CORNELL UNIVERSITY LIBRARY COMPENDIUM NATURAL PHILOSOPHY: ADAPTED TO THE USE OF THE GENERAL READER, AlVD OF SCHOOLS AIVD ACADEMIES. A NEW EDITION, hKTISSS, ENLARGED, AND BMBRACINQ THE LATEST DI3COVERIS8 IN THE SCIENCB. TO WHICH IS NOW ADDED A SUPPLEMENT CONTAINING INSTRUCTIONS TO TOUNS EXPEKIM'SNTEES, WITH A \ COPIOUS LIST OF EXPERIMENTS. BY DENISON OLMSTED, LL.D., PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE. 7ale College. NEW YORK: CLARK, AUSTIN & SMITH, 3 PARK ROW i 3 ANN-STREBtI 1860. Entered according to Act of Congress, in the year 1851, by DENISON OLMSTED, In the Clerk's Office of the District Court of Connecticut. STH-iraiOTYPED BY THOMAS B. SMITH. 21G WILLIAM STRKET, n- i I / PREFACE. This Compendium of Katiu-al Philosophy, having been ex- tensively used as a text-book in the first Academies and High Schools of our country, and of several foreign countries, and having, in its entii-e circulation, exceeded seventy thousand, the author and the pubhsher have felt it incumbent on them, in return for such distinguished patronage, to use their best en- deavore to render the work as useful as possible to those for whom it is d&signed, and deserving of the continued favor of instructors and the friends of education. With this view, it has been stereotyped anew, throughout ; much of the text has been re-wiitten ; many engravings have been added ; and a great amount of matter entirely new has been incorporatea, bringing the subject more fully up to the present advanced state of the science, than can probably be found in any similar work. ]iy adopting a more compact style of printing, as well as by increasing the size of the volume, room has been found to add several entirely new articles, on subjects which the pro- giessive state of Natural Philosophy and its kindred arts has rendered prominent since this work was firet wiitten. Among these are various subjects in practical mechanics, in the arts of locomotion, in Electricity, and in Optics, and especially in Me- teorology and Electro-Magnetism. Meteorology is a subject so well suited to the tastes and capacities of young learners, so fitted to inspire a love of philosophical observation, and so practically useful in its apphcations to many of the ai-ts and conveniences of hfe, that we have greatly enlarged this article, and we beg leave respectfully to commend the sketch here presented to the special notice of instructors and the friends of education, believing that it will be found more full and comprehensive than is usually met with in .works of this class. The new article, also, on Electro-Magnetism has been prepared with care and is adapted to lead the learner to a clear and intelligent understanding of that greatest of the wonders of art, the Electric Telegraph. We have aimed, as heretofore, to comprise in this small vol ume a full view of the most useful truths of Natural Philoso- phy, and their most important practical applications ; but w« have studied to avoid the error attending many of the attempt* to render our science easy of comprehension, — that of exhibit- ing nothing but what is so barren and superficial as to be of little service to the learner. Addressing ourselves to the more inteUigent and cultivated minds of the youth in our High Schools and Academies, and keeping constantly in view practi- cal utihty as well as intellectual improvement, we have been careful to give to each subject of Natural Philosophy a space proportioned to its value in relation to these objects ; and have allotted but a small space to subjects which are more intri- cate than practical, and more curious than useful. Some sub- jects, indeed, of high scientific interest, particularly in the theory of optics, are omitted here, as being not strictly adapted to the generality of pupils for which this work is intended, but a full account of which may be found in our " College Philoso- phy." To render difficult subjects plain and intelligible to the young learner, and to enrich his mind with such knowledge as may at once inspire a love and a habit of philosophical obser- vation and reasoning, and be found in the highest degree avail- able in the actual business of hfe, has been the leading purpose of the many years which the author has devoted to the instruc- tion of the j-outh of his country. Besides the students of academies and high schools, we have had constantly in view two other classes of readers, — firet, educated men, who desire to reom' to the study of Natural Philosophy, rather to refresh their memories upon what they once learned in the regular course of their education, than to toil again through the demonstrations of philosophical truths ; and, secondly, practical men, who consult works of this class for principles which they can employ in the actual business of life. It is hoped, therefore, and confidently believed, that the present work, although of small dimensions, will be found to contain an unusual amount of such information as is required by the professional man, and the mechanic and man of busi- ness, and hence to be pecuharly deserving a place in their re- spective libraries. Yale Collkqe, July, 1851. CONTENTS. Part L— MECHANICS. Page. Chapter I. — Preliminary Principlbs, ft Definition of terms^ 9 Natural Philosophy, ]0 Mechanics, 10 Force 10 Matter, properties of, II Gravity, 11 Inertia, 16 Cohesion, Divisibility, 17 Cuinitressibility, Elasticity, 18 Chapter II.— Of Motion AND Force,. 19 Definition of terms, 19 Absolute and Relative motion, 19 Apparent and Uniform motion, 20 Questions on Uniform motion, 21 Momentum and Force^ 22 Questions on Momentum, 23 Chapter III.— Op the Laws op Mo- tion, 24 First Law, 24 Doctrine of Inertia, 24 Atwood's Machine, 28 Centrifugal Force, 29 Second Law, 33 Quantity of motion, 33 Direction of motion 33 Third Lata 34 Doctrine of action and reaction 34 Collision of bodies, elastic and in- elastic, • 36 Proofs of the laws of motion, 40 Chapter IV. — Or Variable Motion, 41 F\illinff Bodies, 41 Proportion of spaces to times, 41 Proportion of space to acquired ve- locity, 44 Case of bodies projected upwards,... 44 Case of bodies projected downwards,. 45 Questions on Failing Bodies, ■ 46 Bodies revolving in orbits, 48 Chapter V. — Of the Composition AND Resolution OF Motion, 49 Parallelogram of forces, 50 Illustrations, 51 Polygon of forces, 54 Resolution of forces 55 Curve described under two forces,. . . 57 1 _^ Page. Chapter VI. — Op tub Center of Gravity, 58 Position of the center of gravity in plane figures, 59 Center of gravity of any number of bodies, go Line of direction 62 Leaning Tower of Pisa, 64 Rocking stones, 65 Animal motions, 65 Problems solved by the center of gravity, 66 Chapter VII.— Of Projectiles and Gunnery, 67 Random of a projectile, 68 Theory of gunnery, 69 Chapter VIII. — Of Machinery, 70 Lever, 70 Three kinds, 72 Compound Lever, 73 Problems, 74 Balance 75 Bent Lever Balance, 77 Steel-yards, 78 Weighing Machine, 79 Illustrations of the Lever, 80 Bones of animals, 82 Chapter IX.— Op Machinery, 83 Wheel and Axle^. 83 Capstan, 34 Compound Wheel and Axle, 84 Fusee, 85 Problems, 85 Communication of Motion by wheel- iDork, 85 Regulation of Velocity, 88 Clock-work, 89 Wheel Carriages, 91 Chapter X. — Machinery, 94 Pulley^ 94 Fire escapes, 94 Problems, 96 Inclined Plane, 96 Roads 97 Railways, 98 Motion on inclined planes, 99 Velocity on inclined planes, 99 CONTENTS. Page. Slide of Alpuach, 99 Screw 10** Hunter's micrometer screws 102 Compound Machine, 104 Wedge, 105 Illiistralions 106 General Principle of the Mechanical powers, 1^'^ Chapter XL — Machinery, 108 Advantages of machinery, 110 Regulation of machinery, 112 Pendulum, 113 Fly-wheel, 114 Gearing, 116 Universal Joint, 116 Racket wheel, 117 Eccentric, " 117 Reciprocating motion, 117 Crank, 117 Chapter Xn.— Or thk Pendulum, Strength of Materials, and Friction, 118 Pendulum 118 Laws of Vibration, 119 Uses, figure of the earth, 120 Standard of linear measures, 120 Strength of Materials,. ■ 121 P>-tction^ 125 Experiments, 127 Lhws of, 128 Friction of slidins bodies, J29 " rolling " 129 " revolving" 129 Friction wheels, 130 Part II.— HYDROSTATICS. Chapter I. — Fluids at Rest, 133 Hydrostatics, 133 Laws of Fl uids 133 Hydrostatic Press, 134 Leveling, 136 Fluids in a recurved tube, 140 Hydrostatic Paradox, 142 Specific gravitiji 142 Rule,. 144 Examples, 144 Method of finding, 145 Table of specific gravities, 147 Marine Docks 148 Buoyancy 149 Magnitudes of irregular bodies, JoO Chapter II. — Fluids in Motion,-.-. 151 Rivers, 151 Laws of spouting fluids, 152 Friction of fluids, 155 Barker's Mill 156 Water Wheels 157 Overshot wheel 157 Undershot wheel, 158 Breast wheel, 159 Problems on the powers of running water, 160 Page. Chapter IH. — Of Cafillar/ At- traction, Resistance or fuUiDS, AND Waves, 161 Capillary attractioru, 161 Phenomena depending on it 169 Resistance of Fluids^ 163 Motion of fluids in pipes, 164 Wavcs^ 164 Questions on Hydrostatics^ 166 Part III. — PNEUMATICS, ME- TEOROLOGY AND ACOUS TICS. Chapter I.— Of the Mechanical Properties of Air 168 ^ir Pump^ 170 Magdeburg Hemispheres, 173 Experiments, 174 Condenser,. 175 Air Gun, 175 Diving Bell 176 Barometer, 177 Chapter II.— Of the Mechanical AoENciKs OF Air AND Steam 180 Syphon 181 Suction Pump 182 Forcing Pump 183 Fire Engine, 184 Steam EnginC', 185 General Principles, 185 Description 187 Locomotive, 193 Chapter ni. — Of Meteorology,.. . 194 Atmosphere, 1 93 Extent, 195 Weight 195 Density, 196 Temperature, 197 Relations of the atmosphere to Water, 197 Natural evaporation, 198 Dew point, 198 Dew, 199 Fog, 200 Clouds, 201 Rain, 202 Snow, 203 Hail, 203 Relations of the Atmosphere to Heat^ 204 Thermometer, 204 Barometer, 209 Rain gage, 207 Climate^ 207 Causes of Variation, 208 Ventilation, ...^ 209 Draught of a chimney. 209 Circulation of air in mines, 210 Importance of Ventilation, 211 Rules,. 212 Winds and Storms 213 Land and Sea Breezes, 213 Trade winds, 21.4 CONTENTS. Page. Velocity of winds, 214 Force « 2i5 Whirlwinds, 215 Gales, 215 Chapter IV.— Of Acodstics, 216 Vibratory motions, 216 Acoustic figures, 219 Vibrations of elastic fluids, 230 Vibrations of strings, 220 Vibrations of wind instruments,.-.. 222 Pitch 222 Vibrations of a bell, 223 Propagation of Sound, 223 Agency of the air in sound, 224 Velocity of sound, 225 Conducting power of liquids, 226 Conducting power of solids 227 Stethoscope, 228 Reflexion of sound, 228 Echo 229 Structure of halls for speaking or music 229 Roiling of thunder 230 Speaking trumpet, 230 Ear trumpet, 231 Musical sounds, 231 PkUosophical principles of music.. . . - 232 Melody, harmony, chords, discords,. 233 Interference of sounds, 333 Theory of musical instruments, 234 Part lY.— ELECTRICITY. Chapter I.— Of thk General Prin- ciples OP THE Science, 236 Electrical attraction, 336 Electntmeters, 237 Excitation of electricity, 338 Vitreous and resinous, positive and negative, 239 Conductors, 240 Insulation, 241 Sphere of communication 242 Sphere of influence, 242 Induction, 343 Chapter II. — Of Electrical Ap- paratus, 243 Cylinder machine, 343 Plate machine, 245 Hydro-electric machine, 346 duadrant electrometer, 347 Experiments, 348 Law of electrical attraction and re- pulsion, 250 Ley den Jar, 250 Experiments, 252 Chapter III,— Of Electrical Light, Battery, Mechanicaland Chem- ical agencies of Electricity,-- 256 Electrical Lights 356 Electric spark,.. 258 Electricity in a vacuum, 258 Page. Electricity in condensed air, 359 Interrupted circuit, 259 Origin of electric light 360 Battery, 361 Great battery of Haarlem, 362 Mechanical effects of electricity^ 263 Chemical effects, 264 Motions of the electric Jiuid^ 264 Velocity, 264 Chapter IV. — Effects on Animals, Laws, 266 Electric shock, 266 Discharging electrometer, 368 Medical electricity, 208 Cause of electrical phenomena^ 269 Existence of an electric fluid, 270 Hypothesis of a sinsle fluid, 272 Hypothesis of two fluids^ 273 Chapter V. — Atmospherical Elec- tricity, Lightning-rods, Pre- cautions for Safety, 275 Electricity of the atmosphere, 275 Lightning rods, 376 Precautions for safety, 277 Concluding remxirks, 280 Part v.— MAGNETISM AND ELECTRO-MAGNETISM. Chapter I. — Of Magnetism, 282 Oeneral principles^ 282 Magnetic needle, 283 Chapter II.— Of Magnetic Attrac- tion, 284 Attraction and repulsion, 385 Magnetizing by induction, 386 Austral and boreal fluids, 290 Chapter III, — Of the Directive Properties OF the MaCnbt, 391 Declination of the needle, 393 Dipof the needle 294 Magnetic Intensity, 295 Magnetism of the earth, 396 Electricity and Magnetism compared, 297 Artificial Magnets^ 297 Compass, 300 Mariner's Compass, 302 Chapter IV. — Electro-Magnetism, 303 Simple Voltaic apparatus, 304 Grove's Battery, 305 Current of electricity round a wire, .106 Diamagnetic bodies, 307 Induction, 307 Page's Electro-magnetic machine,.. 309 Electric Telegraph, 3l0 .Animal Electricity, 313 Torpedo and Gymnotus, 313 CONTENTS. Part VI.— OPTICS. Chapter I —Preliminary Defini- tions AND Observations, 315 Defmitionsj optics, ray, beam, pen- cil, medium, 315 Velocity ol" light, 3]7 Intensity at different distances, 318 Chapter n. — Reflexion op Light. Definition, 3]9 Laws of reflexion, 320 Plane mirrors, 321 Parallel and inclined, 323 Kaleidoscope, 3:24 Concave mirrors, 325 Co7ivex mirrors, 329 Chapter IIL— Rhpraction of Light. Law of refraction, 331 Multipljing glass, 332 Lenses, 333 Office of a convex lens, 334 Oflice of a concave lens, 334 Images formed by lenses, 335 Spherical observation, 336 Prism, 337 Chapter IV. — Solar Spectrum, Rainbow, Colors, 338 Solar Spectrum, 339 Composition of solar light, 341 Rainbow 343 I Haloes, 344 A us ^spheric refraction, 349 j Page. Colors of bodies, 350 Nature of light 351 Polarization of light, 352 Chapter v.— Vision 352 Camera Obscura, 354 Eye 355 Estimation of distances and magni- ludes, 361 Thaumatrope, 364 Chapter VI.— Microscopes 365 Microscope 365 Field of view, 367 Sapphire microscope 368 Perspective glass, 369 Magic lantern, 373 Solar microscope, 374 Compound microscope, 376 Portable Camera Obscura, 378 Daguerreotype apparatus, 379 Chapter VIL— Telescopes, 380 Telescope, 380 Astronomical telescope, 381 Digiculiies to be overcome, 384 Spherical aberration, 385 Chromatic aberration, 386 Dispersive power, 387 Achromatic telescope, 389 Day telescope, 392 Refiecting telescopes, 394 Ilerschel'a 40 foot reflector, 395 Ross' Leviathan, 396 Cambridge refractor, 396 COMPENDIUM OF NATURAL PHILOSOPHY, PART I.— MECHANICS. CHAPTEK I. PRELIMrN'ART PRINCIPLES. t . JN atural Philosophy is the science which treats of tfie Lawb oj trie material world. The term Law, as here used, signifies the mode in which the pmvers of nature act. Laws aim at determining things with numerical precision, or of assigning the exact propor- tions in which effects take place. Thus, it is a property of light to be reflected from smooth surfaces ; but it is a law of light that the incident and the reflected rays make equal angles with the surface. It is a property of all bodies, when let fall in the atmosphere, to descend towards the center of the earth; but the laws of falling bodies determine, pre- cisely, how much fartlier a body falls in two seconds than in one. Laws are general truths, comprehending a great number of subordinate truths. Thus, it is a fact that heat enlarges the bulk, of a cannon ball ; but this single fact would not constitute a law of heat. The law is, that heat expands all bodies. Natural Philosophy is divided into Mechanics, Electricity, Magnetism, and Optics. Define Natural Philosophy. What does the term Law signify? Give an example of a property of light, as distinguished from a law of light. Same distinction in regard to falling bodies. G-ive an example to show that law3 are general truths. How is natural philosophy divided ' 1 MECHANICS. 2. Mechanics is fJiat branch of Natural Phihsophy, ivldch treats of th". npiUibrium and motion of bodies* This definition refers to Mechanics as a science ; the principle's of the science applied to the purposes of life, as in the con- struction of machinery, constitute Practical Mechanics The arts of life are partly mechanical and partly chemical Mechanical effects involve only' changes of place and ot figure; but chemical effects involve a change of nature Thus the act of mixing the ingredients of bread is mechani cal, because it merely brings things together, producing onh change of place ; the unseen union of the particles of flour yeast, and water, forming dough, a new substance different from any of these, is a chemical change, because it alters the nature of the substances ; making the loaves is mechan- ical, involving only a change of form ; and finally, the bak- ing is a chemical process, because it still farther alters the nature of the body. Body, is any collection of matter existing in a separate form. The wori particle is much used in writings on phys- ical subjects. In Natural Philosophy, we mean by particles, the smallest parts into which a body may be supposed to be divided by mechanical means, without any reference to the different elements of which such particles may be com- posed. Inquiries of the latter kind belong to Chemistry ; and, in general, we recognize no distinctions among the different kinds of matter which constitute various bodies, and classes of bodies, (except what relates to the states of solid and fluid,) leaving to Chemistry all inquiries respecting the composition of bodies, and the changes of nature which bodies undergo by their action on each other. 