquid globule in the spheroidal state, and found that the cen- trifugal force was not able to compel contact. Assuming, then, that the liquid globule is sustained at a small distance above the heated surface by the repulsive force of heat, it is easy to explain the rest. The vapor forming on the lower surface of the sphe- roid would raise it still further from the heated metal, and, escap- ing unequally around the contour of the spheroid, would tend to give to it its singular motions. Then, again, since the liquid is not in contact with the source of heat, it can only be heated by radiation. Now a part of the rays of heat will be reflected from the surface of the liquid ; and, moreover, the greater part of those which penetrate it will pass through it without being ab- sorbed. It is evident, then, that the spheroid will retain but a small portion of the heat radiated from the walls of the metallic capsule; and since it is all the time losing heat by evaporation, 62 614 CHEMICAL PHYSICS. it is not wonderful that its temperature should be reduced several degrees below the boiling-point. By following out the principles of this section to their extreme consequences, we are able to produce some very paradoxical effects. It has before been stated, that water may be frozen by pouring it into liquid sulphurous acid while the latter is in the spheroidal condition, although the capsule containing it may be red-liot. So also, by substituting for liquid sulphurous acid the mixture of solid carbonic acid and ether, even mercury, placed within the red-hot capsule in a small platinum crucible, may be frozen with equal certainty. The wonder disappears from these phenomena when we know that these highly volatile liquids . are not in contact with the heated surface of the capsule, for they simply produce the same effects in their spheroidal condition that they would under other circumstances. A stUl more paradoxical result can be obtained with liquid protoxide of nitrogen. For this experiment, the liquid should be drawn into a tube sus- pended in a bottle containing a few lumps of cliloride of cal- cium, by means of a cork adjusted to the neck. Without this precaution, the moisture of the air would condense as hoar-frost on the tube, and render the wall opaque. If we pour some mer- cury into this tube, it will sink to the bottom and immediately freeze. On the other hand, if a piece of burning charcoal is dropped in, it will float on the liquefied gas, which will assume the spheroidal condition around it ; but, moreover, what is very remarkable, the charcoal will burn with the usual intense bril- liancy in the protoxide of nitrogen gas which surrounds it, and we shall thus have in the same test-tube burning charcoal and frozen mercury. But perhaps the most- marvellous result is the impunity with which the moistened hand may be dipped into melted lead, or even into molten cast-iron as it flows from the furnace. In these cases the adhering moisture is converted into vapor, which forms an envelope to the skin sufficiently non- conducting to prevent the transmission of any injurious quantity of heat during the short period of the immersion. HEAT. 615 STEAM-ENGINE. (304.) It would lead us beyond the design of the present work to enter upon any detailed description of this wonderful application of the laws of vapors. We shall only be able to point out the general principles of the machine, and to illus- trate by figures some of its most important forms. It has al- ready been shown, that when water is confined in a vacuous space, this space becomes filled with vapor, whose tension de- pends on the temperature, and rapidly increases as the tempera- ture rises. It is the object of the steam-engine to convert this tension into mechanical effect. Every steam-engine must, then, consist of two parts : first, the boiler, in which the steam is gen- erated ; secondly, the machine proper, by which the tension of the steam is made to do mechanical work. We shall do well to examine the various forms which are given to these parts separ rately. (305.) The Boiler. — The form of the steam-boiler varies very greatly with the purposes to which it is to be applied, and on its proper construction the safe and economical working of the ma- chine in great measure depends. The boiler is the origin of the power ; it is where the heat evolved by the burning combustible is combined with water, to reappear in the expansive force of steam. The machine proper merely transmits this force, and, like any other machine, it can neither increase nor diminish it, except so far as the force is expended in overcoming friction or other resistances in the machine itself. The two chief requisites for a steam-boiler are evidently, first, the strength required to resist the expansive force of the steam without an unnecessary expense of materials ; and, secondly, the capability of furnishing the amount of steam required by the en- gine in any given time, with the smallest possible expenditure of fuel. The boilers are usually made of plates, either of wrought- iron or of copper, riveted together, and, when necessary, are strengthened by cross iron stays in the interior. Copper is the best material, but iron is almost invariably preferred on account of its cheapness. The thickness of the plates is made such that the boiler will resist a very much greater tension than any to which it can ever be expected to be exposed. It is generally assumed, that, in order to supply a steam-engine, 61-6 CHEMICAL PHYSICS, 35 litres of water must be evaporated in the boiler each hour for every horse-power. Now, we know that at least 650 x 35 = 22,750 units of heat are required in order to convert 35 kilo- grammes of water into steam ; and this amount must therefore be transmitted during an hour through the boiler-plates for every horse-power of the engine. But since, even through the best conductors, heat is transmitted with extreme slowness, so large a quantity can only be made to pass by exposing a large surface to the action of the flame. Hence the extent of the heating sur- face, and not the amount of water contained in a boiler, is the measure of its capacity to generate steam. It is the general rule to allow about 1.7 square metres of heating surface, and about 70 square centimetres of grate-bars to every horse-power. Moreover, in order to obtain the full effect of the combustible, it is essential that the heated products of combustion should be kept in con- tact with the surface of the boiler until the temperature of the smoke is reduced as nearly as possible to that of the water in the boiler. This is accomplished by making the smoke circulate through tortuous flues in contact with the surface of the boiler. The quantity of heat produced by the burning combustible is far, however, from being entirely economized. It has been found, by experiment, tliat the whole amount of heat evolved by burning one kilogramme of bituminous coal is equal to about 7,500 units, which would change into steam ^^"-^w- = 11.5 kilogrammes of water, if it all passed through the boiler-plates into the water ; but so much heat is lost by incomplete combustion, by radiation, by conduction through the mass of the furnace, and, finally, by the smoke, which must be discharged into the chimney, still heated to between 200° and 400° in order to sustain the draught, that practically one kilogramme of coal will not evaporate more than fi:om five to seven kilogrammes of water with the best con- structed furnaces. The conditions of efficient ac- tion just considered are best com- bined in what is termed the Corn- ish boiler, which is represented in Fig. 436. It is cylindrical in form, frequently over forty feet in length, and from five to seven r'S'*3<5. feet in diameter, with two flues, HEAT. 617 which extend the whole length of the boiler ; they are perfectly cylindrical, and of sufficient magnitude to admit a furnace in each. After the heated gases have traversed these iron flues, they are returned around the surface of the boiler by external flues made in the brick-work which supports it. The circuit which the hot gases perform in contact with the boiler surface is, not xmfrequently, 150 feet long, and the heating surface exposed to their action over 3,000 square feet. Another form of boiler much iised for stationary engines in France is represented in Figs. 437 and 438. This boiler is also cylindrical, but in the Fig. 437. place of the internal flues used in the Cornish boiler, the heating surface is increased by means of two tubes bouilleurs, B, Fig. 437, which are connected with the main cylinder by the vertical tubes P, P, P. The flame of the furnace plays directly against the tubes bouilleurs ; the heated gases are then returned under the main cylinder in the flue O, Fig. 438, and are finally dis- charged into the chimney through the side flues x, x, while a damper at R serves to regulate the draught. With a stationary boiler, economy of fuel is, as a general, rule, the great desideratum ; and in most cases that form can be given to it by which this end is best attained. It is different with the boiler of a steamship or of a locomotive engine. With the first, economy of fuel is also the primary consideration, because, other- wise, long voyages would be impossible ; but economy of space must also be considered, and it is therefore essential that the size of the boiler should be restricted to quite narrow limits. With the locomotive, on the other hand, speed is, as a general rule, the , great object, and this must be attained at any cost of fuel. But 52* 618 CHEMICAL PHYSICS. speed implies a very rapid consumption of steam, since for every revolution of the driving-wheel of a locomotive its two cylinders must be filled and vented twice ; hence the chief requisite of a locomotive boiler is, that it should generate the greatest pos- sible amount of steam in a given time. In all cases, the ma- chinist endeavors to combine the requisite conditions as well as the circumstances admit, and the efficiency of his engine depends in great measure on his success. Unfortunately, he is guided almost entirely by empirical rules ; and there are few branches of practical art in which so much remains to be determined and improved, and scarcely any which theoretical science has done so little to advance. The usual form given to the boiler of a locomotive is repre- sented in Fig. 439. The furnace A, called the Jire-box, is within the boiler, and surrounded by water except at the door D and at the ash-pit. The flame is conducted from this fire-box to the smoke-box B through a large number of brass tubes, which are all surrounded by the water of the boiler. There it meets Pig. 439. with a jet of steam coming from the cylinders, which creates a strong draught and drives the waste gases up the chim- ney. The boiler of a locomotive is surmounted by the steam- dome, E.; and a tube with a funnel-shaped orifice, opening near the top of this dome, receives the steam and conveys it to the cylinders through F. This arrangement prevents, to a great degree, the spray, which rises from the water of the boiler and is mixed with the steam in the upper part of it, from reaching the cylinders ; as the steam ascends the steam-dome, this spray falls back, and nothing but pure steam enters the tube. The steam-boiler is always provided with several appendages for the purpose of regulating the quantity of water, for meas- uring the tension of the steam, and for preventing the accu- mulation of a pressure which would endanger the safety of the boiler. HEAT. 619 It is essential for the good -working of the boiler, that the ■water should always cover the whole heating surface; hence it must be maintained above the level of the flues. The water is supplied to the boiler through the pipe a (Fig. 437), which reaches nearly to the bottom. This pipe communicates either with an elevated reservoir, or with a force-pump moved by the engine, the size of the pump being so adjusted that the amoimt of water forced into the boiler during a given time shall be, as nearly as possible, equal to that which escapes in the condition of steam through the steam-pipe v during the same interval. This adjust- ment, however,.is necessarily imperfect ; and hence a great variety of inventions, by which the supply of water is regulated automati- cally, and made to depend on the position of the water-level in the boiler. Various contrivances are in use for indicating to the engineer the height of the water. One of the simplest of these is the glass gauge represented at n (Fig. 437). It consists of a thick glass tube firmly cemented into iron caps, by means of which it communicates with the interior of the boiler. It is so placed, that, when the water is at the proper lev6l, the lower end shall open below the surface of the water, and the upper end above it ; consequently, the water will always stand at the same level in the tube as in the boiler. Another kind of indicator is represented at /'. It consists of a float, which is connected with a counterpoise by a metallic wire passing over a pulley, and through a packing- box in the top of the boiler. The position of the level of the water is indicated either by the position of the counterpoise, or by a needle attached to the axis of the pulley, and moving over a graduated disk. Some boilers are also provided with an alarm- whistle, S, so arranged that it is opened by the float / when the level of the water falls too low. The tension of the steam in the interior of the boiler is indi- cated by a manometer, which may be either of those already described (Figs. 104, 273, or 279). In order to limit the tension of the steam, every boiler is fur- nished with one or more safety-valves, represented at P (Fig. 437), and also in detail in Fig. 440. The valve is kept closed by the weight P, acting on the lever O, and this weight is so adjusted to the area of the valve, that the valve will open as soon as the tension of the steam exceeds a limited amount. The area of the valve is adjusted to the extent of the heating surface of the 620 CHEMICAL PHYSICS. boiler, and to the maximum tension at which the boiler can be worked with safety. It is determined by means of the empirical formula. d 2G sfw- 's -0.412 in which d is the diameter of the valve, B the area of the heating surface of the boiler, and S the maximum tension of the steam. It has been found that a valve with the dimensions given by this formtila will allow all the steam to escape which can be generated by the most active fire ; but, for greater security, a boiler is gen- erally provided with two valves of these dimensions. We can also limit the tension of the steam by fixing a limit to its temperature. Tliis can be done by closing a tubulature adapted to the upper part of the boiler with a plate made of fnsible alloy, whose proportions have been so adjusted (272) that it shall melt when the steam attains the temperature which cor- responds to the maximum tension which the boiler is calculated to sustain. This plate, which is qiiite brittle, is held in its place by an iron collar, and protected by an iron grating, which ena- bles it to resist the pressure of the steam. The use of these plates, however, is liable to serious objections. They not only render the boiler unserviceable for the time, if they yield, but, moreover, the melting-point of the plate is liable to a change from the eliquation of the more fusible metal. (306.) Dimensions of Steam-Boilers. — As in the last sec- tion the dimensions of the steam-boiler were given in French measure, it may be well to add the following English data, taken from the Encyclopaedia Britannica, Article Steam-Engine, pre- mising that by a horse-power is meant a force of that intensity which will raise 33,000 pounds one foot per minute, or nearly 2,000,000 pounds one foot per hour. HEAT. 621 Conditions for each Horse-Power. Ordinary Oomish ■^ standard. Boiler. Quantity of water to be evaporated per hour in cubic feet, 1 1 Volume of water in boiler in cubic feet, . . . 10 or more. Volume of steam in steam-chamber in cubic feet, . 10 or more. Area of fire-grate in square feet, .... 1 2 Area of heating surface in square feet, . . . 15 60 to 70 Circuit of flues in linear feet, 60 150 Results. Bituminous coal per hour for each horse-power, , . lOlbs. 5ilbs. Water evaporated by each pound of coal, . . 6 " 11| " Bituminous coal consumed per hour for each square foot of grate, 10 " 2^ ". (307.) Watfs Condensing-Engine. — The steam-engine, in its present form, was invented, between the years 1763 and 1769, by James "Watt, originally a maker of philosophical Instruments in Glasgow. This invention stands without a parallel in the history of the mechanic arts. Perfect almost from its first con- ception even in its nainutest details, it has since received no improvement involving a single principle unknown to Watt. It is true that we have machines at the present day which, not only in magnitude, but also in the perfection of the mechanical details, and in the beauty and simplicity of the combination of the several parts, far exceed any Watt ever saw ; but all these improvements have been only the necessary development of his first conception. Most of the parts of the condensing-engine are shown in Fig. 441, which, although necessarily imperfect in its details, will serve to illustrate the relation of the parts. The most essential part of the machine is the large cast-iron cylinder (shown on the left-hand side of the cut), within which moves the piston P. The interior of this cylinder is turned on a lathe, so as to be perfectly true, and the sides of the piston are made elastic by what is termed the packing, which prevents any leakage of the steam around the edge. The surfaces of this piston receive directly the pressure of the steam ; and it is therefore to be re- garded as the point of application of the expansive force, and the origin of the motion of the engine. The steam generated in the boiler just described, and conveyed to the machine through the steam-pipe, is first received into the valve-chest b through the 622 CHEMICAL PHYSICS. aperture o, and from this it is admitted alternately into the top and bottom of the cylinder by a sliding-valve, which is moved by the rod b m, passing through a packing-box on top of the valve-chest. Fig. 441. The same valve also opens and closes the vent-hole a, by which the steam, after having done its work in moving tlie piston, is discharged alternately from either end of the cylinder through the eduction-pipe U. When the valve is in the position repre- sented in Fig. 441, tlie steam has free access to the upper part of the cylinder, and presses on the top of the piston, while from the space below the piston a vent is opened throvigh the tube a TJ. Consequently the piston falls ; but when it reaches the bottom of the cylinder, the position of the valve is suddenly changed to that represented in Fig. 442, and a connection is opened between the upper part of the cylinder and the eduction-pipe, while at the same time the steam is admitted below the piston, whose motion is thus reversed. When the piston reaches the top of the cylin- HEAT. 623 der, the position of the Talve is again changed ; and thus continu- ously, so that a reciprocating motion is the result. This motion is qommxinicated hj the piston-rod A, which passes steam-tight rig. 442. through the packing-box d, on the head of the cylinder, to one arm of the large lever L, called the beam, and by the beam it is further transmitted through the connecting-rod I to the crank K, which turns the shaft of the engine, and gives motion to the ma- chinery connected with it. . Fly-Wheel. — When the piston is at the top of the cylinder, the crank is in its lowest position ; and, on the other hand, when the piston is at the bottom of the cylinder, the crank is in its highest position. In either of these positions, called the dead points, it is obvious that the pressure of the steam can communicate no motion to the crank, and the machine would come to rest were it not for the large iron wheel F, called the fly-wheel, which is attached to the shaft and revolves with it. This wheel, which has a large mass of matter in its rim, having once received a certain velocity of rotation on its axis, carries by its inertia the crank and piston through the dead points, and brings them into a position in which the power becomes efifective. ' 624 CHEMICAL PHYSICS. The fly-wheel, moreover, equalizes the motion of the machine, and gives a uniformity to its action it could not otherwise have, owing to tlie unequal leverage at which the connecting-rod acts on the crank in its different positions. Then, again, the uni- form rotation of the wheel acts back upon the piston through the crank with the happiest effect, bringing the piston slowly to rest at the end of each stroke, and thus preventing the jar which would result from a sudden change in the direction of the mo- tion. Indeed, this whole combination is one of the happiest results of mechanics, and wiU repay the most careful study. A fly-wheel is only essential in a stationary engine. In the engine of a steamboat or a locomotive, the same effect is produced by the momentum of the moving mass. Parallel Motion. — The system of jointed rods CD^ (Fig. 441), by which the piston-rod is connected with the beam, called the parallel motion, is an ingenious invention of Watt to prevent any lateral strain on the former. Since the end of the piston-rod must move in a vertical line, while the end of the beam describes the arc of a circle coinciding with this line only at one point, it is easy to see that they could not be directly jointed together ; and it can also be readily shown, by the principle of the composition of forces, that, if they were connected by the rod D alone, a lateral strain would be exerted on the piston-rod which would soon de- range the machinery. By means of the system of rods repre- sented in the figure, the end of the piston-rod is suffered to move in a vertical direction, and the lateral force resulting from the decomposition of the motion, in its transmission to the beam, is balanced by the resistance of the rods C and E, called radius bars, which are connected by joints to the frame of the engine. The parallel motion of "Watt does not completely answer its object, that is, it does not cause the end of the piston-rod to move in an absolutely straight line ; and when the stroke of the piston bears a large proportion to the length of the beam, the deviation from a straight line becomes of practical importance. Hence, a large number of other parallel motions which have been in- vented to remedy this defect. One of the simplest contrivances for the purpose, and the one generally used in this country, consists in directing the motion of the piston-rod by a cross-piece sliding in vertical grooves, which are kept in their place by a stiff frame-work. HEAT. 625 The Eccentric. — It has already been shown that the connec- tions between the ends of the cyhnder and the boiler or vent- tube may be alternately opened and closed by a sliding motion given to the valve ; it now remains to show how this motion is obtained automatically. A wheel (£, Fig. 442), called the eccentric, is so attached to the main shaft of the engine that its centre does not coincide with the axis of rotation. This eccen- tric revolves within a metallic ring, C, and imparts to it a back- ward and forward motion, which is transmitted by the arm Z Z to a bent lever, Soy, and by that to the rods d and b, which act directly on the valve. The extent of the motion of the valve is easily regulated by the length of the arms of the lever, and the moment at which it begins to move in either direction is determined by the position of the eccentric on the shJift. In starting the engine, or in reversing its motion, the valves are moved by hand, and there is always a handle connected with the lever Soy iov the purpose. It is not until after the fly-wheel has acquired a certain momentum, that the arm Z Z of the eccentric is geared on to the lever at S. In order to stop the engine, the arm is ungeared and the motion of the valves regu- lated, as before, by hand. There is no part of the steam-engine on which more ingenuity has been shown than on the valves, and the automatic machinery for opening and closing them. The form of the valve represented in the above figures is the simplest, and , is very generally iised in small engines ; but in large engines there are frequently four separate valves, which are opened and closed independently. The Condenser. — If the eduction-pipe i7 (Pig. 441) opened di- rectly into the atmosphere, the engine would work perfectly well with only the parts which have been now described ; only there would be a loss of power : for a portion of the expansive force of steam would be expended in overcoming the pressure of the air. Watt avoided a part of this loss by an application of the well- known law (287), that the tension of any vapor in vessels com- municating with each other is always that which corresponds to the temperature of the coldest vessel. He connected the educ- tion-tube of his engine with a larged closed iron box ( O, Pig. 441), called the condenser, so that whenever by the motion of the valve the orifice of the eduction-tube is opened, the waste steam rushes at once into the cold vessel, leaving a partial 53 626 CHEMICAL PHYSICS. vacuum in the cylinder, against which tlie fresh steam acts with nearly its full force. The gain, however, thus obtained is not so great as it would at first sight seem, since a portion of the power thus realized is expended in working the pumps connected with the condenser. In order to produce a sudden condensation of the steam, it is necessary to discharge into the condenser a constant stream of water. This water, forced in by the atmospheric pressure through the pipe T (Fig. 441), which ends in what is termed a rose, is showered in fine jets through the chamber. The amount of water which it is thus necessary to introduce is at least twenty times as great as the weight of steam condensed, and would soon fiU the condenser. Hence the necessity of the pump M, worked from the beam of the engine, by which both the hot water and any air that may be mixed with it are rapidly removed, and the water discharged into the hot toell N. The piston of this pump, called the air-pump, has generally about one half of the area and one half of the stroke of the large piston, and the general ar- rangement of its valves may be seen in Pig. 443. The condenser is usually entirely immersed in a tank of water, called the cold well, which is fed, when possible, by an aqueduct, or otherwise by a suction-pump, as R, Fig. 441, worked by a rod attached to the beam of the engine, and drawing its water from some neighboring well. Still a third pump is frequently attached to the beam, which draws water from the hot well and forces it into the boiler. The supply of water to the condenser is regulated by a valve so placed as to be at the command of the engineer, and before stopping the machine it is necessary to close this valve. The machine which has just been described may be regarded as a representative steam-engine. The student must not expect to find the parts of an actual working engine as simple, or com- bined in the same way, as those represented in Fig. 441 ; but having once become familiar with the parts, as they are shown in this figure, he will be able readily to recognize them in a work- ing engine, and to trace out the connection of their motions. (308.) Siri^le-acting Steam-Engine. — W\xQni\iQs,tQ2im-QzigmQ is used for pumping water, which was at first its only practical application, its force is required only in raising the pump-rods with their load of water, their own weight being more than HEAT. 627 sufficient for their descent. If tlie piston and pump rods are attached to opposite ends of a working-beam, the force of the steam is only required in pressing the piston down ; and there is, Fig. 443. therefore, no necessity of admitting the steam to tlie bottom of the cylinder. Engines constructed for this purpose, in which the steam acts only on one side of the piston, are called single-acting engines, to distinguish them from the double-acting engines de- scribed in the last section. They are generally used for pumping water from mines, and are frequently called Cornish engines, because they were brought to perfection in the mining district of Cornwall, in England. A representation of one of these engines is given in Fig. 443. The steam from the boiler enters the valve-chest by the tube T. A rod, d, passing through a packing-box in the top of the valve-chest, moves three valves, m, n, o. The valves m and o open upward, while the valve n opens downward. When the valves are in the position represented in the figure, m and o open and n closed, the steam from the boiler exerts its full effect on the upper surface of the piston, and presses it down ; but just 628 CHEMICAL PHYSICS. before the piston reaches the lowest point of its course, a projec- tion, b, on the rod F, moved by the beam, strikes the arm of a bent lever, d c k, •which, acting on the valve rod at d, causes it to descend, thus closing the valves m, o, and opening tlie valve n, called the equilibrium valve. All connection between the cylin- der and either the boiler or condenser is now closed ; but the two ends of the cylinder freely communicating together, the piston is raised by the weight of the pump-rod Q, while the steam passes from the top to the bottom of the cylinder through the tube C. As the piston now reaches the top of the cylinder, a second pro- jection, a, on the rod F, strikes the end of the bent lever and restores the valves to their first position ; then the piston descends as before, and so continuously. Parallel motion is obtained in these engines by the very simple arrangement represented in the figure, and the condenser is the same as that described in the last section. The efficiency of these engines is estimated by the number of pounds of water which they are capable of elevating one foot by the combustion of one bushel of coal. This number is termed the duty of the engine. By a careful construction and management of the engine and boiler, this duty has been raised as higli as 125,000,000 pounds. (309.) The Non-condensing- F^ine. — This form of the steam- engine differs from those just described only in this, that it has no condenser, and the steam is vented from the cylinder directly into the atmosphere. Although, for the reasons already stated, it cannot be worked so economically as the condensing engine, it has tlie advantage of greater simplicity and compactness, and its first cost is much less than that of its more cumbrous rival. It is therefore frequently preferred when these considerations are of more importance than the saving of a few tons of coal. There is nothing peculiar in the construction of this form of engine, and either of the machines just described might be converted into a non-condensing engine by simply cutting off the eduction-tube and disconnecting the pump-rods from the beam. Of this class the most important is the locomotive engine (Fig. 444), and we have selected it as an example. The construction of the boiler of a locomotive has already been described ; and since we are now acquainted with the construction of the single parts of a steam-engine, it will only be necessary to point them out in the figure. HEAT. 629 X X is the main body of the boiler ; B, the lower part of the fire-box ; Y, the smoke-box ; o, the brass tubes connecting the two ; O, the fire-door, by which the fuel is introduced ; n, the water-gauge, indicating the level of the water in the boiler ; H, the vent-cock, by which the water can be discharged from the boiler ; R, R, the feeders which conduct water from the tender to two force-pumps (not shown in the drawing) , by which it is 630 CHEMICAL PHYSICS. forced into the boiler; Z Z, the dome of the boiler; i, the safety- valves, which are held in place by spiral springs enclosed in the cases e ; g, the steam-whistle ; /, the valve opening into the steam-pipe ; G, a rod which controls the motion of the valve. In the drawing, the engineer holds in his hand the lever by which this rod is turned and the valve opened more or less, as cir- cumstances may require ; a graduated arc, over which the lever moves, enables him to adjust the valve to any position, and thus to regulate the speed of the engine. A is the steam-tube, which conducts the steam from the top of the dome to the two cylin- ders ; this tube passes through the boiler into the smoke-box, where it branches, as shown by dotted lines in the figure ; by this arrangement any condensation of the steam, while passing through the pipe, is prevented. F is one of the cylinders ; there is another on the other side of the smoke-box ; the steam is admitted into the ends of these cylinders and discharged from them, by means of sliding valves worked by eccentrics on the axle of the driving-wheels ; there are generally two sets of these ec- centrics placed in opposite positions on the axle, one set for the forward and the other for the backward motion of the locomotive, and so arranged that they can be thrown ovit of gear or brought into action at the pleasure of the engineer. All this part of the machinery, however, being beneath the boiler, is not visible in the drawing. E is the eduction-tube, by which the steam is discharged from the cylinder into the smoke-pipe Q ; t,t are stop- cocks, by which any water condensed in tlie cylinders may be vented ; P is the piston ; F, the packing-box, through which passes the piston-rod ; r r are guides, corresponding to the par- allel motion of the stationary engine, by which the piston-rod is forced to move in a straight line, and any lateral strain pre- vented ; and, finally, K is the connecting-rod, by which the motion of the piston is communicated to the crank M on the axle of the large driving-wheels. In starting the locomotive, as in the other forms of the steam-engine, the valves must be moved by hand ; a lever, communicating with the valves by means of connecting-rods, marked B and C in the figure, is always pro- vided for this purpose near the front of the engine. It is only when the train is in motion, and its momentum sufficient to i-egulate the movements of the machine, that the eccentrics are thrown into gear. HEAT. 631 (310.) Mechanical Power of Steam. — We can easily calcu- late the mechanical power generated by the conversion of water into steam from the known increase of volume * which accompa- nies this change. For this purpose, let us assume that we have a tall cylindrical vessel, open at the top, the area of whose base is one square decimetre. Let us further assume that the cylinder is filled with water at 4° to the depth of one decimetre, and con- tains, therefore, one litre or one kilogramme of the liquid ; and, lastly, let us assume that a piston without weight, and moving steam-tight without friction in the cylinder, rests on the surface of the water. If now we raise the temperature of this cylinder to 100°, and furnish it with a constant supply of heat, the water will change into steam, occupying 1,698.5 times its former vol- ume, and having a tension of 76 c. m., or one atmosphere ; which will therefore raise the piston 1,697.5 decimetres under the atmospheric pressure, that is, will raise 103.33 kilogrammes to the height of 169.75 metres. The mechanical power thus exerted is, then, equal to 17,540 kilogramme-metres (compare 238). If we' raise the temperature to 120°. 6, and furnish a constant supply of heat, as before, the water will change into steam occupying 896.22 times its former volume, and having a tension of two atmospheres. It will, therefore, raise the piston 895.22 decime- tres under the pressure of the air, when loaded with an additional weight of 103.33 kilogrammes, thus exerting a mechanical power of 206.66 X 89.522 = 18,501 kilogramme-metres. In like man- ner, the other values given in the fourth column of the following table may be easily calculated : — Tempera- ture of SteEun. Tension in Atmos- pheres. Volume of 1 Kilogramme in Litres. Power in Kilogramme- metres. Total Heat absorbed in IlTaporation. Power from 1 Heat Unit in KUog.-metres. ioo!o 1 1,698.5 17,540 637.0 27.53 120.6 2 896.22 18,501 643.3 28.76 144.0 4 474.81 19,583 650.4 SO.ll 170.8 8 252.67 20,804 658.6 31.59 By comparing the conditions assumed above with those in an actual steam-engine, it will be seen that the power given in the * The volume of the steam, as compared with that of an equal weight of water at 4°, can always be obtained by dividing the weight of one cubic metre of water at 4° (one million grammes) by the weight of one cubic metre of steam as given in the table on page 571. 632 CHEMICAL PHYSICS. above table is the greatest possible power which can be obtained by the conversion into steam of one kilogramme of water at the different temperatures ; provided, as we assumed in the descrip- tion of the steam-engine (307), that the tension of the steam does not change from the time it leaves the boiler until it is dis- charged into the condenser, and provided, also, that the steam acts against a perfect vacuum. These conditions are never fully realized in practice, so that even with the best regulated ma- chines we only obtain from one half to two thirds of the theo- retical effect. The total number of units of heat required to change one kilogramme of water into steam of one, two, four, and eight atmospheres' pressure, as calculated by [202], is given in the fifth column of the above table, and the sixth column shows the power obtained in each case by the expenditure of one omit of heat. It will be noticed that the power is nearly the same in all cases, and hence it follows, apparently, that no important gain is obtained by the use of steam of high tension. There is, how- ever, a mode of working the steam-engine in which the gain thus effected is very great. Let us suppose that the boiler is supplying steam of four atmos- pheres, which, as the table shows, it can supply at only a little greater expenditure of heat (in other words, of fuel) than steam of one atmosphere pressure. If the engine were worked with steam of one atmosphere pressure under the conditions described above, each volume of steam eqxiivalent to the capacity of the cylinder, and weighing, as we will suppose, one kilogramme, will do the work of raising 103.33 kilogrammes through a height equal to the length of the stroke of the piston. Speaking ap- proximatively, the same weight of steam of four atmospheres' tension will do an equivalent work during the first quarter of the stroke ; for it will raise four times 103.33 kilogrammes through one fourth of the previous height. Suppose, now, that the con- nection between the cylinder and the boiler is closed at this point, it is evident that the steam will continue to exert an expansive force, although a force lessening gradually as the capacity of the cylinder increases. When- the piston has been raised through one half of the stroke, the volume of the kilogramme of steam will have doubled, and its tension have been reduced to two at- mospheres ; when it has achieved three fourths of the stro'ke, the HEAT. volume will have trebled, and the tension have been reduced to 1^ atmospheres ; and even at the end of the stroke, when the vol- ume has quadrupled, the pressure will still be one atmosphere. Here, then, is a very large gain of power without any additional expenditure of fuel. In practice, these conditions are realized by closing the valve admitting steam into the cylinder after a certain fraction of the stroke, by means of various forms of au- tomatic machinery, called cut-offs. The actual theoretical advan- tage gained in any casecan readily be calculated. It is evidently the greater, the higher the tension of the steam in the boiler and the sooner it is cut off after the beginning of the stroke In no case, however, is the total practical effect as great as the theoret- ical power given in the table on page 631. When thus worked, the engine is said to be worked expansively. We are far from obtaining with the steam-engine the full me- chanical equivalent of heat, even when working under the most favorable circumstances- It will be remembered, that, according to Joule's experiments (238), one unit of heat is capable of gen- erating a power equal to 430 kilogramme-metres, which is 13.6 times greater than 31.59 kilogramme-metres, the greatest pos- sible effect which could be obtained with the steam-engine when not worked expansively, even under a pressure of eight atmos- pheres. Considering, then, that we do not realize, even under the best circumstances, much more than one half of this theoreti- cal effect, it will be seen that we actually obtain with the steam- engine only about one twentieth of the power which the fuel is capable of yielding. To find a more economical means than this of converting heat into mechanical effect, is one of the great prob- lems of the. present age. (311.) Low and High Pressure Engines. — As the tension of the steam used in non-condensing engines (309) is necessarily greater than the pressure of the air, they are frequently called high-pressure engines, while the condensing engines are known as low-pressure engines. These terms, however, do not correctly express their nature, since, although the non-condensing engine must necessarily be worked at a high pressure, yet, as we have just seen, a great advantage is gained by working the condensing engine under a similar pressure ; and, in fact, the so-called low- pressure engines are frequently worked under as great a head of steam as the high-pressure engines. 634 CHEMICAL PHYSICS. PROBLEMS. Heat of Fusion. 352. Three kilogrammes of ice at 0° are mixed with 10 kilogrammes of water at 100°. Eequired the temperature of the mixture after the ice is melted. 353. How much ice at 0° must be added to 200 kilogrammes of water at 1 6° in order to reduce its temperature to 10° ? 354. Solve the same problem, substituting letters for the numbers. 355. How much ice at 0° is required to cool 10 kilogrammes of mer- cury from 100° to 0° ? 356. A mass of tin weighing 55 grammes and heated to 100^ was en- closed in a cavity made in a block of ice. Eequu-ed the amount of ice melted. 357. Eight kilogrammes of ice at 0° were mixed with 35 kilogrammes of water at 59° ; after the ice had melted, the temperature of the water was 33°.3. Required the heat of fusion of ice. 358. In order to determine the heat of fusion of lead, 200 grammes of melted lead at the melting-point were poured into 1,850 grammes of water at 10°. After the lead had cooled, the water was found to have acquired a temperature of 20°.76. Required the heat of fusion of the metal. Tension of Vapors. 359. Before filUng a barometer with mercury, a small quantity of water was poured into the tube. How high wiU the mercury stand in the ba- rometer when the temperature is 20? and the pressure of the air 77 c. m. ? Solve the same problem, assuming that alcohol was used instead of water. 360. Determine the height of the mercury-column in a barometer-tube whose walls are moistened with water at the temperatures and pressures indicated below : — 1. i7= 76.22 cm. t = 20°. 2. ^=75.11 " « = 40°. 3. i/= 74.56 " t = 10°. 4. S'= 77.20 cm. t= 30°. 5. E = 76.54 " t = 60°. 6. H= 78.10 " t = 100°. 361. Solve the last problem, assuming, first, that chloroform, and, sec- ondly, that oil of turpentine, were used instead of water. i862. Calculate by [199] the tension of the vapor of water at the following temperatures : — 10°.24, 15°.45, 40°.25, 60°.58, 150°.5, and 220°.85. 363. Determine the tension of the vapors of alcohol, of ether, and of chloroform at the following temperatures, assuming that the principle of page 582 is correct: 20°.12, 15°.64, 10°.22, and 5°.12. 364. Determine the boiling-point of water under the following pres- sures : 74.24 c. m., 55.54 c. m., 34.20 c. m., 10.50 c. m., and 5 c. m. HEAT. 635 365. Determine the boiling-points of alcohol, ether, and oil of turpen- tine under the same pressures. 366. A cylindrical vessel at the temperature of 120°.6 is filled with vapor of water having a tension of 100 c. m. What will be the tension of the vapor if its volume is reduced to one half by pushing down the piston ? What wiU be the tension of the vapor if its volume is doubled ? 367. A gleiss vessel is fiUed with dry steam which at the temperature of 100° has a tension of 54.22 c. m. To what temperature must the ves- sel be cooled before the steam begins to condense ? What wUl be the ten- sion of the steam, if the vessel is heated to 200° ? 368. In a strong iron vessel, whose capacity equals 5,000 c. m.', 15.24 grammes of water are hermetically sealed. Required the tension of the vapor in the interior of the vessel at the following temperatures : 50°, 100°, 160°, 180°, and 250°. Latent Heat of Vapors. 369. How much free steam must be condensed in order to raise the temperature of 20 kilogrammes of water from 0° to 90° ? How much to raise the temperature of 246 kilogrammes of water from 13° to 28°? 370. How much vapor of alcohol must be condensed in order to raise the temperature of 5 kilogrammes of aldohol from 15° to 30° ? 371. Twenty-five kilogrammes of free steam condensed in a mass of water raised its temperature from 4° to 61°.4. Required the volume of the water before and after the condensation. 372. How many kilogrammes of ice at 0° would be required to con- dense 25 kilogrammes of free steam, and reduce the temperature of the water formed to 0°. 373. Calculate the latent heat of steam at the following temperatures : 25°, 32°, 112°, 175°, 198°, and 222°. 374. Calculate how much heat is required to convert one litre of water at 15° into steam at its maximum tension at 130°- 375. How much heat would be evolved by the condensation of one cubic metre of steam of 140° at its maximum tension into water at 20° ? Steam-Engine. 376. How much mechanical force is generated by the conversion of 25 kilogrammes of water at 0° into steam at 140°, and how much heat is required for the conversion ? 377. The piston of a steam-engine has a diameter of 44 c. m., and it moves 1.15 m. each second. Required the weight which the machine can raise to the height of 8 metres in one second, assuming that there is no resistance, and that the tension of the steam is 2.75 atmospheres. Deter- mine also, the quantity of heat required to furnish the steam employed in producing this effect. 636 CHEMICAL PHYSICS. HTGROMETET. (312.) Formation of Vapor in an Atmosphere of Gas. — If we repeat the experiment with the vessel of one cubic metre ca- pacity described in (284), with only this change, that it is left filled with air, we shall find that the same amount of aqueous vapor will be formed as in a perfect vacuum. For each tem- perature there will be found to exist simultaneously in the cubic metre, first, an atmosphere of air ; secondly, an atmosphere of aqueous vapor, having the weight and tension which are given in the table on page 571. The only difierence between the cir- cumstances attending the formation of vapor in air or any other gas, and in a vacuum, is in the time required. The cubic vessel, when freed from air, would be almost instantaneously filled with vapor of the given tension and weight ; but in the same vessel filled with air, the vapor woiild attain its maximum tension and density only after several minutes. The tension of the mixture of aqueous vapor and air is always equal to the sum of the tensions which each would have if it filled the vessel separately. This tension can then be found for any temperature by adding to the tension of the air, as indicated by a barometer, the tension of aqueous vapor taken from the table of maximum tensions opposite to the given temperature. Thus, if the temperature were 20°, and the barometer indicated a tension of 76 c. m., the tension of the mixture of air and vapor would be equal to 76 -j- 1.739 = 77.789, and a barometer immersed in the vessel would stand at that height. If now we suppose the vessel to be extensible, and exposed on the outside to an invariable pressure of 76 c. m., it is evident that it will be expanded until the tension of the confined mixture is reduced to the same value ; and it is frequently a problem of great practical importance to determine what tlie increased volume will be. In the first place, it is evident that, as the vol- ume of the vessel increases, more water will evaporate, so as to keep the vapor at the maximum tension for the temperature. Hence, in the expanded state, the tension of the vapor will still be 1.789 c. m. It is, therefore, only the air wliich expands, and as the tension of the mixture in its expanded state is equal by assumption to 76 c. m., it is evident that the tension of the air will be equal to 76 — 1.739 = 74.261 c. m. Moreover, since the HEAT. 637 volume of the air (which is, of course, also the volume of the mixture) must be inversely as its tension in the two conditions, we have, by [200] , 1 : F' = 74.261 : 76, .whence V = 1.023 ^:^.» This solution may easily be made general. Let H^ represent the invariable pressure to which the gas is exposed, aiid ^„ the tension of water vapor at the given temperati^re. Then, in the expanded state, the tension of the air is Hg — i|„. We have, by substituting these values in [200], F: F' = izi — f „ : Ho; whence (1.) V'=r w^, and (2.) F= F ^l^. [203.] By means of (1) we can always calculate the increased volume, F', of a gas when saturated with moisture, if the volume of the dry gas is known ; and by means of (2) we can calculate from the measured volume of the moist gas the volume, F, which it would have measured had the gas been perfectly dry. The last problem is one of great importance, and generally presents itself in a form like that of the following exam^ple. A volume of gas confined in a bell-glass over water measures 250 cm." when the temperature is 20° and the barometer 76 c. m. What would be the volume if the gas were perfectly dry ? By substituting the data given in (203. 2) we obtain, F= 250 ''^1^ :^ 244.25 ^^.». [204. J The formula just employed gives in any case the volume of dry gas for the temperature and pressure at which the volume of the moist gas was observed; only it is necessary to remember, in using the formula, that Ho represents the pressure to which the mixture of gas and vapor was exposed at the time the volume was measured. This can always be ascertained by the method described in (169). When the volume pf dry gas has been in this way determined for any given temperature and pressure, it can easily be reduced to 0° and 76 c. m. by means of [98] and [184]. What has been illustrated above in the case of the vapor of 54 638 CHEMICAL PHYSICS. water, is also true of the vapors of other liquids. The same quan- tity of liquid will evaporate into a cubic metre, and a vapor will be formed of the same tension and density, whether the space be empty or filled with gas ; the only difference being that the liquid will evaporate very much more slowly in the last case than in the first. What is true of one liquid must also be true of any num- ber of liquids ; provided only that these do not act chemically on each other, each of them will evaporate and form a vapor of the same tension and density as if the space were a perfect vacuum. At least this is true theoretically, and it would probably be true practically could we enclose the vapor within walls formed by the volatile liquids tliemselves. But in the glass vessels with which we are obliged to experiment, the result, as above stated, is not perfectly realized. This is apparently owing to an adhesive action of the glass, by which the tension of the vapor is reduced below the maximum tension for the temperature. This subject has been carefully examined by Regnault, and we would refer to his memoir* for further details. The principles of this section may be summed up in the two following propositions, first enunciated by Dalton, and therefore known as the Law of Dalton. The last proposition, however, is only a necessary consequence of the first. 1. The tension and the amount of the vapor which will satu- rate a given space at a given temperature are the same, whether the space be completely empty or filled with gas. 2. The elastic force of a mixture of gas and vapor is equal to the sum of the tensions which each would have separately. This law may be illustrated by means of the apparatus repre- sented in Fig. 445. It consists of a glass tube. A, closed at both ends by the iron stopcocks b and d. The lower stopcock is pro- vided with a side tubulature, into which the tube B is cemented, and a graduated scale placed between the tubes serves to meas- ure the relative heights of the columns of mercury they con- tain. In using this apparatus, the tube A is, in the first place, about half filled with dry air, or any other gas from the globe M, which can be screwed on to the stopcock b in place of the tunnel C. The tunnel C is provided with a stopcock of a peculiar construction. The plug of the cock, represented at n, is not * Comptes Eendus, Tom. XXXIX. p. 345. HEAT. 639 pierced, as usual, completely through, but has simply a small cavity on one side. Having now adjusted the quantity of mer- cury in the apparatus so that it shall stand at the same height in both tubes, and having poured a quantity of liquid into the tunnel, we open the cock b and turn the plug of the cock a so that the liquid may be introduced drop by drop into the tube A. The confined gas becomes thus saturated with vapor, and, expanding, depress- es the mercury-column. We then restore the original volume by pour- ing mercury into the tube B. The tension of the mixture of gas and vapor is now evidently equal to the pressure of the air plus the pressure of the mercury-column B o, thus prov- ing that the tension of the confined gas has been increased by the tension of the vapor. By referring to the tables, it will be found that the in- crease of tension is exactly equal to the maximum tension, of the same vapor in a vacuum, when exposed to the same temperature. (313.) Hygrometers. — Every cubic metre of the atmosphere in immediate contact with the earth is, in all respects, similarly situated towards the ponds and rivers of the globe as is the air of the cubic vessel towards the water it contains. Every cubic metre of the atmosphere is capable of holding, for any tempera- ture, the same amount of aqueous vapor, and vapor of the same tension, as the vessel ; moreover, water will continue to evaporate into the atmosphere until the vapor has acquired the tension and specific gravity which correspond to the temperature. There are, therefore, around the globe, as in the cubic vessel, two at- mospheres, one of air and the other of vapor. When the air has taken up all the vapor which it is capable of holding at the temperature, it is said to be saturated or moist ; when less, it is said to be dry. In the last case, it is capable of absorbino- Kg. 445. 640 CHEMICAL PHYSICS. more water, and of course dries up the moisture from sub- stances with which it may be in contact. Thus, if the temper- ature is 20°, the air is saturated with vapor when it con- tains in every cubic metre 17.157 grammes (see table on page 571) ; if it contained only 12.746 grammes it would be dry, since then every cubic metre of air could absorb 4.411 grammes more. But if the temperature falls to 15°, then by the table 12.746 grammes will completely saturate each cubic metre ; so that a cubic metre of air containing 12.746 grammes of vapor is saturated when the temperature is 15°, although dry when it is 20°. The moisture of the atmosphere at any temperature depends, then, not simply on the amount of vapor which it contains, but on the proportion which this amount bears to the whole quantity whicli it could possibly contain at the given temperature. Tlie fraction which is obtained by dividing the actual weight of vapor in a cubic metre of the atmosphere by the weight which it would contain were it completely saturated with aqueous vapor, is called the relative humidity. It follows from Mariotte's law, that the weights of two masses of vapor occupying equal volumes are to each other as their tensions, W: W'^ ^^ : ^'^-j hence the rela- tive humidity may also be obtained by dividing the tension of the vapor actually contained in the air by the tension the vapor would have if the atmosphere were saturated, tliat is, by the maximum tension for the temperature, as given in Table X. In order to iind, then, the relative humidity of the atmosphere at any given time, we in the first place observe its temperature ; and in the second place, we ascertain by experiment the tension of the vapor which it actually contains. The tension is found in the following manner. If we cool down a cubic metre of the atmosphere, we shall come, sooner or later, to a temperature at which the tension of the vapor is at its maximum. Thus, for example, if the temper- ature of the atmosphere is 20°, and the tension of the vapor it contains, and which we wish to find, is 1.2699 c. m., we shall, by cooling one cubic metre to 15°, reach a temperature at which 1.2699 c, m. is the maximum tension, and consequently a tem- perature at which the air will be saturated by the vapor contained in it. If now we cool it below this point, a portion of the vapor will be deposited in the form of mist or dew. The temperature HEAT. 641 then, at which dew would be deposited, were the atmosphere cooled down, is the temperature at which the tension of the vapor contained in it would be at its maximum. This temperature is technically termed the dew-point. It can easily be observed in the following way. Take a brightly polished silver cup and fill it with water. Place in it a sensitive thermometer, which will indicate promptly any changes of temperature, and then add ice in small pieces, waiting until one piece is melted before add- mg another, and constantly stirring the water with the thermom- eter in order to render the temperature uniform throughout the mass. The silver cup, as it is thus slowly cooled, will cool in its turn the thin layer of air which immediately surrounds it, and sooner or later this air will be reduced to the temperature at which the vapor it contains completely saturates it. At that mo- ment the polished surface of the cup will be dimmed by a depo- sition of dew. Note carefully the temperature at which this first takes place ; and then allow the cup to warm, and note carefully the temperature at which the dimness disappears. The two tem- peratures should very nearly correspond, and the mean may be taken as the dew-point. Having found the dew-point, we can easily ascertain the relative humidity of. the air by means of the table of tensions. Opposite to the dew-point we find the actual tension of the vapor in the atmosphere. Opposite to the temperature of the air at the time of the experiment, we find the maximum tension which the vapor could attain ; and since, as we have seen, the weight of vapor is proportional to the tension, we can obtain at once the relative humidity by dividing the first by the last. To illustrate this by an example : — The temperature of the air is 20°. The dew-point, found as just described, is 15°. What is the relative humidity? The maximum tension of vapor at the dew-point is 12.699 m.m., and this is the actual tension of the vapor in the atmosphere. The maximum tension of vapor at 20° is 17.391 m. m., and this is the tension which the vapor would have were the atmosphere satu- rated. ^ = .73 is, then, the relative humidity. The air mosphere, therefore, contains 78 per cent of the whole amount it could possibly contain at 20°. From the relative humidity, it is easy to calculate the amount of vapor contained in a cubic metre. By referring to the table, we ascertain the total amount which the cubic ipetre could contain at the given temperature ; 54* 642 CHEMICAL PHYSICS. and by multiplying this by the fraction expressing the relative humidity, we ascertain the amount which it actually contains. Thus, in the example just given, the total amount of vapor which one cubic metre of air at 20° can contain is 17.145 grammes. It actually contains only 73 per cent of this amount, that is, 17.145 X .73 = 12.515 grammes. It appears, then, that the determination of the amount of vapor in the atmosphere resolves itself practically into the observation Fig. 446. of the dew-point. This can be observed with sufficient acciiracy, for most purposes, with a thin silver cup and thermometer, as described above ; but where greater accuracy is required, the ob- servations can be made more rapidly, as well as with greater cer- tainty, with the hygrometer of Regnault, which is represented in Fig. 446. It consists of two silver thimbles 4.5 c. m. high and 20 m. m. in diameter, made very thin, and brightly polished on the outside. These thimbles are cemented to the bottom of two glass tubes D, E. Each of these contain thermometers gradu- ated to tenths of a degree, kept in place by corks. Through the cork of the tube D passes a small tube. A, open at both ends and extending to the bottom of the silver thimble. The upper HEAT. 643 part of the tube D communicates, through the lateral tubulature and through the stem of the support, with an aspirator, G, by means of which air can be drawn through the apparatus. The tube E, which does not communicate with the aspirator, contains a thermometer for observing the temperature of tlie air. In order to use the apparatus, the tube D is half filled with ether ; then, on opening the stopcock of the aspirator, the water which it contains flows out, and the air required to supply its place flows in at the tube A, bubbling up through the ether. The rapid evaporation caused by this current of air soon cools the temperature of the silver thimble to the dew-point. At the moment a film of moisture appears on the polished surface, the temperature indicated by the thermometer T is carefully noted^ as well also as the temperature of the air given by the thermom- eter t, and we have then the elements for calculating the rela- tive luimidity of the atmosphere. By careful manipulation, the dew-point can be observed with this instrument to one tenth of a Centigrade degree. The second silver thimble, on the tube E, serves not only to protect the bulb of the thermometer, but also, by comparison, enables the observer to detect a slight trace of moisture on the surface of the first, which might otherwise be overlooked. The hygrometer of Daniells, repre- sented in Pig. 447, is based on the same principle as that of Regnault, but is mxich less delicate in its indica- tion. It consists of two bulbs con- nected by a siphon-tube, from which the air has been expelled by hermeti- cally sealing the instrument when filled with ether vapor. The bulb A is about half filled with ether, and contains the bulb of a small thermometer. Moreover, a zone of the bulb is gilt, and burnished so that the deposition of the dew upon it may be easily perceived. The other bulb is covered with muslin. When an ob- servation is to be made, the muslin is moistened with ether, which is dropped very slowly from a bottle. The evaporation of the Fig. m. 644 CHEMICAL PHYSICS. ether from the muslin, by cooling the bulb B and condensing the vapor of ether which it contains, causes a very rapid evaporation from the surface of the liquid in the bulb A. By this means the gilt zone is soon cooled to the dew-point, a deposition of dew indi- cating when the point is reached. The temperature at which the dew is first deposited is carefully observed by means of the en- closed thermometer, and also the temperature at which it disap- pears when the temperature of the bulb A is afterwards allowed to rise. The two observations should not differ much from each other, and their mean is the dew-point. The relative humidity of the air may also be estimated, though with less accuracy, from the rapidity with which water evaporates when exposed to it ; since, as is evident, the drier the air, the more rapid will be the evaporation. The instrument used for this purpose is called a psychrometer, or a wet-bulb hygrometer. It consists of two thermometers, the bulb of one of which is cov- ered with muslin and kept constantly moist, while the bulb of the other is dry. The last indicates the temperature of the air ; but the first always indicates a lower temperature, owing to the latent ' heat absorbed by the evaporation of the water from the surface of the bulb, except when the air is fully saturated with moisture. The difference between the two thermometers will be the greater the more rapid the evaporation, that is, the greater the dryness of the air. Prom the temperatures of the two thermometers we can calculate the tension of the vapor in the atmosphere by means of the empirical formula, 0.429 (x-rQ or a:-fi 0.480 (r-x')^ . in which i5 = maximum tension of vapor at lowest temperature. T = temperature of dry-bulb thermometer, i' = temperature of wet-bulb thermometer. H„ =: height of barometer. 