3. Force is any cause which moves or tends to move a body, or which changes or tends to change its motion. Thus the elastic power of steam in propellmg a boat, the action of the wind upon a sail, of a weight upon a clock, and of an animal in dragging a carriage, are severally examples of forces in actual operation. That part of Mechanics which relates to the action of forces producing equilibrium or rest in bodies, is called Statics ; that which relates to the action of forces producing motion, is called P)yyiamics. * Tliat is, of bodies in a state of rest or motion, and of the forces that keep Ihem m lliese states respectively. Define Mechanics. Define Practical Mechauics. Wliat changes in bodies are Mechanical and -what are Chemical? Give an example. Define dody — also, particle. What science treats of the different kinds of matter 1 Define force. Examples. Define Sialics. Also, Dynamics. PREI.IMINAnV rRINCIPLES. 11 4. The laws of equilibrium and motion undergo certain modifications in consequence o{ the peculiar properties of /lui 1 9. Motion is diange of place. Motion and rest are accidental states of bodies, nor is a body naturally prone to one state, more than to the other. If it is found at rest, it is because it is kept at rest by oppo- site and equal forces ; and if it is found in motion, it is be- cause it has been put in motion by some force extrinsic to itself. The resistances to motion which exist near the surface of the earth, particularly gravity, create a seeming tendency to a state of rest; but in reality rest is no more the natural state of bodies than motion is. 20. Motion is distinguished into absolute and relative Absolute motion is a change of place with respect to any fixed point : relative motion is a change of place in bodies with respect to each other. Thus when two horsemen start Is matter annihilated when hodies are burned ? or when vegetables and animals die ? Are motion and rest natural or accidental states of bodies ? Why is any body at rest ? Why is any body in motion 1 Define absolute viotion — de- fine relaCive motion. 20 MECHANICS. to run a race, their motion is relative with respect to each other, but absolute with respect to the goal. If they keep at the same distance from the goal, they are relatively at rest, When a man walks towards the stern of a ship, he is in mo- tion with respect to the ship, but may be at rest with respect to the shore. When a balloon, carried along by the wind, attains the same velocity as the wind, it is relatively at rest, and appears to the aeronaut to be in a perfect calm, though it may be actually movjng sixty miles an hour. Since the earth, in its annual revolution around the sun, is moving eastward at the rate of 100,000 feet per second, were a can- non ball, at a certain time of day, fired eastward at the rate of 2,000 feet per second, the only effect would be to add 2,000 feet to the velocity which the ball had before in com- mon with the earth ; and were it fired westward, the efiect would be merely to stop 2,000 out of 100,000 parts of its previous motion, while the cannon would proceed onwards leaving it behind. Did not the atmosphere partake of the diurnal motion of the earth, but were it to remain at rest with respect to this motion, the progress of any place to the eastward, would cause a relative motion of the air, or a wind, westward, which would blow with a violence far surpassing that of the most terrible hurricanes. Apparent motion, as distinguished from relative, is that in which the moving body is quiescent, and the seeming mo- tion is owing to a real motion in the spectator. Thus the backward motion of the trees to one riding rapidly, the re- ceding of the shore to one who is sailing from it with a fair wind, and the diurnal motion of the heavenly bodies from east to west, in consequence of the revolution of the specta- tor in an opposite direction : these are severally examples of apparent motion. 2 1 . There are three particulars which are concerned in all the phenomena of motion : namely, the space over which a body moves, the time of its motion, and the velocity with which it moves. If the motion of a body be such, that it describes equal spaces in equal successive parts of time, then it is said to move with uniform velocity. Thus, when a ball rolls just as far the second second as the first, and the third as the second, its velocity is uniform. When the Ula-strate the difference between absolute and relative motion. Examples of motion on board of ship, in a balloon, in the revolution of the earth. De- fine apparent motion. Examples in the backward motion of trees, of the shore, and of tlie diurnal motion of the heavenly bodies. When is a body said to move uniformly 1 Example in a ball rolling. MOTION AND FORCE. 21 spaces described in equal successive parts of time continually increase, it is said to move with an accelerated velocity ; and with a retarded velocity, when those spaces continually decrease. If its motion be so regulated, that it receives equal increments of velocity in equal successive parts of time, then it is said to be uniformly accelerated ; and uni- foi-mlij retarded, if the body suffers equal decrements of velocity in those equal portions of time. The leading principles of uniform motion are compre- hended i^n the three following propositions, which are to be treasured up in the memory. I. The Space equals the product of the time multiplied into the velocity* — Thus, a body moving at the rate of 40 feet per second for 10 seconds would evidently pass over a space equal to ten times 40, that is, 400 feet. II. The Time equals tlie space divided by the velocity. — If, for example, a body has passed over 400 feet at the rate of 10 feet per second, then 10 : 1" : : 400 : *,o/-=40 seconds. III. Tlie Velocity equals the space divided by the time. — Thus, if a body has passed over 400 feet in ten seconds, it must have proceeded at the rate of 40 feet per second : for, 10" : 400 : : i" ;ay=40. Hence, in uniform motions, if any two of the three par- ticulars, space, time, and velocity, be given, the other may be found. This may be illustrated by a few examples. questions on uniform motion. 1. If a body moves uniformly 9 seconds with a velocity of 17 feet per second, through what sjpace MviW it pass? Ans. 153 feet. 2. The space described by a body is 540 feet ; the velocity with which it moves is 6 feet per second; what will be the itme of its motion? Ans. 90 seconds. 3. A body describes 560 feet in 9 seconds, what is its ve- locity ? Ans. 62-f feet per second. * The young learner is apt to be puzzled with such abstract expre=aiong as time multiplied into velocity ; but it may be observed, that by velocity is meant nothing more than the space passed over in one second ; which may evidently be so multi- plied as to equal another space. When does a body move with accelerated velocity ? When with a re- tarded -velocity "^ Three propositions on unifoi-m motion, viz. — What does the space equal ? The time ? The velocity ? Give examples of each ? When the space and time are given, how may we find the velocity 1 When the space and velocity are given, how may we find the time 7 When the time and velocity are given, how may we find the space ? 2'2 MECHANICS. 4. A bird of passage was observed to fly with a uniform velocity of 15 foet per second: over what sj^ace would she pass in 24 hours ? Ans. 245-[^i- miles. 5. A lame man set out to travel around the world. He could walk but one mile an hour for eight hours out of the twenty-four. Provided he could go forward without impedi- ment, on the circumference of a great circle of the globe, which is 25.000 miles round, what time would he require to complete the journey? Ans. 8 years and 205 days. 6. A wind blows uniformly from the equator to the pole (say 6 000 miles) in ten days : what is its velocity per hour? Ans. 25 miles. MOMENTUM AND FORCE. 22. The MOMENTUM of a body is its quantity of motion, and is proportioned to the product of its quantity of matte? and velocity. If two balls, equal in weight, be rolled with the same ve- locity, it is evident that they will together have twice as much motion as either of them alone. Also, ten balls, in like circumstances, would have ten times as much motion as one ball. Nor would it make any difference, as to the amount of motion, whether they moved separately, or were united in one mass. With a given velocity, therefore, the momentum is proportioned to the quantity of matter. But the same balls, moving with twice or thrice as great velocity as before, would have twice or thrice as much motion ; that is, the whole amount of motion, or the momentum, is found by multiplying the quantity of matter by the velocity. Thus a single ball may have as much momentum as one hundred similar balls, if it moves a hundred times as fast as they do ; or, in general, a small mass of matter may have the same momentum with a large mass, if its velocity be as much greater as its weight is less. On the other hand, a body moving very slowly may have a great momentum when its mass is very great. Thus, a large cannon ball, when nearly spent, has been known to take off the leg of a soldier who had put out his foot to stop it ; and a ship-of- war, even when its motion was scarcely perceptible, has dashed in pieces a boat that came in its way.* * Although the moving force of a body is estimated by its mass or quantity of matter multiplied into ita velocity, yet the total amomit of work which abody in mo- Deiine Momentum. Example in balls rolled first, with the same velocity, and afterwards, with diilerent velocities. How may a small mass have the same momentum as a large mass ? MOTION AND FORCE. 23 23. Force M any cause which moves or tends to move a body, or which changes or tends to change its motion (See Art. 3.) The measure of a force is the change of motion which it produces : and the momentum of a body is- determined by the force required to stop it. Momentum is estimated in pounds weight, a weight just sufficient to balance it being supposed to act against it by means of a cord passing over a pulley. Thus, a cannon ball may be said to move with a momentum of 1,000 pounds, because, were a scale loaded with this weight, and attached to one end of a cord, while the other end was attached to the ball, (the cord passing over a pulley,) the ball and the weight would exactly balance one aaother, and the ball would be said to move with a momen- tum of 1,000 pounds. The weight, moreover, would be a force acting against the ball, tending to move it in the oppo- site direction. 24. QUESTIONS ON MOMENTUM. 1. A weighs 50 pounds, and moves at the rate of 60 feet in a second : B weighs 300 pounds, and moves at the rate of 10 feet per second: How are their momenta? Ans. equal; for 50x60 = 300x 10. 2. A weighs 7 pounds, and is moving with a velocity of 9 feet in a second ; B weighs 5 pounds, and moves with a velocity of 1 1 feet in a second : What are their comparative momenta? Momentum of A ; momentum of B : ; 7x9 : 5 X 1 1 ; that is, 63 : 55 Ans. 3. Suppose the battering ram of Vespasian weighed 10.000 pounds, and was propelled with a velocity of 20 feet per second, and that this force was found sufficient to de- molish the walls of Jerusalem : With what velocity must a 32 pound ball move to do the same execution 1 The ball, in order to do the same execution as the batter- ing ram, must have the same force, that is, the same mo- mentum. Now the momentum of the batterinsr ram is kion will perform, (or what ia called its living force,) is proportioned to its mass into tlie square of its velocity. An axe swung with a double velocity will cut four times as much wood ; a spade thrus/ into the ground with a double velocity will genetrate four times as far ; and if a railway train, with a velocity of twenly miles an our, requires to have the steam shut off a mile short of the station-house, in order that it may just come to rest on its arrival, the steam must be shut off at the distance of four miles, if the velocity of the train is forty miles an hour. Define/orce. How is a force measured ? How is a momentum estimated ? Example iu a catinoa ball. 24 MECHANICS. 10,000x20=200.000; and this divided by 32 gives 6,250 for the number of feet per second the ball must move in order to have a momentum of 200,000 pounds. 4. Suppose a grain of light, moving at the rate of 192,000 miles per second, should impinge directly against a mass of ice, floating at the rate of one foot per second : v^^hat weight of ice would the light stop ? Ans. 144822.8.57 lbs.; or more than 64 tons. (1 lb. av. = 7,000 grs.) 5. The porters of Constantinople are said to carry weights on their shoulders of 800 pounds. Suppose two men, each weighing 150 pounds, were to meet, A carrying a load of 800 pounds at the rate of two miles per hour : how fast must B move in order to meet A with equal power? Ans. 12-f miles per hour. CHAPTEK III. OF THE LAWS OF MOTION. 25. There are three fundamental principles of motion, of most extensive application in Mechanics, which are called the Laws of Motion. They are remarkable examples of a happy generalization ; but their very comprehensiveness renders them difficult to be understood by the youug learner ; nor can they be thoroughly mastered, in all their relations, until after considerable proficiency is made in the science of Mechanics. We shall endeavor to make them as plain as possible, by a variety of illustrations. 26. First Law. — A body continues always in a state of rest or of uniform inotion in a right line, till by some exter- 7ial force it is made to change its state. This law contains the doctrine of Inertia, expressed in four particulars. First, that unless put in motion by some external force, a body always remains at rest ; secondly, that when once in motion, it continues always in motion unless stopped by some force ; thirdly, that the motion arising from inertia, is always uniform ; and, fourthly, that this motion is in right lines. If a large and a small body move towards each other in consequepce of their mutual attractions, how much faster will the smaller body move than the larger ? State the First Law of motion. Mention each of the fonr particulars which this law embraces. LAWS OF MOTION. 25 27. That a body at rest will continue at rest, is a con- sequence immediatelj' arising from the inertia of matter. (Art. 12.) That a body in motion will continue to proceed uniformly along the right line in which it began to move, until it is acted upon by some external force, is inferred from the fact, that any deviation from uniform rectilinear motion, in a moving body, is observed to be owing to some external force; and that such deviation is diminished as such exter- nal force is withdrawn ; hence, were it entirely withdrawn, the motion of the body would become altogether uniform, rectilinear, and perpetual. We may see approximations to such a state, in a ball rolled successively on the earth, on a floor, and on smooth ice. Although on account of the nu- merous impediments to motion which exist at the surface of the earth, bodies are unable to maintain for any considerable time, the motion they have acquired, yet we see the first law of motion, so far as it respects the tendency of bodies to persevere in motion, fully confirmed in the continued and unaltered revolution of the heavenly bodies. These are im- pelled by no renewed forces, but revolve from age to age in an undeviating course, simply because they meet with no impediments. 28. We may see various exemplifications of this law in the occurrences that daily present themselves to our obser- vation. And first, with respect to bodies at rest. Their tendency to remain at rest is seen, when a horse starts sud- denly forward, and his rider is thrown backward. In con- sequence of the inertia of matter, before a body can be brought to the required velocity, this velocity must be im- pressed on every particle of matter it contains. Hence, the more numerous its particles, the greater is the resistance, from inertia ; that is, the resistance is proportioned to the quantity of matter. A vast weight may be moved on a horizontal railway by a comparatively small force, provided it can be got into motion, with the required velocity. In transporting large quantities (eighty tons for instance,) of coal, the weight is distributed into a number of differen cars, connected together by a loose chain, in order that the inertia of the several parts may be overcome successively. 29. In consequence of the inertia of matter, the motion How do we infer that a body at rest will continae at rest unless moved by Bome external force ? How do we infer that a body in motion tends to move uniformly and in a right line ? Examples in a ball rolled on ice--m the mo- tions of the heavenly bodies. Examples of inertia in riding— m loads trans- ported on a railway. 26 MECHANICS. applied to a body, does not instantly pervade the mass. Id order to this, motion mu.st be applied gradually, especially if the body is large ; for if it is applied suddenly, it is fre- quently all expended on a part of the mass, the cohesion is overcome, and the body is broken. This explanation may be applied to several familiar facts. When a team starts suddenly forward with a heavy load, the effort is either wholly ineffectual, or some part of the harness or tackling gives way. If we draw a heavy weight by a slender string, a slow and steady pull will move the weight, when a sudden twitch would break the string without starting the mass. The same principle applies to bodies already in motion. Thus, when a horse in a carriage starts suddenly forward, he may break loose as well when the carriage was previous- ly in motiijn as when it was at rest. The inertia of a body is, in fact, the same whether the body is in motion or at rest, opposing the same resistance to its moving with in- creased velocity, as to its beginning to move from a state of rest. 30. Several singular phenomena result from the same cause, showing that time is necessary in order that motion communicated by impulse may pervade the entire, mass. A pistol ball fired through a pane of glass, frequently makes a smooth, well-defined hole, and does not fracture the other parts of the glass. Here the momentum of the ball is com- municated to the particles of glass immediately before it. Had the impulse been gradual, the same motion would have diffused itself over the whole pane, and every part would have felt the shock. A ball fired through a board delicately suspended, causes no vibration in the board. A cannon ball having very great velocity passes through a ship's side, and leaves but a little mark, while one with less speed splinters and breaks the wood to a considerable dis- tance around. A near shot thus often injures a ship less than one from a greater distance. A soft substance, as clay or tallow, may be fired through a plank before the motion has had time to diffuse itself through the contiguous parts. The whole momentum being concentrated upon the part immediately before the body, the cohesion of that part is destroyed. 31. Secondly, let us consider the effects of Inertia as it Does motion instantly pervade the mass? Examples in teams starting from rest or in motion, in firing a -pistol ball, and cannon ball, or soft sub- stances. Give examples of bodies in contact, which acquire a f umioa motion. LAWS OF MOTION. 21 respects bodies in motion. All bodies in contact with each other acquire a common motion ; as, for example, a horse and his rider, a ferrywboat and its passengers, a ship and every thing within it, the earth and all things on its surface. Whenever either of these bodies stops suddenly, the movable bodies connected with it are thrown forward. Were the revolution of the earth on its axis to be suddenly arrested the most dreadful consequences would ensue; every thing movable on its surface, as waters, rocks, cities and animals, not receiving instantaneously this backward impulse, would fly off eastward in promiscuous ruin. Were the diurnal motion of the earth, however, very gradually diminished until it finally ceased, so that time should be afforded to communicate the loss of motion by slow degrees to the bodies on its surface, no such effects would take place. If a passen- ger leaps from a carriage in rapid motion, he will fall in the direction in which the carriage is moving at the moment his feet meet the ground ; because his body, on quitting the vehicle, retains by its inertia the motion which it had in common with it. When he reaches the ground, this motion is destroyed by the resistance of the ground to the feet, but is retained in the upper and heavier part of the body, so that the same effect is produced as though the feet had been tripped. 3S. Thirdly, bodies, in consequence of their inertia, have a tendency to move over equal spaces in equal times ; that is, to move uniformly. In a ball rolled on ice in a pendu- lum continuing to vibrate after the moving force is with- drawn, and in numerous cases similar to these, we observe both in nature and art this tendency to uniform motion ; but in all these cases the motion is not absolutely uniform, but is more or less retarded by the resistances encountered. A much nearer approximation to the truth is obtained by means of an apparatus called Atwood's Machine. (Fig. 5.) Its construction, omitting some parts not essential to the principle, is as follows : The triangular base and upright pillars (which are usually of mahogany) constitute the frame, which is surmounted by a horizontal table or plate of wood A B, perforated with several holes. C is a ver- tical wheel which by a contrivance called friction wheels, (not represented in the figure,) is made to revolve with the least possible resistance from friction. D and E are Effects of inertia on bodies suddenly stopped. Examples, in the earth sud- denly losing its diurnal motion — in leaping from a carriage. Examples of the ten- dency of bodies to move iMiiftyrmly — in a ball rolled on ice — in a pcndulma Describe A^woocTa Maolume. 28 MECHANICS. two weights exactly equal, and connected by a slen- der string passed over the wheel 0. F G is a perpendicular scale grad- uated into inches from top to bot- tom, extending from to 60 or 70, according to the height of the ma- chine. H is a movable ring which slides up and down on the scale, and K is a brass plate sliding in the same manner. There are also sometimes connected with the machine, a pen- dulum, and such parts of a clock as are necessary for beating seconds, in order that the time of each experi- ment may be accurately noted. 33. A great variety of the princi- ples of motion may be established by means of this apparatus, but we are at present concerned only with the method of showing, that a body when once put in motion continues, by in- ertia, to move uniformly, after the moving force is withdrawn. It is obvious that the weights D and E balance each other, and consequently that the power of gravity is entirely removed from D, so that it is at liberty to obey the full and exclusive influ- ence of any force that may be applied to it. If, therefore, an impulse be given, by the finger, for example, to D, when at the top of the scale, it ought in con- formity to the law under consideration to move uniformly along down the scale, passing over the same number of inches in each successive second. Such appears to be the fact ; but in order to give a still greater precision to the experiment, a small brass bar is laid on D, which commu- nicates motion to it, accelerating its progress until it comes to the brass ring H, where the bar lodges and the weight proceeds on with the velocity required. This velocity is found to be uniform ; that is, the weight D after it leaves the ring passes accurately over the same number of inches on the scale in each successive second. 34. FourMy, moving bodies have a constant tendency How is the tendency of bodies to move aniformly, proved by this apparataa ? LAWS or MOTION. 29 Fig. 6. to move in right lines. In nature, there occur, indeed, but few examples of rectilinear motion, but almost every movmg body describes a curve. Thus, the heavenly bodies move in ellipses or ovals ; bodies thrown into the air describe a curve called a parabola ; or if their direction is so altered by a re- sisting medium that their path is no "longer a parabola, it is still changed to some other curve ; and a ship sailing across the ocean, describes a curvilinear path on the surface of the earth. The waving of trees and plants, the courses of rivers, the spouting of fluids, and the motions of winds and waves, are likewise more or less curvilinear. Bodies falling towards the earth by gravity, present almost the only examples we observe in nature of a motion purely rectilinear ; and this is so only in appearance. But notwithstanding the deviations from a right line, observable in actual motion, yet v/e find that there is always some extraneous cause in operation which accounts for such deviations. 35« In consequence of this tendency of moving bodies to proceed in right lines, when a body revolves in a curve, around some center of motion, it constantly tends to fly off" in a straight line, which is a tsmgent* to its orbit. The force which thus carries a body oflf from the center of motion, is called the centrifugal force. A stone from a sling, water escaping from the circumfer- ence of a revolving wheel, and water reced- ing from the center of a tumbler or pail when the vessel is whirled, are familiar instances of the tendency of bodies when revolving in circles to fly off" in straight lines. If a pail, containing a little water, be hung up by the ears, by a cord suspended from the ceiling of a room, on turning the pail and twisting up the cord, and then suffering it to untwist so as to give a rapid revolution to the pail, the water will rise on the sides of the vessel, and, if the motion be sufficiently rapid, it will be thrown out of the vessel in lines which are tangents to the surface of the vessel. If a glass vessel of suitable size and shapef be • A Tangent is a straight line wliicli touches the circumference of a circle. _ + A large bell glass receiver belonging to the air-pump, answers well for this pnr pose. How is the tendency of bodies to move in right lines proved ? Are natu- ral motions usually rectilinear ? Examples. De^ne centrifugalforce. Ex- amples in a sling — in a water pail suspended and whirled. 3* 3C MECHANICS. substituted for the pail, the experiment is observed to better advantage. Such a vessel is represented in the annexed figure, where a be exhibits the fluid, (quicksilver or water for example.) elevated on the sides by the centrifugal force. 36. The action of the centrifugal force may be studied still more advantageously by means of the apparatus called the Whir'ing Tables. These consist of two small circular tables, to which (by means of a wheel turned by hand) is communicated a horizontal revolution around their centers. Bodies laid on the tables in different ways, are made to participate in their rotary motions, and thus the laws of the centrifugal force may be observed. By means of this appa- ratus, the following propositions are established. (1). The centrifugal force of bodies revolving; in a given circle, is proportioned to their densities or specific gravities. If quicksilver, water, and cork be whirled together in a tub or vessel, these bodies arrange themselves in the inverse order of their specific gravities, so that the cork will be at the least, and the quicksilver at the greatest distance from the center of the vessel.* {I.) When bodies revolve in the same circle with different velocities, the centrifugal forces are proportioned to the squares of the velocities. By doubling the velocity of a re- volving body its centrifugal force is quadrupled; and ten times a former velocity, gives one hundred times the former centrifugal force. Millstones, revolving horizontally, com- municate their circular motion to the corn that is introduced betweeu them, near the center. The corn, by the centrifugal force which it gradually acquires recedes from the center and passes out at the circumference. If too great a velocity be given to millstones, they sometimes burst with violence. A horse in swift motion, on suddenly turning a corner, throws his rider ; and a carriage turning swiftly is overset on the same principle. In feats of horsemanship, when the equestrian rides rapidly round a small ring, he inclines his body inwards in different degrees, according to the velocity with which he is moving, and thus counteracts his tendency to fall outwards by the centrifugal force. • Thia experiment may be conveniently performed in the suspended vessel, Fig. 6. Describe the Wliirling Tables. How are bodies placed in experiments on centrifugal force ? State the law in relation to (feimiy. Examples in quick- silver, water, and cork. State the law in relation to different velocities. How much is the centrifugal force of a body, revolving at a given distance from tho center, increased by increasing its velocity ten times ? Examples of centrifu- gal action in millstones — in turning a comer swiftly — in feats of horsemanship. LAWS OF MOTION. 31 37. When spherical bodies revolve on their axes, the equatorial parts, being farther from the center of motion and consequently moving faster than the other parts, have a proportionally greater ceatrifugal force. If the revolving body IS soft so as to yield, it is elevated in the equatorial and depressed in the polar parts. Thus a mass of clay re- volving on a potter's wheel, swells out in the central parts and becomes flattened at the two ends. The earth itself, by its figure, which is an oblate spheroid,* the diameter which passes through the equator being about 26 miles greater than that which passes through the poles, indicates the operation of this principle ; and the planet Saturn, which has a far more rapid revolution on its axis, indicates the same modification of its figure in a still higher degree, being strikingly elevated at the equa- tor and depressed at the poles. Let the circle in Fig. 7 repre- sent a section of the earth, AB being the axis on which it . / /\ p revolves. This rotation causes / O /y'\^ the matter, which composes the / ^ '^^^^^ mass of the earth, to revolve in [ c ) circles CQ. OF, OF, round the different points of the axis as centers, at the various distances at which the component parts of the mass are placed. As they all revolve with the same an- gular velocity, they will be affected by the centrifugal forces, which will be greater or less in proportion as their distances from the center are greater or less ; consequently, the parts of the earth which are situated about the equator, Q, will be more strongly affected by centrifugal forces than those about the poles A, B : the effect of the difference has been, that the component matter about the equator has actually been driven farther from the center than that about the poles, so that the figure of the earth has swelled out at the sides, and appears proportionally depressed at the top and bottom, re- sembling an orange in shape. Fig. 7. Pi. / o ~\ F /\F / o /Al / y ^^\, / //.- ^ \ c ; • A spheroid differs from a globe or sphere, in being flattened in one direction and lengthened in the other. The spheroid is oblatB when its ^%\.xg> is flattened likitan orange, and prolate when elongated like a lemon. State the effects of centrifugal action on the figure pf spherical hf 'Tft Examples, in the eartli and planets, illustrate by figure 7. 32 MECHANICS. 38. The centrifugal force of the earth's rotation also affects detached bodies on its surface. If such bodies weie not held upon the surface by the earth's attraction, they would be immediately flung off by the whirling motion in which they participate. The centrifugal force, however, really diminishes the effect of the earth's attraction on those bodies, or what is the same, diminishes their weight, so that, were a body weighing 289 pounds at the equator, carried to the north pole, it would there weigh 290 pounds, if it were at the same distance from the center of the earth ; but being nearer the center when at the pole than at the equator, it gains still more weight, so that, from both causes, there is a gain of one pound in 194. If the earth were not revolv- ing on its axis, the weight of bodies in all places equally distant from the center would be the same ; but this is not so when the bodies, as they do, move round with the earth. They acquire from the centrifugal force a tendency to fly off from the axis ; which increases with their distance from that axis, (Art. 37,) and is therefore greater the nearer they are to the equator, and less as they approach the pole. But there is another reason why the centrifugal force is more eflicient, in the opposition which it occasions to gravity, near the equator than near the poles. This force does not act from the center of the earth, but its direction is in a line per- pendicular to the earth's axis. Thus, in Pig. 7, the centri- fugal forces act, not in the lines CF, CF, but in the lines OF, OF, &c. This force is therefore not directly opposed to gravity, except on the equator itself On leaving the equa- tor and proceeding towards the poles, it is less and less op- posed to gravity. If the diurnal motion of the earth around its axis were about seventeen times faster than it is, the cen- trifugal force would, at the equator, be equal to the power of gravity, and all bodies there would entirely lose their weight ; and if the earth were to revolve still quicker than this, they would all fly off The consideration of centrifugal force proves, that if a body be observed to move in a curvilinear path, some effi- cient cause must exist which prevents it from flying off, and which compels it to revolve round the center. 'Thus the bodies in the solar system are constantly impelled or drawn How does centrifugal action affect the weights of bodies ? Upon what two causes does the loss of weight in the equatorial regions depend ? If a body were first weighed at the equator and then at the poles, how much would it gain ? What would be the effect were tlie diurnal motion of the eai'th 17 times greater ? LAWS OF MOTION. 