610 — i' = latent heat of the vapor of water (compare 300). X = tension of aqueous vapor at the time of observation. From the value of x the relative humidity can be easily calculated by dividing by the maximum tension, as before described. The above are the formulae of Regnault as modified from the original formula of August. They are in a measure empirical, HEAT. 645 and founded on theoretical considerations, for which we must refer to the original memoir. The last formula, as Eegnault found, gives accurate results when the air is not more than four tenths saturated. Otherwise, the first should he used. For tem- peratures below freezing, which suppose the wet bulb to be cov- ered with a film of ice, the value 610 — t' must be changed to 610 -j- 79 — r' = 689 — t', since the amount of heat required to change ice into vapor is greater by 79 imits (the heat of fusion) than that which would be required to change water into vapor of the same temperature and tension. For the value of ^„, it is generally sufficient to take the mean barometric pressure of the place of observation. In the Meteorological Tables prepared by Professor Arnold Guyot, and published by the Smithsonian Insti- tution, will be found tables by which, from the indications of the psychrometer, the tension of vapor and relative humidity may be ascertained by inspection. As the indications of the psychrometer are discovered by simple inspection, it would entirely supersede all other hygrometers were the formula by which the tension of vapor is deduced from the observed data perfectly trustworthy. They are sufficiently so for the purposes of meteorology, but results obtained with Eegnault's hygrometer are in all cases to be preferred. Still a third class of hygrometers is based upon the fact that many solids swell on imbibing moisture, and contract again on drying. This is the case with most dry organic substances, such as whalebone, wood, parchment, and hair. The hygrometer of Deluc consists of a very thin piece of whalebone, which, in expanding and contract- ing, moves an index ; and a variety of toys, in which a change in the degree of humidity of the air is shown by the motion of a pasteboard figure, are made on the same principle. But the only trustworthy or even approximatively accurate hygrometer of this class is the hair hygrometer of Saussure, as modified by Eegnault. It is rep- resented in Fig. 448, and consists essentially of a human hair, c, previously freed from fat by being soaked in ether, and so fixed in a copper frame that its expansion and contraction will move a needle over a graduated arc. Each Mg. M8. 646 CHEMICAL PHYSICS. instrument is graduated experimentally by placing it in a con- fined space kept in a known state of humidity by the presence of sulphuric acid of different degrees of strength. Unlike the other hygrometers, this instrument gives at once the relative humidity of the air, and its indications are independent of the temperature. Unfortmaately, however, it is liable to variations, and must be adjusted from time to time by means of the solu- tions employed in graduating it. The last, but the most accurate, method of determining the amount of vapor in the air, consists in drawing through a tube containing chloride of calcium, or some other powerful absorb- ent, a measured volume of air, by means of an aspirator. The increased weight of the tube will give at once the weight of vapor contained in the known volume of air. This process is much too complicated, however, to admit of general application ; but it may be used to advantage where great accuracy is required, or in verifying the results of the other more expeditious methods.* (314.) Drying Apparatus. — It is frequently necessary in the practice of chemistry to remove from a solid body the moisture adhering to its surface, or otherwise mechanically united with it. This is, generally, readily accomplished by exposing the solid to dry air, into which the moisture evaporates. If the solid will bear the temperature of 100° without undergoing change, we can use the drying oven already described (294) ; but if not, we effect the same object at the ordinary temperature by placing the solid un- der a bell-glass, over a dislr containing concen- trated sirlphuric acid. In this case the rapid- ity of the evaporation is greatly accelerated by exhausting the air. The arrangement rep- resented in Fig. 449 may be used for this purpose, and also for concentrating solutions of chemical compounds which would be altered Fig. 449. by a high temperature. In drying goods on a large scale in the arts, it is important to keep in mind two facts : first, that the capacity of air for holding moisture increases very rapidly with the temperature; and, secondly, that a very considerable time must elapse before * For a fall account of the methods of hygrometry as revised by Regnault, see his " fendes sur rHygrometrie," Anuales de Chimie et de Physique, 3' Se'rie, Tom. XV. HEAT. 647 the air is saturated, — the longer, the lower the temperature. An advantage is therefore gained by keeping the air in the drying chamber at as high a temperature as is compatible with the cir- cumstances, and preventing it from escaping until it is absolutely saturated -with humidity. In no case, however, can water be evaporated by heated air in a drying stove as economically as in a close boiler. ORIGIN OP HEAT. (315.) Sources of Heat. — The sun's rays are the great source of heat on the surface of the globe. The amount of heat which thus enters the earth's atmosphere from the sun during a year has been estimated by Pouillet to be equal on an average to 231,675 units for every square centimetre of the earth's surface. In order to give an idea of this quantity, Pouillet states that it would be sufficient to melt a layer of ice enveloping the earth 30.89 metres thick. Of this amount, however, the surface of the earth only receives about two thirds, the rest being absorbed by the atmosphere. Besides the heat which it is constantly receiv- ing from the sun, the earth has also a great store of heat within its own mass, called the central heat. It has already been stated, that the spheroidal figure of the earth is probably owing to the fact, that the globe was once a fluid mass ; and we have reason to believe that it is so now, with the exception of a comparatively thin crust on the surface. From observations made in mines and Artesian wells, we find that the temperature of the crust rapidly increases as we descend from the surface of the earth. The rate of increase varies in different places, but may be stated, on an average, to be about one degree for every 80 or 40 metres. At this rate of increase, assumed to be the same at all depths, the temperature of the crust at the depth of about 2,700 metres must be that of boiling water, and at a depth of 35 kilometres that of melting iron, while at 70 kilometres all known mineral substances would be in complete fusion. It is probable, there- fore, that the thickness of the crust of the earth is not greater than T-iw of its radius, and might be represented by a sheet of pasteboard on a large artificial globe. Nevertheless,' the conduct- ing power of the crust is so slight, that the effect of the central heat is hardly felt on the surface ; and Fourier has' calculated 648 CHEMICAL PHYSICS. that it does not elevate the mean temperature of the surface ipore than ^^ of a degree. Besides these constant sources of heat, there are many others wliich are more or less accidental and intermittent. In general, any motion of the molecules of a body, whether it accompanies a chemical or a physical change, is attended either by an evolu- tion or by an absorption of heat ; but in almost* every case the heat thus evolved may be traced back, either directly or indi- rectly, to the sun. The accidental sources of heat may be di- vided into two classes, the physical and the chemical. (316.) Physical Sources. — Of the physical sources of heat, the most important is friction. Count Rumford succeeded in boiling water by the friction from boring a cannon, and an appa- ratus has been invented in Prance for generating steam by means of heat produced in a similar way. It has already been shown (238) that there is an exact equivalence between the heat gener- ated by friction and the mechanical power used in producing it ; and it is possible that, whore motive power is abundant and fuel expensive, such a machine might be used to advantage. Another physical source of heat is percussion, as is illustrated by the common flint-lock, and by a number of familiar facts. For example, a small bar of iron may be heated to redness on an anvil by blows of the hammer actively applied, and a bar of lead may even be melted in this way. In like manner all metals, when rolled out into plates, drawn into wire, or submitted to any other mechanical process by which the relative position of their molecules is changed, liccome more or less heated. The heat evolved in all these cases appears to be due to an internal friction between the particles of the solid, so that this source of heat does not differ essentially from the last. A third source of heat is mechanical condensation. If we diminish the volume of a body by mechanical means, its tempera- ture is at once raised, and an amovmt of heat is evolved which is probably in all cases equal to that which would be required to ex- pand the body Ijy an equivalent amount (compare 237). Since both solids and liquids are but slightly compressible, we cannot produce with them any very marked calorific effects by condensa- tion. It is different with gases. They are very compressible, and their temperature can be greatly raised by sudden condensation. This is illustrated by i\\Q fire-syringe (Fig. 450). It consists of a HEAT. 649 cylinder of glass, and of a piston, which closes it hermetically and by which the air it contains may be condensed. On pushing in the piston with a quick and forcible motion, the heat evolved by the condensar tion of the air raises the temperature suffi- ciently to inflame a piece of tinder, which is placed in a cavity provided for the pur- pose on the under side of the piston. This requires a temperature of at least 300°. A bright light is noticed in the cylinder at the moment of the maximum condensa- tion, caused by the burning of a portion of the oil with which the piston is lubri- cated. The only other mechanical sources of heat usually enumerated in this connec- tion are the absorption of gases or liquids by porous solids, the change of the state of aggregation of a substance, and elec- tricity. The first of these is probably identical with the one last considered, the heat in every case originating from condensation caused by the adhesion of the liquid or gas to the surface of the solid ; the second has already (277 and 299) been studied at length, and the last will be considered in another portion of the work. (317.) Chemical Sources. — All chemical combination is at- tended with the evolution of heat ; indeed, this is the chief source of artificial heat on the surface of the globe. When the combinar tion takes place slowly, as when iron rusts in the air, the heat is dissipated as fast as it is evalved, and does not elevate sensibly the temperature of the combining substances ; but when the combination is rapid, the heat accumulates in the bodies, and pro- duces the phenomena of combustion. Combustion is, therefore, simply a process of chemical combination, in which heat is evolved so much more rapidly than it is conveyed away through the usual channels, that the temperature of the substances is retained above the point of ignition. All combustion with which we are generally familiar consists in the chemical combination of the burning sub- stance with the oxygen of the air ; but we may have phenomena 55 Fig. 450. 650 CHEMICAL PHYSICS. of intense ignition witliout oxygen, as when antimony is dropped in powder into a jar of chlorine, or when phosphorus is mixed with iodine. The quantity of heat evolved during chemical com- bination varies very greatly with the nature of the substances employed ; but it is always constant for the same substances, and is exactly proportional to the weight of each which is used in forming the compound. Thus, for example, from one kilogramme of the following substances there is always evolved the amount of heat indicated in the following table when they combine with oxygen, or, in other words, when they burn. TJnita of Heat. UnitaofHeat Hydrogen, . 34,462 Oil of Turpentine, . 10,662 Marsh Gas, 13,063 Ether, 9,027 Olefiant Gas, . . 11,858 Alcohol, . 7,184 Beeswax, . 10,496 Wood Charcoal, . 8,080 Spermaceti, . . 10,342 Gas Coke, . 8,047 Stearic Acid, . 9,716 Native Sulphur, . 2,261 It has, moreover, been proved that the amount of heat evolved during chemical combination is precisely the same whether the union be rapid or slow, and also whether the compound be formed at once by direct combination or by several successive processes. But all these subjects can be discussed to much greater advan- tage after the student is familiar with the laws of chemical com- bination ; we shall, therefore, defer the further consideration of them until then. The same is true, also, of the heat evolved by the processes of animal life ; for this is probably due to a slow combustion which takes place in the animal body under the influ- ence of vitality. PROPAGATION OP HEAT. (318.) Heat may be transmitted from one body to another througli space, as it is transmitted from the sun to the earth, or it may be communicated from particle to particle by direct con- tact, as when a bar of iron is heated by placing one end in contact with ignited coals. The first of these methods is called radiation, the second conduction. It is probable, however, that conduction is only a form of radiation, the heat being, in all cases, radiated from particle to particle through the intervening spaces, which may be exceedingly large as compared with the size of the par- ticles themselves (75). HEAT. 651 (319.) Radiation. — When we stand in the bright sunshine or before a blazing fire, and feel the effect of the rays of heat impinging on our bodies, we are led to perceive that heat is emit- ted from the surfaces of hot bodies, and that it has the power of traversing space and transparent media like the atmosphere. But it is also probable that rays of heat are emitted from the surfaces of all bodies and at all temperatures, however low, the only difference between hot and cold bodies being that the first radiate more heat than the last. In a room where there is a condition of thermal equilibrium, each object receives as much heat as it radiates, and therefore retains its own temperature. If one object, however, becomes warmer than the rest, — the stove, for example, — then it radiates more heat than it receives, until the equilibrium is again established. This theory explains the appar- ent radiation of cold, which we feel when standing before a large mass of ice. It is not that the ice radiates cold, since it actually radiates heat ; but as the body receives from the ice less heat than it radiates towards it, we feel a sensation of cold. The phenomena of radiant heat are in all respects similar to those of light, and, as is well known, the rays of both agents are found mixed together in the sunbeam and in the emanations from most luminous objects. Like light, radiant heat is transmitted with an incredible velocity in straight lines, and its intensity diminishes as the square of the distance from the source. If the rays of heat fall on a polished surface they are reflected, and the angle of reflection is always equal to the angle of incidence. If they enter a transparent medium they are refracted, and for the same substance the sine of the angle of refraction always bears a constant ratio to the sine of the angle of incidence. If they are passed through a prism of rock salt, they are divided into rays of different refrangibility, which stand to each other in the same relar tion as the different colors of the solar spectrum ; and, lastly, when reflected or refracted at a certain angle by different substances,, the heat rays become polarized and present properties similar to those of polarized light. But yet, although the thermal rays thus closely resemble the rays of light, there are essential differences between the two. It does not follow, because a medium transmits light unchanged, that it will transmit heat with equal readmess ; thus, for example, a crystal of alum, even if perfectly transpar- ent to light, is almost opaque to heat ; and, on the other hand, 652 CHEMICAL PHYSICS. a crystal of smoky quartz, which will hardly transmit a ray of light, is quite transparent to heat. Most solid and liquid media which are transparent and colorless as regards light, act on the rays "of heat in the same way that colored glasses act on light ; transmitting rays of certain degrees of refrangibility, but not others. Thus, for example, a pane of colorless glass will trans- mit nearly all the rays of heat from the sun, while it will inter- cept the greater part of those from a coal fire, and absolutely aU the rays which radiate from a steam-pipe heated to 100° ; and the same is true to a still greater degree of water. The only sub- stance which is perfectly transparent to rays of heat from every source is rock-salt, and this can be used in "experiments on heat In the same way that glass is used in optical experiments. The phenomena of radiant heat are best explained by the undulatory theory, which assumes that they are caused by undulations in an imponderable mediiim filling all space ; and they cannot be prof- itably studied until the student is acquainted with the mechanical theory of light. We shall, therefore, notice in this connection only a few familiar facts connected with the subject. The unequal power which different bodies possess of radiating heat appears to depend on the condition of the surface, and not on the nature of the substance of which the body consists. As a general rule, the greater the density of the substance at the sur- face, the less is the radiating power of the body. Thus, the bur- nished surfaces of the metals are the poorest radiators, while -the surfaces of paper and similar loose materials are the best. The very best radiator of all is a surface covered with lampblack. If we represent the radiating power of such a surface by 100, that of a silver surface, hammered and well burnished, will be only 3. Those surfaces which radiate heat the best also absorb it the most readily, and it has been proved that the absorbing power of a sur- face is equal to the radiating power, if the difference between the temperature of the radiating and absorbing surfaces is not great. On the other hand, the power which a surface possesses of reflect- ing heat is always in the inverse ratio of its power of absorption ; that is, the best absorbents are the poorest reflectors, and the reverse. Hence heat is best reflected by surfaces of metals which have been hammered and polished ; but so entirely does the power of reflecting or absorbing heat reside in the surface, that a sheet of gilt paper answers the purpose of a reflector nearly as HEAT. 653 well as a mass of solid gold. The power which a surface has of absorbing heat varies with the nature of the source from which it emanates, while its radiating power remains constant ; the two are equal only under the condition above stated. Hence it is not sin- gular that, while the radiating power of any surface is unaffected by its color, the readiness with which bodies absorb the heat of the sun depends, in great measure at least, if not entirely, upon it. This last fact was noticed by Dr. Franklin. He placed pieces of the same kind of cloth, but of different colors, on the snow, where they were equally exposed to the direct rays of the sun. The black cloth absorbed the most heat and sunk deepest into the snow, while the white cloth produced but little effect. The other colored cloths produced intermediate effects ; and they may be arranged according to their absorbing powers as follows : black, violet, indigo, blue, green, red, yellow, white. Numerous illustrations of the above principles may be found in the familiar facts of every-day life. Water can be heated most rapidly in a dull iron kettle, whose bottom is covered with soot, while it can be kept hot longest in a bright silver teapot. The hot air from a furnace is best conveyed to the different apartments of a building in tinned iron pipes, which are poor radiators, while the smoke-pipe of a stove is best made of rough sheet-iron, for the opposite reason. The melting of a bank of snow is accel- erated by sprinkling over its surface coal-dust, because its very feeble power of absorption is in that way greatly increased. Light-colored garments are preferable in summer, because they do not readily absorb the solar rays ; in winter, when the object is to retain the heat in the body and prevent ridiation, the color is unimportant. The phenomenon of dew, first correctly explained by Dr. Wells, is another beautifal illustration of the principles of radiation. The earth is constantly radiating heat into space. During the daytime this loss is compensated by the constant supply of heat from the sun ; but as soon as the sun sets, the supply ceases, while the radiation still continues. Consequently, the tempera- ture of all objects on the surface exposed to the clear sky is rap- idly reduced; if. their temperature falls below the dew-point (313) of the atmosphere, dew is deposited upon them as on a glass of iced water, or, if the temperature falls below the freezing-point, the dew takes the form of hoar-frost. On cloudy nights, little or no 65* 654 CHEMICAL PHYSICS. dew is deposited, because the clouds reflect back the rays of heat to the earth. The same effect is produced by the glass sashes or straw mattings which are used by gardeners to protect young plants from the late frosts of spring. The direct rays of the sun readily pass through the glass during the daytime, but tlie glass reflects back the heat of less intensity which is radiated from the earth during the night. On windy nights, also, little or no dew is deposited, because the layer of air in contact with the radiating crust of the earth is so frequently renewed that its temperature does not fall to the dew-point ; and for the same reason dew is more copiously deposited in a valley or a sequestered dell than on the top of a hill ; and it is in such places, also, that the early frosts of autumn are first felt. As we should naturally expect, we find that in any given place the dew is deposited most copiously on the best radiators, which are, at the same time, the poorest conductors ; thus, while dew is deposited in abun- dance on the shrubs and the grass, which derive most benefit from the moisture, it is not wasted on the dry path and road, whose hard, beaten surfaces render them poorer radiators, while at the same time their higher conducting power enables them to withdraw heat from the strata below, and thus in part make good the loss which the radiation may have caused. " In India, near the town of Hooghly, about forty miles from Calcutta, the principle of radiation is applied to the artificial production of ice. Flat, shallow excavations, from one to two feet deep, are loosely lined with rice straw or some similar bad conductor of heat, and upon the surface of this layer are placed shallow pans of porous earthen-ware, filled with water to the depth of one or two inches. Radiation rapidly reduces the tem- perature below the freezing-point, and thin crusts of ice form, which are removed as they are produced, and stowed away in suitable ice-houses until night, when the ice is conveyed in boats to Calcutta. Winter is the ice-making season, viz. from the end of November to the middle of February." * (320.) Conduction. — That dense and compact solids like the metals are good conductors of heat, while light and porous solids like wood and the various textile fabrics are poor conductors, is a matter of common experience. The general fact may be * Miller's Elements of Chemistiy, Part I. p. 201. HEAT. 655 illustrated by means of the apparatus of Ingenhousz, represented in Fig. 451. The different rods attached to the front of the brass box, made of various ma- terials, are covered with a thin layer of wax ; and on turning boiling water into the box, the wax melts on the rods, after a certain time, to unequal distances, depending on their relative conducting power. If we heat one end of a metallic rod with a lamp, as repre- sented in Fig. 452, the temperature of the different parts of the rod will gradually increase, until a point is reached at which the heat lost by radiation is equal to the heat received from the flame by conduction through the bar. If now we test the temperature Jig. 451. Jig. 452. of the different parts of the bar by means of thermometers placed at equal intervals, say of one decimetre each, it will be found that it very rapidly decreases as we go from the source of heat ; and if the distances from the source of heat increase in an arith- metical progression, the excess of the temperatures of the suc- cessive sections of the bar above the temperature of the air will be found to diminish in a geometrical progression. Moreover, it is evident that the rate of decrease will be more rapid in propor- tion as the conducting power of the bar is more feeble ; and we can determine the relative conducting powers of two bars by measuring the distances from the source of heat of the sections which have the same temperature, for it can easily be proved 656 CHEMICAL PHYSICS. 100 Steel, . 11.6 73.6 Lead, . 8.5 53.2 Platinum, . 8.4 14.5 Eose's Metal, 2.8 11.9 Bismuth, . . 1.8 that the conducting powers are to each other as the squares of these distances. Experimenting in this way, and using a delicate thermo-electric pile for measuring the temperatures of the dif- ferent sections of the bars, Messrs. Wiedmann and Franz de- termined the relative conducting powers of various metals, as follows : — Silver, Copper, Gold, Tin, . Iron, The conducting power of stones, brick, and other earthy materials, is very much less than that of the metals, and the conducting power of wood and other organic tissues is so very feeble that they are usually regarded as non-conductors. It may be assumed as a rule, although it has many exceptions, that the denser a body the better it conducts heat. Homogeneous solids and crystals belonging to the regular sys- tem conduct heat equally in all directions ; but in crystals not belonging to the regular system, the conduct- ing power varies in the direction of unequal axes. This fact is easily shown by a simple experiment devised by Senarmont. He took two slices of a quartz crystal (Fig. 453), one cut perpendicxilar to the vertical axis, and the other parallel to it ; through the centre of each plate he drilled a small conical aperture for the reception of a silver wire, one end of which, heated in the flame of a lamp, served as a central source of heat. Previously to the application of the heat, he had covered the slices of the crystal with beeswax. He found that on the first the wax melted in the form of a circle round the wire, showing that quartz conducts heat equally in the direction of its equal and lateral axes ; but on the second the wax melted in the form of an el- lipse, whose longer diameter coincided with the vertical axis of the crystal, which proved that the conducting power is greater rig. 453. HEAT. 657 in this direction than in the one at right angles to it. Similar facts are also true of organized structures ; thus, wood conducts heat much better in the direction of its fibres than across them. Count Rumford concluded, from his experiments, that liquids were absolutely non-conductors ; but later experiments have shown that they do conduct heat, but only very imperfectly. De- spretz* experimented on a vertical column of water contained in a wooden cylinder one metre high and 21.8 c. m. in diameter, whose upper surface he exposed to a constant source of heat. By means of thermometers passing through tubulatures on the sides of the cylinder, he observed the temperatures of horizontal sections of the liquid at equal distances from each other. At the end of 32 hours the thermometers were stationary, and the dif- ferences between the temperatures indicated by the successive thermometers and the temperature of the air were found to form a decreasing geometrical series, as in a solid bar. This experi- ment proves conclusively that water conducts heat ; but, never- theless, the conducting power is so feeble, that water may be boiled for many minutes at the top of a test-tube without oc- casioning the slightest inconvenience to the person who holds the lower end. Gases are still poorer conductors of heat than liquids ; but yet they are not absolutely non-conductors, and they differ very greatly from each other in this respect. This is proved by the fact that a hot body cools more rapidly in an at- mosphere of hydrogen than in air, and also by a similar fact, first noticed by Grove, that a platinum wire can be made to glow in air with a feebler galvanic current than it can in hydrogen. In order to heat a mass of liquid or gas, we always apply the heat to the lowest portion of the containing vessel ; then, as already explained (268), currents are established by which the particles are brought into actual contact with the source of heat. This process is sometimes distinguished as a third method of communicating heat, and called convection. (321.) Illustrations. — The laws of conduction furnish the ex- planation of many familiar facts, and receive many important applications both in the arts and in every-day life. Our sensa- tions of heat and cold are very much influenced by the conduct- ing power of the substances with which the body comes in contact. * Annaleg de Chimie et de Physique, 3' Serie, Tom. LXXI. 658 CHEMICAL PHYSICS. A hearth, for example, feels colder to the bare feet than a wooden floor, and this, again, colder than a woollen carpet, even when all are at the same temperature. The obvious explanation is, that stone is a better conductor than either wood or wool, and there- fore removes the heat from the body more rapidly. The body, if properly protected by poor conductors, may be exposed with im- punity to air heated to 150°, while it would be burnt by contact with a rod of metal heated to only 50°. The oven-girls of Ger- many, protected by thick woollen garments, enter without incon- venience ovens where all kinds of culinary operations are going on, although the touch of any metallic articles while there would surely burn them. Water in pipes laid at a slight depth under ground is not frozen during the severest winter, because the soil is a poor con- ductor ; and iron safes are rendered fire-proof by making them with double walls, and filling the intervening space with non- conducting materials. Doors of furnaces, ladles, and teapots are provided with wooden handles, to protect the hand from the heated metal ; and hot dishes are placed on woollen or straw mats, which prevent the polished surface of the table from being scorched. So also vessels of glass or porcelain are heated on a sand-bath, and when removed from the fire are always rested on some non-conductor, as they are liable to crack when suddenly heated or cooled. The efficacy of clothing in preventing the escape of the heat of the body depends, not only on the non-conducting power of the material itself, but also on that of the air which is imprisoned by it. Hence it is that wool, fur, and eider-down, which retain large bodies of air within their texture, are so well adapted to protect the body against the extreme cold of winter. The order of the conductibility of the different materials used for clothing is as follows : linen, silk, cotton, wool, furs. Accordingly, cotton sheets feel warmer than linen ones, and blankets warmer than either. In summer, coarse linen goods are used, "because they allow the heat to escape from the body more readily than other materials, while a dress of fine and close woollen is the best pro- tection from the cold of winter except furs. It is in consequence of the non-conducting property of gases, that double doors and windows, which include a layer of air be- tween them, are so useful in preventing the heat of our houses HEAT. 659 from escaping outwards ; and the double walls of ice-houses, refrigerators, or water-coolers, for preventing the heat from en- tering. For the same reason, snow, which encloses large quanti- ties of air, prevents the escape of the heat from the earth, and limits the penetration of frost. It is a well-known fact, that the ground always freezes deeper in winters without snow than when it abounds. But it is unnecessary to multiply these illus- trations further. (322.) Coefficient of Conduction. — The number of miits of heat which pass in one second through a solid wall 1 m. m. thick and having an area of 1 in?,, when the difference between the temperatures of the two faces of the wall is equal to 1°, is called the coefficient of conduction of the substance of which the wall consists. The coefficient of conduction of lead was determined by Peclet by means of a very ingenious apparatus,* and found to be 3.82. Prom this, the coefficients of conduction of other solids can be calculated when their conductibility as compared with lead is known. We give, in the first column of the follow- ing table, the relative conductibility of several solids, as deter- mined by Despretz ; and in the second column, the coefficients of conduction, which have been calculated as just described. The results of Despretz, however, are not probably as accurate as those of Wiedmann and Franz, given above. I. n. I. n. Gold, . . 