33 towards the sun by a force which we denominate gravity. If this force did not act constantly, they would resume their motion in the right line in which they were originally pro- jected, when they were first launched into space, and would continue moving in it forever. 39. Second Law. — Motion, or change of motion, is pro- ■oortional to the force impressed, and is produced in the right line in which that force a^ts. First, motion is proportional to the force impressed. This IS very satisfactorily shown by means of Atwood's Machine, (Fig. 5.) When the box D is loaded with bars of diflerent weights, (the bars being left on the ring, H, as in Art. 32,) the box descends along the scale, in consequence of the mo- tion given it by the bar, with velocities exactly proportional to the weights of the bars respectively. Secondly, motion is the direction of the force impressed. Notwithstanding the diversity of motions to which every terrestrial body is constantl}' subject, the effect of any force to produce motion, is the same, when the spectator has the same motion with the body, as though that body were ab- solutely at rest. In other words, all motions are compound- ed so as not to disturb each other ; each remaining, relatively, the same as if there were no others. If we are in a ship, moving equably, any force which we can exert will produce the same motion relative to the vessel, whether it be or be not in the direction of the vessel's motion. If we stand on the deck, supposed to be level, and roll a body along it, the same effort will produce the same velocity along the deck, whether the motion be from head to stern, or from stern to bead, or across the vessel. Also a body dropped from the top of the mast will not be left behind by the motion of th« ship, but will fall along the mast as it would if the mast were at rest, and will reach the foot of it at the same time. If a body be thrown perpendicularly upwards, it will rise directly over the hand, and fall perpendicularly upon it again ; and if it be thrown in any other direction, the path and mo- tion relative to the person who throws it will be the same as if he were at rest. 40, Since, according to the second law of motion, the change of motion is proportional to the force impressed, it What IB the Second Law of Motion? How is the first part of this law proved by experiment ? Is the effect of a force altered by the body's being previoasly in motion! Example, on board of vessel. Case of a ball rolled in different directions— of a body dropped from mast head— of a body thrown directly upwards. Case of a body thrown iu any other direction. 34 MECHANICS. follows that the smallest force is capable of moving the largest bodies. Agreeably to this doctrine; a blow with a hammer upon the earth ought to move it, and that it would do so may be inferred from the following reasons. (1.) We can conceive the earth to be divided into parts so small, that the blow would produce upon one of them even a sensible motion. Then it would produce on two of the parts half as much velocity ; and upon all the parts together a velocity as much less than upon one, as their number was greater than unity. This velocity might be appreciable in numbers, although too small to be observed by the senses. (2.) Very heavy weights may be actually put in motion by small forces. Leslie asserts that a ship of any burden may, in calm weather and smooth water, be gradually pulled along, even by the exertions of a boy. (3.) The repetition of very small blows, finally produces sensible effects upon large bodies. The wearing away of stone by the dropping of water, the abrasion of marble im- ages by the kisses of pilgrims, and especially, the demoli- tion of the strongest fortresses by the repeated blows of the battering ram, are examples of the powerful effects produ- ced by small impulses, each of which must have contributed its share, since the addition of any number of nothings is nothing still. Since motion is ordy in proportion to the force impressed, no force can, by means of any mechanical contrivance, pro- duce a motion greater than itself, or which accumulates in a higher ratio than that in which the force is increased. If an increased velocity is generated by a given force through the intervention of machinery, the mass moved is propor- tionally diminished, so that the momentum still remains proportioned to the force. V") >t^/ 41. Third Law. — When bodies MCt\ip^ mcftr-oAer, action and reaction are equal and in opposite directions. If I strike one hand upon the other at rest, I perceive no difference in the sensations experienced by each. The re- sistance to the hand which gives the blow is equal to the impulse given. A boatman presses against the bank with his oar, and receives motion in the opposite direction, which being communicated through him to the boat, makes it re- Is the smallest force capable of moving: the largest body ? Eifect of a blow with a hammer on the earth. Three reasons stated in favor of the doctrine. Can a force ever generate motion that shall increase faster than the force is increased? What is the Third Law of Motion! Example, one hand stracls npon the other. Why does pressing the bank with an oar move a boat? LAWS OF MOTIOM. 35 cede from the shore. He strikes the water, the reaction of which, at every impulse, carries the boat forward in the op- posite direction. An infirm old man presses the ground with his staff, and thus by lightening the pressure on his lower limbs, makes his arras perform a part of the labor of walking. A bird beats the air with its wings, and by giv- ing a blow whose reaction is more than sufficient to balance the weight of his body, rises with the difference. When tlie wings are small and slender, as those of the humming- bird, and disproportioned to the weight of the body, the de- fect is compensated by more frequent blows, giving nimble motions suited to their short but swift excursions, while the long wings of the eagle are equally fitted, by their less rapid but more effectual blows, for their distant journeys through the skies. Hence, propelling and rowing a boat, flying, and swimming, are processes analogous to each other, depending on the principle of reaction. If a man stands in a boat and pulls upon a rope which is fastened to a post on the shore, the force of the man is ex- pended on the post in one direction, and the post, by its re- action, draws the man in the opposite direction, namely, towards the shore. Call the man A, and let another man B, take the place of the post. If B pulls with a force just equal to that of A, he will do nothing more than the post did be- fore, and therefore the two men together will bring the boat ashore no sooner than A would have done it alone in the former case. If A pulls with more force than B. he pulls B towards him, and the reaction of the force which carries the boat ashore, is the same as before, namely, the force of B. If B were to pull with more force that) A, he would pull A out of the boat, were not A attached firmly to the boat, in which case the velocity of the boat would be augmented. By attentively considering this and all analogous cases, we shall perceive that whenever two bodies act against each other, they give and receive equal momenta, and the mo- menta being in opposite directions, it follows, that bodies do not alter the quantity of motion they have, estimated in a given direction, by their mutual action on each other. 42. These familiar illustrations may serve to give a general notion of the doctrine of action and reaction, as con- tained in the third law of motion ; but this law is suscep- Why does striking the water do the same 1 Why does a staff aid m walk- ing'/ Explain the philosophy of flying, and swimming. Case of a man m« boat pulling at a rope which is fastened to a post. 30 MECHANICS. tible of more precise experimental proof by means of the fol- lowing apparatus. (Fig. 8.) Two equal bodies, whose quan- ^ '^'^ V b ' 1 jj|.jgg j,|- matter or Pig. 8. weights are respect- ively represented by A and B, are suspen- ded contiguously to each other by strings of equal length. A is pulled from its per- pendicular position, and let fall upon B at rest. The space through which each body passes in a giv- en time, as indicated by the graduated arc XY is a measure of its velocity, and in all cases the velocity multiplied into the weight, is a measure of the momentum. (Art. 22.) From experiments with this apparatus, the following truths are established : (1.) That, when A is equal to B, the two bodies move together after impact with half the velocity of A before impact ; and since the quantity of matter in both is double that of A, the two bodies moving with half the velocity of one of them, have the same momentum, that is, the same after impact as before : and consequently as much motion as A imparted to B by its action, just so much B took from A by its reaction. (2.) That, when A is greater than B it still holds true that the momentum of the mass composed of both bodies united, is the same after impact as before : consequently B extinguishes in A just as much mo- tion as it receives from it. (3.) That when the two bodies move in opposite directions, the quantity of motion after im- pact is equal to the difference of their momenta before im- pact. Thus, if A and B are equal, and they meet with equal velocities, each receiving what it gives in an opposite direction, both are brought to a state of rest. If B has half the velocity of A, then it will extinguish an equal amount How is the law of reaction established by experiment? Describe the apparatus. When A is let fall upon B at rest, (the two bodies being equal,) with Trhat velocity do they move after impact 1 When A is greater than B, feow 1 the momentum after the blow? How much motion does B extin- guish in A 1 When the two bodies meet in opposite directions, how are their momenta after impact ? LAWS OF MOTION. • 37 in A, and will return in company with A with half its origi- nal velocity. 43. In the collision of perfectly elastic bodies, (Art. 17.) the velocity lost by the one and gained by the other, is TWICE that tvhich it would have been, had they been perfectly non-elastic. ♦ Let us take the case of two equal bodies, as two ivory balls, supposing each to be perfectly elastic, and calling one A and the other B. First, let A overtake B moving in the same direction ; then the excess of A's velocity will be im- parted to B, so that B will move off with the original ve- locity A, and A will move with that of B ; that is, the two will interchange their velocities. Secondly, let the two bodies meet from opposite directions ; each will return with the original velocity of the other. Thirdly, let A strike upon B at rest ; then A will stop, and B will proceed with the motion A had before. Again, let us take the case of a row of equal elastic bodies, as A B C D E F X •"•'■ O OCXDOO O A will communicate its motion to B and stop; and thus each of the bodies will successively transmit its motion to the next body, and be brought to rest, while the last body, X, will move off with the original velocity of A. 44. It is a general law in the material world, that no body loses motion in any direction, without communicating an equal quantity to other bodies in that same direction, and conversely, that no body acquires motion in any direction, without diminishing the motion of other bodies by an equal quantity, in the same direction. Whatever motion, there- fore, one body receives towards another, whether it is drawn towards it by attraction, or by a rope, or by any other method, precisely the same quantity of motion it imparts to the other body in the opposite direction. If a man in a boat pulls at a rope attached to another boat of equal weight, the boats will move towards each other with equal velocities ; but a man in a boat pulling a rope attached to a large ship State the proposition respecting the collision of two perfectly elastic bodies Case of two equal bodies, A overtaking B moving the same way. Case where they meet from opposite directions. Case of a row of equal bodies, motion being communicated to the series from the first body. Case of a boat and a ship. 4 38 MECHANICS. seems only to move the boat, but he really moves the ship a little, although its velocity is as much less than that of the boat as its weight is greater. A pound of lead and the earth attract each other with equal forces, and the two bodies approach each other with equal momenta. (See Art. 8.) This law of motion applies not only to the impact of bodies, but to every case in which one body acts upon an other. It holds good, not only when bodies come into actual contact, but when they act upon one another at any distance w^hatever. A body A, for instance, is sustained by another body B, and both bodies remain at rest; if the pressure ex erted by the two bodies were not equal, it is evident that some motion would ensue ; which is contrary to the suppo- sition. If motion does ensue, then the case becomes, in a great measure, analogous to that of impact; and the effects produced, estimated in a similar manner, are found to ob- serve the same law. The mutual attractions of bodies are also subject to this law. Thus, if two equal magnets, con- nected with two equal and similar pieces of cork, be made to float upon the surface of the water, as soon as they come within the sphere of attraction, they are observed to move towards each other in a right line, with equal velocities, and consequently with equal momenta; and as the resist- ance which each body meets with from the fluid, is evi- •dently the same, we infer that their actions upon each other are equal. Since momentum is proportioned to the joint product of the velocity and quantity of matter, a great momentum may be obtained, either by giving a slow motion to a great mass, or a swift motion to a small body. A striking illustration of this is afforded by example 4, p. 24, where, on the sup- position that a grain of light moving with its usual velocity, were to impinge directly against a mass of ice floating at its ordinary slow rate, the grain of light would be competent to stop about sixty-five tons of ice. Islands of ice move with such vast momentum, that they instantly demolish the largest ship of war. if it comes in^ their way. 45. If a body in motion strikes a body at rest, the strik- ing body must sustain as great a shock from the collision as if it had been at rest, and struck by the other body with the same force. For the loss of force which it sustains in Case of a pound of lead and the earth. Is the law of action and reaction confined to cases of impact ? How exemplified in pressure— in mutual at- tractions 1 In what two ways may a gi-eat momentum be gained? Examnlo in a grain of light striking an island of ice. LAWS OF MOTION. 39 one direction, is an effect of the same kind as if, being at rest, it had received as much force in the opposite direction. If a man walking rapidly, or running, encounters another standing still, he suffers as much from the collision as the man against whom he strikes. When two bodies moving in opposite directions meet, each body sustains as great a shock as if, being at rest, it had been struck by the other t)ody with the united forces of both. For this reason, two persons walking in opposite directions, receive from their en- counter a more violent shock than might be expected. If they be of nearly equal weight, and one be walking at the rate of three and the other of four miles an hour, each sus- tains the same shock as if he had been at rest, and struck by the other running at the rate of seven miles an hour. This principle accounts for the destructive effects arising from ships running foul of each other at sea. If two ships of 500 tons burden encounter each other, sailing at ten knots an hour, each sustains the shock which, being at rest, it would receive from a vessel of 1,000 tons burden sailing ten knots an hour. It is a mistake to suppose that when a large and a small body encounter each, the smaller body re- ceives a greater shock than the larger. The shock which they sustain is the same ; but the larger body is better able to bear it. When the fist of a pugilist strikes the body of his antagonist, it sustains as great a shock as it gives ; but the part being more fitted to receive the blow, the injury and pain are inflicted on his opponent. This is not the case, however, when fist meets fist. Then the parts in col- lision are equally sensitive and vulnerable, and the effect is aggravated by both having approached each other with great force. The effect of the blow is the same as though one fist, being held at rest, were struck with the combined force of both. 46. The question may be asked, why are the effects so much more injurious to fall from an eminence upon a naked rock, than upon a bed of down? In both instances our fall is arrested, and we sustain a contrary and equal reaction; yet in the one case we might suffer hardly any injuiy, while in the other, we should be bruised to death. The reason of the difference is this : when we fall on a bed of down, the Bxample of one man encountering another. Acconnt for the destructive effects of ships running foal of each other at sea. Does the small body receive a greater shock than the larger ? Why does the blow given by the fist hurt the person struck more than the assailant ? Why are the effects so much more injurioas to fall upon a naked rook than upon a bed of down 1 40 MECHANICS. resistance is applied gradually ; when we fall on a rock it is applied instantaneously. We do not strike the bed with the same force that we do the rock ; we move along with the bed, and of course do not lose our motion at once, and, we receive in the opposite direction merely what we lose. A violent blow, if equally diffused over the human body, may be sustained without injury. Thus, if an anvil be laid on the breast, a man may receive on it a heavy blow with a great hammer with impunity. There are many instances where action and reaction mutually destroy each other, and no motion results. Thus, when a child stands in a Fig. 10. boat and pulls by a rope attached to the stern, he labors in vain to make the boat advance. Dr. Arnott tells us of a man who attached a large bellows to the hinder part of his boat, with the view of manufactur- ing a breeze for himself,- being ignorant that the reaction would carry the boat backward as much as the impulse of artificial wind carried it forward. A force which begins and ends with a machine has no power to move it. 47 . The three Laws of Motion, which, on account of their extensive application to the phenomena of motion, we have endeavored to render familiar to the learner by a vari- ety of illustrations, are to be regarded as the fundamental principles of mechanics. Their truth rests on three different kinds of evidence : 1. They are conformable to all experience and observation. 2. They are confirmed by various accurate experiments. 3. The conclusions deduced from them have always proved true in fact, without exception. x - Case of a violent blow diffased over the whole body. Examples, wlifer* action and reaction matually destroy each other. Upon what three kinds o( evidence rests the truth of the three Laws of Motion t CHAPTER IV. OF VARIABLE MOTION. _ ; 48. When a moving body is subject to me eii^y of a force which acts on it without interruption, but in a different manner at each instant, the motion is called in general vari- able motion. ■ We have instances of variable motion in the action of gunpowder on a ball while it 'is passing through the barrel of a gun, and in the action , of the wind on the sails of a ship. In each of these cases, the velocity of the moving body is constantly augmented, yet the degree of augmentation is diminishing iintil it finally ceases. When a moving body receives each successive instant the same increase of velocity, it is said to be uniformly accele- rated. If a small wheel were revolving without resistance, and. at the end of every second, I should apply a given im- pulse, the wheel would be uniformly accelerated ; for, by its own inertia, it would retain all its previous motion, and, by the second law of motion, the repetition of the same force, at equal intervals, would increase its velocity at a uniform rate. If the intervals at which this force was repeated were indefinitely diminished, the same kind of effect would take place ; and the same would evidently be the case, were the force' to operate without cessation. Such a force is that of gravity, the consideration of which will be pursued in the following sections. FALLING BODIES. 49. In consequence of gravity, all bodies near the earth fall towards its center. We are _ not to infer from this fact, that there is any peculiar force, (like that of a large magnet for example,) residing at the center, but merely that the effect of the earth, taken as a whole, is the same as though its matter were condensed into the center. Thus in Fig. 1 1, Define Variable Motion. Examples, in a mnsket ball— in the action of the wind npon a sail. When is a moving body said to Be uniformly accelerated ? Example, in a revolving wheel Gravity a constart force. In what direc- tion do bodies fall by gravity 1 Why towards the center of the earth ? Ex- plain by figure 11 42 MECHANICS. if we consider how a body at A would be attracted towards the earth, recollecting that every parti- cle of matter in the earth exerts its share in the effect, we shall perceive that while the matter on one side would attract it to the right of the line AB, the matter on the other side would attract it to the left of the same line; consequently, both together would carry it directly for- ward in the line AB towards the center ; and the same would be true were the body A placed in any other point exterior to the earth. The leading truths respecting falling bodies will be stated in the form of propositions, which the learner is requested to commit accurately to memory. The illustrations sub- joined to each, will, it is believed, render perfectly intelligible whatever may not be fully understood from the proposition as enunciated. 50. TJie spaces described by bodies falling from a state of rest under tlie influence of gravity, are proportioned to tlm SQUARES OP THE TIMES, during which they are falling. Thus, if a body be let fall from the top of a tower, or from the brow of a precipice, it will fall in two seconds not merely twice as far as in one second, hvAfour times as far ; in three seconds nine times as far ; in ten seconds one hundred times as far ; and so on, the spaces being proportioned, not simply to the times I, 2, 3, and 10, but to their squares, 1, 4, 9, and 100. It is found by actual experiment that the space through which a body falls in one second from a state of rest, is 16-[^4 feet. Hence, it is easy to estimate the space corresponding to any other time ; for the space belonging to two seconds must be 4xl6-,-'j, or 64| feet; to three seconds, 9xl6-iV, oi 144-1 feet; and to ten seconds, 100xl6-i^, or 1608i feet To find the number of feet, therefore, through which a body falls, the time being known, we have the following Rule. Mvltiply the square of the number of seconds by 1 6-^4. Ex. 1. A body has been falling 7 seconds: through what space has it fallen ? Ans. 788-iV- State the proposition respecting the relation between the spaces and times How much farther will a body fall in two seconds than in one ? Give the rule for the number of feet throagh which a body falls in a given time. VARIABLE MOTION. 43 Ex. 2. In what time would a man fall from a balloon 3 miles high ? By the Rule, putting T for the time, T^Xl6-i\=3x 5280= 15840; and 1'=— -=984.87, Hence, taking the square root of both sides of the equation, T=31.38 seconds, or a little more than half a minute. _ 51. A body descending by gravity is in the same situa- tion as a ball rolled on smooth ice, which should receive a new impulse every moment. Eetaining all its previous motion and receiving more continually, its speed would shortly become very great ; arid were these new accessions of velocity without intermission arid uniform (as is actually the case with gravity) the velocity acquired would be pro- portioned to the time the ball had been moving ; so that at the end of two seconds it would be twice as great as at the end of one second ; at the end of ten seconds ten times as great ; and so on. It appears from the foregoing principle, that the progress of a falling body is rapidly accelerated. In nature, however, the resistance of the air prevents a body which falls through it, from acquiring so great a velocity as it would otherwise do ; still we see indications of the principle of acceleration, in the impetuosity with which bodies fall from any consid- erable height above the earth. Meteoric stones falling from the sky, sometimes bury themselves deep in the ground. Aeronauts that have fallen from balloons have been dashed in pieces. It is, however, a rare occurrence to see a body falling from any great height perpendicularly ; most in- stances of accelerated motion which come under our obser- vation, are bodies falling down inclined planes, where the same law of acceleration prevails. A fragment of rock de- scending from the side of a mountain, has its speed aug- mented as it goes, until its momentum becomes irresistible, and large trees are prostrated before it. 52« If a body after it has fallen from rest^ through any space, slhovM then cease to receive any farther impulse from gravity, hut should proceed on uniformly with the last ac- quired velocity, it would describe twice the space in the same time. How is the effect of gravity illustrated by the motion of a ball on smooth ice 1 Do falling bodies rapidly increase in velocity ? What hinders this in- crease 1. Examples, of the impetuosity of falling bodies. Do we often mr 3t with bodiei falling from a great height perpendicularly? Case of a rock descending a mountain. State the proposition respecting the motion of a body proceeding with the last acquired velocity. 44 MECHANICS. Thus, at the end of one second, having fallen IG-^ feet, it would have acquired a velocity which, in the next second, would carry it 32J- feet; at the end oi four seconds, its space being (4'X 16-iV=) 257i, it would, without any far- ther impulse, descend during the next four seconds 514| feet. 53. The spaces described by falling bodies are also pro- portioned to the squares of the velocities which they acquire in falling over those spaces. Ex. 1. Through what space must a body fall to acquire a velocity of 60 feet per second? In falling from rest 16tV feet a body acquires a velocity of 32^^ feet ; therefore, the square of the velocity acquired, that is, the square of 32-J-, will bear the same ratio to its space, namely, 16-iV feet, that the square of 60 bears to the space required ; that is, (32i)' : 16t1j : : (60)" : 55.96 feet. Ans. Rule : To find tlie space when the velocity is given, divide the square of the velocity by 64-J-. Ex. 2. From what height must a body fall to acquire a velocity of 50 feet per second ? Ans. 38.86 feet. Ex. 3. What velocity would a body acquire by falling 500 feet ? TTj By the Eule, I =500 ; hence ¥"=500x64^=32166-1 64^ therefore V=v/32166f =179.35 feet per second. 54. As in the descent of a body, the force of gravity generates equal increments in equal times, so in ifs ascent, equal portions of velocity will be destroyed in equal times ; that is, as a body is uniformly accelerated as it falls, so it is uniformly retarded as it rises. Hence, If a body be projected perpendicularly upwards, with the velocity which it has acquired in falling from any lieight, it will rise to the height fr07n which it fell, before it begins to descend again. It will also occupy the saine tiine in rising as in falling. Ex. 1. To what height will a body rise, when projected perpendicularly upwards with a velocity of 120 feet per second ? As it will rise to the same height as that from which it must have fallen to acquire this velocity, we have only to How far would a body move the second second with the velocity acquired dnring the first? How far in foar seconds, having fallen 4 ? State the relation between the spaces and the acquired velocities. Give the rule for finding the space from the acquired velocity. State the case of a body thrown upwards. How high will it rise 7 What time will it occupy in rising ? VARIABLE MOTION. 45 ,(120)'. find this space. According- to Art. 63,^-— j- =223.83 Ans. Ex. 2. How high will a body rise when thrown perpen- dicularly upwards with a velocity of 100 feet per second? Ans. 155.44 feet. 55. The law of descent of falling bodies, as enunciated in Art. 50, goes on the supposition that the body begins its descent from a state of rest, and that it afterwards receives no impulse from any force beside gravity ; but we may have occasion to estimate the motion of a falling body which re- ceives, either at first or during its descent, an impulse from some extraneous force. In this case we must add the amount of the impulse to the ordinary force of gravity, as expressed in the following proposition. The space described in a given time by a body projected downwards with a given velocity, is equal to tlve space which would be described with that velocity contirvued uniformly for that time, together with the space through which a body would fall from rest by the action of gravity for the same time. Ex. 1. A body is projected downwards with a velocity of 30 feet in a second ; how far will it fall in four sec- onds? First, by a uniform motion of 30 feet for four seconds, the body would dpscribe 120 feet. Secondly^ by gravity it would in the same time describe 2574- Hence, the entire space is ... . 377f Ex. 2. A body after falling three seconds passes by a window in a tower, from which a person standing in the tower, gives it a blow downwards, which increases its ve- locity 20 feet per second, after which it falls during two seconds more, and then reaches the ground ; what is the height from which it fell ? First, the descent by gravity for 5 seconds, is 402-i'ij feet Secondly, the uniform motion of 20 feet for two seconds is 40 Whole space, 442-iV Ex. 3. Suppose a body to be projected downwards with a State the proposition respecting a body projected downwards with a given velocity. 46 MECHANICS. velocity of 17 feet per second : how far will it fall in five seconds ? Ans. 487-,^ feet. QUESTIONS ON FALLING BODIES. 1. From a black cloud a flash of lightning- was observed, and 12 seconds afterwards it began to rain : on the suppo- sition that the rain began to descend on the instant of the flash, what was the lids^ht of the cloud? Ans. 2.316 feet.* 2. A body fell into a'well which was 250 feet deep : how long was it in falling, and what velocity did it acquire? Ans. toM;=3.942 seconds ; ve/oc;V?y= 126.82 feet per second. (See Art. 50, Ex. 2, and Art. 53, Ex. 3.) 3. Wishing to ascertain the difference in the depth of two wells, I dropped a pebble into one of them, and heard it strike the water in six seconds ; and then into the other, and heard it strike in ten seconds ; what was the difference in their depths ? Ans. 1029i feet. 4. A boy wishing to know the height of his kite, found that he could just send an arrow to it, by giving to the arrow the velocity of 125 feet per second: what was the height of the kite ? Ans. 242.9 feet. 5. From the top of a tower, a boy knocked his ball per- pendicularly upwards. After six seconds, it returned, when he gave it a blow downwards, which increasing its velocity ten feet per second, it reached the ground in four seconds after it received the downward blow : what was the height of the tower? Ans. 683-^ feet. 56. The laws of falling bodies are susceptible of very accurate experimental proof, by means of Atuood's Machine. (Art. 32.) Before the invention of this apparatus, there were two difficulties in the way of such a verification, name- ly, the little time occupied in descending through such per- pendicular heights as the experimenter can command, and the resistance of tlie air, which, when the velocity becomes great, acts as a powerfully retarding force. We can rarely command a perpendicular eminence of more than 400 feet, and yet the time of passing over this space is only about five seconds, a period too short to enable us to mark dis- tinctly the respective rates at which the successive intervals are described. Atwood's Machine affords the means of ob- * No allowaace is made in problems of this kind for resistance of the air. By what apparatus may the laws of falling bodies be verified ? What were the two difficulties in the wa^ befor« this machine W4 ccutHved > VARIABLE MOTION, 47 viating both these difficulties, and of verifying the laws of falling bodies with great accuracy. The object of the ma- chine, so far as it respects experiments on falling bodies, is to render the descent of bodies so gradual, that the relations between the times and spaces can be accurately observed. By recurrence to the figure, and to the description given in Art. 32, we shall readily see how this object is accomplished. The weights D and E are each equal to 31-J- ounces, and of course the quantity of matter in both is 63 ounces. Now, since one of these weights rises as the other descends, the force of gravity retards the one as much as it accelerates the other, and they are in effect the same as though they were entirely destitute of gravity. If a small weight, as one ounce, were let fall freelij from the top of the machine, it would fall through this small space almost in an instant, and we should be unable to mark the rate at which it pass- ed over the successive portions of the scale FGr ; but if it be laid on the weight D, it must carry D along with it ; that is, it must make D descend, and E ascend, and therefore the motion belonging to one ounce, will be distributed through 64 ounces, and the velocity retarded in the same ratio. Consequently, the weight D will descend only -^ part as fast as a body falling freely ; and as a body falling freely descends about sixteen feet or 192 inches in one second, the weight D will descend -ig2j2=3 inches in the same time. The comparative progress of this weight, and of a body falling freely for several successive seconds, will be seen in the following table. Time, in seconds, 1 2 3 4 5 6 Body falling freely, in feet, 16V-.- 64i 144| 25 7i 402-iV 579 Do. in Atwood's Mach. in inches. 