100.0 21.28 Tin, . 30.39 6.46 Platinum, . 98.1 20.95 Lead, . 17.95 3.82 Silver, . . 97.3 20.71 Marble, . . 2.36 0.48 Copper, 89.8 19.11 Porcelain, . 1.22 0.24 Iron, . . 37.4 7.95 Saked Clay, . . 1.14 0.23 Zinc, 36.3 7.74 When the coefficient of conduction is known, we can easily calculate the amount of heat in units which will pass through a given metallic plate in a given time, by means of the following formula, which for want of space we must assume without proof. C=K . S E [205.] In this formula, K represents the coefficient of conduction, S the * Annales de Chimie et de Physique, 3= S&ie, Tom. II. 660 CHEMICAL PHYSICS. area of the plate, E its thickness, and t, t' the temperatures of its two faces. It is evident that the quantity of heat passing through such a metallic plate in a second of time increases in direct proportion with the conductibility of the metal, with the area of the plate, and with the difference of temperature between its faces ; and it is also evident that the amount of heat dimin- ishes in direct proportion to the thickness. It has already been stated (305), that, in making boilers for evaporating water or other liquids, it is necessary to pay regard to the laws of conduction ; and it is evident from the above for- mula that the greater the conducting power of the metals, the larger the area of the heating surface, and the thinner the boiler- plates, the more rapid will be the evaporation. Hence the advan- tage of copper over iron boilers, and also the reason that water will evaporate so much more rapidly in a silver dish than in one either of glass or porcelain. CHAPTER V. WEIGHING AND MEASURING. (323.) Recapitulation. — Most methods of chemical investigar tion and all processes of quantitative chemical analysis involve the accurate determination of the amounts of small masses of mat- ter, either by measure or by weight. The mass of a body, that is, the quantity of matter which it contains, is necessarily inva- riable ; but its weight and its volume are liable to constant va^ nations, arising from changes either of temperature or of the pressure of the atmosphere, and from other causes. It has been one great object of the present volume to develop the principles on which these variations depend, and to study the laws which they obey. We have thus been led to different methods by which the observed volumes and weights of bodies may be reduced to cer- tain assumed standards, such as a temperature of 0° C. and a pressure of 76 c. m. ; and it will be the object of the remaining chapter of this volume to illustrate these methods by a few examples. SOLIDS. (324.) Weight. — The weight of a solid is easily determined by means of the balance. The theory of this instrument has been already given at length (73), and the methods of using it are so simple and obvious that they need not be described in detail.* Were it not for the presence of the atmosphere, the balance would give at once the exact relative weight (71) of a body ; but weighing the body, as we must, immersed in the air, the difference of the buoyancy which the air exerts on the weights and on the body may make the apparent weight slightly different from the actual weight. We can always, however, re . duce the observed weight to the weight in vacuo by means of * For the best methods of manipulating a delicate balance, and for the precautions required in accurate weighing, the student may consult the standard work of Fresenius on Quantitative Analysis. 56 662 CHEMICAL PHYSICS. [91], when either the volumes or the specific gravities of both the weights and tlie body are known. For this purpose, the heights of the barometer and thermometer are observed at the time of weighing, and from these observed data the weight of one cubic centimetre of air (w), required in making the reduction, is easily calculated by [215], or obtained by inspection from Table XIV. In weighing either solids or liquids, however, the correc- tion for the buoyancy of the atmosphere is at best very small, and may be entirely neglected except in the very few cases where the greatest refinement is required ; as, for example, in adjusting standard weights. For the method to be followed in such cases, the student will do well to consult the admirable memoir of Professor Miller* on the restoration of the English standards. (325.) Specific Gravity. — The specific gravity of a substance has been defined as the ratio of its weight to that of an equal volume of pure water at 4°, the temperature at which the volume of tlie solid is measured being 0°. The general methods by which the specific gravity of solids is determined have been already described (144-146), and we have only to consider the methods by which results obtained at other temperatures may be reduced to the standard temperatures. In order to obtain the specific gravity of a solid, we determine, in the first place, the relative weight ( TF) of the body ; and when very great accuracy is required, the weight observed in the air may be reduced as just described. We next seek, by one of the methods of (145) and (146), the weight of pure water CPT') displaced by the body when the temperature of the water is 4°, and that of the solid 0° ; and, lastly, we calculate the specific gravity by dividing the first weight by the last. Practically, the value of W' is always determined at some temperature, <°, higher than the standard temperatures, and the same for both solid and water ; and, before nsing it in calculating the specific gravity, it is necessary to determine what would be its value assuming that the water was at 4° and the solid at 0°. In Table XVI. we have given the specific gravity of water at different temperatures referred to water at 4° as unity. Representing, then, the specific gravity at t° by 5, and also the weight of water displaced respectively at t° and 4° by W(> and W^o, we shall * Philosophical Transactions, Part III. London, 1856. WEIGHING AND MEASURING. 663 have, evidently, (assuming that the volume of the solid is in- variable,) Wi<. : W,. = 1 : d, or F^o = TT,. i- . [206.] But the volume of the solid is not invariable, and it displaces at 0° (the standard temperature for the solid) less water than at t°. Representing the volumes of the solid at 0° and f by F^ and V,o respectively, we have, by [166] , Vq" = Vf , ^ . Since the two weights of water displaced by the solid when at 0° and f must be proportional to the volumes of the solid at these tempera- tures, (assuming now that the temperature of the water is invaria- bly at 4°,) we shall also have W^o ; PT^ = Ve : _, \r. . Hence, and by [206], TF'. = Tr..l. ^^. [207.] Having thus obtained the weight of water at 4° displaced by the solid at 0°, this value, IFV, is to be used in place of W' in [87]. The last factor of [207] is always very nearly unity, and can in most cases be neglected without appreciable error. When the coefficient of expansion is not accurately known, and great accu- racy is required, the value of K may be eliminated from [207] by making- two determinations of the weight of water displaced at temperatures differing as widely from each other as the cir- cumstances will permit. In very accurate determinations the temperature of the water should be observed to the tenth of a Centigrade degree ; and if the value of 8 is not given in the table for the observed temperature, it can easily be determined by interpolation. Compare (289).* * The most accurate method of determining the specific gravity of a solid is the one with the hydrostatic balance (146), which should always be used when the nature of the substance will admit of it. The body is best suspended from the pan of the balance by a single fibre of silk, or by a very fine human hair, and the temperature of the water observed by means of a very delicate thermometer, adjusted so that the bulb may be nearly in contact with the body, and so that the division may be read by a telescope placed outside of the balance-case. When the solid is in powder, it can be supported under water in a small glass cup suspended to the pan of the balance by a platinum wire. In this case, it is necessary to weigh, first, the cup under water, im- mersed to a point marked on the platinum wire. We then weigh the cup containing 664 CHEMICAL PHYSICS. (326.) Volume. — The Tolume of a solid can rarely be deter- mined with accuracy by direct measurement. It is therefore generally calculated from the weight and the specific gravity by means of the formula [56] . Several examples of such calcula- tions have already been given among the problems. the powder immersed to the same point, taking care that the temperature is the same as before. The difference between these weights is, evidently, the weight of water dis- placed by the solid at the observed temperature, which must be reduced to the standard temperatures by [207]. Lastly, we wash the powder into a tared beaker-glass, evapo- rate the water, and determine the weight of the solid. The only objection to this method of experimenting arises from the fact that the resistance of the water to the motion of the cup renders the balance less sensitive and prompt in its indications. When the solid is in powder, very accurate results can be obtained with a specific- gravity bottle (145). The neck of the bottle should be made with a thick rim, ground square at the top, and the glass stopper should be so fitted as not to have a channel between the two in which water can collect. In order to determine its specific gravity, a known weight, W, of the powder is introduced into the bottle with water, and after the entangled air has been removed by an air-pump, the bottle, is suspended in a large beaker of water whose temperature is very slightly higher than that of the room. This temperature, t, is carefully observed by means of a delicate thermometer, whose bulb is placed near the bottle. After an equilibrium is established, the stopper is inserted into the neck of the bottle while it is still under water. The bottle can then be removed, and, after having been wiped dry, weighed at leisure. This is the weight TFa of [86]. For every specific-gravity bottle, we determine once for all the weight, Wo, of water which it contains at 0°. This is a constant for that bottle, and from it we can easily calculate the weight of the bottle filled with water at t°, or Wi, by the formula, Wi = W' + Wo{l + Ki)3, [208.] in which W is the weight of the glass, K the coefiicient of expansion of glass, and S the specific gravity of water at t°, referred to water at 0° as unity, as given by Table XVI. The weight of the water displaced at t° is now determined by the formula W't<> =Wi + W— W2, which is then reduced to the standard temperature by [207]. The chemist frequently has occasion to determine the specific gravities of solids which are soluble in water. Tor this purpose he selects some inactive liquid, such as alcohol, glycerine, or oil of tvu^jentine, and first finds, by one of the methods just de- scribed, the weight of this liquid displaced by the body, exactly as when using water, the temperature being carefully observed. He then determines the specific gravity of the liquid used at the same temperature as before, and from these data easily calculates the specific gravity of the solid. The student will be able to devise a formula for the purpose. In all delicate determinations of specific gravity it is essential to use several grammes of the substance, since otherwise a very small error in the weighing will cause an im- portant error in the result. It is also essential to remove any air which may be entangled in the interstices or cavities of the solid. This can be done either by boiling the liquid in which the solid is immersed, or by placing the vessel containing the liquid and solid under the receiver of an air-pump and exhausting the air. WEIGHING AND MEASUEING. 666 LIQUIDS. (327.) Weight and Specific Gravity. — The weight of a liquid can be most accurately determined by direct weighing, and the weight of the liquid in the atmosphere may be reduced to the weight in vacuo exactly as in the case of solids ; only the tare of the flask in which the liquid is enclosed must be taken under the same circumstances of temperature and pressure as those under which the liquid is weighed. Such niceties, however, are very rarely necessary. The specific gravity of a liquid determined at an observed temperature, t* by either of the methods described in (145) and (146), can easily be reduced to the standard temperature when the law of expansion of the liquid is known. For this pur- pose, we first calculate the volume of the liquid at f (Fi")? ^^ volume at 0° being unity, by means of the empirical formula expressing the law of expansion (255) ; and since the specific gravity at different temperatures must be inversely as the volume, we have and [209.] iSp.Gr.)v = CSp.Gr.)^ T^=. In most cases with which the chemist meets in practice, however, the law of tepansion is not known. It is then best to determine by direct experiment the specific gravity of the liquid at the stand- ard temperature. An apparatus invented by Regnault (Fig. 454) may be used with advantage for this purpose. It is merely a specific-gravity bottle, so shaped that it can readily be surrounded by melting ice and the volume of the liquid measured with great accuracy. It is, in the first place, filled, like a thermometer- tube, with the liquid to be examined, which is then cooled to 0° by surrounding the apparatus supported on its stand with pulver- * By " specific gravity of a liquid at the temperature t" is meant the weight of the liquid divided by the weight of an equal volume of water, the liquid being measured at (« and the water at 4°. In using a specific-gravity bottle ( 145 ), we have only to determine for each substance the weight, W, of liquid which exactly fills the bottle at t°. Having previously determined, once for all, the weight of water at 4° which the bottle will con- tain at the same temperature, we can easily calculate by fI66] the weight of water at 4° which the bottle would hold at t°. In using the hydrostatic balance, the results may be reduced in a similar way. 56* 666 CHEMICAL PHYSICS. ized ice. After an equilibrium of temperature is established, the excess of the liquid is removed with bibulous paper, until the liquid stands at a point marked on the fine tube which forms the neck of the bottle. The apparatus is now closed with its glass stopper, and it may then be removed from the ice, wiped dry, and weighed at leisure. By subtracting from this weight the tare of the glass and the brass stand, we obtain the weight of liquid which the apparatus holds at 0°, which, di- vided by the weight of water it con- tains at 4° (previously determined), gives the exact specific gravity. (328.) Volume. — The volumes of liquids are generally determined by direct measurement. For this purpose a great variety of grad- uated glasses are used, which are described in detail in most works on Chemical Manipulation or Chemical Analysis.* These instruments for chemical purposes are usually gradii- ated in cubic centimetres, and are only standard at 0°. The process of measurement is, however, seldom so accurate as to make it important to regard the change of volume which the glass undergoes from changes of temperature. The same, how- ever, is not true in regard to the liquid itself ; where great accuracy is required, it is important to observe the temperature at which the measurement is made, and to reduce the observed volume to the standard temperature by means of the empirical formula (255), which expresses the law of expansion of the given liquid. The volume of a liquid can be determined with greater accu- racy by [56] ; that is, by dividing the weight of the liquid by its specific gravity for the temperature at which the volume is re- quired. This method is frequently used, in chemical investiga- tions, for measuring the volume of a glass vessel. For this pur- rig. 454. * A very complete description of this class of instruments will be found in Dr. Mohr's Titrirmethode. WEIGHING AND MEASURING. 667 pose, we determine with a delicate balance the weight of mercury or distilled water which the vessel contains at an observed tem- perature. This weight, divided by the specific gravity of mercury or water for the given temperature, gives the volume of the vessel at that temperature. If the weight is accurate to one centigramme, the volume may thus be measured within. the thou- sandth or the hundredth of a cubic centimetre, according as mercury or water was used in the determination. Knowing now the volume of the vessel at a given temperature, t, and also the coefficient of expansion of glass (245), we can easily calculate by [167] the volume at any other temperature "(241). GASES AND VAPOES. (329.) Weight. — The weights of equal volumes of the best known gases and vapors have been determined with great care by several experimenters, and it is now seldom necessary to repeat the determination. Those of air, oxygen, nitrogen, hydrogen, and carbonic acid were determined by Regnault, and are among the most accurate constants of science. The method which he used will serve to illustrate the general method followed in such cases. Eegnault weighed the gases in a large glass globe, whose volume, V, had been measured in the way just de- scribed. In order to avoid the always uncertain correction made necessary by changes in the buoyancy of the atmosphere during the coutse of the experiments, he equipoised this globe by another globe of the same size and made of the same kind of glass (see Fig. 258) ; so completely did this simple provision effect its object, tliat in one experiment he saw the equi- librium maintained during fourteen days, in spite of great change in the temperature, pressure, and moisture of the air. The ex- periments were conducted in the following way. The globe, having been surrounded with melting ice (Fig. 455), and connected by a lead tube with the manometer 1 1' and also with an air-pump through the branch Fig. 456. tube a m, was first filled with perfectly pure and dry gas. This was 668 CHEMICAL PHYSICS. effected by exhausting it several times, and, after each exhaustion, con- necting it with the vessel in which the gas was generating through a series of U tubes, by which the crude gas was dried and purified. The globe was then exhausted again as perfectly as possible, and the tension of the small amount of gas remaining in it ascertained by measuring the height a /J with a cathetometer. Represent this by h„. This measurement hav- ing been made and the stopcock closed, the globe was disconnected from the manometer, removed from the ice, and, having been carefully cleaned, suspended to one pan of a very strong and dehcate balance, and coun- terpoised by a second globe as above described. The globe was then returned to its first position, and the connection having been made as before, it was again fUled with the same gas under the pressure of the air. Represent the pressure, as given by the barometer, by Si,. Lastly, the globe was a second time suspended from the balance, and the increase of weight determined, which we will call W. This evidently was the weight of a volume of gas equal to the volume of the globe measured at 0°, and under a pressure of ^ — k„. The weight of one cubic centimetre of the gas at 0°, and under a pressure of 76 c. m., was then calculated by the formula, The results obtained by Regnault were as follows : — SDBcific Weight of 1 Litre Name of Gas. «„_!»,, measured at Gravity. 0° and 76 cm. Air, 1.00000 1.293187 Nitrogen, .... 0.97137 1.256167 Oxygen, .... 1.10563 1.429802 Hydrogen, . . . 0.06926 0.089578 Carbonic Acid, . . . 1.52901 1.977414 It was discovered by Gay-Lussac, that all gases combine with each other in very simple proportions by volume. This remark- able law will be considered at length in another portion of this work. It is sufficient for the present to say, that it gives us the means of calculating from the weight of one litre of oxygen the weight of one litre of any other gas when the chemical equiva- lent and the combining volume are known. In this way the values given in the fifth column of Table II. have been calcu- lated. They are not exactly equal to those obtained by direct experiment, probably because the different gases are unequally compressed by the weight of the atmosphere. The actual weights as observed can always be obtained by multiplying the " specific WEIGHING AND MEASUBING. gravity by observation," given in Tables III. and IV., by 1.29206. the weight of one litre of air. The weight of one litre of a vapor at 0° and 76 c. m. is of course a fiction, since all those gases generally known as vapors (292) would be condensed to liquids under these conditions of temperature and pressure. It is convenient, however, in many calculations, to know the weight which one litre of a vapor would have at the standard temperature and pressure, assuming that it could retain its aeriform condition under these circumstances ; the weights of the vapors are therefore given in Table II. in connection with those of the gases. Knowing,, then, the weight of one litre, and hence also of one cubic centimetre, of all the more important gases and vapors at 0° and at 76 c. m., when perfectly dry, we can easily calculate from these constants the weight of one cubic centimetre of any of these gases when saturated with aqueous vapor, and at any given temperature and pressure. The following formula for the purpose is easily deduced from [100] ^ [184], and [203], re- membering that the weight of one cubic centimetre of any given mass of gas must be inversely as its volume. "' = ^- l+a00366. •^- t211.] • This formula gives the weight of the gas only, not including the weight of aqueous vapor mixed with it ; if the gas is dry, ^ becomes 0, and of course disappears. Using the weight of one litre of aqueous vapor at 0° and 76 c. m. given in Table II., we can easily calculate by [211] the weight of one cubic metre of aqueous vapor at difierent pressures and temperatures. It was in tMs way that the values given on page 571 were obtained. They are not absolutely accurate, because, as we have before seen, the vapor deviates from the law of Mariotte before reaching its maxi- mum tension, while the formula assumes that it strictly obeys the law. The weight of one cubic centimetre of a gas depends, to a slight extent, on still another cause not yet considered, namely, the va- riations in the intensity of the force of gravity over the surface of the earth. What the effect of such variation must be can easily be seen by taking an assumed case. Suppose, then, that the intensity of the earth's attraction were exactly doubled, it is evident that the total weight of the atmosphere, and hence 670 CHEMICAL PHYSICS. its pressure, -would be doubled. Moreover, the density of all gases exposed to this pressure would be doubled also ; and all this change would take place without any variation in the height of the barometer ; for although the pressure of the air would be thus increased, the weight of the mercury-column which meas- ures this pressure would be increased in the same proportion. A similar effect to this, although only to a very slight extent, is produced by the small variations in the force of gravity on the earth's surface. Other things being equal, the relative weight of one cubic centimetre of a gas at different places is proportional to the force of gravity at these places. w : w' ^ g : g' and w' == iv — • [212.] The weights determined by Regnault, and given on page 668, are only exact for Paris,* where g = 9.8096 ; but from these the weight for any other latitude or elevation can easily be calcu- lated by [40] and [47]. The weights given in the fiftli column of Table II. were calculated for the latitude of the Capitol at Washington (38° 53' 34") and the sea level. They can be re- duced for any other place by the following formula, easily derived from [212], [40], and [47] : — 1 — 0.00259 cos 2 X ro-io t w' = w -. 2A— r ? [213.] 0.99945(1+63^) but such reduction is seldom necessary. (330.) Specific Gravity of Gases. — It is usual to refer the specific gravity of gases to air, as a standard of comparison, in- stead of water, and the specific gravity of a gas may be defined as the ratio of its weight to that of an equal volume of dry air, both being measured at 0° and under a pressure of 76 c. m. Regnaulfs Method. — The most accurate method of determining the specific gravity of a gas is due to Regnault. It consists in determining with the apparatus described above (329) the weight of the given gas which a large glass globe will contain at 0° and 76 c. m., and then divid- ing this weight by that of an equal volume of air previously determined in the same way. This method requires no further description, as the process of determining the weight of the gas has already been given in detail. It admits of great accuracy, and should always be used in normal determinations. * The latitude of Regnault's laboratory, at Pai'is, is 48° 50' 14", and the elevation above the sea level about 60 metres. WEIGHING AND MEASURING. 671 Bunsen's Method. — Wien, however, the very greatest accuracy is not required, as in the investigations usually made in the laboratory on gas- eous bodies, their specific gravity can be obtained by dividing the weight of the gas by the weight of the same volume of dry air taken at the same temperature and under the same pressure. This ratio is, strictly speaking, the specific gravity only when the gas obeys exactly the law of Mariotte, and has the same coefficient of expansion as air ; but it is, nev- ertheless, in most cases near enough for all practical purposes. Bunsen's method* is an application of this principle. He employs, for determining the specific gravity of a gas, a common Ught flask, g, Fig. 456. The vol- Fjg. 456. ume of this flask should be about 200 or 300 cubic centimetres, and the neck, a, thickened before the blowpipe, should be drawn out so as to have an aperture of the thickness of a straw, into which a glass stopper is ground air-tight by means of emery and turpentine. Through this neck, which is furnished with an etched scale in millimetres, mercury is poured by means of a funnel readying to the bottom of the flask, until the whole is filled. As soon as this is accomplished, the flask is transferred, with its mouth downwards, into the mercury-trough A A, and gas is allowed to enter, until the level of mercury in the neck of the flask stands a few millimetres higher than in the trough. In order to prevent the gas from becoming mixed with air, it is evolved from as small a vessel as possible, and allowed to enter the flask through a narrow delivery tube, and in the moist state.t The gas is dried in the flask itself by a small piece of fused * This description is taken from Bunsen's Gasometry (Rosooe's translation), varying only the method of computing the results, t If the gas under examination corrodes mercury, the flask cannot be filled in this 672 CHEMICAL PHYSICS. chloride of calcium, h, -which has previously been made to crystallize on the side of the flask by bringing it into contact with a single drop of water and alternately heating and cooling the glass. This small piece of chlo- ride of calcium serves also to free the mercury and the sides of the flask from all adhering moisture. In order to be able to close the flask at any time without warming it with the hand, the little lever cy" is employed. On the end of this lever the stopper is so fastened in a cork, that it passes into the neck of the flask without closing it ; and the lever is hdd in its right place by a wedge, d, pushed under the finger-plate c. As soon as the flask has attained the constant temperature, t, of the laboratory,* the volume t of the gas, V, the height of the barometer, H^, and the height, h^, of the column of mercury in the neck above the level of the metal in the trough, are carefully observed. It is now necessary to determine the weight of this volume V. For this purpose, the wedge d is taken away ; the flask g is thereby closed, and by withdrawing the pin e, it can then be removed, together with the lever c f, from the trough. Having discon- nected the lever from the stopper, and carefully cleaned the exterior surface of the flask, it is then weighed. Let W represent this weight, H't, the height of the barometer, and t' the temperature of the balance at the time. The glass stopper is now removed, and replaced by an india-rubber tube, a, Fig. 457, connected with a drying tube, I. The apparatus thus arranged is placed under the receiver of an air-pump, and, by alternately ex- hausting and admitting the air, the gas in the flask is replaced by dry air. The drying appa- ratus is then disconnected, and the flask weighed again. Call this weight W- Since the air rig. 457. has free access both to the inte- way ; but since such gases are almost invariably hearier than air, it can be filled by displacement. The fla^k being placed in an upright position, and the delivery tube extending quite to the bottom, the gas is allowed to flow in and overflow the mouth until all the air has been expelled. The tube is then slowly withdrawn, the flow of gas still continuing, and the mouth of the flask closed by its stopper. * These experiments should be conducted in a cellar-room, in which a constant temperature can be maintained for several hours. t Before using the flask, it is once for all carefully calibrated, and the volume corre- sponding to each division on the neck inscribed in a table, which is kept with the in- strument. WEIGHING AND MEASURING. 673 rior and the exterior surface of the flask, it is evident that W is sun- ply the weight of the glass of the vessel and of the small amount of mercury and chloride of calcium which it contains, less the weight of air which these materials displace. It is also evident that IT must be equal to W increased by the weight of the volume of gas, V, contained in the flask, and diminished by the weight of air displaced by this volume of gas when the flask was weighed. The weight of the gas is, then, equal to W—W'-{-W";m which W" is the weight of V cubic centimetres of dry air at t'° and ff'^ c. m., calculated by [211]. To obtain the specific gravity, we have now only to divide the weight of the gas by the weight of an equal volume of air measured under the same conditions of temper- ature and pressure at which the gas was measured, that is, at f and {ffi, — ho) cm. This can also be calculated by [211]. Eepresenting then this last weight by W", we have for calculating the specific gravity the three following equations : — o ^ W— W + W" [214.] W" = 0.0012921 V W" = 0.0012921 V 1 S'o. 1-f 0.003661!' 1 • 76' Ha — ho 1 + 0.003664 ■ 76 [215.] [216.] As an example of the method of calculation, we cite the following fronj Bunsen's work. A determination of the specific gravity of bromide of methyl, with a small flask of about 44 c.m.° capacity, furnished the fol- lowing data : — r =7.9465 gram. .ff'o = 74.21 cm. F=42.19c:m.» 2ro=74.64c.m. ^■' = 7.8397 " i' =6°.2 < =16°.8 /%„ = 2.43 « Calculation of W".* Calculation of W'".* t< = 6°.2 ar. co. 9.99025 t = 16°8 ar. co. 9.97409 iri= 74.21 log. 1.87046 ir„—Ao= 72.21 log. 1.85860 76. ar. co. 8.11919 8.11919 F = 42.19 log. 1.62521 1.62521 0.0012932 log. 7.11166 7.11166 Tr" = 0.052092 log. 8.71677 TT'" = 0.048837 log. 8.68875 ^_ jf/ _|_ W" = 0.158892 log. 9.20110 Specific gravity of Bromide of Methyl, 3.253 log 0.51235 * The values of W" and W" can be calculated much more rapidly, although with less accuracy, by means of Table XIV. 57 674 CHEMICAL PHYSICS. (331.) Specific Gravity of Vapors* — As will appear in an- other portion of this work, the determination of the specific gravity of vapors is one of the most important processes of prac- tical chemistry. We always make the determinations at a tem- perature considerably above the boiling-point of the substance ; f and since under these circumstances a vapor has all the prop- erties of a gas (292), it follows that its specific gravity may be found by dividing its weight by the weight of an equal volume of air measured under the same conditions of temperature and pressure. The method of determining these two weights usually followed in the case of vapors is precisely similar to that used in the case of gases and described in the last section, and the same formulae may be used in calculating the results. It dif- fers from it only in the details of the manipulation, and in the fact that, on account of the high temperature to which the vapor is heated, it is necessary to take into account the change in the * We use the term vapor here in its ordinary sense. t The number of degrees above the boiling-point at which a vapor first acquires fully the properties of a permanent gas varies very greatly with ditl'erent substances. Thus, under the normal pressure of the air, the vapors of water and alcohol obey the law of Mariotte at a temperature only a few degrees above their boiling-points, while the vapor of sulphur does not obey the law until heated to at least 500° above its boil- ing-point. Unless the experimenter is confident in regard to the properties of the sub- stance under examination in this respect, it is best to make two determinations of the specific gravity at temperatures differing by twenty or thirty degrees. If the two do not agree within the limit of error of the method employed, it is an indication that the temperature is not sufficiently high. This is illustrated by the experiments of Cahours on the specific gravity of the vapor of monohydrated acetic acid. He found that the specific gravity did not become constant until the temperature rose above 240° C, that is 120° above its boiling-point. The following table contains his results : — Temp. Sp. Gr. 125° 3.180 130 3.105 140 2.907 150 2.727 160 2.604 170 2.480 180 2.438 190 2.378 Temp. Sp. Gr. 200° 2 248 220 2.132 240 2.090 270 2.088 310 2.085 320 2.083 336 2.083 It is evident that a determination of the specific gravity of the vapor of acetic acid made at a temperature below 240° would have given too large a result, and one which would have been the more enoneous as the temperature was lower. An error of the same kind, made in the determination of the specific gravity of the vapor of sulphur, introduced an anomaly into the simple law of equivalent volumes which has only recently been explained. "WEIGHING AND MEASURING. 675 capacity of the vessel used by an example. Suppose specific gravity of alcohol vapor, The method may be best explained , then, that we wish to ascertain the Kg. 458. We take a light glass globe having a capacity of from 300 to 500 ^^.«, and draw the neck out in the flame of a blast lamp, so as to leave only a fine opening, as shown in Fig. 458 at a. We then weigh the globe, which gives us the weight W of [214]. The second step is to ascertain the weight of the globe filled with alcohol vapor at a known temperature and under a known pressure. For this purpose, we introduce into the globe a few grammes of pure alcohol, and mount it on the support rep- resented in the figure. By loosening the screw, r, we next sink the balloon beneath the oil contained in the iron vessel, V, and secure it in this position. We now slowly raise the temperature of the oil to between 300° and 400°, which we observe by means of the thermometer, B. The alcohol changes to vapor and drives out the air, which, with the excess of vapor, escapes at a. When the bath has attained the requisite temperature, we close the opening a by sud- denly melting the end of the tube at a by means of a mo^ith blowpipe, and as nearly as possible at the same moment observe the temperature of the bath and the height of the barometer. We have now the globe filled with al- cohol vapor at a known temperature and under a known pressure. Since it is hermetically sealed, its weight cannot change, and we can therefore allow it to cool, clean it, and weigh it at our leisure. This will give us the weight of the globe filled with alcohol vapor at a temperature t and under a pressure H. This is the weight IF of [214]. We also notice the height of the barometer H' and the temperature of the balance-case t' during this second weighing, and when we have measured the capacity of the globe V, we can easily calculate by [215] the value of W". Knowing now W — W -\- W", the weight of alcohol vapor which filled the globe at f and under a pressure He. m., the next step is to find W", the weight of an equal volume of air under the same conditions of temperature and pressure. By (241) the volume of the globe at the temperature t was V{l-\- Kt), and by substituting this in [216], we get at once, since K = 0, W" = 0.0012932 F (1 -f Kt) H, l_|_0.00366if ■ 76' 7fi' [217.] by which we can easily determine the weight required. The last step is 676 CHEMICAL PHYSICS. to find the capacity of the globe, which, although we have supposed it known, is not actually ascertained experimentally until the end of the process. For this purpose we break off the tip of the tube a under mer- cury, which, if the experiment has been carefully conducted, rushes in and fiUs the globe completely. We then empty this mercury into a care- fully graduated glass cylinder, and read off the volume. We have now all the data for calculating the specific gravity, and the calculation may be conducted precisely as on page 073, only substituting [217] for [216]. We have assumed that the vapor expelled all the air from the globe, and hence that the globe filled completely with mercury on breaking the tip end of the neck. This, however, is rarely the case ; there is almost always left in the globe a bubble of air, and sometimes the volume of air remaining is quite considerable. In such cases, however, we may stiU obtain approximatively accurate results ; it is only necessary to decant the air into a graduated beU over a pneumatic trough, and measure ex- actly its volume, v, at an observed temperature, t", and under a pressure oi H". Its weight, TFJ, can now be calculated by [215], and from this weight we readily deduce the weight of vapor which the globe contained at the moment of closing its orifice ; this weight of vapor was evidently W — W' -j- W" — Wi- The volume which the small amount of air left in the globe occupied at the moment of closing the orifice (that is, at f and He. m.) can also be calculated from the formula, 1_(_ 0.00366 < H" 1 4- 0.003 66 i!" Ha [218.] which can readily be deduced from [98] and [184]. The volume of the balloon at this time was, as we have seen, V (1 -\- Kt). Hence the vol- ume of the vapor must have been V{\-\-K{) — ;•'. Substituting this value for V {l-\-Kt) in [217], we get for the weiglit of the vapor in the globe at the time of closing, r. = 0.0012932 [ra + A^O-^'l oiok66 • f.-' [219.] 1+0.00366 ■ 76' and for the specific gravity. Sp.Gr. ^-^'+^"-^1 . [220.] The results which are thus obtained are not, however, perfectly trustwor- thy, and it is always best to avoid these corrections by so conducting the experiments that only a very small amount of air at most shall be left in the globe. This end is secured by adapting the size of the globe to the quantity of liquid which is available for the determination. In calculating the specific gravity of a vapor from the observed data, we WEIGHING AND MEASURING. 677 must be careful, in the first place, to reduce all the barometric heights to 0° by Table XVIII. In the second place, the temperature of the bath, as indicated by the mercury-thermometer, must be corrected for the part not immersed [156], and the corrected temperature reduced by the table on page 439 to the true temperature. When great accuracy is required, it is best to measure the temperature of the bath directly with an air-thermome- ter. This is immersed in the oil at the side of the globe, and the orifices of both thermometer and globe are closed at the same time (264). In com- puting the results, we use the formula [189], and without actually calcu- lating the temperature, substitute the value of "|~ in [217]. We have assumed that the bath in whi"h the globe is heated is filled with a fixed oil, which is the most convenient liquid if the temperature required does not exceed 250°. When heated above this temperature, the fat oils emit very disagreeable vapors ; and for temperatures between 250° and 500° it is necessary to fill the bath with some easily fusible alloy, such as Rose's metal or Soft solder. The pressure exerted by the melted metal is necessarily very great, and tends to deform the globe, so that we are obliged to abandon this method of experimenting as soon as the glass begins to soften, which takes place a little above 500° By slightly modifying the apparatus, however, Eegnault has been able to obtain accurate results at temperatures as high as 600° or 650°. His method, which is only used for substances which boil at a very high tem- perature, is as follows. The volatile substance is introduced into the cylindrical reservoir a' V (Fig. 459) of the tube a' d, which is made of the most infusible glass, and supported in an iron frame, m m! m", at the side of a similar tube, a b. This last tube, which may be closed by the stopcock r, serves as an aiiv Fig. 459. thermometer. The two tubes are heated together in an air-bath, made, as represented in Fig. 460, of two or three concentric cylinders of sheet-iron enclosed in an outer cylindrical case of cast-iron. The frame m m" fits the inner cylinder/^ h, i, and when in place the metallic disk m" n" just closes its mouth, /«', leaving the ends of the two tubes projecting m front of the bath. This apparatus is heated in a horizontal position on a semi- cylindrical grate, and so arranged that it can be surrounded with burning coals. The temperature is first rapidly raised ; but after the volatile sub- stance has distilled over and the excess has been collected in the cold por- tion of the tube c' d, the temperature is increased very slowly, and before 57* 678 CHEMICAL PHYSICS. the glass softens, the process is arrested by closing the stopcock of the air- thermometer and withdrawing the frame with its two tubes from the bath. We now determine the temperature to which the tubes were heated, by J rig. 460. the method already described in detail (265). We next ascertain the weight of vapor which was contained in the reservoir a! V at the moment of withdrawing the tube from the air-bath. For this purpose we remove the excess of the substance which condensed in the part of the tube c'rf, and then weigh the whole tube, first with the substance it contains, and secondly after the substance has been removed. The difference of these weights is the weight of the vapor which filled the reservoir a' V c' at a known temperature and pressure. Lastly, to find the volume of the res- ervoir, we determine the weight of water which fiUs it at a known temper- ature ; and we then have all the data for calculating the specific gravity of the vapor. The formulae already given may be easily modified for the purpose. If the substance under examination absorbs oxygen at a high temperature, it is best to fill the whole tube a' d with nitrogen, and to adapt with a cork to the open end a small tube drawn to a point. The use of the air-thermometer (which involves a great expenditure of time) in the determination of the specific gravity of vapors of substances which boil at a high temperature, is avoided in another modification of the general method proposed by Deville and Troost. They use a glass bal- loon, and heat it in an atmosphere of vapor rising from boiling mercury or sulphur. The temperature of these vapors is so constant, that it is not necessary to use a thermometer, — that of the first at 350°, and that of the second at 440°. For still higher temperatures they use a balloon of porce- lain, which is heated in the vapor of boiling cadmium (860°) or boiling zinc (1040°) ; but for the details of the apparatus and of the method, we must refer to the original papers.* Method of Gay-Lussac. — The method of determining the specific gravity of vapors just described is liable to one very serious source of error. In order to insure that all the air will be expelled from the globe, it is necessary to use a considerable amount of liquid ; and it is evident that any impurity which this liquid may contain will be left behind in the globe, and tend to falsify the weight. This source of * Comptes Rendus, Tom. XLV. p. 821 ; also Tom. XLIX. p. 239. WEIGHING AND MBASUEING. 679 error is entirely aToided by a method invented by Gay-Lussac ; but unfortunately the method is applicable only to liquids which boil at a comparatively low temperature. It consists in measuring with accu- racy the volume of vapor formed by a known weight of liquid. The liquid is first enclosed in a very thin glass bulb, A, Fig. 461, which is her- metically sealed, and the weight of the liquid is determined by weighing the bulb both before and after it has been filled. This bulb is then passed up into a graduated bell-glass, G, filled with mer- cury, and standing in an iron basin also partly filled with the same liquid. Around the bell is placed a glass cylinder, whose lower end, resting in the mercury contained in the basin, is com- pletely closed. This cylinder is filled with water, and the apparatus thus arranged is mounted on a charcoal furnace. The glass bulb is soon broken by the expansion of the liquid, and when the temperature is sufficiently elevated the liquid changes into vapor, which depresses the mercury-column. The heat is still increased until the water in the cylinder boils, when the bubbles of vapor rising through the liquid estab- lish a uniform temperature of 100° throughout the whole mass. We then observe accurately the volume of the vapor and the pressure to which it is exposed. To obtain the last, we subtract from the height of the barometer, JHii, the difference of level between the surface of the mercury in the basin and that in the bell. This difference of level is measured by a cathetom- eter with the aid of the levelling-screw r. Compare (159). With these data we can easily calculate the specific gravity. We reduce, first, the volume of the vapor to 0° and 76 c. m. by [166] and [107], and we then calculate the specific gravity by [55] and [58]. For the different pre- cautions required in this process, and for the slight variations required under different circumstances, the student is referred to Regnault's Ele- ments of Chemistry, American edition. Vol. 11. p. 408. (332.) Volumes of Gases. — In consequence of the very small density of gases, their volumes can be determined much more accurately by measure than by weight. The measurement of the volume of a gas is effected in eudiometers, or graduated tubes, Pig. 462, which are generally about 2 c. m. in diameter and from 25 c. m. to 80 c. m. long. These tubes are frequently graduated Fig. 461. 680 CHEMICAL PHYSICS. into cubic centimetres, but it is more accurate to divide them into millimetres and to determine afterwards the corresponding volumes by calibration. The graduation is easily made, with the dividing machine before described, on a thin coating of wax Fig. 462. spread over the surface of the tube, and the divisions are after- wards etched with hydrofluoric acid. The tube is then calibrated by pouring into it repeatedly the same measured quantity of mercury through a long funnel, and after each addition accu- rately noting the division to which it rises in the tube. From these data it is easy to calculate the volume corresponding to each graduation ; and a table is then prepared, from which these volumes can be subsequently ascertained by inspection. The measurements of gases are best performed over a small mercurial trough, like that represented in Fig. 462, which was contrived by Bunsen, and is admirably adapted to the purpose. The trough has two transparent sides of plate-glass, through which the level of the mercury is easily observed. The eudiometer is first filled with mercury by means of a long funnel reaching to the bottom of the tube ; and after closing its mouth, it is inverted and placed in the position represented in the figure, when the gas can readily be introduced from the collecting tubes. When practicable, a drop of water is brought into the head of the eudiometer before filling it with mercury, so that the collected gas may be perfectly satu- rated with aqueous A'apor. Every determination of the volume of gases requires the fol- lowing four primary observations : — WEIGHING AND MEASURING. 681 1. The level of the mercury in the eudiometer. 2. The level of the mercury in the trough measured on the etched divisions of the eudiometer. 3. The height of the barometer. 4. The temperature. The eudiometer is first brought to a perpendicular position by means of a plumb-line, and the observations are then made by the help of a small telescope placed at a distance of from six to eleven feet. The axis of the telescope is brought to a horizontal posi- tion, and all error from parallax thus avoided. It is unneces- sary to add, that the heights of the mercury columns must always be read off at the highest point of the meniscus. The observed volumes of gas are reduced by calculation to the volumes in a dry state at 0° and under a pressure of 76 c. m. by means of the equation Hq — K — ^ (1 + 0.00366 r!) 76' which is easily obtained from [107], [184], and [203]. The following measurements, by Bunsen, of a volume of air sat- urated with aqueous vapor, may serve as an example of the calculation : — V=V' Temperature of the air, 20°.2 Lower level of mercury, Upper " " Difference of level. Reduced height li^. c. m. 66.59 31.73 24.86 24.78 Height of barometer, Correction for temperature, Reduced height H,,, Tension of vapor, ^, Ha — ^0 — fi) c. m. 74.69 0.25 74.44 1.76 47.90 The division 317.3 corresponds to a volume by table of 292.7 Correction for meniscus, ...... 0-4 The corrected volume V, 293.1 V, ...... log. 2.46701 H^-h — ^i,- ■ ■ • log. 1.68033 (1 _|- 0.00366!!) by Table XI., . ar. co. 9.96902 76, ar. co. 8.11919 Reduced volume F= 172.01, . log. 2.23555 For the practical details of the methods connected with the manipulation and measurement of gases, we would refer the student to Professor Bunsen's work on Gasometry. This dis- tinguished experimentalist has very greatly improved all these processes, and has given them an accuracy unsurpassed by any of the most refined methods of chemical investigation. 682 CHEMICAL PHYSICS. PROBLEMS. Hygrometry. 378. A glass globe, having been filled at 0° and 76 c. m. partly with air and partly with water, and afterwards sealed, is heated to 100°. Re- quired the pressure exerted on the interior surface of the vessel, provided that there is an excess of water left in the globe. 379. What would be the pressure, if ether were used in the last ex- ample instead of water ? 380. Into a vacuous vessel, whose capacity equals 2.02 litres, there were introduced one litre of dry air and sufficient water to leave after evaporation 20 c.m.° in the liquid state. Required the tension of the mixture of air and vapor in the interior of the vessel. 381. A given quantity of dry air weighs 5.2 grammes at 0° and 76 c. m. pressure. What would be its volume at 30° and 77 c. m. pressure when saturated with vapor ? 382. What is the weight of a cubic metre of air at 30° and 77 c. m. pressure ? The relative humidity of the air is assumed to be 0.75. 383. The volumes of air given in the table below were measured when saturated with vapor at the temperatures and pressures annexed. It is required to reduce these volumes to what they would have been at 0° and 76 c. m. pressure, had the gas been perfectly dry. H= 76.3 cm. 1= 30°. H = 5.6 " t= 20°. fl^ = 78 " « = -20°. 384. The volumes of air given in the following table were measured at 0° and 76 cm. pressure when perfectly dry. It is required to deter- mine what would have been the volume at the temperature and pressure annexed were the gas saturated with moisture. 1. 250 c. m.^ H= 75.6 cm. ( = 15°. 4. 500 c. m. 2. 120 " 77=25.4 " t = 20°. 5. 725 " 3. 75 " fl"= 5.6 " t = 10°. 6. 340 " 1. 200 cm.-* fi"=75.4cm. t = 15°. 4. 75 c. m.'' fl'=77.2cra. (= -10°. 2. 500 " 7r=45.5 " t = 100°. 5. 60 " H= 80.2 " t = -40°. 3. 25 " H= 15.8 " t = 130°. 6.140 " iZ" =79 4 " f = -100O. 385. In the following problems are given, first, the temperature of the atmosphere, f ; secondly, the dew-point, t'°. It is required to determine in each case the relative humidity of the atmosphere and the weight of vapor in one cubic metre. 1. ( = 30° t' = 18°. 4. t = 30° (' = 28°. 7. «= 0° t'= 4°. 2. t = 20° (' = 11°. 5. t = 25° t' = 20°. 8. t = -6° t' = 10°. 3. ( = 5° i' = 0°. 6. t = 10° (' = 6°. 9. « = 41o tl = 39°. 386. In the following problems are given, first, the temperature of the dry-bulb thermometer ; secondly, that of the wet-bulb. Required in each case the relative humidity of the air. WEIGHING AND MEASURING. 683 1. t = 30° (' = 28°. 4. « = 28° (' = 26°.7. 7. i = 0° V = -3°. 2. t = 20° tl = 12°. 5. t = 15° t' = 12°.3. 8. t = 5° t' = -8°. 3. « = 10° V = 2°. 6. t = l2° ('= 8°. 9. « = 20° t' = -20° .8 387. Assuming that the air is four fifths saturated with aqueous vapor at the temperature of 20°, how much water would fall from each cubic metre if the temperature suddenly fell to 11° ? 388. When the temperature of the air was 30°, the dew-point was observed to be at 28° ; the temperature of the aur suddenly fell to 20°. How much rain would fall on a square kilometre from a height of 200 metres, assuming that the atmosphere were of uniform density and hy- grometric condition throughout the whole height ? Sources of Heat. 389. How much wood charcoal must be burnt in order to evaporate 50 kilogrammes of water, assuming that the water is already at the boiling- point, and that all the heat evolved is economized in the process ? 390. How much alcohol must be burnt in order to melt 5 kilogrammes of sulphur, assuming that the sulphur is already at the melting-point, and that the heat is all economized ? 391. How much coke would be required to raise the temperature of the air of a room measuring 6 m. X 7 m. X 3.5 from 5° to 25°, assuming that none of the heat evolved was lost ? 392. How many cubic metres of illuminating gas (marsh gas) must be burnt to raise the temperature of 40 kilogrammes of water from 0° to 100° ? How much, in order to convert the water into steam ? Conduction of Heat. 393. It is required to make a copper boiler by which 100 kilogrammes of water may be evaporated each hour. What must be the extent of boiler surface, assuming that the thickness of the copper is 2 m. m., and that the difference of temperature between the two surfaces of the copper plate is 100° ? 394. If the boiler were made of iron 5 m. m. thick, what must be the extent of the boiler surface ? "WEIGHING AND MEASURING. Specific Gravity of Solids. 395. The specific gravity of zinc was found to be 7.1582 when the temperature of the water was 15°. What would have been the specific gravity at 4° ? 396. The specific gravity of antimony was found to be 6.681 when the temperature of the water was 15°. What would have been the specific gravity at 4° ? 684 CHEMICAL PHYSICS. 397. The specific gravity of an alloy of zinc and antimony was found from the following data : — Weight of the alloy, 4.4106 grammes. " " specific-gravity bottle, . . . 9.0560 " " " " " full of water at 4°, 19.0910 " " " bottle, alloy, and water at 14°.6, . 22.8035 " 398. Find the specific gravity of metallic zinc from the following data : — Weight of the zinc 12.4145 grammes. " " bottle ' . 9.0560 " " " " fullofwaterat 18° . . . 19.0790 " " " " zinc and water at 12°.4, . 29.7663 " Volume of Solids. 399. Gold-leaf is made as thin as one ten-thousandth of a millimetre. How great a surface could be covered with 10 grammes of such leaf ? 400. A cylinder of iron weighing 21 kilograrmnes is 2.5 m. high. What is its diameter ? 401. The base of the grand pyramid of Egypt measured 23.48 m. on each side ; its original height was 146.18 m. Required its weight, as- suming that it was solid, and that the stone of which it is constructed has a Sp. Gr. = 2.75. 402. Required the price of an iron pipe, knowing that its interior di- ameter is equal to 0.254m., that its thickness equals 0.014 m. and its length 213.4 m. The specific gravity of cast-iron is 7.207, and its price 4 cents a pound. 403. A silver wire 1.5 m. m. in diameter weighs 3.2875 grammes. It is required to cover it with a coating of gold 0.4 m. m. in thickness. What will be the weight of the gold ? Volmne of Liquids. 404. What is the volume of 40 kilogrammes of mercury at 100° ? If the liquid is contained in a cylindrical vessel 6 c. m. in diameter, how high would it stand above the horizontal base ? 405. A glass flask with a narrow neck was weighed full of mercury at the temperature of 10°, and found to weigh 560.234 grammes. The flask itself weighed 84.374 grammes. Required the volume of the flask. 406. Calculate the volume at 0° of the globe employed by Regnault in dctermininrr the absolute weight of one litre of air and of other gases from the following data (see Fig. 454) : — Weight of the glass globe at 4°. 2 and 75.789 cm., . . . . 1,258. 55 gram. after having been filled with water at 0°, . 11,126.05 " Temperature of tlie chamber at the time of weighing, ... 6° Height of the barometer at the same time, 76.177 c. m. Ans. 9,881.06 37^.' WEIGHING AND MEASURING. 685 Weight of Gases. 407. Calculate the weight of one litre of dry air at 0° and 76 c. m. from the following determination by Eegnault (329). The globe used was the same as in the last example. Globe fidl of Air and surrounded hy Ice. Height of barometer at the time of closing the stopcock, . . . 76.119 cm. Weight added to globe to equipoise it in balance (Fig. 258), . . 1.487 gram. Globe exhausted of Air and surrounded by Ice. Tension of air remaining in globe as indicated by the manometer at the moment of closing the stopcock, 0.843 c. m. Weight required for equipoise 14.141 gram. Ans. 12.7744 gram. 408. Calculate the weight of one litre each of hydrogen and carbonic acid at 0° and 76 cm. from the following determinations of Regnault. The data are given in the same order as in the last problem. Hydrogen. Carbonic Acid. Globe full of gas, Ho =75.616 cm. Globe full of gas, fli =76.304 cm. W = 13.301 gram. W = 0.6335 gram. Globe exhausted, ^o = 0.340 c. m. Globe exhausted, h, — 0.157 cm. TF" = 14.1785 gram. TF"= 20.211 gram. Ans. 0.88591 gram. Ans. 19.5397 gram. 409. Reduce the weights obtained from the last two problems to the latitude of 45° and the sea-level. See page 670. 410. Reduce the weights to what they would be at Quito. Latitude, 0° 13'.5. Elevation above sea-level, 2,908 metres. 411. In the following table are given, first, the volume of the gas ; secondly, the pressure to which it is exposed ; thirdly, its temperature. Assuming that the gas is saturated with vapor of water, it is required to calculate the weight in each case. V. H. t. Air 245 ^T^ 76.12 c m. 15°. Hydrogen, ... . 564 " 64.32 " 12°. Carbonic Acid, 202 " 45.20 " 4°. Chlorine, 50 " 75.89 " 30°. Protoxide of Nitrogen, . . .465 " 66.23 " 8°. Steam, 500 " 76.54 " 213°. Alcohol Vapor, .... 1,500 " 54.22 " 152°. Ether Vapor, 250 " 75.20 " 100°. 412. A glass globe weighed, when open to the air, 225.169 grammes ; filled with water at the temperature of 0°, it weighed 785.169 grammes. Required the weight of air which the globe would contain at 300° and under a pressure of 77 c. m. 413. What is the weight of one cubic metre of aqueous vapor at its maximum tension at the following temperatures : 10°, 15°, 120°, 200°, and 250° ? 58 686 CHEMICAL PHYSICS. 414. What is the weight of the vapor contained in one cubic metre of the atmosphere under the conditions given in problem 385 ? Specific Gravity of Gases and Vapors. 415. Calculate the specific gravity of hydrogen and carbonic acid at 0° from the data given in problems 407, 408, and 409. 416. Ascertain the specific gravity of alcohol vapor from the following data : — Weight of glass globe, W, ... . 50.8039 gram m es. Height of barometer, H', 74.754 c. m. Temperature, (', . . . 18°. Weight of globe and vapor, TT'", . . . 50.8245 grammes. Height of barometer, H, .... 74.764 c. m. Temperature, t, . . ... 167°. Volume, F, 351.5 oTI^' 417. Ascertain the specific gravity of camphor vapor from the follow- ing data : — Weight of glass globe, W'-, ■ ■ 50.1342 grammes. Height of barometer, H', . . 74.2 c. m. Temperature, t\ 13°.5. Weight of globe and vapor, W, ■ . 50.8422 grammes. Height of barometer, fl", ... . 74.2 cm. Temperature, t, 244°. Volume, F, . . 295 ^T^.' Volume of Gases. 418. A volume of air saturated with moisture gave the following meas- urements. Reduce to the standard temperature and pressure. Level of mercury in pneumatic trough, .... 52.34 c. m. " " eudiometer, 24.25 " Volume corresponding to 24.25 division, .... 350 c. m.' Temperature of the air, 15°.4. Height of barometer, 76.54 c. m. 419. A volume of air saturated with moisture at 3°.l and 57.59 c. m. pressure, was found to measure 368.9 c..m.°- After absorbing the oxygen with a paper ball moistened with pyrogaUate of potash, and drying the residual gas with a ball of caustic potash, it was found to measure 313.8 ^^.% the temperature being 3°.l and the pressure 53.58 c. m. Required the percentage composition of the gas. 420. A volume of gas (choke-damp), measured moist at 13.°5 and 62.40 pressure, was found to be 171.2 cTla.^. After absorbing the car- bonic acid with a ball of caustic potash and drying the gas, it was found to measure 107.3 c. m.^ the temperature being 13.5° and the pressure 61.96 cm. Finally, after absorbing the oxygen with pyrogaUate of pot- ash, and drying, the gas was found to measure, at 13°.9 and 60.58 c. m. pressure, 147 c. m.^ Required the percentage composition of the gas. APPENDIX LIST OF TABLES. Table *Page I. Weights and Measm-es 11 II. Specific Gravity and Weight of One Litre of various Gases and Vapors, calculated for Latitude of Washington from Keg- nault's Experiments 668 in. Specific Gravity of Gases. (Ann. du Bureau des Long., 1855.) IV. Specific Gravity of Vapors. " " " V. Specific Gravity of Liquids. " " " VI. Specific Gravity of Solids. " " " VII. Coefficients of Absorption of various Gases in Water and Alco- hol. (Bunsen.) 392 Vin. Tension of the Vapor of Alcohol. (Kegnault.) . . . 582 IX. Tension of Aqueous Vapor from —32° to 230°. (Regnault.) . 570 X. Tension of Aqueous Vapor from — 2° to 35°. (Regnault.) . 570 XL Valueof 1+0.00366 < between —2° and 59°. (Bunsen.) . 528 Xn. Value of 1 -(- 0.00367 < between 60° and 299°. (Gerhardt.) 528 Xm. Value oil-\-k (i' — t) for Glass. (Gerhardt.) . . 493, 695 XIV. Weight of One Cubic Centimetre of Air. (Gerhardt.) . . 673 XV. Expansion of Solids. (Mtiller.) 496 XVI. Volume of Water at different Temperatures. (Kopp.) 526, 662 XVII. Reduction of Thermometer. (Graham.) 436 XVin. Reduction of Barometer. 511 XIX. Reduction of Water Column to Mercury. (Bunsen.) . 513 XX. Logarithms of Numbers. XXI. Antilogarithms. * These numbers indicate the pages of the work on which the use of the table is de- scribed. TABLES. TABLE I. MEASURES AND WEIGHTS./ ENGLISH MEASURES. Measures of Length. The inch is the smallest lineal integer now used. For mechanical purposes it is divided either duodecimally or by continual bisection ; but for scientific purposes it is most convenient to divide it decimally. The larger units are thus related to it : — Links. Inches. 1 = 8 = 80 = 320 = 880 = 1760 = 5280 = 8000 =63360 1 = 10 = 40 = 110 = 220 = 660 = 1000 = 7920 1 = 4= 11 = 22 = 66 = 100 = 792 1 = 2.75= 5.5= 16.5 ^ 25 = 198 1 = 2 = 6 = 9A= 72. 1 = 3 = 4,\= 36 1 = 1H= 12 ,000125=.001 = .01=.04= .11= .22= 0.66= 1 = 7.1 Measures of Surface. Acre Kooda. Square Chains. Sijaare Vards. Square Feet. 1 = 4 = 10 = 4840 = 43,560 i ^ 2.5 = 1210 =■ 10,865 1 = 484 = 4,356 1 = 9 Measures of Volume. Cubic Yard. Cubic Feet. Cubic Inches. 1 = 27 = 46,656 1 = 1,728 58« 690 TABLES. Imperial Measure. The Imperial Standard Gallon contains ten pounds avoirdupois weight of distilled water, weighed in air at 62° Fahr. and 30 in. Barom., or 12 pounds, 1 ounce, 16 pennyweights, and 16 grains Troy, = 70,000 grains' weight of distilled water. A cubic inch of distilled water weighs 252.458 grains, and the imperial gallon contains 277,274 cubic inches. Distilled Water. Grains. Avoir, lb. Cubic Inches. Pint. Quart. 