3 12 27 48 75 108 Hence it appears that in six seconds, while a body would fall freely through 579 feet, it would in the same time de- scend only nine feet in Atwood's Machine. But the latter is a uniformly accelerated velocity, and subject to the same What is the object of this machine 1 Explain how it renders the depcent of bodies so slow'. How far does the weight descend in one second? How far would a body fall freely in six seconds, and how far during the same time in Atwood's Machine ! 48 MECHANICS. laws as the former, and it may therefore be employed to m vestigate the laws of falling bodies. The results correspond remarkably with theory, so that when the mstrument i? well constructed and managed skilfully, the descendmg weight clicks upon the stage or brass plate K, at the very instant required. 57. It is not alone by the direct fall of bodies that the gravitation of the earth is manifested. The curvilineai motion of bodies projected in directions different from the perpendicular, is a combina- tion of the effects of the, uni- form velocity which has been given to the body by the im- pulse which it has received, and the accelerated or retard- ed velocity which it receives from the earth's attraction. Suppose a body placed at any point P (Fig 12.) above the surface of the earth, and let PA be the direction of the earth's center. If the body were allowed to move without receiving any impulse, it would descend to the earth in the direction of PA, with an accelerated motion. But suppose that at the moment of its departure from P it receives an impulse in the direction of PB ; then it would fall towards the earth, between the actions of the two forces, in the curve line PD. The greater the velocity of projection in the direc- tion PB, the greater the sweep the curve will take. Thus it will successively take the forms PD, PE, PP, &c., until, when the velocity of projection is increased to a certain amount, the body will sweep quite clear of the earth, and like the moon revolve around it. Thus, a cannon ball shot horizontally from the top of a lofty mountain, would go three ; or four miles. If there were no , atmosphere to resist its motion, the same original velocity would carry it thirty or forty miles before it fell ; and if it could be despatched with about ten times the velocity of a cannon shot, the centrifu- gal force would exactly balance the force of gravity, and the How is ^avity manifested in curvilinear motions 1 Ulastrate by figure 12. How far would a cannon ball proceed when shot from the top of a high mountain, if it were not for the resistance of the air ? 'With how much greater velocity must the ball be fired to'*make it go quite round the earth J COMPOSITION AND RESOLUTION OF MOTION. 49 ball would go quite round the earth. Such a velocity would carry the ball round the world in less than an hour and a half.* 58. Hence it is obvious, that the phenomenon of the revolution of the inoon round the earth, is nothing more than the combined effects of the earth's attraction, and the im- pulse which it received at its creation ; and were any of the heavenly bodies to explode, we may conceive that the frag- ments would proceed in a rectilinear direction, until ap- proaching, severally, within the sphere of influence of some large body, whose attraction would combine with their pro- jectile force, they would forever afterwards continue to re- volve around that body, as the satellites revolve around the primary planets. 59. The attraction of gravitation is manifested by com- paratively small masses of matter. The effect of a high mountain is perceptible upon a plumb line, causing it to deviate sensibly from a perpendicular, so that the same star near the zenith would change its apparent place when view- ed on opposite sides of the mountain. CHAPTER V. OF THE COMPOSITION AWD RESOLUTION OF MOTION. 60. Simple motion is that which arises from the action of a single force ; compound motion is that which is pro- duced by several forces acting in different directions. Strict- ly speaking, we have no example of a simple motion, since in the absolute motion of all bodies, their own proper motion is combined with that of the earth in its diurnal and annual revolutions, and we know not with how many others. In an enlarged sense therefore all motions are compound. But in the foregoing distinctions we have reference only to rela- tive motions, as those which take place among bodies on the earth. * I hour, 23 minutes, aiid 33 seconds. In what time woaM it perform the whole revolution ? By what forces does the moon revolve about the earth? Is the attraction of gravitation manifested by comparatively small masses of matter, such as a high moun- tain? o V J9 Define simple motion. Are simple motions often observed ( 5 50 MECHANICS. When a body is acted upon at the same time, by two of more forces, whose directions are not in the same straight line, it is evidont that it will deviate from the course in which it would have moved by the single action of either of those forces, and will proceed in some intermediate direction. Let us first consider the case of a body acted upon by two forces. If I place a small ball at one of the corners of the table, and give it a snap with my thumb and finger, in a direction parallel to one edge of the table, it will of course move along that edge ; or if I give the impulse with the thumb and finger of the other hand, in the direction of the edge which is at right angles to the former, the ball will move along this edge ; but if I give both these impulses at the same moment, the ball will move diagonally across the table from corner to corner. If the force applied to each be accurately proportioned to the length of the corresponding side of the table, (as it may be by means of springs fixed to the corner of the table.) the ball will reach the opposite corner in the same time as it would have taken it to describe either side separately. This fact is generalized in the following funda- mental proposition. 61. Two impulses, which, when communicated sepa- rately to a body, would make it describe tlie adjacent sides of a parallelogram in a given time, will, w/ien tliey are com- municated at tlie same instant, cause it to describe tlve di- agonal in tlie same time ; . and tlie motion in the diagonal will be uniform. This principle is called the parallelogram of forces. Suppose a body, placed at A ^'g- "• (Fig. 13,) to be. acted upon by two forces, one of which would cause it to move uniformly over the line AB, and the other over the line AC in the same time; then if both forces act at the same instant upon the body, it will by their joint action move uniformly over the diagonal AD, in the same time it would have taken to describe AB or AC by the forces act- Describe the motion of a ball across the table, first under one, and then un- der two impulses. State the fundamental proposition respecting the com- position of motion. Explain the foregoing proposition by figure 13. What IS this principle called ? When a body would describe two sides of a trian- gle under two forces acting separately, what line will it describe under two forces acting simultaneously \ COMPOSITION AND RESOLUTION OP MOTION. 51 ing separately. By the second law of motion, every force applied to a body produces the same change of motion as though it were the only force applied. Consequently the force applied in the direction of AC. will carry a body just as far towards the line CD, as though the force which acts irj the direction AB were not applied. In the same manner, by the other force it will be carried just as far towards BD as though there were no other force acting upon it. Hence, the body will be found both in the lines CD and DB, when acted upon by the two forces conjointly, in the same time that it would reach those lines respectively, if acted on by each force separately. Being therefore at the end of this time in both the lines, it must he at their inter- section, that is, at the point D. 62. Since AB is equal to CD and parallel to it, the two forces may be considered as acting in the direction of the two sides AC and CD of the triangle ACD ; and hence ivJien a body would describe tJie two sides of a triangle by two forces acting separately, it will in the same time, describe the third side by the two forces acting jointly. The motion which is produced by the action of two or more forces is called the resultant. Thus the diagonal AD, IS the resultant of the two forces represented by AB and CD. 63. We daily observe examples strikingly illustrative of the principle just explained. In crossing a river, the boatman heads up the stream, and so combines the direction of the boat with that of the current, as to move directly across in a line which is the diagonal between the two di- rections ; or he describes the third side of a triangle by the action of two forces which would severally carry him over the other two sides. Rowing, swimming, and flying are severally instances of motion in the diagonal between two forces. In feats of horsemanship, when the rider leaps up from the saddle, we are surprised not to see the horse pass from under him ; but he retains the motion he has in com- mon with the horse, and does not in fact ascend perpen- dicularly, but obliquely, rising in one diagonal and falling "in another. Two men in a boat under rapid sail, sitting on opposite sides, and tossing the ball from one to the other, catch the ball in the same manner as though they were at rest. While, indeed, the ball is crossing the boat, the oppo- site man advances ; but the ball also participating in the Define the term resultant. Examples, in crossing a river, in rowing swimmings, flying ; in feats of horsemanship ; in tossing a ball in a boat. 52 MECHANICS. same common motion of the boat, advances meanwhile in the same manner, and in reaching the other side, actually moves diagonally, with respect to the surrounding space, though with respect to the boat, its motion is directly across. A body let fall from the top of a mast, when the ship is un der sail, falls along down the mast and strikes at its foot m the same manner as though the ship were at rest, partaking of the common motion of the ship, and therefore describing a diagonal between this forward direction and that of gravity. The bow and arrow af- fords an example of a body moving in the di- agonal of a parallelogram under the action of two forces. Let CED (Fig. 14,) be a bow, which is stretched by the string CGD, the arrow being applied at the middle point G-. Then, as the tendency of the bow to spring back is the same on each side, consequent- ly the' forces acting in the direction of GC and GD are equal. Let them be represented by Gm and G;i, and complete the parallelogram G« K«i ; then GK will be the resultant, and will represent the actual force by which the arrow is propelled. GK is evidently greater the more the bow is bent, which accords with experience. In the flight of a bird we recognize the same principle. The bird strikes the air in the directions AD and BD, (Fig 15,) and the reaction of the air strikes the wings in the di rections DA and DB. Taking DE and DF to represent these two equal forces and completing the parallelogram, DG represents the combined effect of both, or that force un der which the bird moves. It will be seen that the diagonal DG is greater as the angle at D is more acute, and conse- Examplo in a body let fall from the top of a mast. How do the bow and arrow exemplify the parallelo^am of forces ? Illustrate by figure 14. How is the resultant increased or diminished ? How does the night of a bird ex- hibit the principle ? COMPOSITION AND RESOLUTION OF MOTION. 53 quently that the effect of the blows is greatest when they are most direct, that is, most nearly parallel to Fig. 15. the path ,in which the Lira is flying. The force of the blows, there- fore, is greatest at first, and decreases as the wing approaches the body. If the wing were of the same shape on both sides, before and behind, and if it return- ed in the same time, then it would lose as much in one direction as it gained in the other, and the bird would remain at rest. But the wing opens to give the blow, and then closes up and returns on its edge. Steamboats have sometimes been constructed with paddles, instead of wheels, which, like the wings of a bird, presented their broad side to the water in giving the blow, but re- turned on their edge. A skilful rower manages his oar on the same principle. It is also evident from the figure, that if the force DP were suspended, DE would turn the bird round in the direc- tion ABD. We here see the manner in which birds turn themselves or change their course of direction ; and a steam- boat, in a similar manner, turns .about or changes her course by either suffering one wheel to remain at rest while the other continues acting, or in rendering the velocity of the two wheels unequal. G4:. ^a hody he impelled by any number offerees which, while acting separately, would, in a given time, make it de- scribe all the sides of a polygon, except tJie last side, when all iliese forces act at the saine instant, tlie body ivill be m,ade to describe the remaining side in the same time. This principle is called the polygon of forces. Thus in Fig. 16, a body placed at A, and acted on by two forces represented in quantity and direction by AB and BC, In what manner must the blow be given to produce the greatest effect? Why is not the motion gained by the blow lost while the wing returns 7 Explain the principle on which a bird turns or changes her direction— also as applied to a steamboat. State the proposition respecting the poh/gon of forces. 5* 54 MECHANICS. would describe the side AC. Therefore, AC may be taken as the equivalent of those two forces, or as the representative of a force equal to them both, and Fig. 16. producing precisely the same effects as they would do. For the same reason, the two forces AC and CD would cause the body to describe AD ; and AD, therefore, represents a force equivalent to the three forces AB, BC, CD. and may be substituted for them; and. in like manner, AE may be substituted for AD and DE. Therefore under the action of the several forces AB, BC, CD, and DE, the body would describe the last side AE. If the number of forces were equal, in quantity and di- rection, to all the sides of the polygon, then the body would remain at rest under their joint action. For the forces acting in the direction of AE, would, in this ease, be exactly bal- anced by those acting in the direction of EA. Thus AC would be the resultant of AB and BC ; AD that of AB, BC, and CD ; and AB that of AB, BC, CD, and DE ; consequently the forces represented by these four lines, if acting together, would unitedly produce a force equal to AE, and would therefore be balanced by a single force acting in the direction EA. 65. A given motion may be Tig. 17. considered as caused by two, three, or any number of forces, as will be evident from the follow- ing figure. AB will represent a motion resulting either from the combined action of forces repre- sented in quantity and direction, by AD and DB, or from AC and CB, or from the sides of various other triangles of which AB may be considered as the third side. In the same manner, any one side of the polygon, (Pig. 16,) may be considered as the representative of a motion produced by forces corres- ponding to all the other sides of the figure. IlluBtrate by figure 16. How may a given motion be considered as caused ? Illustrate by figure 17. How may any one side of a polygon bo considered as produced ? COMPOSITION AND RESOLUTION OF MOTION. 55 Fig. 18. 66. A given force may be resolved into an unlimited numhev of others, acting in all possible directions. Thus (Fig. 17,) AD and DB, or AC and CB may be sub- stituted for AB, representing forces which are equivalent to that represented by AB ; and any force represented by one side of the polygon (Pig. 16.) may be resolved into forces corresponding to all the other sides, the united effect of which is only equal to that of this side. The sailing of a ship affords an instructive illustration of the principles of the composition and resolution of motion. To one unacquainted with the principles, it is apt to appear mysterious that a ship is able to sail with a wind partly ahead, and still more that two ships are able to sail in ex- actly opposite directions by the same wind. Let us see how this takes place. Let AB (Fig 18,) represent the keel of a ship, and CD the sail ; and let the wind come in from the side, in the di- rection of HD. Let DE represent the whole force of the wind, and resolve it into two forces, viz. into EF perpendic- ular, and FD par- allel to the sail DC. Then it is manifest that EF alone rep- resents the effective force of the wind upon the sail. But EF is not wholly em- ployed in urging the ship forward, since it is oblique to her course ; therefore, again resolve BF into FG parallel with the course and GE at right angles with it. The force represented by GE is lost by the lateral resistance of the water, or is counteracted by the helm, while FG is employed in propelling the ship on her way. By inspecting Fig. 18 it will readily be seen that another ship may sail in the opposite direction by the same wind ; Into what forces may any given force be resolved ? Illustrate by figure 17. How are the composition and resolution of motion exemplified in the sailing of a ship 1 Illustrate by figure 18. 56 MECHANICS. only the sail is raised on the left side when the ship is heading one way, and on the right side when it is heading the other way. When the wind strikes the sail at right angles, only one resolution is necessary ; for if FE repre- sents the whole force of the wind, FG will represent the force which propels the ship forward, while GE will rep resent the part which is lost by the lateral resistance of the water. Since, resolving the force of the wind after the foregoing manner, the effective part of the force, viz. FG, will not wholly disappear until the wind is directly ahead, it might seem possible to sail much nearer the wind than is found to be actually practicable. But though on account of the pe- culiar shape of vessels, the forward resistance is much less than the lateral, yet it is somethings and therefore requires more or less of the force that acts parallel to the keel to overcome it. 67. A body acted upon at tlie same time by three forces, represented in quantity and direction by the three sides of a triangle taken in order, (or by lines parallel to these.) will remain at rest. This principle is called the triangle of forces. Since AD (Fig. 19,) represents -^'^' ^^- ^„ a force which is equivalent to those corresponding to the two sides A(J, CD, if upon a body placed at A, two such forces were to act while a third force cor- responding to the side DA were to act upon it in the direction DA, the body being acted upon by two opposite and equal forces would remain at rest.* A kite at rest in the air is commonly mentioned as an example of this, the three forces being, the direction of the wind, the weight of the kite, and the action of the string. Let AF be a kite, held by the string AS. Let DF represent the force of the wind blowing horizontally, and resolve it into two forces, viz. DC perpendicular, and CF parallel to the kite. Then DC will be the only effective part of the wind, since that part which acts parallel to the kite can have • The three forces are properly represented by AC and AB acting against DA ; bnl CD is parallel and equal to AB, and may therefore be substituted for it. Show how two ships may sail in opposite directions by the same wind. Wh^ cannot a ship sail closer to the wind than a certain angle ? State tha proposition respecting the triangle of forces. Illustrate by figure 19. Ex- ample, in a kite at rest. COMPOSITION AND RESOLUTION OF MOTION. 57 no influence on its motions. Again, resolve CD into two forces, namely, CE perpendicular and DE parallel to the Fig. 20. Fig. 21. horizon. Then CE will represent the upward force of the wind, and DE its force in a horizontal direction. Now when the string AS makes such an angle with the kite that its downward force, added to the weight of the kite, shall equal CE, and its horizontal force shall equal DE, the kite will be at rest. 68. When two motions which are not in the same straight line are combined, one. of which is uniform and the other accelerated, the moving body describes a curve. ' Thus, (Fig. 21,) when a body is thrown obliquely upwards in the direction of PN, the force of ofravity will draw it continually away from that line towards the earth ; and as gravity is a force which increases the motion of a falling body every instant, the body will at first recede slowly from the line PN, but more and more rapidly as it advances, de- scribing a curve whose deviation from the line of projection contin- ually increases, as POQ. Now, the spaces PM and PN, repre- senting the uniform motion in the line of projection, are to one another as the squares of the spaces MO and NQ. (Art 50,) which, being equal to PL and PV, represent the times of descent towards the earth. But a curve described between two forces bearing this relation to each other, is known to be the curve called a Illustrate by figure 20 When do two oombined motione describe a curv« 1 Dlnatrate by figure 21. 58 MECHANICS. parabola, being one of the curves which result from the sections of a cone. The parabola, therefore, is the curve belonging to all bodies projected from the earth into the at- mosphere, as is seen when a stone is thrown upwards, or a fluid spouts obliquely. Forces differently proportioned to each other, describe different curves, as circles, ellipses, &c. Thus, the planets revolve around the sun in ellipses, between the force of projection and that of attraction towards the central luminary. • CHAPTER VI. OF THE CENTER OF GRAVITY. 69. The center of gravity of a body is that point, about which, if supported, all the parts of a body {acted upon only by tlie force of gravity) would balance each other in any position. Thus, a staff poised across the finger, rests only when the finger is under the center of gravity. The principles which have been discovered respecting the composition and resolution of forces, and respecting the center of gravity, have alike contributed greatly to simplify the doctrines of Mechanics. It is characteristic of a great and penetrating mind, to devise means of divesting intricate subjects of their complexity, and thus to bring easily within the grasp of the mind, subjects otherwise too much involved to be within its comprehension. By the rule of simple multiplication, we easily multiply any number by one thousand ; indeed, it is nothing more than to annex three ciphers to the number itself; but how tedious would be th's process, were the rule of multiplication undiscovered, and we were unacquainted with any other method of arriving a.t the result, except to add the given number to itself one thousand times. In like manner, by means of the rules for the composition of motion, we are enabled to reduce a thousand different motions to one ; and by the doctrine of the center of gravity we are taught how we may make a "Wliat Curve is described under the united forces of projection and gravity ? Under what two forces do the planets revolve abont the sun ? Define the center of gravity. Give an example — of what nse are the doctrines of the composition and resolution of forces, and of the center of gravity ? lUustrate by a case of multiplication. CENTER OP GEAVITY. 59 force, situated at one single point, equivalent to an infinite number of forces, -situated in as many different points ; and, instead of pursuing the endless diversities of motion to which the different parts of a complicated system of bodies may be subject, we are taught how to follow merely the motions of a single individual point. 7 O. Ill regular plaiie figures, such as squares, parallel- ograms, circles, Sfc. the center of gravity is the same with the center of tlie figure. Lines drawn in the following figures Fig. 22. bisecting the opposite sides, also bisect each other in the center of the figure, and divide the whole figure into four equal parts. When the figure rests on G, every two ol these opposite parts act against each other, and being equal, exactly balance one another. The same is true of such regular solid figures as a cube, a sphere, a cylinder, &c. 7 1 . To find the center of gravity by experiment, several different methods present themselves. We will first suppose the body to be in the shape of a piece of board, of uniform thickness. Suspend it by one corner, and from the same Corner let fall a plumb line, and mark its line of direction on the surface of the board. Suspend the board from any other point, and mark the line .of direction of the plumb line as before, and the point where these lines intersect each other, must obviously be the center of gravity, since that center is in both of the lines. But when the body is not of uniform thickness, but is any irregular solid, suspend the body by a thread, and let a small hole be bored through it, in the exact direction of the thread, so that if the thread were continued below the point where it is attached to the body, it would pass through this hole. The body being successively suspended by sev- eral different points in its surface, let as many small holes be bored through it in the same manner. If the body be Where is the center of gravity in regular plane figiires 1 How can we find the center of gravity of a board, or any regular solid ? How do we find the center of gravity of an irregular solid ? 60 MECHANICS. then cut through, so as to discover the directions which the several holes have taken, they will be all found to cross each other at one point within the body. Or the same fact may be discovered thus : a wire which nearly fills the holes being passed through any one of them, it will be found to inter- cept the passage of a similar wire through any other. 72. A convenient method of finding the center of gravity of a body is, to balance it in different positions across a thin edge, as the edge of a knife or a prism. The same thing may be effected, when the shape of the body will admit of it, by laying it on the edge of a table, and letting so much of it project over the edge, that the slightest disturbance will cause it to fall. The center of gravity is the point in which the several lines marked on the body, where the edge cuts it. intersect one another. From some or all of the foregoing trials, the center of gravity of bodies may be nearly ascer- tained ; but in order to find it with absolute exactness, we are frequently obliged to resort to intricate mathematical processes. By whatever method the center of gravity of a body has been ascertained, we shall find that when that is supported, the body will remain at rest in every position. Thus a globe will stand securely on a very small perpendicular sup- port, since that support will necessarily be under the center of gravity ; a lever, as the beam of a balance, poised on its center of gravity, \\'A\ be at rest in every position it takes while turning around the fulcrum ; and however irregular the body may be, it will, when balanced on its center of gravity, obstinately maintain its position. X 73. We may find the distance of the common center of gravity of any number of bodies from a given point, upoa the following principles. First, suppose the bodies have their centers of gravity in the same right line, as in figure 23, then the distance of the common center of gravity of all the bodies from the point Fig. 23. O A B C D -® X ®- How do we find the center of gravity by means of a sharp edge as s prism or the edge of a table! Why does a globe stand firm on a narrow support ! Case of a lever having the center of gravity at the fulcrum How mav we find the distance of the common center of gravity of any number of bodies from a given point ! ■> j ">«=r CENTER OF GRAVITT. 61 0, will be found hy multiplying each body into its distance from tJiat point, and dividing the sum of the products by the sum of the bodies. In figure 23, A, B, C, D, are bodies of different weights connected together by a wire which is balanced on the center of gravity Gr. Now we may find the distance of G from any point in the same line, by multiplying A into AO, B into BO, C into CO, and D into DO, and dividing the sum of these products by the sum of the bodies, A, B, C, and D. Secondly, suppose that the bodies are not in the same right line, but are situated like a number of balls of differ- ent weights hanging at different distances from the ceiling of a room. Thus, we may find the distances of their com- mon center of gravity from the perpendicular wall of a room, by m,ultiplying each body into its distance from tht wall, and dividing the sum of the products by the sum oj the bodies. 7 4. When a body is supported by a prop placed unde'i its center of gravity, the pressure will be the same, wliethei the whole quantity of matter is uniformly diffused through the space occupied by the body, or is all concentrated in the center of gravity. In consequence of this law of the center of gravity, the reasonings on mechanical subjects are often greatly simpli- fied. Thus, instead of estimating the pressure and other mechanical effects of a large body like the earth by con- sidering the united effects of all its separate parts, we may often arrive at a far more simple conclusion by considering all the matter of the earth as residing in the center of gravity, and reasoning respecting it accordingly. When bodies that compose a system are in motion, their common center of gravity will move in the same manner as if a body equal to the sum of the bodies were placed in that point, and the same forces act on it as acted on the bodies separately. 75. Two weights or pressures acting at the extremities of an inflexible rod void of gravity, vdll be in equilibrium about a given point, when their distances from that point are to each other inversely as those weights or pressures. Example, in the distance of the center of gravity of any numher of bodies (rom the wall of a room. Wliat is the effect of supposing the matter all con- centrated in the center of gravity ? When a system of bodies are in motion, how does their common center of gravity move ? How must two weights acting at the ends of an inflexible rod be situated with respect to the center of gravity in order to be in equilibrium 7 6 62 • MECHANICS, Thus. (Fig. 24.) if a weight of one pound, and another of ten pounds, are connected by a wire, and balanced by *^ ' laying the wire across Fig. 24. a thin edge, it will be found that the smaller weight is ten times a.' fai from the support, ox fulcrum, as the largei weight is. 76. Whatever be the form (n dimensions of a body upon a plane parallel to thehorizon, it will remain at rent, iftlie line drawn from its center of gramty perpendumlar to tlm horizon, {called the line of direction.) falls within its For let ABCD (Fig. 25.) represent the section of a body, passing through its center of gravity G, and draw G-F per- pendicular to HO the plane upon which it stands ; then, since the tendency of the body to descend is the same as it Fig. 25. DA D B F F B its whole weight were concentrated in G, it will rest or fall according as & is supported or not ; i.e. according as F falls vrithin or without the base BC ; moreover, the stability of the body will depend upon the distance at which the point F falls within the base. 77. If a body be suspended from, any point, it mil not rest till the line which joins the center of gravity and point of suspension, is perpendicular to the horizon. For let ABCD (Fig. 26.) represent the section of a body as before, Gr its center of gravity, S the point of suspen- "WTiat is the line of directioix % In order that a body may stand iirm on a horizontal base, bow must the line drawn fi"om the center of gravity perpen- dicularly to the horizon, fall with respect to the base ? Illustrate by figure 25, If a suspended body swing freely on a point, on coming to rest how is the line situated which joins the ceate- of gravity and point of suspension ? CENTER OP GRAVITY. 63 Fig. 26. sion ; join SGr, and draw SOW perpendicular to the horizon ; produce SG to N, and draw GR par- allel to SW ; then, since the weight of the body may be considered as collect- ed in fi. its tendency to motion will be along the line GrR. Let G-R there- fore represent this tendency, which re- solve into GrN in the direction SG-. and RN, perpendicular to it ; the part GN is counteracted by the reaction from the point of suspension S, and NR is employed in producing motion in the direction of the circular arc GO ; G therefore (and consequently the hody) will not remain at rest till NR van- ishes, i.e. till the angle NGR (=:OSG) vanishes, or SG coincides with SO. 78. When a body is suspended by an inflexible rod from a center of motion, and revolves around it in a circle perpendicular to the horizon, it will be at rest only when the cerUer of gravity is either directly below, or directly above the center of motion. For it is only in these two cases that the center of gravity will be in the line which is drawn through the center of motion perpendicular to the horizon. The stationary point above the center of motion is very unstable, since the slightest disturbing force throws the body out of the line of direction, when, by the force of gravity, it immediately descends to the lowest point it can reach, and vibrates about that point until it finally settles itself with the center of gravity immediately under the point of sus- pension ; and whenever it is thrown out of this position, the same vibrations are renewed until it resumes it. When, therefore, the center of gravity is at the lowest point it is capable of reaching, the equilibrium is stable, since the body obstinately maintains that position. On this principle, gates which have their center of gravity raised as they are opened, shut spontaneously. 79. The stability of a body not only requires that the center of gravity should be low, but that the line of direc- tion should fall within the base. The farther it falls from the extremity of the base, the more stable is the position. Ulastrate by figure 26. WTien a body swings around a center of motion in a circle which is perpendicular to the horizon, at what two points will it remain at rest ? Which of these points is stable, and which unstable 1 Ex- emplilied in gates. 