8,750 = 1.25= 34.659 = 1 2.5 = fi9..S18 = 2 = 1 Galls. Pecks. Bush. Qr. 17,500 = 70,000 = 140,000 = 660,000 = 10 = 20 = 80 = 69.318 = 277.274 = 554.548 = 2,218.192 = 16 = 4=1 = 8=2 = 64 = 32 = 8 = 1 4 = 1 4,480,000 = 640 =17,745.536 = 512 = 256 = 64 = 32 = 8 =1 Apothecaries' Measure. The gallon of the former wine measure and of the present Apotheca- ries' measure contains 58,333.31 grains' weight of distilled water, or 231 cubic inches, the ratio to the imperial gallon being nearly as 5 to 6, or as 0.8331 to 1. Minims. Gr. of Dist.Wat. Cab> Inch. = 61,440 = 58,333.31 = 231 = 7,680 = 7,291.66 = 28.8 = 480 = 455.72 = 1.8 = 60 = 56.96 = 0.2 Hon. Pints. Ounces. Drachms. 1 = 8 = 128 = 1024 1 = 16 = 128 §1 = 8 31 ENGLISH WEIGHTS. Avoirdupois Weight. Pound. Ounces. Drachms. Grains. 1 — 16 = 256 =. 7000 1 16 -= 437.5 1 — 27.34375 Apothecaries' Troy Weight. PouncL Ounces. Draclims. Scruples. Grains. 1 = 12 = 96 i= 288 = 5760 1 = 8 = 24 = 480 1 = 3 1 = 60 20 TABLES. 691 1 Kilometre 1 Hectometre 1 Decametre 1 Metre 1 Kilometre 1 Metre 1 Centimetre FRENCH MEASURES. Measures of Length. 1000 Metres. 100 " 10 « 1 « 1 Metre 1 Decimetre 1 Centimetre 1 Millimetre 0.6214 Mile. 3.2809 Feet. 0.3937 Inch. Logarithms. 9.793 3712 0.515 9930 9.595 1742 1.000 Metre. 0.100 " 0.010 « 0.001 " At. Co. Log, 0.206 6188 9.484 0070 0.404 8258 Measures of Volume. 1 Cubic Metre = 1 Cubic Decimetre = 1 Cubic Centimetre = 1000.000 Litres. 1.000 « 0.001 " 1 Cubic Metre = 35.31660 Cubic Feet. 1 Cubic Decimetre = 61.02709 Cubic Inches. 1 Cubic Centimetre = 0.06103 " « 1 Litre = 0.22017 Gallon. 1 Litre = 0.88066 Quart. 1 Litre = 1.76133 Pints. Logarithms. 1.547 9790 1.785 5226 8.785 5226 9.342 7581 9.944 8083 0.245 8407 Ar. Co. log. 8.452 0210 8.214 4774 1.214 4774 0.657 2419 0.055 1917 9.754 1593 FRENCH WEIGHTS. 1. Kilogramme ^1000 Grammes. 1 Hectogramme = 100 " 1 Decagramme = 10 " 1 Gramme = 1 " 1 Gramme = 1.000 Gramme. 1 Decigramme = 0.100 " 1 Centigramme = 0.010 « 1 MiUigramme = 0.001 « 1 Kilogramme = 2.67951 Pounds (Troy). 1 Gramme = 15.44242 Grains. Logarithms. Ar. Co. Log. 0.428 0554 9.571 9446 1.188 7154 8.8112846 TABLE FOR THE REDUCTION OF THE BAROMETRIC SCALE. 28 inch. = 71.1187 cm. 29 " =73.6587 « 30 « =76.1986 « 31 « =78.7386 « 71 cm. = 27.953 inch. 72 « =28.347 " 73 « =28.741 « 74 " =29.134 « 1 inch = 2.539954 c m. 75 cm. = 29.528 inch. 76 « =29.922 « 77 « =30.315 « 78 " =30.709 « 1 cm. = 0.3937 inch. 692 TABLES. LOGARITHMS FOR KEDUCrNG THE MOST COMMON WEIGHTS AND MEASTJBES. Measures of Length. Metre. Parisian Foot. Austrian Foot. Prussian Foot. English Foot. 0. 0.511 6687-1 0.499 8277-1 0.496 7270-1 0.484 0071-1 0.488 3313 0. 0.988 1590-1 0.985 0583-1 0.972 3384-1 0.500 1723 0.011 8410 0. 0.996 8993-1 0.984 1794-1 0.503 2730 0.014 9417 0.003 1007 0. 0.987 2801-1 0.515 9929 0.027 6616 0.015 8206 0.012 7199 0. Measures of Surface. Square Metre. Parisian Sq. Foot. Austrian Sq. Foot. Prussian Sq. Foot. Englisli Sq. Foot. 0. 0.976 6625 1.000 3445 1.006 5459 1.031 9857 0.023 3375-1 0. 0.023 6820 0.029 8834 0.055 3232 0.999 6555-2 0.976 3180-1 0. 0.006 2014 0.031 6412 0.993 4540-2 0.970 1166-1 0.993 7986-1 0. 0.025 4398 0.968 0143-2 0.944 6768-1 0.968 3588-1 0.974 5602-1 0. Measures of Volume. Cubic Metre. Pariaan Cub. Foot. Austrian Cub. Foot Prussian Cub. Foot. Englisli Cub. Foot. 0. 1.464 9938 1.600 5168 1.509 8189 0.547 9786 0.535 0062-2 0. 0.035 6230 0.044 8261 0.082 9848 0.499 4832-2 0.964 4770-1 0. 0.009 3021 0.047 4618 0.490 1810-2 0.955 1749-1 0.990 6979-1 0. 0.038 1597 0.452 0214-2 0.917 0162-1 0.952 5382-1 0.961 8403-1 0. Weights. Kilogramme. Austrian Pound. Prussian Pound. Eng. Troy Pound. English Pound AToirdupois. 0. 0.748 1973-1 0.669 9776-1 0.571 9792-1 0.656 6547-1 0.251 8027 0. 0.921 7803-1 0.823 7818-1 0.908 4574-1 0.330 0224 0.078 2197 0. 0.902 0016-1 0.986 6771-1 0.428 0208 0.176 2182 0.097 9984 0. 0.084 6756 0.343 3453 0.091 5426 0.013 3229 0.915 3244-1 0. TABLES. 693 TABLE II. SPECIFIC GRAVITY AND ABSOLUTE WEIGHT OF ONE LITRE OF SOME OF THE MOST IMPORTANT GASES AND VAPORS. Calculated for the Latitude of Washihgton. Names of Gases. H Sp. Gr. Observed. Sp. Gr. Oomputed. Weight of 1 Litre = 1,000 CO. Logaritlims. Ar. Co. LogaritlimB. Air, 1 1.00000 1.29206 0.111282 9.888718 Alcohol, 4 1.613 1.58938 2.05357 0.312510 9.687490 Ammonia gas, . 4 0.5967 0.58738 0.75893 9.880201 0.119799 Antimony, 1 16.90823 21.84640 1.339380 8.660620 Antimonide of hydrogen, . 4 4.33072 5.59554 0.747842 9.252158 Arsenic, 1 10.65 10.36553 13.39285 1.126873 8.873127 Arsenide of hydrogen. 4 2.695 2.69504 3.48215 0.541847 9.458153 Boron, .... 1 1.50646 1.94643 0.289238 9.710762 Bromine, .... 2 5.54 5.52827 7.14285 0.853872 9.146128 Bromohydric acid. 4 2.79870 3.61607 0.558237 9.441763 Carbon, .... 1 0.8469* 0.82924 1.07143 0.029963 9.970037 Carbonic acid, 2 1.5290S 1.52131 1.96433 0.293215 9.706785 Carbonic oxide, 2 0.96779 0.96745 1.25000 0.096910 9.903090 Chlorine, 2 2.47 2.45317 3.16964 0.501010 9.498990 Chloride of boron, . 4 3.942 4.05636 5.24107 0.719420 9.280580 Chloride of silicon, 3 5.939 5.87380 7.58928 0.880201 9.119799 Chlorohydric acid, . 4 1.2474 1.26114 1.62947 0.212045 9.787955 Cyanogen, . 2 1.8064 1.79669 2.32143 0.365755 9.634245 Cyanohydric acid, . 4 0.9476 0.93290 1.205.S6 0.081116 9.918884 Ether, .... 2 2.586 2.55689 3.30365 0.518994 9.481006 Fluorine, .... 2 1.31297 1.69643 0.229536 9.770464 Fluoride of boron. 4 2.3124 2.34608 3.03127 0.481625 9.518375 Fluoride of silicon, . 8 3.600 3.59338 4.64287 0.666786 9.333214 Fluohydric acid, . 4 0.69104 0.89286 9.950782 0.049218 Hydrogen, 2 0.06926 0.06910 0.08929 8.950782 1.049218 Iodine, .... 2 8.716 8.77614 11.33930 1.054586 8.945414 lodohydric acid. 4 4.443 4.42262 5.71429 0.756962 9.243038 Marsh gas, . 4 0.5576 0.55283 0.71429 9.853872 0.146128 Mercury, .... 2 6.976 6.91035 8.92858 0.950782 9.049218 Nitrogen, 2 0.97137 0.96745 1.25000 0.096910 9.903090 Nitrous oxide, . 2 1.5269 1.52028 1.96429 0.293205 9.706795 Nitric oxide, 4 1.0388 1.03655 1.33928 0.126873 9.873127 defiant gas. 4 0.9852 0.96745 1.25000 0.096910 9.903090 Oxygen, 1 1.10566 1.10566 1.42857 0.154902 9.845098 Phosphorus, 1 4.42 4.28442 5.53571 0.743174 S.256826 Phosphide of hydrogen, 4 1.178 1.17476 1.51786 0.181231 9.818769 Selenium, 1 5.52827 7.14285 0.853872 9.146128 Silicon, .... 1 2.90235 3.75000 0.574031 9.425969 Sulphur, . . . - Sulphide of hydrogen, . 1 2.2 2.21132 2.85714 0.455932 9.544068 2 1.1912 1.17476 1.51786 0.181231 9.818769 Sulphurous acid, 2 2.247 2.21131 2.85714 0.455932 9.544068 Water, .... 2 0.6235 0.62193 0.80357 9.905025 0.094975 * Computed from tlie speciflo gravity of carbonic acid, observed by Ecgnault. 694 TABLES. TABLE III. SPECIFIC GRAVITIES OE GASES AT 0° C; BAEOMETER, 76 cm Specific Specific Names. Gravity by Gravity by Observers. Observation. Calculation. Air, 1.000 [gault. Oxygen, . ... 1.106 Dumas and Boussin- Hydrogen, 0.0691 . . tt tc it Marsh gas, ... 0.555 0.559 Thomson. Methyle, 0.490 Olefiant gas, .... 0.978 0.980 Th. de Saussure. Bicarbide of hydrogen of Fara- day, . ... 1.920 1.960 Faraday. Phosphide of hydrogen, 1.214 1.193 Dumas. Arsenide of hydrogen, 2.695 2.695 11 Chlorine, 2.470 . . Gay-Lussac & The- Oxide of chlorine, or hypochloric [nard. acid, . . 2.340 Hypochlorous acid of Balard, . , , 2.980 Nitrogen 0.972 . . Dumas and Bonssin- Protoxide of nitrogen, 1.520 1.525 Colin. [gault. 1.0388 1.036 Berard. Cyanogen, .... 1.806 1.818 Gay-Lnssac. Chloride of cyanogen, . . . 2.116 It Ammonia, 0.596 0.591 Biot and Arago. Oxide of carbon, .... 0.957 . , Cruikshanck. Carbonic acid, . . 1.529 Dumas and Boussin- Chloro-carhonic acid, 3.399 [gault. Sulphurous acid, .... 2.234 , . Thenard. Acid, chlorohydric, 1.247 1.260 Biot and Arago. bromohydric, . 2.731 iodohydric, 4.443 4.350 Gay-Lussac. 1.191 . . Gay-Lussac & The- selenohydric, . . 2.795 Bineau. [nard. tellurohydric. • . 4.490 " fluoboraeic. 2.371 . . John Davy. fluosilicic. 3.573 . , ti chloroboracic. 3.420 , . Dumas. Monohydrate of methyle, 1.617 1.601 Dumas and Peligot. Chlorohydrate of methyle. 1.731 1.737 tt tt it riuohydrate of methyle, 1.186 1.170 It tt (t TABLES. 695 TABLE IV. SPECIFIC GRAVITIES OF VAPORS EEDTTCED BY CALCULATION TO 0° C, AND BAROMETER 76 c. m. Specific Speeiflo Names. Gravity by Gravity by Observers. Dbserration. Oalculation, Air, 1.000 Bromine, 5.540 5.390 Mitscherlich. Iodine 8.716 8.700 Dumas. Sulphur, 6.617 6.650 (1 Phosphorus, 4.420 4.320 (( Arsenic, 10.600 10.360 Mitscherlich. Mercury, ..... 6.976 6.970 Dumas. Acid, arsenious, . 13.850 13.300 Mitscherlich. sulphuric anhydrous, S.OOO 2.760 11 selenious, .... 4.030 . . tc hyponitrous 1.720 O O I— I B « O CO o I— I 6h fa W o o H w H fa O fa O 1 1 tDWQO-^0»oO*nOiftoicoi^^inoo--Tj»n(McOiri^cOifscoO«^>ncoOtX)r-»ccrj(No coaooooooor-r~r-t^tooto«)ooicr*«'H'0'-'r*cococoGocoo»i-tm'«iltOCO(MTfCft COCN — OOiOOOOr-CDiOm-^COCOCM — — OOOiOiOlOOODr- 1 r^t^^r^eot^^cnoiF^r-eooon^oeomaoo'* COOOOOOfNOiOCOO — ■*^— 'irtC^C^O^i-iiow O(M'*r^i-HTtC000C000'#O«)C0Ol^ioe:i.— O r- r-tDvnir5Trcoco(NOii-Hf-;.--ppocr)Oimcnoi ^^^^^r^i-Jr-Jrir^i-ir^^^rMi-Jddddd 1 1 s Ol (?1 OS CT> Ol OT CT> Oi OS Ol Oi 0> Ol CT) OS Oi Ol OS COOOOOCOOOOOOOQOOOQOOOOOOOQOOOQOCOQOOOOOCO 1 ^r-i^Ot^co-i«>nair»ooscooi-*o>a>Tt<'#oooo '-'00-^i-«C\|'*tOOO — inOOCOOOCOOOrf^OOinCO ^OOiOOt^^Din-^WmOJ— '"-"OOOSOIOSOOOOOO OOOOOOOOOOOOOOOOOOOOO d d d d d'd ddddddd odd d dodo § 1 d M mow— ir-coascDcoCT>tOTfi— iasr^iOKi--'OCiooi--.cDc£j«o CN<— lOlOOtOincoC^^OSOOr-tO-^tCOtM— iOOir-'X)mr}>0?(M OSOiaOCOCOCOOOOOQO«^l^r-t^r-t^t^t^t-tDt£)iXitDOtD(X> to to lO iO ^ W tD to CD to CO to to to tD tO tO tD tD tD tO tO tO tO tO oooooooooooqooooooooooooo (4 ooooooooooooooooooooooooo 0>0>OSO*OSOiOJO>OSOsOSOiOSOiO^OSOiOSOSaiO>030iO^OS ooooooooooooooooooooooooo S'6odoS(6<6do■cno^~■*^ostoxJ"r-osr^l^ic^)(MOos^-. tomm^n■^■^Tttcococof^^c^CT^^— ii-HOOOOOoosoi o<6 d<:i(Ddodd<^ s a irt^(?j'*CD-d«MC0tf5Ot^l^aJC0OQ0C0^tDC^C0 COOOCOOOCOOiO — r--tOtotom»f:)inmTt'-+Tji-^-t>i* oppSqooqpoppqqoooooco dddddodddoddddododddd 8. 1 3 S3 °Oi-<-HO00C0e0<0^WC0O}C0OOCNiftO»O ddeot^^i^»oeo-(Oir^iATt<(N— QD(om-^c>ii-<0) ooa)o»o>oaaococoQOGOt»t^t^i>t^^»cococoto rH a> Tt irt tN ID »o ^ rr M CD r* ■* o6^»od»rii-^od»n(N--Idosdd(N-^r^dTj!cft-^dcocO'^ cj.-HosaotowcotN.-tocnt^r^coiftTt ^_l>. (N OS O^ 00 CO eb r-^ wri CO* — " c> co' eo ■«* co* »-* oi od w m* co oi d o> t^ d ■<* co oi ^ ^0cO(0(X>«D»OiOW»f5iOiO-*TrTii-*-*'^TtC0C0C0C0C0C0C0 ll 1 i-iCT«DcocotocococDco(N»n<-TltOQ0r-t^O>ddiO 1 a (O •* CO CO « (N (N CO ift (D 00 C4 in 00 co(N(N^oosoocoi>.ix>»ninTjfeoco(N^oq(^qQot^t^eo rrTJ5Tt-.^^cocococ6cococococococococ6coc*c4©ic>iCT(?i 1 J d H — oot^r^oooeoQOTf<.-oscooi^-*QOcoooor^(^ f-coor-'^tNOstOTfiNast^iO'^iMOOsaotDin'^ cooooot^ir^r^iaDtoIG^(NO1tNO1(71(M(NC4(N(M(Nd'd'oddddSddtd'dG ffl g i ■J o 1 a ooscooO'#cflcoaor*c»m»noo»nmosr^coeo»-*coosos(N intCyoDincoco^oOiniNOOsotNinoco-^J'coco-^r-oi oscoSG*itSSjr^St^cooo-*oin(MQO-*.-.r--*^oo»ni«cN(?iCT(Noi(N«« i coccoot0t^coNoo(N«r-eor-co(NiftrtcococD« eDr-coo(NinQO^»noscoaocoosinf--c^GOCOOstOG30s^:S:i'^ oiostD-^r^Qorracooi^in(Not:'GS^St~^?'P?2JS."t,':^ XjI-P-iF-H — ooooososososcoooaocoi>'r-r-.i--cDto*-a>o>o^w«2ISS^22CTWCTw^ 59* 702 TABLES. TABLE VIII. TABLE OF THE TENSION OF THE VAPOE OF ABSOLUTE ALCOHOL, ACCORDING TO REGNAULT.* OC. Tension. oC. Tenaion. OC. Tension. OC. Tension. o jn. m. m. m. o m. m. o m. m. 0.0 12.73 4.0 16.62 8.0 21.31 12.0 27.19 0.1 12.82 4.1 16.73 8.1 21.45 12.1 27.36 0.2 12.91 4.2 16.84 8.2 21.53 12.2 27.53 0.3 13.01 4.3 16.95 8.3 21.72 12.3 27.70 0.4 13.10 4.4 17.05 8.4 21.85 12.4 27.87 0.5 13.19 4.5 17.16 8.5 21.99 12.5 28.04 0.6 13.28 4.6 17.27 8.6 22.12 12.6 28.21 0.7 13.37 4.7 17.38 8.7 22.25 12.7 28.38 0.8 13.46 4.8 17.48 8.8 22.39 12.8 28.55 0.9 13.56 4.9 17.59 8.9 22.52 12.9 28.72 1.0 13.65 5.0 17.70 9.0 22.66 13.0 28.89 1.1 13.74 ^.1 17.82 9.1 22.80 13.1 29.07 • 1-2 13.84 5.2 17.93 9.2 22.94 13.2 29.25 1.3 13.93 5.3 18.04 9.3 23.08 13.3 29.43 1.4 14.03 5.4 18.16 9.4 23.23 13.4 29.61 l.j 14.12 5.5 18.27 9.5 23.37 13.5 29.79 1.6 14.22 5.6 18.38 9.6 23.51 13.6 29.97 1.7 14.31 5.7 18.50 9.7 23.65 13.7 30.15 1.8 14.41 5.8 18.61 9.8 23.79 13.8 30.23 1.9 14.50 5.9 18.73 9.9 23.94 13.9 30.51 2.0 . 14.60 6.0 18.84 10.0 24.08 14.0 30.69 2.1 14.70 6.1 18.96 10.1 24.23 14.1 30.88 2.2 14.79 6.2 19.03 10.2 24.38 14.2 31.07 2.3 14.89 6.3 19.20 10.3 24.53 14.3 31.26 2.4 14.99 6.4 19.32 10.4 24.68 14.4 31.45 2.5 15.09 6.5 19.44 10.5 24.83 14.5 31.64 2.6 15.19 6.6 19.56 10.6 24.99 14.6 31.84 2.7 15.29 6.7 19.68 10.7 25.14 14.7 32.03 2.8 15.39 6.8 19.80 10.8 25.29 14.8 32.22 2.9 15.49 6.9 19.92 10.9 25.44 14.9 32.41 3.0 15.59 7.0 20.04 11.0 25.59 15.0 32.60 3.1 15.69 7.1 20.17 11.1 25.75 15.1 32.80 3.2 15.79 7.2 20.30 11.2 25.91 15.2 33.01 3.3 15.90 7.3 20.43 11.3 26.07 15.3 33.21 3.4 16.00 7.4 20.55 11.4 26.23 13.4 33.41 3.5 16.10 7.5 20.68 11.5 26.39 15.5 33.61 3.6 16.21 7.6 20.81 11.6 26.55 15.6 33.82 3.7 16.31 7.7 20.93 11.7 26.71 15.7 34.02 3.8 16.41 7.8 21.06 11.8 26.87 15.8 34.22 .S.9 16.52 7.9 21.19 11.9 27.03 15.9 34.42 * This table is calculated from recent experiments of Regnault. TABLES. 703 OC. Tension. OC. Tension. OC. Tension. OC. Tension. o m. m. o m.m. m.m. m.m. 16.0 34.62 20.0 44.00 24.0 55.70 28.0 70.02 16.1 34.84 20.1 44.27 24.1 56.04 28.1 70.49 16.2 35.05 20.2 44.54 24.2 66.37 28.2 70.89 16.3 35.27 20.3 44.81 24.3 56,70 28.3 71.29 16.4 35.48 20.4 45.08 24.4 57.03 28.4 71.69 16.5 35.70 20.5 45.35 24.5 57.37 28.5 72.09 16.6 35.91 20.6 45.61 24.6 57.70 28.6 72.49 16.7 36.13 20.7 45.88 24.7 58.03 28.7 72.89 16.8 36.34 20.8 46.15 24.8 58.36 28.8 73.29 16.9 36.56 20.9 46.42 24.9 58.70 28.9 73.69 17.0 36.77 21.0 46.69 25.0 59.03 29.0 74.09 17.1 37.00 21.1 46.98 25.1 59.38 29.1 74.53 17.2 37.23 21.2 47.26 25.2 59.73 29.2 74.96 17.3 37.45 21.3 47.55 26.3 60.08 29.3 75.39 17.4 37.68 21.4 47.83 25.4 60.43 29.4 75.82 17.5 37.91 21.5 48.12 25.5 60.78 29.5 76.25 17.6 38.14 21.6 48.40 25.6 61.13 29.6 76.68 17.7 38.36 21.7 48.69 25.7 61.48 29.7 77.12 17.8 38.59 21.8 48.97 25.8 61.83 29.8 77.55 17.9 38.82 21.9 49.26 25.9 62.18 29.9 30.0 77.98 78.41 18.0 39.05 22.0 49.54 26.0 62.53 18.1 39.29 22.1 49.84 26.1 62.90 18.2 39.53 22.2 50.14 26.2 63.27 18.3 39.77 22.3 60.44 26.3 63.64 18.4 40.01 22.4 50.74 26.4 64.01 18.5 40.25 22.5 51.04 26.5 64.37 18.6 40.49 22.6 51.34 26.6 64.74 18.7 40.73 22.7 51.64 26.7 65.11 18.8 40-97 22.8 51.94 26.8 65.48 18.9 41.21 22.9 62.24 26.9 65.85 39.0 41.45 23.0 52.54 27.0 66.22 19.1 41.71 23.1 52.86 27.1 66.60 19.2 41.96 23.2 63.17 27.2 66.99 19.3 42.22 23.3 53.49 27.3 67.38 19.4 42.47 23.4 53.81 27.4 67.77 19.5 42.73 23.5 54.12 27.5 68.15 19.6 42.98 23.6 64.44 27.6 68.54 , 19.7 43.24 23.7 64.75 27.7 68.93 19.8 43.49 23.8 55.07 27.8 69.31 19.9 43.75 23.9 55.38 27.9 69.70 • 704 TABLES, TABLE IX. TABLE FOR THE TENSION OF AQUEOUS VAPOR FOR TEMPERA- TXJRES FROM —32° TO +230°, BY BEGNAULT. Temperature. Tension in Centimetres. Temperature. Tension in Centimetres. Temperature. Tension in Centimetres. o —32 0.0320 o +19 1.6346 +105° . 90.6410 30 0.0386 20 1.7391 110 107.5370 25 0.0605 21 1.8495 116 126.9410 20 0.0927 22 1.9659 120 149.1280 15 0.1400 23 2.0888 125 174.388 10 0.2093 24 2.2184 130 203.028 — 5 0.3113 25 2.3550 135 235.373 0.4600 26 2.4988 140 271.763 + 1 0.4940 27 2.6605 145 312.555 2 0.5302 28 2.8101 150 ■ 358.123 3 0.5687 29 2.9782 155 408.856 4 0.6097 30 3.1548 160 465.162 5 0.6534 35 4.1827 165 527.454 6 0.6998 40 5.4906 170 596.166 7 0.7492 45 7.1391 175 671.743 8 0.8017 50 9.1982 180 754.639 9 0.8574 55 11.7478 185 845.323 10 0.9165 60 14.8791 190 944.270 11 0.9792 65 18.6945 195 1051.963 12 1.0457 70 23.3093 200 1168.896 13 1.1162 75 28.8517 205 1295.566 14 1.1908 80 35.4643 210 1432.480 15 1.2699 85 43.3041 215 1580.133 16 1.3536 90 52.5450 220 1739.036 17 1.4421 95 63.3778 225 1909.704 18 1.5357 100 76.0000 230 2092.640 Tension of Vapor of Water, according to Didong and Arago. Temperature. Tension in Atmosplieres. Pressure in Eilogrammes onlc. m.2 Temperature. Tension in Atmosplieres. Pressure in Eilogrammes onlSTmTa o 100 121.4 135.1 145.4 160.2 172.1 190.0 203.6 214.7 1 2 3 4 6 8 12 16 20 1.033 2.066 3.099 4.106 6.198 8.264 12.396 16.528 20.660 226.3 265.89 311.36 363.58 423.57 462.71 492.47 516.75 25 60 100 200 400 600 800 1000 25.825 51.650 103.3 206.6 413.2 619.8 826.4 1033.0 TABLES 705 TABLE X. TABLE FOR THE TENSION OF AQUEOUS VAPOR FOR TEMPERA- TURES FROM —2° TO +35° C, ACCORDING TO REGNAULT. OC. Tension. OC. Tension. oo. Tension. OC. Tension. m.m. o m.m. o m.m. o m.m. —2.0 8.935 +2.0 5.302 +6.0 6.998 +10.0 9.163 1.9 3.985 2.1 5.340 6.1 7.047 10.1 9.227 1.8 4.016 2.2 5.378 6.2 7.095 10.2 9.288 1.7 4.047 2.3 5.416 6.3 7.144 10.3 9.350 1.6 4.078 2.4 5.454 6.4 7.193 10.4 9.412 1.5 4.109 2.5 5.491 6.5 7.242 10.5 9.474 1.4 4.140 2.6 5.530 6.6 7.292 10.6 9.537 1.3 4.171 2.7 5.569 6.7 7.342 10.7 9.601 1.2 4.203 2.8 5.608 6.8 7.392 10.8 9.663 1.1 4.235 2.9 5.647 6.9 7.442 10.9 9.728 1.0 4.267 3.0 5.687 7.0 7.492 11.0 9.792 0.9 4.299 3.1 .5.727 7.1 7.544 11.1 9.837 0.8 4.331 3.2 5.767 7.2 7.595 11.2 9.923 0.7 4.364 3.3 5.807 7.3 7.647 11.3 9.989 0.6 4.397 3.4 5.848 7.4 7.699 11.4 10.054 0.5 4.430 3.5 5.889 7.3 7.751 11.5 10.120 0.4 4.463 8.6 5.930 7.6 7.801 11.6 10.187 0.3 4.497 8.7 5.972 7.7 7.857 11.7 10.255 0.2 4.531 3.8 6.014 7.8 7.910 11.8 10.322 —0.1 4.563 3.9 6.055 7.9 7.964 11.9 10.389 0.0 4.600 4.0 6.097 8.0 8.017 12.0 10.457 +0.1 4.633 4.1 6.140 8.1 8.072 12.1 10.526 0.2 4.667 4.2 6.183 8.2 8.126 12.2 10.596 0.3 4.700 4.3 6.226 8.3 8.181 12.3 10.665 0.4 4.733 4.4 6.270 8.4 8.236 12.4 10.734 0.5 4.767 4.5 6.313 8.5 8.291 12.5 10.804 0.6 4.801 4.6 6.357 8.6 8.347 12.6 10.875 0.7 4.836 4.7 6.401 8.7 8.404 12.7 10.947 0.8 4.871 4.8 6.445 8.8 8.461 12.8 11.019 0.9 4.905 4.9 6.490 8.9 8.517 12.9 11.090 1.0 4 940 5.0 6.534 9.0 8.574 13.0 11.162 1.1 4.973 5.1 6.5S0 9.1 8.632 13.1 11.235 1.2 5.011 5.2 6.625 9.2 8.690 13.2 11.309 1.3 5.047 5.3 6.671 9.3 8.748 13.3 11.383 1.4 5.0S2 5.4 6.717 9.4 8.807 18.4 11.456 1.5 5.118 5.5 6.763 9.5 8.865 18.5 11.530 1.6 5.133 5.6 6.810 9.6 8.925 18.6 11.605 1.7 5.191 5.7 6.857 9.7 8.985 13.7 11.681 1.3 5.228 5.8 6.901 9.8 9.045 13.8 11.757 1.9 5.265 5.9 6.951 9.9 9.105 13.9 11.882 706 TABLES. OC. Tension. OC. Tension. OC. Tension. OC. Tension. m. m. m. m. o m. m. m.m. + 14.0 11.908 +18.0 15.357 +22.0 19.659 +26.0 24.988 14.1 11.986 18.1 15.454 22.1 19.780 26.1 25.138 14.2 12.064 18.2 15.552 22.2 19.901 26.2 25.288 14.3 12.142 18.3 15.650 22.3 20.022 26.3 25.438 14.4 12.220 18.4 15.747 22.4 20.143 26.4 25.583- 14.5 12.298 18.5 13.845 22.5 20.265 26.5 25.7.38 14.6 12.378 18.6 15.945 22.6 20.389 26.6 25.891 14.7 12.458 18.7 16.045 22.7 20.514 26.7 26.045 14.8 12.538 18.8 16.145 22.8 20.639 26.8 26.198 14.9 12.619 18.9 16.246 22.9 20.763 26.9 26.351 15.0 12.699 19.0 16.346 23.0 20.888 27.0 26.505 15.1 12.781 19.1 16.449 23.1 21.016 27.1 26.663 15.2 12.864 19.2 16.552 23.2 21.144 27.2 26.820 15.3 12.947 19.3 16.655 23.3 21.272 - 27.3 26.978 15.4 13.029 19.4 16.758 23.4 21.400 27.4 27.136 15.5 13.112 19.5 16.861 23.5 21.528 27.5 27.294 15.6 13.197 19.6 16.967 23.6 21.659 27.6 27.455 15.7 13.281 19.7 17.073 23.7 21.790 27.7 27.617 15.8 13.366 19.8 17.179 23.8 21.921 27.8 27.778 15.9 13.451 19.9 17.285 23.9 22.053 27.9 27.939 16.0 13.536 20.0 17.391 24.0 22.184 28.0 28.101 16.1 13.623 20.1 17.500 24.1 22.319 28.1 28.267 16.2 13.710 20.2 17.608 24.2 22.453 28.2 28.433 16.3 13.797 20.3 17.717 24.3 22.588 28.3 28.599 16.4 13.885 20.4 17.826 24.4 22.723 28.4 28.765 16.5 13.972 20.5 17.935 24.5 22.858 28.5 28.931 16.6 14.062 20.6 18.047 24.6 22.996 28.6 29.101 16.7 14.151 20.7 18.159 24.7 23.135 28.7 29.271 16.8 14.241 20.8 18.271 24.8 23.273 28.8 29.441 16.9 14.331 20.9 18.383 24.9 23.411 28.9 29.612 17.0 14.421 21.0 18.495 25.0 23.550 29.0 29.782 17.1 14.513 21.1 18.610 25.1 23.692 29.1 29.956 17.2 14.605 21.2 18.724 25.2 23.834 29.2 30.131 17.3 14.697 21.3 18.839 25.3 23.976 29.3 30.305 17.4 14.790 21.4 18.954 25.4 24.119 29.4 30.479 17.5 14.882 21.5 19.069 25.5 24.261 29.5 30.654 17.6 14.977 21.6 19.187 25.6 24.406 29.6 30.833 17.7 15.072 21.7 19.305 25.7 24.552 29.7 31.011 17.8 15.167 21.8 19.423 25.8 24.697 29.8 31.190 17.9 15.262 21.9 19.541 25.9 24.842 29.9 31.369 TABLES. 707 OO. Tension. oC. Tension. 0. Tension. OO. Tension. m. m. m. m. o m. m. o m. m. +30.0 31.548 +31.0 33.405 +32.0 85.359 +33.0 37.410 30.1 31.729 31.1 33.596 32.1 35.559 33.1 37.621 30.2 31.911 31.2 33.787 32.2 35.760 33.2 37.832 80.3 32.094 31.3 33.980 32.3 35.962 33.3 38.045 30.4 32.278 31.4 34.174 32.4 36.165 33.4 38.258 30.5 32.463 31.5 34.368 32.5 36.370 33.5 38.473 30.6 32.650 31.6 34.564 32.6 36.576 33.6 38.689 30.7 32.837 31.7 34.761 32.7 36.783 33.7 38.906 30.8 33.026 31.8 34.959 32.8 36.991 33.8 39.124 30.9 33.215 31.9 35.159 32.9 37.200 33.9 39.344 34.0 39.565 34.3 40.230 34.6 40.907 34.9 41.595 34.1 39.786 34.4 40.455 34.7 41.135 35.0 41.827 34.2 40.007 34.5 40.680 34.8 41.364 TABLE XI. TABLE FOR THE CALCULATION OF THE VALUE OF 1 + 0.00366 (. «. Number. Log. t. Number. Log. o —2.0 0.99268 9.99681 0.0 1.00000 0.00000 1.9 0.99305 9.99697 +0.1 1.00037 0.00016 1.8 0.99341 9.99713 0.2 1.00073 0.00032 1.7 0.99378 9.99729 0.3 1.00110 0.00048 1.6 0.99414 9.99745 0.4 1.00146 0.00063 1.5 0.99451 9.99761 0.5 1.00183 0.00079 1.4 0.99488 9.99777 0.6 1.00220 0.00095 1.3 0.99524 9.99793 0.7 1.00256 0.00111 1.2 0.99561 9.99809 0.8 1.00293 0.00127 1.1 0.99597 9.99825 0.9 1.00329 0.00143 1.0 0.99634 9.99841 1.0 1.00366 0.00159 0.9 0.99671 9.99857 1.1 1.00403 0.00175 0.8 0.99707 9.99873 1.2 1.00439 0.00191 0.7 0.99744 9.99888 1.3 1.00476 0.00207 0.6 0.99780 9.99904 1.4 1.00512 0.00222 0.5 0.99817 9.99920 1.5 1.00549 0.00238 0.4 0.99854 9.99937 1.6 1.00586 0.00254 0.3 0.99890 9.99952 1.7 1.00622 0.00270 0.2 0.99927 9.99968 1.8 1.00659 0.00285 —0.1 0.99963 9.99984 1.9 1.00695 0.00301 708 TABLES. (. Number. Log' t. Number. Lof. o +2.0 1.00732 0.00317 +6.0 1.02196 0.00943 2.1 1.00769 0.00333 6.1 1.02233 0.00959 2.2 1.00805 0.00349 6.2 1.02269 0.00975 2.3 1.00842 0.00365 6.3 1.02306 0.00991 2.4 1.00878 0.00381 6.4 1.02342 0.01006 2.5 1.00915 0.00397 6.5 1.02379 0.01022 2.6 1.00952 0.00412 6.6 1.02416 0.01038 2.7 1.00988 0.00428 6.7 1.02452 0.01054 2.8 1.01025 0.00444 6.8 1.02489 0.01069 2.9 1.01061 0.00459 6.9 1.02525 0.01084 3.0 1.01098 0.00474 7.0 1.02562 0.01099 3.1 1.01135 0.00490 7.1 1.02599 0.01115 3.2 1.01171 0.00506 7.2 1.02635 0.01131 3.3 1.01208 0.00521 7.3 1.02672 0.01147 3.4 1.01244 0.00537 7.4 1.02708 0.01162 3.5 1.01281 0.00553 7.5 1.02745 0.01177 3.6 1.01318 0.00568 7.6 1.02782 0.01193 3.7 1.01354 0.00584 7.7 1.02818 0.01208 3.8 1.01391 0.00600 7.8 1.02855 0.01223 3.9 1.01427 0.00615 7.9 1.02891 0.01238 4.0 1.01464 0.00631 8.0 1.02928 0.01253 4.1 1.01501 0.00647 8.1 1.02965 0.01269 4.2 1.015.37 0.00663 8.2, 1.03001 0.01284 4.3 1.01574 0.00678 8.3' 1.03038 0.01300 4.4 1.01610 0.00694 8.4 1.03074 0.01315 4.5 1.01647 0.00710 8.5 1.03111 0.01330 4.6 1.01684 0.00725 8.6 1.03148 0.01346 4.7 1.01720 0.00741 8.7 1.03184 0.01361 4.8 1.01757 0.00766 8.8 1.03221 0.01377 4.9 1.01793 0.00772 8.9 1.03257 0.01392 5.0 1.01830 0.00788 9.0 1.03294 0.01407 5.1 1.01867 0.00803 9.1 1.03331 0.01423 5.2 1.01903 0.00819 9.2 1.03367 0.01438 5.3 1.01940 0.00834 9.3 1.03404 0.01454 5.4 1.01976 00850 9.4 1.03440 0.01469 5.5 1.02013 0.00865 9.5 1.03477 0.01484 5.6 1.02050 0.00881 9.6 1.0.3514 0.01500 5.7 1.02086 0.00896 9.7 1.03550 0.01515 5.8 1.02123 0.00912 9.8 1.03587 0.01530 5.9 1.02159 0.00927 9.9 1.03623 0.01545 TABLES. 709 t. Number. Log. t. , Number. Log. -t-io.o 1.03660 0.01561 o +14.0 1.05124 0.02170 10.1 1.03697 0.01577 14.1 1.05161 0.02185 10.2 1.03733 0.01592 14.2 1.05197 0.02200 10.3 1.03770 0.01607 14.3 1.05234 0.02215 10.4 1.03806 O.01623 14.4 1.05270 0.02230 10.5 1.03843 0.01639 14.5 1.05307 0.02246 10.6 1.03880 0.01653 14.6 1.05344 0.02261 10.7 1.03916 0.01669 14.7 1.05380 0.02276 10.8 1.03953 0.01683 14.8 1.05417 0.02291 ip.9 1.03989 0.01698 14.9 ■ 1.05453 0.02306 11.0 1.04026 0.01714 15.0 1.05490 0.02321 11.1 1.04063 0.01729 15.1 1.05527 0.02336 11.2 1.04099 0.01744 15.2 1.05563 0.02351 11.3 1.04136 0.01759 15.3 1.05600 0.02366 11.4 1.04172 0.01775 15.4 1.05636 0.02381 11.5 1.04209 0.01790 15.5 1.05673 0.02396 11.6 1.04246 0.01805 15.6 1.05710 0.02411 11.7 1.04282 0.01820 15.7 1.05746 0.02426 11.8 1.04319 0.01836 15.8 1.05783 0.02441 11.9 1.04355 0.01851 15.9 1.05819 0.02456 12.0 1.04392 0.01867 16.0 1.05856 0.02471 12.1 1.04429 0.01882 16.1 1.05893 0.02486 12.2 1.04465 0.01897 16.2 1.05929 0.02501 12.3 1.04502 0.01912 16.3 1.05966 0.02516 12.4 1.04538 0.01928 .16.4 1.06002 0.02531 12.5 1.04575 0.01943 16.5 1.06039 0.02546 12.6 1.04612 0.01958 16.6 1.06076 0.02561 12.7 1.04648 0.01973 16.7 1.06112 0.02576 12.8 1.04685 0.01989 16.8 1.06149 0.02591 ■ 12.9 1.04721 0.02004 16.9 1.06185 0.02606 13.0 1.04758 0.02019 17.0 1.06222 0.02621 13.1 1.04795 0.02034 17.1 1.06259 0.02636 13.2 1.04831 0.02049 17.2 1.06295 0.02651 13.3 1.04868 0.02064 17.3 1.06332 0.02666 13.4 1.04904 0.02079 17.4 1.06368 0.02681 13.5 1.04941 0.02095 17.5 1.06405 0.02696 13.6 1.04978 0.02110 17.6 1.06442 0.02711 13.7 1.05014 0.02125 17.7 1.06478 0.02726 13.8 1.05051 0.02140 17.8 1.06515 0.02741 13.9 1.05087 0.02155 17.9 1.06551 0.02756 60 710 TABLES. £. Number. ^og. (. Number. Log. +18.0 1.06588 0.02771 +22.0 1.08052 0.03363 18.1 1.06625 0.02786 22.1 1.08089 0.03378 18.2 1.06661 0.02801 22.2 . 1.08123 0.03393 18.3 1.06698 0.02816 22.3 1.03162 0.03408 18.4 1.06734 0.02831 22.4 . 1.08198 0.03422 18.5 1.06771 0.02846 22.5 1.08235 0.03437 18.6 1.06808 0.02861 22.6 1.08272 0.03452 18.7 1.06844 0.02876 22.7 1.08308 0.03466 18.8 1.06881 0.02891 22.8 1.08345 0.03481 18.9 1.06917 0.02906 22.9 1.08381 0.03496 19.0 1.06954 0.02921 23.0 1.08418 0.03510 19.1 1.06991 0.02936 23.1 1.08455 0.03525 19.2 1.07027 0.02951 23.2 1.08491 0.03539 19..3 1.07064 0.02965 23.3 1.08528 0.03554 19.4 1.07100 0.02980 23.4 1.08564 0.03568 19.5 1.07137 0.02995 23.5 1.08601 0.03583 19.6 1.07174 0.03009 23.6 1.08638 0.03598 19.7 1.07210 0.03024 23.7 1.08674 0.03612 19.8 1.07247 0.03039 23.8 1.08711 0.03627 19.9 1.07283 0.03053 23.9 1.08747 0.03642 20.0 1.07320 0.03068 24.0 1.08784 0.03656 20.1 1.07357 0.03083 24.1 1.08821 0.03671 20.2 1.073^*5 0.03098 24.2 1.08S57 0.03685 20.3 1.07430 0.03113 24.3 1.08894 0.03700 20.4 1.07466 0.03128 24.4 1.08930 0.03714 20.5 1.07503 0.03142 24.5 1.08967 0.03729 20.6 1.07540 0.03157 24.6 1.09004 0.03744 20.7 1.07576 0.03172 24.7 1.09040 0.03758 20.8 1.07613 0.03187 24.8 1.09077 0.03772 20.9 1.07649 0.03201 24.9 1.09113 0.03787 21.0 1.076S6 0.0321S 25.0 1.09150 0.03802 21.1 1.07723 0.0.3231 25.1 1.09187 0.03817 21.2 1.07759 0.03246 25.2 1.09223 0.03831 21.3 1.07796 0.03261 25.3 1.09260 0.03846 21.4 1.07832 0.03275 25.4 1.09296 0.03860 21.5 1.07869 0.03290 23.5 1.09333 0.03875 21.6 1.07906 0.03305 25.6 1.09370 0.03889 21.7 1.07942 0.03320 25.7 1.09406 0.03904 21.8 1.07979 0.03334 25.8 1.09443 0.03918 21.9 1.08015 0.03349 25.9 1.09479 0.03933 TABLES. 711 t. Number. ■ Log. f. Nftabei. Log. +26.0 1.09516 0.03918 +30.0 1.10980 0.04524 26.1 1.09553 0.03963 30.1 1.11017 0.04538 26.2 1.09589 0.03977 30.2 1.11053 0.04552 26.3 1.09626 0.0.3992 30.3 1.11090 ff.04567 26.4 1.09662 0.04006 .30.4 1.11126 0.04581 26.5 1.09699 0.04021 30.5 1.11163 0.04595 26.6 1.09736 0.04035 30.6 1.11200 0.04610 26.7 1.09772 0.04050 30.7 1. 11236 0.04624 26.8 1.09809 0.04064 30.8 1.11273 0.04638 26.9 1.09845 0.04079 30.9 1.11309 0.04653 27.0 1.09882 0.04093 31.0 1.11346 0.04667 27.1 1.09919 0.04107 31.1 1.11383 0.04681 27.2 1.09955 0.04122 31.2 - 1.11419 0.04695 27.3 1.09992 0.04136 31.3 1.11456 0.04710 27.4 1.10028 0.04150 31.4 1.11492 0.04724 27.5 1.10065 0.04165 31.5 1.11529 0.04738 27.6 1.10102 0.04179 31.6 1.11566 0.04753 27.7 1.10138 0.04193 31.7 1.11602 0.04767 , 27.8 1.10175 0.04208 31.8 1.11639 0.04781 27.9 1.10211 0.04222 31.9 1.11675 0.04796 28.0 1.10248 0.04237 32.0 1.11712 0.04810 28.1 1.10285 0.04251 32.1 1.11749 0.04824 28.2 1.10321 0.04266 32.2 1.11785 0.04838 28.3 1.10358 0.04280 32.3 1.11822 0.04852 28.4 1.10394 0.04295 32.4 1.11858 0.04866 28.5 1.10431 0.04309 32.5 1.11895 0.04881 , 28.6 1.10168 0.04323 32.6 1.11932 0.04S95 28.7 1.10304 0.04338 32.7 1.11968 0.04909 28.8 1.10541 0.04352 32.8 1.12005 0.04923 28.9 1.10577 0.01367 32.9 1.12041 0.04938 29.0 1.10614 0.04381 33.0 1.12078 0.04932 29.1 1.10651 0.04395 33.1 1.12115 0.04966 29.2 1.10887 0.04410 33.2 1.12151 0.04980 29.3 1.10724 0.04424 33.3 1.12188 0.04994 29.4 1.10760 04438 33.4 1.12224 0.03008 29.5 1.10797 0.04453 33.5 1.12261 0.05022 29.6 1.10834 0.04167 33.6 1.12298 0.03036 29.7 1.10870 0.04482 33.7 1.12334 0.05050 29.8 1.10907 0.04496 33.8 1.12371 0.03065 29.9 1.10943 0.04510 33.9 1.12407 0.05079 712 TABLES. t. Numte# Log. t. Number. Log. +34.0 1.12444 0.05094 o +37.0 1.13542 0.05516 34.1 1.12481 0.05108 37.1 1.13579 0.05530 34.2 1.12517 0.05122 37.2 1.13615 0.05544 34.3 1.12554 0.05136 37.3 1.13652 0.05558- 34.4 1.12590 0.05150 37.4 1.13688 0.05572 34.5 1.12627 0.05164 37.5 1.13725 0.05585 34.6 1. 12664 0.05178 37.6 1.13762 0.05599 34.7 1.12700 0.05193 37.7 1.13798 0.05613 34.8 1.12737 0.05207 37.8 1.13835 0.05627 34.9 1.12773 0.05221 37.9 1.13871 0.05B41 35.0 1.12810 0.05235 38.0 1.13908 0.05655 35 1 1.12847 0.05249 38.1 1.13945 0.05669 35.2 1.12883 0.05263 38.2 1.13981 0.05683 35.3 1.12920 0.05277 38.3 1.14018 0.05697 35.4 1.12956 0.05291 .38.4 1.14054 0.05711 35.5 1.12993 0.05305 38.5 1.14091 0.05725 35.6 1.13030 0.05319 38.6 1.14128 0.05739 35.7 1.13066 0.05333 38.7 1.14164 0.05753 35.8 1.13103 0.05347 38.8 1.14201 0.05767 35.9 1.13139 0.05361 38.9 1.14237 0.05781 36.0 1.13176 0.05375 39.0 1.14274 0.05795 36.1 1.13213 0.05389 39.1 1.14311 0.05809 36.2 1.13249 0.05403 39.2 1.14347 0.05823 36.3 1.13286 0.05417 39.3 1.14384 0.05837 36.4 1.13322 0.05431 39.4 1.14420 0.05850 36.5 1.13359 0.05446 39.5 1.14457 0.05864 36.6 1.13396 0.05460 39.6 1.14494 0.05878 36.7 1.13432 0.05474 39.7 1.14530 0.05892 36.8 1.13469 0.05488 39.8 1.14567 0.05905 36.9 1.13605 0.05502 39.9 1.14603 0.05919 40 1.14640 0.05934 50 1.18300 0.07298 41 1.15006 0.06072 51 1.18666 0.07433 42 1.15372 0.06210 52 1.19032 0.07566 43 1.15738 0.06348 53 1.19398 0.07700 44 1.16104 0.06485 54 L19764 0.07833 45 1.16470 0.06621 55 1.20130 0.07965 46 1.16836 0.06758 56 1.20496 0.08097 47 1.17202 0.06893 57 1.20862 0.08229 48 1.17568 0.07029 58 1.21228 0.08360 49 1.17934 0.07164 59 1.21594 0.08491 TABLES. 713 TABLE XII. TABLE FOR THE CALCULATION OF THE VALUE OF 1 + 0.00367 t. t. log. Di£f. t. log. Diff. (. log. Diff. 60 0.08643 131 * 100 0.13577 117 140 0.18007 105 61 0.08772 131 101 0.13693 116 141 0.18112 105 62 0.08903 131 102 0.13809 116 142 0.18217 105 63 . 0.09033 130 103 0.13925 116 143 0.18322 105 64 0.09162 129 104 0.14041 116 144 0.18426 104 65 0.09291 129 105 0.14156 115 145 0.18530 104 66 0.09420 129 106 0.14271 115 146 0.18634 104 67 0.09548 128 107 0.14385 114 147 0.18738 104 68 0.09676 128 108 0.14499 114 148 0.18841 103 69 0.09803 127 109 0.14613 114 149 0.18944 103 70 0.09930 127 110 0.14727 114 150 0.19047 103 71 0.10057 127 111 0.14841 114 151 0.19150 102 72 0.10183 126 112 0.14954 113 152 0.19252 102 73 0.10309 126 113 0.15067 113 153 0.19354 102 74 0.10434 125 114 0.15179 112 154 0.19456 102 75 0.10559 125 115 0.15291 112 155 0.19558 102 76 0.10684 125 116 0.15403 112 156 0.19660 102 77 0.10809 125 117 0.15515 112 157 0.19761 101 78 0.10933 124 118 0.15626 111 158 0.19862 101 79 0.11057 124 119 0.15737 111 159 0.19963 101 60 0.11180 123 120 0.15848 111 160 0.20063 100 81 0.11303 123 121 0.15959 111 161 0.20163 100 82 0.11426 123 122 0.16069 110 162 0.20263 100 83 0.11548 122 123 0.16179 110 163 0.20363 100 84 0.11670 122 124 0.16289 110 164 0.20463 100 85 0.11792 122 125 0.16398 109 165 0.20562 99 86 0.11913 121 126 0.16507 109 166 0.20661 99 87 0.12034 121 127 0.16616 109 167 0.20760 99 88 0.12155 121 128 0.16725 109 168 0.20859 99 89 0.12275 120 129 0.16833 108 169 0.20958 99 90 0.12395 120 130 0.16941 108 170 0.21056 98 91 0.12515 120 131 0.17049 108 171 0.21154 98 92 0.12634 119 132 0.17156 107 172 0.21252 98 93 0.12753 119 133 0.17263 107 173 0.21350 98 94 0.12872 119 134 0.17370 107 174 0.21447 97 95 0.12990 118 135 0.17477 107 175 0.21544 97 96 0.13108 118 136 0.17584 107 176 0.21641 97 97 0.13226 118 137 0.17690 106 177 0.21738 97 98 0.13343 117 138 0.17796 106 178 0.21834 96 99 0.13460 117 139 0.17902 106 179 0.21930 96 60' 714 TABLES. 1. log. Ditf. t. log. Diff. t. log. Diff. 180 0.22026 96 220 0.25705 88 260 0.29027 82 181 0.22122 96 221 0.25793 88 261 0.29178 Si 182 0.22218 96 222 0.25881 8^ 262 0.29260 82 . 183 0.22314 96 223 0.25969 88 263 0.29341 81 184 0.22409 95 224 0.26057 88 264 0.29422 81 185 0.22504 95 225 0.26144 87 265 0.29503 81 186 0.22599 95 226 0.26231 87 266 0.29584 81 187 0.22693 94 227 0.26318 87 267 0.29664 80 188 0.22787 94 228 0.26405 87 268 0.29745 81 189 0.22882 95 229 0.26492 87 269 0.29825 80 190 0.22976 94 230 0.26578 86 270 0.29905 80 191 0.23070 94 231 0.26665 87 271 0.29985 80 192 0.23163 93 232 0.26751 86 272 0.30064 79 193 0.23257 94 233 0.26837 86 273 0.30144 80 194 0.23350 93 234 0,26922 85 274 0.30224 60 195 0.23443 93 235 0.27008 86 275 0.30303 79 196 0.23536 93 236 0.27094 86 276 0.30383 80 197 0.23628 92 ■ 237 0.27179 85 277 0.30462 79 198 0.23721 93 238 0.27264 85 278 0.30541 79 199 0.23813 92 239 0.27349 85 279 0.30620 79 200 0.23905 92 240 0.27434 85 280 0.30698 78 201 0.23997 91 241 0.27519 85 281 0.30776 78 202 0.24088 92 242 0.27603 84 282 0.30855 79 203 0.24180 91 243 0.27688 85 283 0.30933 78 204 0.24271 91 244 0.27772 84 284 0.31011 ■78 205 0.24362 91 245 0.27856 84 285 0.31089 78 206 0.24453 91 246 0.27940 84 286 0.31167 78 207 0.24544 90 247 0.28023 83 287 0.31245 78 208 0.24634 92 248 0.28107 84 288 0.31323 78 209 0.24724 90 249 0.28190 83 289 0.31400 77 210 0.24814 90 250 0.28274 84 290 0.31477 77 211 0.24904 90 251 0.28357 83 291 0.31554 77 212 0.24994 90 252 0.28439 82 292 0.31631 77 213 0.25084 90 253 0.28522 83 293 0.31708 77 214 0.25173 89 254 0.28605 83 294 0.31785 77 215 0.25262 89 255 0.28687 82 295 0.31862 77 216 0.25351 89 256 0.28769 82 296 0.31938 76 217 0.25440 89 257 0.28851 82 297 0.32014 76 218 0.25529 89 258 0.28933 82 298 0.32091 77 219 0.25617 88 259 0.29015 82 299 0.32167 76 TABLES. 715 TABLE XIII. Expansion of Glass. TABLE FOK THE CALCULATION OP THE VALUE OE l+K(ti t>—t. log. Diff. fi — t. log. Did. 100 0.00117 200° 0.00234 12 110 0.00129 12 210 0.00246 12 120 0.00140 11 220 0.00257 11 130 0.00152 12 230 0.00269 12 140 0.00164 12 240 0.00281 12 150 0.00176 12 250 0.00293 12 160 0.00187 11 260 0.00304 11 170 0.00199 12 270 0.00316 12 180 0.00211 12 280 0.00328 12 190 0.00222 11 290 0.00339 11 TABLE XIV. TABLE FOR THE CALCULATION OF THE WEIGHT OF ONE CUBIC CENTIMETRE OP AIR. Weight at 0° = 0.0012932. H^ = 76 c. m. t. log. Diff t. log. Diff. a 7.11166 o 15 7.08739 151 1 7.11007 159 16 7.08688 151 2 7.10848 159 17 7.08538 150 3 7.10690 158 18 7.08388 150 •4 7.10533 157 19 7.09239 149 6 7.10376 157 20 7.08090 149 6 7.10220 156 21 7.07942 148 7 7.10064 156 22 7.07794 148 8 7.09909 155 23 7.07647 147 9 7.09755 154 24 7.07500 147 10 7.09601 154 25 7.07354 146 11 7.09447 154 26 7.07208 . 146 12 7.09294 153 27 7.07063 145 13 t.09142 152 28 7.06918 145 14 7.08990 152 29 7.06774 144 The following corrections must be added to the above logarithms when the barometer stands higher than 76 c. m., and subtracted from them when' it stands lower. The correction for tenths and hundredths of centimetres is found by moving the decimal point one or two figures to the left. Diff. in cm. Oorr. Diff. in cm. Corr. Diff. in cm. Corr. 1 0.0057 4 0.0228 7 0.0399 2 0.0114 . 5 0.0285 8 0.0456 3 0.0171 6 0.0342 9 0.0513 716 TABLES. .TABLE XV. EXPANSION OF SOLIDS. Name of Substance. Interval of Coefficienta of Expansion. Temperature. Decimal Fractions. Vulgar Eract. Linear Expansion determined by Lavoisier and Laplace. English Flint-Glass, . . 0° to 100° 0.00081166 TsW Glass tube (without lead), 0.00087572 ttVj Steel (not hardened), . 0.00107880 ^T Steel (hardened), 0.00123956 iriT Soft Iron, 0.00122045 ^TB' Gold, . 0.00146606 ^i^ Copper, 0.00171220 3^F¥ Brass, 0.00186760 -d^ Silver, .... 0.00190868 ■52T Tin, . ; :, ,< 0.00193765 TTS Lead, . 0.00284836 sli By Dulong and Petit Platinum, (0° to 100° |o to 300 0.00088420 1 TTTTT 0.00275482 Tin CO to 100 0.0008j6133 ttVt Glass, .j to 200 0.00184502 lir (o to 300 0.00303252 32 9' Iron, (0 to 100 1 to 300 0.00118210 1 b4,6 0.00440528 227 Copper, (0 to 100 jo to 300 0.00171820 Ti^ 0.00564972 T+T By Wollaston. Palladium, . . . . | 0° to 100° 0.00100000 Twtr By Brunner. — Expansion for me Degree. Ice, ... . 1 —6° to 0° 0.0000375 tIt Cubic Expansion determined by Kopp. Substance. Formula. Copper, Cu Lead, Pb Tin, Sn Iron, Fo Zinc, Zn Cadmium, Cd Bismuth, Bi Antimony, Sb Sulphur, S Galena, PbS Zinc-blende, ZnS Iron pyrites, . FeSj Rutile, TiOa Tin stone. SnOa Iron-glance, FeaOa Magnetic iron ore, FeaOi Cub. Expan. for 1° C. 0.000051 0.000089 0.000069 0.000037 0.000089 0.000094 0.000040 0.000033 0.000183 0.000068 0.000036 0.000034 0.000032 0.000016 0.000040 0.000029 Substance. Fluor-spar, Aragonite, Calc-spar, Bitter-spar, Iron-spar, Heavy-spar, Celestine, Quartz, Orthoclase, Soft soda glass. Another sort. Hard potash- glass, Formula. CaF CaO, C02 CaO, 002 ( Ca0,C02 •! \ +MgO, COa ) ( Fe (Mn, Mg) O, ) \ CO, ] BaO, SO3 SrO, SO3 SiOa j ( KO, SiOa 1 1 -fALiOa, SSiOaf Cub. Expan. for 1° C. 0.000062 0.000065 0.000018 0.000035 0.000035 0.000058 0.000061 0.000042 0.000039 0.000026 0.000017 0.000026 0.000024 0.000021 TABLES. 717 TABLE XVI. VOLUME ASD DENSITY OF WATER. — BY KOPP. Tempera- Volume of Water Sp. Gr. of Water Volume of Water Sp. Gr. of Water ture. (at 0» = 1). (atO° = l). (at4°=l). {at4° = l). o 1.00000 1.000000 1.00012 0.999877 1 0.99995 1.000053 1.00007 0.999930 2 0.99991 1.000092 1.00003 0.999969 3 0.99989 1.000115 1.00001 0.999992 4 0.99988 1.000123 1.00000 1.000000 5 0.99988 1.000117 1.00001 0,999994 6 0.99990 1.000097 1.00003 0.999973 7 0.99994 1.000062 1.00006 0.999939 8 0.99999 1.000014 1.00011 0.999890 9 1.00005 0.999952 1.00017 0.999829 10 1.00012 0.999876 1.00025' 0.999753 11 1.00021 0.999785 1.00034 0.999664 12 1.00031 0.999686 1.00044 0.999562 13 1.00043 0.999572 1.00055 0.999449 14 1.00036 0.999445 1.00068 0.999322 15 1.00070 0.999306 1.00082 0.999183 16 1.00085 0.999155 1.00097 0.999032 17 1.00101 0.998992 1.00113 0.998869 18 1.00118 0.998817 1.00131 0.998695 19 1.00137 0.998631 1.00149 0.998509 20 1.00157 0.998435 1.00169 0.998312 21 1.00178 0.998228 1.00190 0.998104 22 1.00200 0.998010 1.00212 0.997886 23 1.00223 0.997780 1.00235 0.997637 24 1.00247 0.997541 1.00259 0.997419 25 1.00271 0.997293 1.00284 0.997170 26 1.00293 0.997035 1.00310 0.996912 27 1.00319 0.996767 1.00337 0.996644 28 1.00347 0.996489 1.00365 0.996*367 29 1.00376 0.996202 1.00393 0.996082 30 1.00406 0.995908 1.00423 0.99578T 35 1.00370 40 1.00753 43 1.00954 50 1.01177 1 55 1.01410 60 1.01659 63 1.01930 70 1.02225 75 1.02541 80 1.02858 83 1.03189 90 1.033J0 95 1.03909 100 1.04299 718 TABLES. TABLE XVII. FOE CONVERTING DEGREES OF THE CENTIGRADE THERMOME- TER INTO DEGREES OF FAHRENHEIT'S SCALE. Cent. Fahr. Cent. —58° Fahr. Cent. Fahr. Cent. Fahr. Cent. Fahr. —100° — 14S.0 — 72°.4 —16° +3°.2 +26 +78°.8 +68 + 154.4 99 146.2 57 70.6 15 5.0 27 80.6 66 156.2 98 144.4 56 68.8 14 6.8 28 82.4 70 158.0 97 142.6 55 67.0 13 8.6 29 84.2 71 159.8 96 140.8 54 65.2 12 10.4 30 86.0 72 161.6 95 139.0 53 63.4 11 12.2 31 87.8 73 163.4 94 137.2 52 61.6 10 14.0 32 89.6 74 165.2 93 135.4 51 59.8 9 15.8 33 91.4 75 167.0 92 133.6 50 58.0 8 17.6 34 93.2 76 168.8 91 131.8 49 56.2 7 19.4 35 95.0 77 170.6 90 130.0 48 54.4 6 21.2 36 96.8 78 172.4 89 128.2 47 52.6 5 23.0 37 98.6 79 174.2 88 126.4 46 50.8 4 24.8 38 100.4 80 176.0 87 . 124.6 45 49.0 3 26.6 39 102.2 81 177.8 86 122.8 44 47.2 2 28.4 40 104.0 82 179.6 85 121.0 43 45.4 — 1 30.2 41 105.8 83 181.4 84 119.2 42 43.6 32.0 42 107.6 84 183.2 83- 117.4 41 41.8 + 1 33.8 43 109.4 85 185.0 82 115.6 40 40.0 2 35.6 44 111.2 86 186 8 81 113.8 39 38.2 3 37.4 45 113.0 87 188.6 80 112.0 38 36.4 4 39.2 46 114.8 88 190.4 79 110.2 37 34.6 5 41.0 47 116.6 89 192.2 78 108.1 36 32.8 6 42.8 48 118.4 90 194.0 77 106.6 3.5 31.0 7 44.6 49 120.2 91 195.8 76 104.8 34 29.2 8 46.4 50 122.0 92 197.6 75 103.0 33 27.4 9 48.2 51 123.8 93 199.4 74 101.2 32 25.6 10 50.0 52 125.6 94 201.2 73 99.4 31 23.8 11 51.8 53 127.4 95 203.0 72 97.6 30 22.0 12 53.6 54 129.2 96 204.8 71 95.8 29 20.2 13 55.4 55 131.0 97 206.6 70 94.0 28 18.4 14 57.2 56 132.8 98 208.4 69 92.2 27 16.6 15 59.0 57 134.6 99 210.2 68 90.4 26 14.8 16 60.8 58 136.4 100 212.0 67 88.i 25 13.0 17 62.6 59 138.2 101 213.8 66 86.8 24 11.2 18 64.4 60 140.0 102 215.6 65 85.0 23 9.4 19 66.2 61 141.8 103 217.4 64 83.2 22 7.6 20 68.0 62 143.6 104 219.2 63 81.4 21 5.8 21 69.S 63 145.4 105 221.0 62 61 60 59 79.6 77.8 76.0 74.2 20 19 18 17 4.0 2.2 —0.4 + 1.4 22 23 24 25 71.6 73.4 75.2 77.0 64 65 66 67 147.2 149.0 150.8 152.6 106 107 108 109 222.8 224.6 226.4 228.2 TABLES. 7iy Cent. Fahr. Cent. Fahr. . Cent. Fahr. Cent. Fahr. CeAt. Fahr. +110 +230.0 +158° +316°.4 +206° +402°.8 +254° +489.2 +302° +575°.6 111 231.8 159 318.2 207 404.6 255 491.0 303 577.4 112 233.6 160 320.0 208 406.4 256 492.8 304 579.2 113 235.4 161 321.8 209 408.2 257 494.6 305 581.0 114 237.2^ 162 323.6 210 410.0 258 496.4 306 582.8 115 239.0 163 325.4 211 411.8 259 498.2 307 584.6 116 240.8 164 327.2 212 413.6 260 500.0 308 586.4 117 242.6 165 329.0 213 415.4 261 501.8 309 688.2 118 244.4 166 330.8 214 417.2 262 503.6 310 590.0 119 246.2 167 332.6 215 419.0 263 505.4 311 591.8 120 248.0 168 334.4 216 420.8 264 507.2 312 593.6 121 249.8 169 336.2 217 422.6 265 509.0 313 595.4 122 251.6 170 338.0 218 421.4 266 510.8 314 597.2 123 253.4 171 339.8 219 426.2 267 512.6 315 599.0 124 255.2 172 341.6 220 428.0 268 514.4 316 600.8 125 257.0 173 343.4 221 429.8 269 516.2 317 602.6 126 258.8 174 345.2 222 431.6 270 518.0 318 604.4 127 260.6 175 347.0 223 433.4 271 519.8 319 606.2 128 262.4 176 348.8 224 435.2 272 521.6 320 608.0 129 264.2 177 350.6 225 437.0 273 523.4 321 609.8 130 266.0 178 352.4 226 438.8 274 525.2 322 611.6 131 267.8 179 354.2 227 440.6 275 527.0 323 613.4 132 269.6 180 356.0 228 442.4 276 528.8 324 615.2 133 271.4 181 357.8 229 444.2 277 530.6 325 617.0 134 273.2 182 359.6 230 446.0 278 532.4 326 618.8 135 275.0 183 361.4 231 447.8 279 534.2 327 620.6 136 276.8 184 363.2 232 449.6 280 536.0 328 622.4 137 278.6 185 365.0 233 451.4 281 537.8 329 624.2 138 280.4 186 366.8 234 453.2 282 539.6 330 626.0 139 282.2 187 368.6 235 455.0 283 541.4 331 627.8 140 284.0 188 370.4 236 456.8 284 543.2 332 629.6 141 285.8 189 372.2 237 458.6 285 545.0 333 631.4 142 287.6 190 374.0 238 460.4 286 546.8 334 633.2 143 289.4 . 191 675.8 239 462.2 287 548.6 335 635.0 144 291.2 192 377.6 240 464.0 288 550.4 336 636.8 145 293.0 193 379.4 241 465.8 289 552.2 337 638.6 146 294.8 194 381.2 242 467.6 290 554.0 338 640.4 147 296.6 195 383.0 243 469.4 291 555.8 339 642.2 148 298.4 196 384.8 244 471.2 292 557.6 340 644.0 149 300.2 197 386.6 245 473.0 293 559.4 341 645.8 150 302.0 198 388.4 246 474.8 294 561.2 342 647.6 151 303.8 199 390.2 247 476.6 295 563.0 343 649.4 152 305.6 200 392.0 248 478.4 296 564.8 344 651.2 153 307.4 201 393.8 249 480.2 297 566.6 345 653.0 154 309.2 202 395.6 250 482.0 • 298 568.4 346 654.8 155 311.0 203 397.4 251 483.8 299 570.2 347 656.6 156 312.8 204 399.2 252 485.6 300 572.0 348 658.4 157 314.6 205 401.0 253 487.4 301 573.8 349 660.2 720 TABLES. )— I O Ph I N W W K 1^ • H 1— 1 w 1— 1 H H- 1 O ^ H M 'A Ui w 1-1 o h-; o pq >H oj jD H u fH O !2; (■■) H (J P P W M CO t<> in CO ^ Oi b- lO CO r-( Ci *> in CO rl 00 CD -^ N © CD (N « in in CD l> CO Oi O) M CO -* "l- in CD t> 00 CO ^ a S M N w (N N (N M M IM CO •^ CO ■-H 03 CO -^ CO ^ 05 o (N CO TJ* in CO CO i> 00 Oi fH M (M CO -T in CO l> a£J CO « CO CO CO CO CO CO CO CO CO CO -Tp •rf TS< -^ 'v -1* -^ Tf -^ I— ( rH i-H rH rH 3 o O o o o q q q q 'R *R "-^ q © 6 d d d d d d d 6 d d d d d d d d s i^ 06 CO d d d d ^ ,4 1^ i> i> t- t> i> 00 00 00 00 00 00 00 00 00 00 CO 00 00 \a « "J 0:1 l> in CO w Cl 00 CD •^ (M CO CO ^ (N © 00 CO 10 (N (W CO ■<*• in CO i> l> 00 Ol M (M CO "^ lO CD CD l> 00 m a 00 a o oo CO 00 00 00 00 00 00 00 00 Ol 01 01 Ci C3 CI Ci Ci CI CI 1 o o 000 000 © © d <^ o o q q q q 000 000 © o d d d d d d d d d d d d d a> <6 d d d d d ^ CO 00 t^ in '^ (M 00 i^ in -t C^ 1-1 01 00 CO in -f< CO l> CO 03 01 00 C3 .-. c^ CO -^ s a o CO 00 CO 00 ai OJ Oi a-i C3 0:1 01 Oi 01 (51 CJ 000 © 3 o o i-t 3 6 <=> o o © q q q q q 000 © © d d d d d d d d d d d d d d d d d d d d d d id q lO q in q in q in in q in q in q in q in © in q tii «^ fS^ (TJ oi CO CO -r -* in in CD CD t> t> QO CO d d d d r4 « in in in in in in m in in in in m in 10 in in in in in CO CO CO _, o 00 CD ■^ (M 00 CD -f< c^ 00 CD "* CO I-H CT> »> 10 CO ^ IN w CO -* in CD CO l> CO OJ (M CO -^ -r* m CO t- CO pq as -1* -f -T '^ ■^ -^ -f -^ ^ -T< in in m lO in in in in in m in O o © © © © © i 9 o o q 000 © © q © o d d d d d d d d d d d d d odd ^ ^ S d d eo IfS eo M Ol CO CO in CO (N 01 t- CD Ift CO (M © 05 t, CO M ^ in CD t- 00 03 IM CO CO ^ in CD (> CO d CI © f-i m as 'f -f Tf -f ■-t ■T* -7" in in in in in in in in m m in in CO CO 3 o o 000 © © © © 3 c "= o o 000 © © © © © o d d d d d d d d d d d d d <6 ^ fS d d a "? q in q in q in in ift in f> in in q in © 10 © tii 's CO CO t^ 1^ CO 00 ci oi d d p^ ^ o CI CO -t Tf 10 CD t^ 00 CJl (M (M CO -f in CO CO t- P3 a o o l-H 1-H o 000 © © © © o 9 o o q 000 © © © © © o d^ d d d d d d d d d d d d S <6 c> <6 <6 S d d 95 t^ CO " 06 06 d d © d >-i pH 1-H TABLES. 721 U) ■^ (N o OD (© -* CO i-i OJ h- Ift CO Oi in 1^ in f o CO t^ m ■T -^ 'tr "V Tt> lO in in tn w to ID in in in in in in «p © 1— 1 l-l fH o O o o O o o o o o o o © © © © © © © © © © o o o o o o o o o o o o o o o o o o o © © © © © © © © © o CO »> CD -f CO ^ o CO h- »c '^ CO l-[ o en i^ in Tf fM r^ m (^ in -f ni (M CO -p TP 00 O) o o G^ CO lO rv) -r -T UJ U3 m id LO CD CO CO CO fD (—1 1-4 o

t^ CO CO Ol OS o o p^ 1^ (M c^ CO CO -t T lO tn fP c-> r- t^ nn fT> rri (-) QD cs Oi Ol Oi Ol CI cs OS OS Cs Cl Oi a Oi d ei cs © n ^1 cs t- lO « r-4 Oi t^ in CO ^ a> t> CO •«3< 03 © CO CO -It Cincor-icst^co -i'N©ooco-i'M©coco *tw©cob«inco^ei Q0O5©i-ioioie0'^ iocDi^t^cnai©t-H-^(N co^ininto»>cocio:_ lOiococDcocDCOco cococococDcor*t^»>^- ^r*i>fr»fr-t>-t*t-"r-co o©©oo©©© ©o©o©o©oo© ©oo©o©©oo© o©©©©©©© ©©©©©©oo©© ©©©©©©©©©© ©©©©©©©© 0©©©©©0©©© ©©©©©©©©©© ■cDT}( eo^©cs»>co'*coi-io QOh-»^coFHocoi^ CTCo-^wincbt'QO cs©'-^^oi«**'»nco»> t^cooso^c^cocorf SSScocococbS cor^i>t^t^c^*^i^(^i> i;j;*'^oo°ooocDcococo SSooSSoo o©©©©©©©©© ooo©o©oooo ©©©§©§©© ©©©0999999 9999999999 ©©©©©©©© ©©©©©©©-©©© ©©©©©©©©©© in©in©in©in© in©»n©in©in©in© in©in©in©in©ino Or-^rHfiqWCOCOTf-flri inCOCDb-b-QOQOCJ©© S S S 2 2 S « ^il g s » ?: s s s s s s « ^ & s § s f; £ S 5? gggggggg §g§g8§§g§g §0' §§§§§§§. doo6c><66<6 6666000000 0000000000 sisisiii igiissssss ggggggssso 00000000 oooooqoooo oqooooooo- 66666666 6666000000 000000000 >ooinoinoiBO moiooiBqioqioq iBOinqinoioqioq 61 722 TABLES. TABLE XIX TABLE FOR THE REDUCTION OF THE PRESSURE OF A COLUMN 01? WATER TO A COLUMN OF MERCURY. 1 Pressure of Water, in Millimetres. Pressure of Mercury, in Mallinietres. Pressure of Water, in Millimetres. Pressure of Mercury, in Millimetres. Pressure of Water, in Millimetres. Pressure of Mercury, in Millimetres. 1 0.07 41 3.03 81 5.98 2 0.15 42 3.10 82 6.05 3 0.22 43 3.17 83 6.13 4 0.30 44 3.25 84 6.20 5 0.37 43 3.32 85 6.27 6 0.44 46 3.39 86 6.35 7 0.52 47 3.47 87 6.42 S 0.59 48 3.54 88 6.49 9 0.66 49 3.62 89 6.57 10 0.74 50 3.69 90 6.64 11 0.81 51 3.76 91 6.72 12 0.89 52 3.84 92 6.79 13 0.96 53 3.91 93 6.86 14 1.03 54 3.99 94 6.94 15 1.12 55 4.06 95 7.01 16 1.18 66 4.13 96 7.08 17 1.26 57 4.21 97 7.16 18 1.33 58 4.28 98 7.23 19 1.40 59 4.35 99 7.31 20 1.48 60 4.43 100 7.38 21 1.55 61 4.50 200 14.76 22 1.62 62 4.58 300 22.14 23 1.70 63 4.65 400 29.52 24 1.77 64 4.72 500 36.90 2.5 1.84 65 4.80 600 44.28 26 1.92 66 4.87 700 51.66 27 1.98 67 4.94 800 59.04 28 2.07 68 5.02 900 66.42 29 2.14 69 5.09 1000 73.80 30 2.21 70 5.17 31 2.29 71 5.24 32 2.36 72 5.31 33 2.44 73 5.39 34 2.51 74 5.46 35 2.58 75 5.54 36 2.66 76 5.61 37 2.73 77 5.68 38 2.80 78 5.76 39 2.88 79 5.83 40 2.95 80 5.90 LOGARITHMS AND ANTI-LOGARITHMS. LOGARITHMS OF NUMBERS. 10 1 2 3 4 5 6 7 8 9 Proportional Parts. 1 2 i 4 § 6 7 8 9 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 4 8 12 17 21 25 29 33 37 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 4 8 11 15 19 23 26 30I34 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 3 7 10 14 17 21 24 28J31 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 3 6 10 13 16 19 23 26 29 14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 3 6 9 12 15 18 21 24 27 15 1761 1790 1818 1847 1873 1903 1931 1959 1987 2014 3 6 8 11 14 17 20 22 25 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 3 5 8 11 13 16 18 21 24 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2 5 7 10 12 15 17 20 22 18 2553 2577 2601 2625 2643 2672 2695 2713 2742 2765 2 5 7 9 12 14 16 19 21 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 2 4 7 9 11 13 16 18 20 20 3010 3032 3034 3075 3096 3118 3139 3160 3181 3201 2 4 6 8 11 13 15 17 19 21 3222 3243 3263 3284 3304 3324 3345 3365 3386 3404 2 4 6 8 10 12 14 16 13 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 2 4 6 8 10 12 14 15 17 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 2 4 6 7 9 11 13 15 17 24 3802 3820 3838 3356 3874 3892 3909 3927 3945 3962 2 4 5 7 9 11 12 14 16 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 2 3 5 7 9 10 12 14 15 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 2 3 5 7 8 10 11 13 15 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 2 3 5 6 8 9 11 13 14 28 4472 4487 4502 4513 4533 4548 4564 4579 4594 4609 2 3 5 6 8 9 11 12 14 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 3 4 6 7 9 10 12 13 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 3 4 6 7 9 10 11 13 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 3 4 6 7 8 10 11 12 32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 3 4 5 7 8 9 11 12 33 5185 5198 5211 5224 5237 5250 5263 5276 5239 5302 3 4 5 6 8 9 10 12 34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 3 4 5 6 8 9 10 11 35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 2 4 5 6 7 9 10 11 36 5563 5575 55S7 5599 5611 5623 5635 5647 5658 5670 2 4 5 6 7 8 10 11 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5736 2 3 5 6 7 8 9 10 38 5798 5809 5821 5832 5843 5855 5366 5377 5833 5899 2 3 5 6 7 8 9 10 39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 2 3 4 5 7 8 9 10 40 6021 6031 6042 6053 6064 6075 6035 6096 6107 6117 2 3 4 5 6 8 9 10 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 2 3 4 5 6 7 8 9 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 2 3 4 5 6 7 8 9 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 2 3 4 5 6 7 8 9 44 6435 6444 6454 6464 6474 6434 6493 6503 6513 6522 2 3 4 5 6 7 8 9 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 2 3 4 5 6 7 3 9 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 2 3 4 5 6 7 7 8 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 2 3 4 5 5 6 7 8 48 6812 6821 6330 6339 6848 6857 6866 6875 6884 6893 2 3 4 4 5 6 7 8 49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 2 3 4 4 5 6 7 8 50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 2 3 3 4 5 6 7 8 51 7076 7034 7093 7101 7110 7118 7126 7135 7143 7152 2 3 3 4 5 6 7 8 52 7160 7168 7177 7185 7193 7202 7210 7213 7226 7235 2 2 3 4 5 6 7 7 53 7243 7231 7259 7267 7275 7284 7292 7300 7308 7316 2 2 3 4 5 6 6 7 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 2 2 3 4 5 6| 6; 7 ■ — =^^- ■-■■ ^• LOGARITHMS OF NUMBERS. 1^ ll 1 2 3 4 5 6 7 8 9 Proportional Parts. 1 2 8 4 § 6 7 8 9 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 2 2 3 4 5 5 6 7 56 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 2 2 3 4 5 5 6 7 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 2 2 3 4 5 5 6 7 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 2 3 4 4 5 6 7 59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 2 3 4 4 5 6 7 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 2 3 4 4 5 6 6 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 2 3 4 4 5 6 6 62 7924 .7931 7938 7945 7952 7959 7966 7973 7980 7987 2 3 3 4 5 6 6 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 2 3 3 4 5 5 6 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 2 3 3 4 5 5 6 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 2 3 3 4 5 5 6 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 2 3 3 4 6 5 6 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 2 3 S 4 6 5 6 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 2 3 3 4 4 5 6 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 2 2 3 4 4 5 6 70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 2 2 3 4 4 5 6 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 2 2 3 4 4 5 5 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 2 2 3 4 4 5 5 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 2 2 3 4 4 5 5 74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 2 2 3 4 4 5 5 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 2 2 3 3 4 5 5 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 2 2 2 3 3 4 5 5 77 8865 8871 S876 8882 8887 8893 8899 8904 8910 8915 2 2 3 3 4 4 5 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 2 2 3 3 4 5 79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 2 2 3 3 4 5 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 2 2 3 3 4 5 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 2 2 3 3 4 5 82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 2 2 3 3 4 5 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 2 2 3 3 4 5 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 2 2 3 3 4 5 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 2 2 3 3 4 5 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 2 2 3 3 4 5 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 2 2 3 3 4 4 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 2 2 3 3 4 4 89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 2 2 3 3 4 4 90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 2 2 3 3 4 4 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 2 2 3 3 4 4 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 2 2 3 3 4 4 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 2 2 3 3 4 4 94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 2 2 3 3 4 4 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 2 2 3 3 4 4 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 2 2 3 3 4 4 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 2 2 3 3 4 4 93 99^2 9917 9921 9926 9930 9934 9939 9943 9948 9952 2 2 3 3 4 4 99 995^ 9961 9965 9969 9974 9978 9983 9987 9991 9996 2 2 3 3 3 4 ANTILOGARITHMS. ^-! Proportional Parts. mS'I a 1 2 3 4 6 7 8 9 II iSS U 1 ■ ; 1016 1 2 § 4 5 G 7 8 9 j .00 1000 1002 1005 1007 1009 1012 1014 1019 1021 1 1 2 2 2 1 .01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 1 2 2 2 .02 1047 1050 1052 1054 1057 1059 1062 1064 1067 1069 1 2 2 2 .03 1072 1074 1076 1079 1081 1084 1086 1089 1091 1094 1 2 2 2 .01 1096 1099 1102 1104 1107 1109 1112 1114 1117 1119 1 2 2 2 .05 1122 1125 1127 1130 1132 1135 1138 1140 1143 1146 2 2 2 2 .06 1148 1151 1153 1156 1159 1161 1164 1167 1169 1172 2 2 2 2 .07 1175 1178 1180 1183 1186 1189 1191 1194 1197 1199 2 2 2 2 .08 1202 1205 1208 1211 1213 1216 1219 1222 1225 1227 2 2 2 3 .09 1230 1233 1236 1239 1242 1245 1247 1250 1253 1256 2 2 2 3 .10 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 2 2 2 3 .11 1288 1291 1294 1297 1300 1303 1306 1309 1312 1315 , 2 2 2 3 .12 1318 1321 1324 1327 1330 1334 1337 1340 1343 1346 .. - 2 2 2 3 ; .13 1349 1352 1355 1358 1361 1365 1368 1371 1374 1377 2 2 2 3 3 .14 1380 1384 1387 1390 1393 1396 1400 1403 1406 1409 2 2 2 3 3 .15 1413 1416 1419 1422 1426 1429 1432 1435 1439 1442 2 2 2 3 3 .16 1445 1449 1452 1455 1459 1462 1466 1469 1472 1476 2 2 2 3 3 .17 1479 1483 1486 1489 1493 1496 1500 1503 1507 1510 2 2 2 3 3 .18 1514 1517 1521 1524 1523 1531 1535 1538 1542 1545 2 2 2 3 3 .19 1549 1552 1556 1560 1563 1567 1570 1574 1578 1581 2 2 3 3 3 .20 1585 1589 1592 1596 1600 1603 1607 1611 1614 1618 1 2 2 3 3 3 .21 1622 1626 1629 1633 1637 1641 1644 1648 1652 1656 2 2 2 3 3 3 .22 1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 2 2 2 3 3 3 .23 1698 1702 1706 1710 1714 1718 1722 1726 1730 1734 2 2 2 3 3 4 ! .24 1738 1742 1746 1750 1754 1758 1762 1766 1770 1774 2 2 2 3 3 4 .25 1778 1782 1786 1791 1795 J799 1803 1807 1811 1816 2 2 2 3 3 .26 1820 1824 1828 1832 1837 1841 1845 1849 1854 1858 1 2 2 3 3 3 .27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 2 2 3 3 3 .28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 2 2 3 3 4 .29 1950 1954 1959 1963 1968 1972 1977 1982 1986 1991 2 2 3 3 4 .30 1995 2000 2004 2009 2014 2018 2023 2028 2032 2037 2 2 3 3 4 .31 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 2 2 3 3 4 ■32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 2 2 3 3 4 .33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 2 2 3 3 4 .34 2188 2193 2198 2203 2208 2213 2218 2223 2228 2234 1 2 2 3 3 5 .35 2239 2244 2249 2254 2259 2265 2270 2275 2280 2286 2 2 3 3 4 4 5 .36 2291 2296 2301 2307 2312 2317 2323 2328 2.333 2339 2 2 3 3 4 4 5 .37 2344 2350 2355 2360 2366 2371 2377 2382 2388 2393 2 2 3 3 4 4 5 .38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 2 2 3 3 4 4 5 .39 2455 2460 2466 2472 2477 2483 2489 2495 2500 2506 2 2 3 3 4 5 5 .40 2512 2518 2523 2529 2535 2541 2547 2553 2559 2564 2 2 3 4 4 5 5 .41 2570 2576 2582 2588 2594 2600 2606 2612 2618 2624 2 2 3 4 4 5 5 II .42 2630 2636 2642 2649 2655 2661 2667 2673 2679 2685 2 2 3 4 4 5 6 .43 2692 2698 2704 2710 2716 2723 2729 2735 2742 2748 2 3 3 4 .4 5 6 .44 2754 2761 2767 2773 2780 2786 2793 2799 2805 2812 2 3 3 4 4 5 6 .45 2818 2825 2831 2838 2844 2851 2858 2864 2871 2877 2 3 3 4 5 5 6 .46 2884 2891 2897 2904 2911 2917 2924 2931 2938 2944 2 3 3 4 5 5 6 .47 2951 2958 2965 2972 2979 2985 2992 2999 3006 3013 2 3 3 4 5 5 6 .48 3020 3027 3034 3041 3048 3055 3062 3069 3076 3083 2 3 4 4 5 6 6 .49 3090 3097 3105 3112 3119 3126 3133 3141 3148 3155 2 3 4 4 5 6 6 ANTILOGARITHMS. li Proportional Parts. 1 2 3 4 5 6 7 8 9 M il i^'C 3206 1 2 § • 4 § 6 7 8 9 1 .50 3162 3170 3177 3184 3192 3199 3214 3221 3228 1 2 3 4 4 5 6 .51 3236 3243 3251 3258 3266 3273 3281 3289 3296 3304 2 2 3 4 5 5 6 .52 3311 3319 3327 3334 3342 3350 3357 3365 3373 3381 2 2 3 4 5 5 6 ' 1 .53 3388 3396 3404 3412 3420 3428 3436 3443 3451 3459 2 2 3 4 5 6 6 7 1 .54 3467 3475 3483 3491 3499 3508 3516 3524 3532 3540 2 2 3 4 5 6 6 .55 3548 3556 3565 3573 3581 3589 3597 3606 3614 3622 2 2 3 4 5 6 7 7 .56 3631 3639 3648 3656 3664 3673 3681 3690 3698 3707 2 3 3 4 5 6 7 8 .57 3715 3724 3733 3741 3750 3758 3767 3776 3784 3793 2 3 3 4 5 6 7 8 .58 3802 3811 3819 3828 3837 3846 3855 3864 3873 3882 2 3 4 4 5 6 7 8 .59 3890 3899 3908 3917 3926 3936 3945 3954 3963 3972 2 3 4 5 5 6 7 8 .60 3981 3990 3999 4009 4018 4027 4036 4046 4055 4064 2 3 4 5 6 6 7 8 .61 4074 4083 4093 4102 4111 4121 4130 4140 4150 4159 2 3 4 5 6 ,7 8 9 .62 4169 4178 4188- 4198 4207 4217 4227 4236 4246 4256 2 3 4 5 6 7 8' 9 .63 4266 4276 4285 4295 4305 4315 4325 4335 4345 4355 2 3 4 5 6 7 8i 9 .64 4365 4375 4385 4395 4406 4416 4426 4436 4446 4457 2 3 4 5 6 7 8 9 .65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 2 3 4 5 6 7 8 9 .66 4571 4581 4592 4603 4613 4624 4634 4645 4656 4667 2 3 4 5 6 7 9 10 .67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 2 3 4 5 7 8 9 10 .68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 2 3 4 6 7 8 9 10 .69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 2 3 5 6 7 8 9 10 .70 5012 5023 5035 5047 5058 5070 5082 5093 5105 5117 2 4 5 6 7 8 9 11 .71 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 2 4 5 6 7 8 10; 11' .72 5218 5260 527a 5284 5297 5309 5321 5333 5346 5358 2 4 5 6 7 9 101 11 i. .73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 ) . 3 4 5 6 8 9 lOlU i .74 5495 5508 5521 5534 5546 5559 5572 5585 5598 5610 1 3 4 5 6 8 9 10 12 .75 5623 5636 5649 5662 5675 5689 5702 5715 5728 5741 1 3 4 5 7 8 9 10 12 .76 5754 5768 5781 5794 5808 5821 5834 5848 5861 5875 1 3 4 5 7 8 9 11 12 .77 5888 5902 5916 5929 5943 5957 5970 5984 5998,6012 1 3 4 5 7 8 10 11 12 .78 6026 6039 6053 6067 6081 6095 6109 6124 61386152 1 3 4 6 7 8 10 u 13 .79 6166 6180 6194 6209 6223 6237 6252 6266 6281 6295 1 3 4 6 7 9 10 11 13 .80 6310 6324 6339 6353 6368 6383 6397 6412 6427 6442 1 3 4 6 7 9 10 12 13 .81 6457 6471 6486 6501 6516 6531 6546 6561 6577 6592 2 3 5 6 8 9 11, 12| 14 i •82 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 2 3 5 6 8 ■9 11 12; 14 ; .83 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 2 3 5 6 8 9 11, 13; 14 1 .84 6918 6934 6950 6966 6982 6998 7015 7031 7047 7063 2 3 5 6 8 10 11:13; 15 .85 7079 7096 7112 7129 7145 7161 7178 7194 7211 7228 2 3 5 7 8 10 12 13; 15 .86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 2 2 3 5 7 8 10 12 13 15 .87 7413 7430 7447 7464 7482 7499 7516 7534 7551 7568 3 5 7 9 10 12 14, 16 .88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 2 4 5 7 9 1" 12 14 16 .89 \ 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 2 4 5 7 9 11 13 14 16 .90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 2 4 6 7 9 11 13 15' 17 .91 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 2 4 6 8 9 11 13 15 17 .92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 2 4 6 8 10 12 14 15117 .93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 2 4 6 8 10 ;12 14 I6II8 .94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 2 4 6 8 10 12 14 16 ,18 .95 8913 8933 8954 8974 8995 9016 9036 9057 9078 9099 2 .4 6 8 10 12 15 17 19 .96 9120 9141 9162 9183 9204 9226 9247 9268 9290 9311 2 4 6 8 11 13 15 17 19 ! .97 9333 9354 9376 9397 9419 aui 9462 9484 9506 9528 2 4 1 9 U 13 15 17 20 ' .98 1 9550 9572 9594 9616 9638 9661 9683 9705 9727 9750] 2 4 7 9 11 13 16 18120 1' .99 9772 9795 9817 9840 9863 9886 9908 9931 9954 9977 1 2 5 "7 ■ 9 11 14 16 18 !20 |1 INDEX. Absolute Weight. (See Weight.) Absorption of gases by solids, 879. " ^' " laws of, 381. " " by liquids. (See Solu- " of liquids by solids, 363. [bility.) Absorption-Meter, 402. Analysis of mixed gases by, 409. Acceleration, definition of, 23. " of gravity, 65. Action and reaction, law of, 49. Adhesion, 842. (And see Osmose.) " between gases, 412. " " liquids, 383, " " and gases, 891. " solids, 342. " " and gases, 379, 383. " " " " liquids, 344. " phenomena of, classified, 342. Air. (See Atmosphere.) Air-Pump, with valves, 829. " without valves, 325. " degree of exhaustion, 327. Air-Thermometer, 633. (See Thermosoope.) " Eegnanlt's, 584. Alcoometer, Gay-Lussac's, 254. Alloys, expansion in solidifying, 553. " melting-point of, 550. Alumina, crvstallization of, 120. Analogies of Nature, 9. Annealing, 207, 211. " of glass, 212. Antimony, ratio of crystalline axes of, 122. Arago and Dulong, experiments on Mari- otte's law, 293. " " experiments on tension of aqueous vapor, 575. Archimedes's Law, 235. " " demonstration of, 237. " " illustration of, 236. Arsenic, crystallization of, 120. Arsenious Acid, crystallization of, 120. Artesian Wells, 233, 647. Aspirator, 325, 392. Atmosphere, buoyancy of, 268. " dew-point of, 641. " effects of expansion of, 640. " pressure of, 266, 279. " probable limit of, 307. " relative humidity of, 640. " waves of, 286. Atomic Theoiy, 110. Atoms, size of, Boscovisch's opinion of, 110. " " Newton's opinion of, 110. Attraction of Earth. (See Gravity.) 62 Axes of crystals, 121, 123. " lateral and vertical, 122. " ratio in crystals of antimony, 122.. " " " bichromate of pot- ash, 124. [122. " " " carbonate of lime, " " " gypsum, 123. [124. " " " sulphate of copper, " " " ' " iron, 128. " " " sulphur, 123. " " " tin, 122. " similar, 125. Babinet, formula of, 305. Balance, accuracy and sensibility of, 102. " centre of gravity of, how adjusted, " degree of sensibility of, 105. [101. " description of, 100. " hydrostatic, 248. " regarded as a lever, 101. " " " pendulum, 102. [94. " spring, indicates absolute weight, Balloons, 270. " ascensional force of, 271. Barometer, Aneroid, 285. " Bourdon's metallic, 190. " common, 284. " Fortin's, 282. " history of, 275. " oscillations of, 286. " Eegnault's, 280. " theory of, 278. " used in measuring heights, 304. " " meteorology, 287. " various uses of, 285. Barometrical Observations, corrected for ca- pillarity, 284, 355. " " corrected for tem- perature, 284, 511. Bevelling, 131. Bichromate of potash," ratio of crystalline axes of, 124. Billiards, illustrative of elasticity, 201. Bodies, collision of unelastic, 49. " " elastic, 196. Body, definition of, 3. Boiler. (See Steam-Boiler.>) Boiling-Point, determination of, 669. " influenced by pressure, 666, " table of, 566. [577. " of water, 566. " " effect ofsalts on, 568. " " influenced by con- taining vessel, 668. 730 INDEX. Boiling-Point, use in measuring heights, 567. Boracic Acid, how used in crystallizing, 120. Boscovisch's opinion of atomic theory, 110. Bourdon. (See Barometer antZ Manometer.) Buoyancy of gases, 268. " " liquids, 235, 247. Bramah's Press, 220. Br^guet's Metallic Thermometer, 504. Britannia Bridge, expansion of, 503. Brittleness, definition of, 205. Brix, latent heat of vapors, 604. Bronze, tempering of, 212. Bunsen, absorption-meter, 402. " solution of gases in liquids, 393. " specific gravity of gases, 671. By eflEusion, 414. " tension of condensed gases, 593. " volume of gases, 679. Cagniaed de la TorrE, experiments on dense vapors, 601. Calcite, hardness of faces of, 210. " ratio of crystalline axes of, 122. " rhombohedrons of, 152. Capillarity, 346. " absoi-ption of liquids by porous solids, 363. " amount of pressure, 361. " effects of pressure, 352. " form of meniscus, 347, 349. " general phenomena of, 346, 354. " illustrations of, 353, 362. " influence of temperature on, 360. " numerical laws of, 355. " pressure resulting from molecu- lar forces, 349. " verification of laws of, 357. Capillary Tubes, height of liquid in, 364, " Plates, 357, 359. [358, 860. Carbonate of soda, laws of its solubility, 876. " lime. (See Calcite.) Carbonic Acid, condensation of, 596, 609. Cathetometer, 186, 281. Cements, 343. Centre of Gravity, properties of, 60. *' " position of, 61. " oscillation, definition and proper- ties of, 70. " pressure, 220j 240. Centip-ade Thermometrio Scale, 436. Centrifugal force, 79. " " at equator, 82. " " measure of, 80. " " modifying gravity, 81. Centripetal force, 78. Charcoal, absorption of gases by, 380. Chemical Change, distinguished from solu- tion, 371. " Physics, definition of, 6. Chemistry, how distinguished from Physics, " the three questions of, 5. [5. Chimney, theory of, 541. Cleavage, laws of, 205. " planes of, 119, 204. Clock, description of, 72. CoefEcient of absorption of gases, 392. " " compressibility of liquids, 217. '■ " conduction of heat, 669. " " cubic expansion, 492. " " elasticity, 186. " " expansion of gases, 528. Coefficient of expansion of water, 527. " " " of mercury, 510, 514. " " linear expansion, 491. Cohesion, 119, 342. Coinage, 208. Collision of elastic bodies, 196. " " unelastic bodies, 49. Column. (See Mercury Column.) Combustion, heat from, 649. Components and Resultants, 88. Compressibihty of gases, 116, 273, 648. " " laws of, 287. » " limit to, 301. " *' (SeeM.iriotte'sLaw.) " of liquids, 215. " of matter, illustrations of. Condensation of gases, 692. [113. " ^' apparatus of batte- rer, 598. " " apparatus of ThUo- rier, 696. " " by cold, 593. " " by pressure, 594. " Faraday's experi- ments on, 699. " " Faraday's method, 695. [648. " " heat resulting from. Condensed Gases, boiling-points of, 692. " " freezing-points of, 699. " " latent heat of, 609. [610. " " low temperature from, " ** maximum tension of, 593, " " table of, 595. [595. Condensing-Pump, 333. Conduction of Pleat, coefficients of, 669. " " illustrations of, 665. " " in crystals, 656. " " in gases, 667. " " " Grove's experi- ments on, 667. " " in liquids, 667. " " " Despretz's ex- periments on, 657. " " in liquids, Rumford's experiments on, 657. " " in solids, conductors good and bad, 654. " " in solids, experiments of Wiedmami and Franz, 666. " " in solids, Ingenhousz's apparatus, 655. " " in solids, laws of, 665. " " in various metals, 656. Co-ordinates, definition of, 20 Copper, tempering of, 212. Cornish Boiler, 616. Coulomb, laws of elasticity, 192. Couples, definition of mechanical, 47. Cryophorus, 609. Crystal, axes of, 121. " centre of, 124. " definition of, 121. " parameters of planes of, 124. " planes of, 121. " similar axes of, 125. " " planes of, 126. " size of, 121. " (See Fonn.) Crystalline form, 119. INDEX. 731 Crystalline form, identity of, defined, 188. " stnicture, 119. Crystallization, process of, 119. " water of, 372. Crystallography, 119. " terms of, 121. Crystals, cleavage of, 119, 204. " conduction of heat in, 666. " determination of, 175. *' expansion of, 498. " groups of, 173. " irregularities of, 170. " models of, 132. " modifications of, 131, 175. " " laws governing, " simple and compound, 129. [132. " symbols of, 128. " systems of, 121, 175. " twin, 173. (See Form.) Dalton's Apparatus for tension of vapors, 572. " Laws, 638. Dauiell's Hygi-ometer, 643. Densimeter, 252. Density, definition of, 18. (See Mass.; " how related to weight, 91. Despretz, conduction of heat in liquids, 657. " expansion of water, 523, 526, 549. " experiments on Mariotte's Law, 291. Dew, theory of, 653. Diffusion bottles, 419. " tube of Graham, 420. " of gases, 419. " " Dalton's theory of, 422. " " illustrations of, 423. " of liquids, 383. [384. " ''' Graham's experiments on, " " illustrations of, 384. " " laws of, 385. " " (See Osmose). Dimorphism, 184. Distillation, process of, 588. Dividing engine, 443. Divisibility of matter. (See Matter.) Ductility, 205. " order of, 207. Dnlong and Petit, experiments on expansion of mercury, 508, 514. " specific heat of gases, 483, 489. " (See Arago.) Dynamics, definition of, 34. Eakth, centre of gravity of, 84. " eccenti-icity of, 83. " origin of form of, 85. " spheroidal figure of, 83. Effusion of gases, 412. [413. " " " experiments of Graham, " " " law of, 414. " " " use in determining Sp. Gr., 414. Elastic bodies, collision of, 196. Elasticity, coefficient of, 186. " definition of, 115. « limits of, 115, 193. " limited*nd unlimited, 115. " of compression, 187. " " crystals, 195. Elasticity of flexure, 187. " " " applications of, 189. " " liquids, 115, 215. " " solids, 185. " " tension, laws of, 185. " " torsion, 191. " " " applications of, 193. " " " laws of, 192. " perfect and imperfect, 115. " varieties of, 115. Elements, chemical definition of, 3. Engine, dividing, 443. " steam, 615 et sea. Equilibrium, mechanical, definition of, 34. " of fioating bodies, 242. " of liquids, 228. [62. " stable, unstable, and neutral, Expansion, coefficient of, 491. " force of, 499. " by heat, 430. " " " cubic, 431, 492. " " " linear, 431, 491. " heat absorbed in, 475, 480. " of gases, 528. " " " expansion of air, 540. " " " air-thermometer, 533. " " " air-pyrometer, 639. " " " coefficients of, 528. " " " general laws of, 532. " " " methods of determin- ing, 630. " " liquids, 507. " " " above the boiling- point, 519. " " " absolute and appar- ent, 507. " " " change of rate with temperature, 517. " " " experiments of Drion, 619. " " " experiments of Kopp, 516. " " " experiments of Pierre, 616. " " " formula for alcohol, ether, and oil of turpentine, 518. " " " represented by curves, 518. " " solids, 494. " " " applications of, 504. ' " " determination of cubic, 495, 515. [494. " " " determination of linear, " " " case of crystals, 498. " " " " glass, 497, 498. " " " experiments of Kopp^ 496. " " " experiments of La Place and Lavoisier, 494. " " " illustrations of, 500. " " " order of compressibili- ty and expansibility, 497. « " " related to fusibility,497. " " " variation with temper- ature, 497. " " mercury, 508. « " " coefficients of, 510. " " " correction of barom- eter, 511. 732 INDEX. Expansion of mercury, determination of ab- solute, 508. " " " determination of ap- parent, B13. [510. " " " empirical foi-mula of, " " " method of determin- ing absolute, Dulong and Petit, 608, Keg- nanlt, 509. " " " Relation between ap- parent and absolute, 615. " " water, 520. " " " curve of, 521, 624. " " " coefficient of, 627. " " " determination of maxi- mum density, 522. " " " empirical formulae for, 626. " " " experiments of Des- pretz, 623. " " " experiments of Pliicker and Geissler, 523. " *' " point of maximrmi den- sity, 520. " " " (See Maximum Density.) Extension, definition of, 10. " how measured, 11. Fahrenheit, thermometric scale of, 435. Faraday, experiments on condensed gases, 595, 699. Floating bodies, laws of, 241. Fluidity, definition of, 215. Force, change of point of application, 38. " definition of mechanical, 32. " intensity and quantity of, 37, 53. " laws governing direction of, 32. " living, 52. " measure of, 34. " moving, 37. (See Momentum.) " origin of idea of, 6. " synonymous with volition, 7. " unit of, 36, 93. Forces, centre of parallel, 48. " centrifugal and centripetal, 77. " composition of, 38, 42. " " " parallel, 43, 47. " decomposition of, 40. *' illustration of parallel, 46. " parallelogram of, 39. " represented by lines, 38. " acting in the same direction, result- ant of, 39. Forces, Molecular, 117, 342. [351, 352. " " pressure exerted by, 349, Form, crystalline, 119, 127. " dominant and secondary, 130. " essential and accidental, 119. " hemihedral, 128. " holohedral, 127. " principal, 143, 151, 153, 159. " tetartohedral, 129, 156. " (See Hemihedral and Holohedral.) Forms of crystals. Dimetric, 142. Hexago- nal, 147. Monoclinic, 163. Monometric, 132. Triclinic, 168. Trimetrio, 158. Formulae : — Absolute expansion of mercury, 509. " weight, 87. Aur-thermometer, 536 - 539. Formulae : — Air-pump, 327, 828. Analysis of gases by absorption, 411. Apparent expansion of mercury, 613, 514. Apparent and absolute coeflScient of expansion, 615. Ascensional force of balloon, 272. Barometrical observations corrected for temperature, 511, 512. Capillarity, 357, 358. Centrifugal force, 80 - 83. Coefficient of expansion and specific gravity, 496. [616. Coefficient of expansion of solids. Collision of elastic bodies, 196-198. " unelastic bodies, 49 -61. Compensating pendulum, 506. Conduction of heat, 659. Correction of thermometric observa- tions, 449. Couples, 47. Decomposition of forces, 41. Density and weight, 91. Dimensions of safety-valve, 620. Effusion of gases, 415. Elasticity of flexure, 188. " tension, 186. " torsion, 192. Expansion by heat, 492, 493. " of gases, 529. " " determination of, Heat of fusion, 560. [531, 532. Hydrometer, 251, 252. Intensity of gravity, 65. " " at different lati- tudes, 77. La Place's and Babinet's, 305. Latent heat of steam, 607. Mariotte's flask, 323, 324. " law, 287, 288. Mass and density, 18. Measure of forces, 36. Measurement of height by barome- eter, 304, 305. Momentum, 37. Parallel forces, 45. Parallelogram of forces, 40. Pendulum, 68, 69, 73, 76, 76. Person's law, 661, 563. Power or quantity of a force, 63. Pressure of atmosphere, 279. " liquids, 219, 227, 232. Psychrometer, 644. Eeduction of thermometric scales, 436 446. " of volumes of gases to standard pressure, 314. " of volume of moist gases, 637. Relative and absolute weight, 95. [96. Relative specific weight and density, Relative specific weight and relative weight, 96. Relative weight and mass, 95, 96. Safety-tubes, 316, 317. Size of thermometer-bulb, 446. Solution of gases, 394. " of mixed gases, 406, 407, 409. Solubility of salts, 367. Specific gravity, 247-249, 257. INDEX. 733 Formula : — Specific gravity and mass, 92. Sp. Gr. and specific -weight, 92. " and weight, 91. " of gases, 673. " of liquids corrected for tem- perature, 665. " of solids corrected for tem- perature, 663. " of vapors, 675, 676. " referred to air and water, 93. " weight and volume, 92. Specific heat of gases under constant volume, 481. " " method of mixture, 468. Specific weight, 90. Syphon, 321. [586. Tension and temperature of vapors, " " volume of vapors, 688. " of agueous vapor, 581. Uniform motions, 23. Uniformly accelerated motion, 24, 25a " retarded motions, 26, 27. Variation of gravity with height, 86. Velocity of sound, 482. Volume of alcohol, etc., 518. ^ " of gases, 681. " of mercury, 611. " of water, 527. [670. Weight of gas, reduced for latitude, " of one srsr" of gas, 668, 669. " of bodies in air, 269. Woolf 's apparatus, 319, 320. Franklin, on absorption of heat, 653. French System of Weights, 89. Freezing mixtures, 656. " • point, 548. " " of water, 549. . " " " effect of salts on, 649. Friction, heat of, 648. Fulcrum, 97. Furnace, hot-air, 542. Fusion of solids, 548, 653. (See Melting and Freezing Points, oimHeatof JTusion.) Fusion of soUds, vitreous, 648. [567. " " change of volume attending, Galileo, proposition of composition of ve- locities, 28. Gallon, imperial, 14. Gases, absorption of, by solids, 379. " compressibility of, 115, 273, 287. " condensation of. (See Condensation.) " conduction of heat by, 657. " definition of quantity of, 394. " direction of pressure of, 266. " effusion of. (See Effusion.) [115. " elasticity of, perfect and unlimited, " expansion of. (See Expansion.) " fluidity of, 263. " formation of vapor in, 636. " how distinguished from liquids, 273. " " " vapors, 585. " mechanical condition of, 263. " method of weighing, 270. " passage of, through membranes, 425. " permanent elasticity of, 274. " pressure due to gravity, 265. " solubility of. (See Solubility.) " specific gravity of, 93, 273, 670. " tension of, definition, 263. 62* Gases, transmission of pressure, 264. " transpiration of, 417. " volume of, 679. (See Weighing and Measuring.) " " how reduced to standard pressure, 313. " " moist, how reduced, 637. " weight of, 270, 667. Gasometers, 314. Gay-Lussac, solubility of sulphate of soda, 374, 375. Geometry, subject-matter of, 11. Glass, annealing of, 212. " expansion of, at different tempera- tures, 498, 499. Glauber Salts. (See Sulphate of Soda.) Gold-Leaf, illustrates divisibility pf matter, " manufacture of, 206. [109. Goniometer, Application, 177. " Reflective, 178. " " Babinet's, 183. " " Haidinger's, 183. " " Mitscherlich's, 182. " " Endberg's, 182. " " Suckow's, 183. " " Wollaston's, 179. Goniometry, Miller's method of, 181. [384. Graham's experiments on diffusion of liquids, " " " of gases, 420. " " effusion, 413. " " osmose, 389. " " transpiration, 417. Grailich and Pekarek's Sclerometer, 209. Gramme, definition ofj 89. Grassi, on compressibility of hquids, 217. Gravitation, law of, 86. Gravity, acceleration of, 65. " Borda's and Cassini's experiments on, 74. " causes of variation of earth's, 77. " centre of, 60. " definition of, 66. " direction of earth's, 57. " intensity of, 64. " " how -measured, 66. " " represented by g, 65. " irregularities of, 77. " measured by pendulum, 73. " point of application of earth's, 68. " proportional to quantity of matter, " resultant of forces of, 59. [65. " value of, at different latitudes, 76. " varies with distance, 86. " (See Specific Gravity.) Gypsum, form of crystals of, 174. ^' ratio of crystalline axes of, 123. Hallstkom, expansion of water, 523. Hardness, definition of, 208, " how measured, 208. " of crystals, 209. " scale of, 209. " soleroipeter, 209. Heat, a repulsive force, 118. " absorbed by expansion, 475, 480. " an expansive force, 430. " central, 647. " definition of, 430. " mechanical equivalent of, 484, 633. " theories of, 430. " (See Conduction, Radiant, & Sources.) 734 INDEX. Heat of Fusion, 555. " " freezing mixture, 556. " " how determined, 559. " " Person's law, 660. Hemihedral Forms, 128, 135, 138, 145, 149, Hemi-octaliedrons, 163. [161, 167. Hemi-prisms, 165. Hemitropes, 174. Holohedral Form., 127, 133, 142, 147, 158, 163. Hopkins, effect of pressure on melting-point. Hydrometer, 249. [550. " Baum^'s, 253. " Fahrenheit's, 251. " Nicholson's, 250. " Rousseau's, 255. Hydrostatic Balance, 248. " Paradox, 228. " Press, 220. ' Hygrometer, 639. " Daniell's, 643. " Deluc's, 645. " Hair, 645. " Eegnault's, 642. " Saussure's, 645. " Wet-bulb, 644. Hygrometry, 636. " Dalton's laws, 638. " dew-point, 641. " drying apparatus, 646. " formation of mixed vapors, 638. " " of vapor in air, 636. " relative humidity of air, 640. " tension of vapor in air, 636. " volume of moist gases, how re- duced, 637. Hypothesis, how related to law, 7. Impenetkabilitt, definition of, 19. India-rubber, adhesion of, 343. " used for joints, 343. Inertia, delinition of, 32. Iodine, crystallization of, 120. .TouLE, mechanical equivalent of heat, 484, 633. Kater, experiments on the pendulum, 12,71. Kilogramme, origin and history of, 15. lilino-diagonal axis, 123, 164. Kopp, change of volume in fusion, 551. " cubic expansion, 496. " expansion of liquids, 516. " volume of water at different tempera- tures, 526. La Place, formula of 305. " velocity of sound, 482. Latent Heat. (See Heat of Fusion.) Latent Heat of Vapor, 603. " " application in case of steam, 611. " " Brix's experiments on, " " cryophonis, 609. [604. " " determination of, 603. " " illustrations of, 608. " " in equal volumes, 606. " " in steam at different temperatures, 606. " " Leslie's experiment on, 609. " " porous water-jars, 608. Latent Heat of Vapor, Eegnault's experi- ments on, 607. " " solid carbonic acid, 610. " " spheroidal condition of liquids, 611. " " Watt's theory, 606. Latitude, variation of gi-avity with, 76. " " of weight of gases with, 670. Lavoisier and Laplace, measurement of lin- ear expansion, 494. Law, criterion of its validity, 8. " Dalton's, 638. " definition of, 7. " Mariotte's, 287. " nature of a physical, 7, 300. " of gravitation, 86. " Person's, 560. " relation of, to Divine Mind, 7. " Watt's, 606. Laws of capillarity, 355. " cleavage, 205. " crystalline symmetry, 132. " diffusion of gases, 420. " " hquids, 383. " Dulong, 484, 489. " elasticity, 186. " liquid equilibrium, 229. " " pressure, 227. " solution of gases, 392. " torsion, 192. " transpiration, 417. Length, units of, English, 11. French, 14. Leslie's experiment, 609. Lever, arms of, 98. " conditions of equilibrium of, 98. " general theory of, 97. " three kinds of, 97. Leverage, definition of, 100. Light, plane of polarization rotated by. crys- tals, 162, 167. Liquid state, 117. Liquids, adhesion to solids. (See Solids.) " centre of pressure of, 220. " characteristic properties of, 215. " compressibility of^ 114, 216. " diffusion of 383. (See Diffusion.) " direction of pressure of, 219. " elasticity of, 115, 215. " expansion of. (See Expansion.) " how distinguished from gases, 273. " laws of buoyancy of, 235 - 247. " " equilibrium of, 228-232. " " pressure of, 224-227. " mechanical condition of, 215. " pressure due to gravity, 223. " principle of Archimedes, 235. " specific gravity of, 247 et seq., 665. " spheroidal condition of, 361. " transmission of pressure, 218. " volume of, 666. (See Weighing and " Measui'ing. ) Litre, 17. Locomotive Boiler, 618. " Engine, 628. Loewel's experiments on solubility of carbo- nate of soda, 876. " " on solubility of sul- phate of soda, 374. " " on supersaturated so- lutions, 378. ISDEX. 735 Makko-diaoonal Axes, 123. Malleability, 206. " order of, 207. [208. " variations with temperature. Manometer, Eegnault's, 308. " metallic, of Bourdon, 189. " with confined air, 310. Marcet's Globe, 574. Mariotte's Flask, 323. " Law, application of, 301. " " deviations from, 290, 299, 532, 586,602. " " experiments on, Arago and Dulong, 293. " " " Despretz, 291. " " " Natterer, 299. " " " Oersted, 290. " " " Eegnault, 296. " " history of, 290. " " illustrations of, 288. " " relation to expansion of gas- es, 532, 586. " " statement of, 287. Mass, definition of, 18. " relation to density, 18. " unit of, 91. Matter, compressibility of, 113. " definition of, 3. " divisibility of, an accidental prop- erty, 109. " essential nature of, not understood, 3. " " and accidental properties of, 10. " expansibility of, 113. " general and specific properties of, 3. " illustrations of its porosity, 110. " physical and chemical properties, 5. Maximum density of water, 520. " " " effects of salts on, 526. " " " history of dis- covery of, 522. " " " important bear- ings of, 525. Measure, English system of, 11. (See Yard.) " French system of, its history, 14. Measuring. (See Weighing and Measuring.) Mechanics, subject-matter of, 32. Melting-Point, 548. " effect of pressure on, 550. " of alloys, determination of. Meniscus, form of, 347, 349. [554. Mercurial Thermometers, 432. " , " arbitraiy scale, 446. " " calibration of, 443. " " change of zero-point, 441. " " comparison of dif- ferent, 439. " " construction of stan- dard, 442. " " defects of, 436. " " filling of, 433. « " graduation of, 433. " " observations, how corrected, 448. " " size of bulb of, 445. Mercury column, how measured, 280. " " expansion of. (See Ex- pansion.) Metacentre, definition of, 244. Metals, crystallization of, 120. Metre, an arbitrary measure, 16. " origin and history of, 14. " subdivisions of, 17. Mitscherlich, expansion of crystals, 498, " goniometer, 182. Modifications of crystals, 131. " 'i laws of, 132. Mohs's scale of hardness, 209. Molecular forces, two classes of, 117. (See Forces.) Moment, definition of, 100. Momentum, definition of, 37. Motion, a relative term, 21. " an essential property of matter, 21. " compound, 27. " curvilinear, how resulting, 29. " origin of idea of, 21. " parallelogram of, 27. " possible in several directions at once, " uniform, and varying, 23. [22. " uniformly accelerated, 23. " " retarded, 26. [598. Natteeek, apparatus for condensing gases, " experiments on compressibility of gases, 299. Newton,'discovery of law of gravitation, 87. " formula for velocity of sound, 482. " opinion on atomic theory, 110. Oetho-diagonal Axis, 123. Osmometer, 387. Osmose, 387. " explanation of, 388. " Graham's experiments on, 389. " how allied to chemical affinity, 391. Pakametees of crystalline planes, 124. Pendulum, ampUtude of oscillation, 68. Bessel's experiments on, 76. Borda's and Cassini's experi- ments on, 74, 76. centre of oscillation of, 70. definition of, 66. formula of, 68, 69. Han-ison's gi-idiron, 505. how affected by the air, 75. isochronism of, 68. Kater's experiments on, 12, 71. laws of oscillation of, 69. Martin's compensation, 506. measure of force of gravity, 73. " of time, 71. simple and compound, 66, 69. theory of, 67. virtual length of, 70. 'Physical changes, how distinguished from chemical, 4. " properties, how distinguished fi:om chemical, 5. Physics, how distinguished from Chemistry, Planes of cleavage, 119. [5. " similar, 126, 175. ^ . " symbols of crystalline, 128. " terminal and basal, 159. Plumb-Line, use of, 57. Pneumatic Trough, 311, 680. Polyhedron, 121. Polymorphism, 184. Pores, size of, Herschel's opinion, 113. 736 INDEX. Porosity, 110. " Florentine experiments on, 112. " illustrations of. 111. " implies compressibility, 113. Position of a body, bow defined, 20. " origin of idea of, 20. Pound, Troy and Avoirdupois, 90. " United States standard, 90. Power of a force, 37, 52. Pressure of the atmosphere, 266. " " " measured by ba- rometer, 279. Kadiant Heat, 651. " " absorption of, 652. '* *' analogous to light, 651. " emission of, 653. [6B3. " " Franklin's experiments, " " freezing water by radia- tion, 654. " " hot-beds, 654. " " laws of, 661. " *' phenomena of dew, 653. " " radiation of cold, 651. " " reflection of, 652. " " transmission through me- dia, 652. Kefrigerator, 543. Eeguault, comparison of thermometers, 439. " deteraiination of tension of va- pors, 575. [295. experiments on Mariotte's law, " " on specific heat, 466, [467,469,471,474,476. " hygrometer, 642. " hygrometry, 644, 645. " latent heat of aqueous vapor, 607. " method of weighing gases, 270. " specific gravity of gases, 667. " " " of vapors, 6T6. " weight of gases, 667. Relative Weight. (See Weight.) " specific weight, 96. Rest, a relative term, 21. Rhombohedron, 149. RoUing-Mill, 206. Rumford, conduction of heat in liquids, 657. " heat of friction, 648. Rupert's Drops, 212. Rupture, resistance to, 201. " law of, 202. Safety-tubes, theory of, 315. " valve, 619. Savart, elasticity of crystals, 196. Scalenohedron, 153. Sclerometer, 209. Section, principal, 151, 159. Set, definition of, 116, 194. Silliman, diffusion apparatus, 423. Similar axes, 125. " edges, 131. " planes, 126, 175. " , solid angles, 131. Siphon, theory of, 320. Solid state, 117. SoUds, absorption of liquids by porous, 363. " " of gases by, 379. " adhesion between, 342. " " to liquids, Gay-Lussac's ex- periments, 345. Solids, characteristic properties of, 119. " compressibility oi^ 118. " conduction of heat in, 655. " elasticity of, imperfect and limited, " fusion of. (See Fusion.) [116. " porosity of, 110. " specific gravity of, 91, 247, 662. " volume of, 664. " weight of, 87, 100, 661. (See Weigh- ing and Measuring.) Solubility of carbonate of soda, 376, 377. " of sulphate of soda, 372 - 375. " of gases, causes of variation, 398. " " coefficient of absorption, 392. " " determination of coeffi- cient, 398. " " expression by empirical formulae, 393. " " mixed gases, 405. [394. " " variation with pressure, " " variation with tempera- ture, 393. " " (See Absorption-Meter.) " of solids, curves of, 367. " " determination of, 369. " " empirical formula , of, 366. " " uninfluenced by fusion, 369. " " variation with tempera- ture, 365. Solution, how distinguished from chemical change, 871. " of gases, 392. " of solids in liquids, 365. *■ supersaturated, 376. Sources of Heat, 647. central heat, 647. calculations of Fourier, 647. chemical, 649. condensation, 648. friction, 648. percussion, 648. sun, 647. Sp. Gravity, 91, 247. " bottle, 247. " methods of determining, 247- 267. " of gases, 93, 273. [414. " " determined by effusion, " " referred to air, 93. " relation to specific weight in French system, 92. Sp. Heat, 464. " of gases, 476, 478. " " under constant pressure, 477. " " under constant pressure, does not vary with tem- perature or pressure, 477. " " under constant volume, 480. " " under constant volume, determination from ve- locity of sound, 482. " " under constant volume, Dulong's experiments, 483. " " under constant volume, Dulong's laws, 484, 489. INDEX. 737 Sp. Heat of platinum, and determination of nigh temperatures, 473. " of solids and liquids, 466. " connected with their chem- ical equivalents, 471. " determination of, 466, 487. " greater in liquids than in solids, 475. " greatest in water, 476. " of the elements, 466. " unit of heat, 464, 472. Sp. Weight, 90. " relative, 96. Spheroidal condition of liquids, 361, 611. " " Boutigny's experi- ments, 613. " " illustrations of, 614. " " temperature in, 612. " " freezingof water in, 614. Spirit-Level, 232. Spring-Balance, 94, 189. Standards of measure. ( See Yard and Metre. ) " of weight. (See Gramme and Pound.) Statics, deiinitiou of. 34. Steain, 672. (See Vapors.) " application of latent heat of, 611. " bath, 591. " expansion at formation of, 603. " latent heat of, at diiferent tempera- tures, 606, 632. " " " Eegnault's results, 607. " " " theory of Watt as to, " mechanical power of, 631. [606. " volume of, 631. Steam-BoUer, 615. " appendages of, 618. " Cornish, 616. " dimensions of, 620. " " heating surface, " French form of, 617. [616. " fusible plug, 620. " locomotive, 617. " requisites of, 615. " safety-valve, 619. Steam-Engine, 615. " condenser, 625. " cut-oflfs, 633. " fly-wheel, 623. " high-pressure, 628, 633. " locomotive, 628. " low-pressure, 621, 633. " mechanical power of, 631. " non-condensing, 628. " parallel motion, 624. " the eccentric, 625. " Watt's condensing, 621. Substances, definition of, 3. Sugar, hemihedral forms of, 168. [169. Su5)hate of copper, crystalline form of, 124, " of iron, crystalline form of, 123. " , of lime, crystalline form of, 123. " of soda, laws of solubility, 372, 375. " " osmotic equivalent of, 888. " " soluble modifications of, 374. " " supersaturated solution of, 376. " " use of, in freezing mixtures, 657. Sulphide of hydrogen, coefficient of absorp- tion of, 399. Sulphur, how crystallized, 120. " ratio of crystalline axes of, 123. Sulphurous Acid, coefficient of absorption of, , 401. " " condensation of, 693. Supersaturated Solution, 376. Surface, units of. Enghsh, 13. French, 17. Syphon, theory of, 320. System, dimetric, 122, 142. " hexagonal, 122, 147. " monoclinic, 123, 163. " monometric, 121, 132. " triclinic, 123, 168. " trimetric, 123, 158. Systems of crystals, 121. Tables ; — Absorption of gases by charcoal, 880 j by Meerschaum, plaster of Paris, and silk, 381. BoUing-points of condensed gases, 592. " " liquids, 566. " " saline solutions, 668. Coefficients of compressibility of liquids, " of elasticity, 187. [217. '? of expansion of glass at dif- ferent temperatures, 497. " of expansion of mercury, 510. Comparison of difiereut mercurial ther- mometers, 439. " of mercurial with aii^ther- mometers, 439. ** of thermometers filled with different liquids, 451. Compressibility of gases by Arago and ' Dulong, 294. " " by Natterer, 299. " " byEegnault,296. Conducting power of metals, by Des- pretz, 669; by Wiedman and Franz, 656. Determination of crystals, 176. Diffiision of solids in solution, 385. Dimension of steam-boilers, 621. " of the earth, 83. Effect of pressure on melting-point, 550. Effusion and Diffusion of gases, 414. Expansion of matter by heat, 431. " in vaporization, 603. " of gases, 528. " of uquids, 617. [519. " " above boiling-point. Freezing-points of condensed gases, 599. French linear measure, 17. " system of weights, 89. Greatest density of vapors, 601. Groups of equi-difiiisive substances, 386. Heat of combustion, 660. " fusion, 556. Height of liquids in capillary tubes, 358, 361. Intensity of gravity at different lati- tudes, 76. Latent heat of aqueous vapors, by Watt, 606 ; by Keguault, 608. " " of ;yapors, 605. Limit of elasticity, 195. Mechanical power of steam, 631. Melting-points, 648. " of alloys, 550. 738 INDEX. Tables: — Person's law, 562. Pressure and specific gravity of the air at increasing altitudes, 306. - Scale of hardness, 209. Solubility of carbonate of soda, 377. " of chloride of potassium, 366. " of gases, 393. " of nitre, 366. " of sulphate of soda, 375. Sp. Heat of elements, 466. " of equal volumes of gases, 483. " of gases and vapors, 478. " in solid and liquid state, 475. " of liquids at different temper- atures, 474. " of modifications of carbon, 476. " of platinum at different tem- peratures, 473. " of solids at different tempera- tures, 478. " of water at different tempera- tures, 472. Temperature of liquids in spheroidal condition, 612. Tenacity, ductility, malleability, 207. Tension of aqueous vapors, 571. " of condensed gases, 593. " " " at 0°, 595. " of vapors of liquids, 583. Tints of heated steel, 211. Transpirability of gases, 418. Weight of gases, 668. Tartaric Acid, hemihedral forms of, 167. Tartrate of soda and ammonia, hemihedral forms of, 162. Temperature, absolute zero, 564. definition of, 463. detei-mined by specific heat of platinum, 473. influence of, on solubility, 366. lowest observed, 462, 565. measured by a thermometer, of celestial space, 564. [432. obtained with condensed gas- es, 610. thermal equilibrium, 463. tnie, 639. Tempering, 211. " of bronze, 212. " of copper, 212. " of glass, 212. Tenacity, 203. " means of measuring, 202. " order of, 207. Tension of gases. (See Gases.) " of vapors. {See Vapors.) Tetartohedral Forms, 129, 156. Theory, atomic, 110. Theories, how related to laws, 7. Thermometer, air, 455, 534. " alcohol, 451. " filled with various liquids, 451. " fixed points of, 433. " house, 460. " maximum and minimum, 462. " mercurial, 432. " metallic, of Br^guct, 604. " Negretti and Zambra's, 453. " Rutherford's, 462. " scales of, 435. Thermometer, scales of, reduction of, 436. " Walferdin's, 454. " water, 438. " weight, 513. " (See also Air, and Mercurial.) Thermo-multiplier, Melloni's, 457. Thermoscopes, Leslie's, 456. " Eumford's, 457. " Sanctorius's, 456. Time, how measured, 22. " origin of the idea of, 22. " units of, 22. Tin, ratio of crystalline axes of, 122. Torricelli's experiments, 275. Torsion Balance, 193. " elasticity of, 191. Transpiration of gases, laws of, 417. Troughton, standai-d yard, 13. Truncation, 131. Twin crystals, 173. Unit of force, 36, 93. " heat, 464, 472. " length, 11, 14, 17. " mass, 91. " surface, 13, 17. " volume, 13, 17. " weight, 89. Vapok, aqueous tension of, 571. " ■' " Dalton's appara- tus, 672. " apparatus of Gay-Lussac, 574. " " Regnault, 575. " empirical formulas for, 581. " formation in atmosphere of gas, 636. {Aiid see Hygrometry.) " geometrical cuiwe of, 580. " laws governing, 580. " Marcet's globe, 574. " Papin's digestei", 591. " {See Latent Heat of Vapor.) Vapors, expansion attending formation of, formation of, 570, 5S2. [603. " gi-eatest density of, 600. " how distinguished from gases, 585. " maximum tension of, 584. '• smallest density of, 602. " specific gravity of, 674 et seq. " tensions of, compared, 684. " weight of, 669. Velocities, composition of, 28. Velocity, definition of, 23. Vis vii'a, 53. Volume, definition of, 10. " how estimated, 14. " units of English, 13. French, 17. Volumeter, Gaj^-Lussac's, 252. Wash-Bottle, 825. Water, change of volume in freezing, 552. " effect of pressure on melting-point, 560. " expansion of (See Expansion.) " freezing-point of, 549. " maximum density of (See Maxi- mum Density.) " pump, 334. [526. " volume of, at different temperatures, Watt, law of, 606. " steam-engine of, 621. INDEX. 739 Weighing and Measuring, 661. Sp. Gr. of gases, Bnnsen's method, 671. " " Eegnault's method, 670. " of liquids, 91, 249, seq. " " corrected for tem- perature, 666. " of solids, 91, 247. " " con-eoted for tem- perature, 662. " of vapors, 674, seq. [678. " " Deville's method, " " Dumas's method, 675. " " Gay-Lussac's meth- od, 678. " " Eegnault's method, 676. Volume of gases, 679. " of liquids, 666. " of solids, 664. Weight of gases, 270,667. " ofsolids, 87, 100, 661. " of vapors, 669. Weight, absolute, 87. " " distinct from mass, 88. " " liable to variation, 89. " " measure of quantity of matter, 88. " of a body in air, 268. " relative, 94. " " a constant quantity, 96. " " measured by the balance, ■94. " specific, 90. " of a unit of mass, 91. Weights described, 94. Wells's theory of dew, 653. Welter's tube, 317. Wertheim, experiments on elasticity, 187. Wire-MiU, 205. Woolf 's Bottles, 318. Yakd, act of Parliament concerning, 11. " American standard, 13. " origin and history 0^ 11. " standard, destroyed by fire, 12. THE END.