64 MECHANICS. Hence the stability of a pyramid when standing on its broad base, and its instability when inverted. For the same reason, all broad vessels, as steamboats, are difficult to up- set, while vehicles with narrow bases are easily overturned. AYhen a load is so situated as to raise the ce^er of gravity, it increases the liability to upset, because it in- creases the facility with which the line of direction , is thrown without the base. Thus carts loaded with hay, or bales of cotton, are very liable to be overturned. The same is true of stages carrying passengers or baggage on the top. On the other hand, a large ship well supplied with ballast is capsized with great difficulty, since the center of gravity of all parts of the ship is so low as to render it difficult to throw the line of direction wjthout the base. Yet if the center of gravity is very low, a ship will rock excessively in a rough sea, since the upper parts near the deck move over a greater space in proportion a.s their distance from the center of gravity is greater. 80. There are many remarkable structures which lean or incline a little ; but so long as the line of direction falls within the base, and the parts of the mass have sufficient tenacity among themselves to hold tegether, the structure will stand. The famous Leaning Tower of Pisa, was built intentionally inclining, to frighten and surprise ; with a height of one hundred and thirty feet, it overhangs its base sixteen feet. Yet since the lower parts are of greater dimensions than the upper, and the walls thicker below than above, and of heavier materials, the center of gravity is so low that the line of direc- tion falls far enough within the base to give the whole structure sufficient stability, while its apparent tendency to fall greatly enhances the emotion of the spectator from its summit. Many ancient Cause of the stability of a pyramid? Examples of strnctares rendered stable on the same principle. What is the effect on the stability of a body produced by raising the center of gravity 1 Examples in loads of hay wages, ic. Explain why a ship rocks when the center of gravity ig very low. What is the peculiar structure of the Leaning Tower of Pisa. CENTER OF GRAVITY. 65 spires and other tall structures, are found to have lost some- thing of their perpendicularity. Rocking stories are rocks which are sometimes found so exactly poised upon their center of gravity, that a very small force is sufficient to put them in motion. The rocking of a balloon when it begins to ascend, affords an illustra- tion of the tendency of bodies to vibrate around the center of gravity. 81. The motions of animals are regulated in conformity with the doctrines of the center of gravity. A body is seen tottering in proportion as it has great altitude and a narrow base ; but it is a peculiarity in a man to be able to support his figure with great firmness, on a very narrow base, and ..under constant changes of attitude. The faculty is acquired slowly, because of the difficulty. The great facility with which the young of quadrupeds walk, is ascribed to their broad supporting base. Many of our most common motions and attitudes, depend for their ease and gracefulness, upon a proper adjustment of the center of gravity. 'The erect pos- ture of a man carrying a load upon his head — leaning to one side when a heavy weight is carried in the opposite hand — leaning forward when a weight is on the back — or backward when the weight is before ; — these are severally Pig. 28. examples in point. When a man rises, from his chair, he orings one foot back, and leans the body forward, in order to bring the center of gravity over the base ; and without aajusting it in this manner, it is hardly possible to rise. A man standing with his heels close to a perpendicular wall, Explain the case of rocking stones — rocking of a balloon. Explain the motions of animals in conformity with the doctrine of the center of giavity. 6* 66 MECHANICS. cannot bend forward sufficiently to pick up any object that lies on the ground near him, without himself falling forward. The art of rope m wire dancing, depends in a great de- gree upon a skilful adjustment of the center of gravity. The rope dancer frequently carries in his hand a stick loaded with lead, which he so manages as to counterbalance the in clinations of his body which would throw the line of direc tion out of the base. Upon a similar principle the eques- trian balances himself on one foot on a galloping horse. 82. The vegetable creation is subject also to these gen- eral laws of nature. Trees by the weight and height of their tops would seem peculiarly liable to fall ; but their roots afford a corresponding breadth of base, while the great size and density of their trunks, and the symmetri- cal disposition of the branches, conspire to increase their stability. 83. The position of the center of gravity of any number of separate bodies, is never altered by the inutiuil action of those bodies on each other. If for example, two bodies, by mutual attraction, approach each other, the center of gravity remains at rest, until finally the bodies meet in this point. If, by their mutual action, they contribute to make each other revolve in orbits, it is around their common center of gravity. Thus the earth and moon revolve around a com- mon center of gravity, which remains fixed ; the same is true of the sun and all the bodies that compose the solar system. Were the centrifugal force to be suspended, and the bodies abandoned to the mutual action of each other, they would all meet in their common center of gravity. This naturally results from the principle that the momenta on opposite sides of the center of gravity are equal, and that bodies by their mutual action produce equal momenta in each other. 84. The doctrines of the center of gravity, suggest the readiest method of solving a great number of practical problems. We annex a single example. Suppose three persons were carrying a stick of timber (A by himself supporting one end, and B and C by a hand- spike lifting together towards the other end,) and it were How is the art of rope or wire dancing related to this subject ? Ho\7 is the same principle illustrated in the structure of trees and plants ? How is the position of the center of gravity of any number of bodies affected by their mutual action? fROJECTILBS AND GTJNNEIir. 67 required to determine at what distance from the end of the stick the handspike must be placed, in order that the three rig. 20. > persons might bear equally. — A stick of timber being a body of regular shape and uniform density, has its center of gravity coincident witli the center of magnitude. We may therefore proceed on the supposition that the entire weight is collected in the center. Now in order that B and C may together lift twice as much as A. they must be twice as near the center. But the distance of A from the center is half the length of the stick ; therefore the distance of the required point from the center is one fourth the length of the stick, and consequently it is one fourth the same length from the end of the stick. To test this case by experiment, we might rest one end of the stick upon a support, and ascertain, by a pair of steelyards, the weight at a distance from the other end equal to -^ the length of the stick. It would be found equal to f the weight of the whole stick. CHAPTER VII. OF PROJECTILES AND GUNNERY. 85. A projectile is any body thrown into the atmosphere. A. ball fired from a cannon, a stone thrown by the hand, ana in arrow shot fi'om a bow, are severally examples of projec- tiles. According to article 69, projectiles rise and fall in the curve of a parabola, under the combined forces of piojection, which tends to carry them uniformly forward, and of gravity, which brings them with accelerated velocity to- wards the earth. Give an example of solution of problems. What is a projectile ? Give examples. In what curve does a projectile rise and fall? Under the astiau of what forces does it move 1 68 MECHANICS. The random of a prqjectik is the horizontal distamco be- tween the point from which it is thrown, and that where it falls to the earth. For example, when I throw a stone obliquely into the air, it rises and falls in a curve, (the parabola) and the distance from the place where I stand to the place where it falls, measured on the surface of the earth, is its random. The random is greatest when the angle of elevation is 45 de- grees, and is the same at elevations equally distant above and below 45 degrees. It is the same, for instance, at 60 and at 30 degrees. (See Fig. 30.) A projectile rises to the greatest height when thrown per pendicularly upwards, and it remains, in this case, longest in the air ; or the time of flight is greatest when a body is projected directly upwards. Fig. 30. 86. When a body is thrown horizontally from any eleva- tion, with a velocity equal to that which it would have ac- quired by falling from that elevation to the earth, its random is tviice as great as that height. Thus, if I throw a ball from a chamber window, with a velocity which it would have acquired in falling from the window to the ground, it will fall at a distance from the foot of the building equal to twice the height of the window. The foregoing principles hold good only when projectiles move without resistance. But this is far from being the fact, since the resistance of the air. especially to a body moving swiftly through it. is very great ; and hence the dis- cordance between theory and experiment is such, that the What is the random, of a projectile 1 At what angle is the random great- est ? At what two angles are the randoms equal ? When does a projectile rise to the greatest height ? When is the time of flight greatest ? What is the random of a body thrown horizontally from a chamber window ? Do the theoretical principles of projectiles hold good in practice ? PROJECTILES AND GUNNERY. 69 mathematical principles of projectiles are found to be wholly inapplicable to practice. It is ascertained, in general, that projectiles moving slowly describe curves which are nearly parabolas ; while such as move swiftly deviate very far from this curve. The para- bolic figure described in the case of projectiles which move slowly, may be observed in tracing the path of a small stone thrown into the air, and more especially in the curves described by jets of water spouting upwards, as in fountains. But when the jet is more rapid, and spouts at a high angle, as forty-five degrees for example, we can plainly see that the curve deviates greatly from a parabola. The remote branch of the curve is seen to be much less sloping than the rising branch ; and in very great jets, which are to be seen in some great water-works, the falling branch is almost per- pendicular at its remote extremity ; and the highest point of the curve is far from being in the middle between the spout and the place where the water falls. The unequal division of the curve by its highest point, may also be ob- served in the flight of an arrow or a bomb shell. The following facts also show the<5jpcordance between the parabolic theory of gunnery and experience. A cannon ball, fired in such a direction and with such a velocity, that its random or horizontal range ought to be twenty-four miles, comes to the ground short of one mile. The times of rising and falling, if that theory held good, ought to be equal ; but the time of rising is greater than that of falling at great elevations, and at small elevations less than that of falling. According to the theory, the greatest random is at an angle of elevation of forty-five degrees, but in practice it is found to be much below this. The greatest random of an arrow, is when the elevation is about thirty-six or thirty- eight degrees. What carve is described by projectiles moving sUyioly 1 Ditto wheii moving; swiftly 1 Examples, in a stone thrown into the air, and in spouting fluids. Discordance between theory and practice exemplified in the motion of a cannon ball. At what angle of elevation is the random of an arrow greatest? CHAPTER VIII. OF MACHINERY— THE LEVER. 87. The organs employed in communicating- motion are tools, machines, and engines. Tooh are the simplest m- suumentsof art; these, when complicated in their structure, become machines ; and machines, when they act with great power, take the name of engines. Among the ancients, machines were confined chiefly to the purposes of arckitec- ture and war ; and they were moved almost exclusively by the strength of animals. Thus, in building one of the great Pyramids of Egypt, vast masses of stones were raised to a great height, amounting together to 10,400.000 tons. In this labor were employed 100,000 men for twenty years. The advantage which man has gained by pressing into his service the great powers of nature, instead of depending on his own feeble arm. is evinced by the fact, that by the aid of the steam engine, one man can now accomplish as much labor as 27,000 g[|yptians, working at the rate at which they built the pyramids. In war also, while the use of gun- powder was unknown, engines of great power were invented for throwing stones and javelins, and for demolishing for- tifications. Such were the Catapulta, the Ballista. and the Battering Kam. of the Komans. Yet it is remarkable, that during many ages, while such powerful auxiliaries were employed in architecture and in war, the ancients should have made so little use as they did of machinery in the ordinary processes of the arts. The practice of grinding corn by hand, which was chiefly performed by women, was prevalent at Kome until the time of Augustus, when we find the first mention of water mills. The elements of machinery are found in what are called the Mechanical Powers. They are six in number, viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Screw, and the Wedge. THE LEVER. 88. The Lever is an inflexible bar or rod, some point Distinguish between tools, maciiinea, and engines. To what purposes were machines chiefly confined among the anciqats ? How wore they moved 7 Example in building the great Pyramid of Egypt. Compare the labor of a man aided by the steam engine with the Egyptians. Enumerate the Mechanical Powers. MACHINERY. 71 of which being supported, the rod itsdf is movable freely about that point, as a center of motion,. This center of motion is called tJie fulcrum ob prop. When two forces act on one another by means of any ma- chine, that which gives motion is called tJte power ; that which receives it, the weight. In treating of the Mechanical Powers, the first inquiry is what are the conditions of an equilibrium ; that is, when do the power and weight exactly balance each other? This point being ascertained, any^ addition to the power puts the weight in motion. The investigation first proceeds on the supposition that the action of the mechanical powers is not impeded by their own weight, or by friction and resistance, a suitable allowance being afterwards made for the various impediments. 89. Two loeights will balance each other upon the arms of a lever, when tliey are to each other inversely as their re- spective distances from the fulcrum. Thus in Fig. 31, if W is as much heavier than P as AC ^'S- 3i- is greater than BC, the two ° weights will exactly balance pg f one another. Here the pro- dsct of P into AC, is equal to .^ the product of W into BC, and in all cases where the product of the weight into its distance from the fulcrum, is equal to the product of the power into its distance, the weight and the power will be in eq«ilibrium. Fig. 38. O A B C D -® — IS. ®- This is true even where there are several weights on each side as in figure 32. If the products A and B into the re- spective distances from Gr, be equal to the similar products Define the lever, the fnlcram, the power, the weight. What is the first in- quiry in treating of the mechanical powers ? Do we take into the accoant fric- tion, resistance of the air, 4:o. ? WTien will two weights balance each other on the arms of a lever? Explain the principle by Fig. 31. How does the pro- duct of the power into its distance from the fulcrum compare with that of the weight into its distance ? Does the same principle of equilibriu. hold when there are several weights on each side 1 72 MECHANICS. of C and D, the weights on one another. the opposite sides will balance Fig. 33. Fig. 34. 2. 90. Levers are divided in- to three different orders, ac- cording to the position of the power and weight with respect to the fulcrum. 1. In a lever of the firs kind, the fulcrum is between the power and the weight, as in Fig. 31. 2. In a lever of the second kind, the weight is applied between the power and the fulcrum, as in Fig, 33. 3. In a lever of the third kind, the power is applied be- tween the weight and the ful- crum, as in Fig. 34. The same law of equilibrium (Art. 89.) holds good in the three kinds of levers ; and where the power is at a greater distance from the fulcrum than the weight, as in the first and second kinds, it is proportionally less than the weight; and where it is nearer the fulcrum than the weight, as in the third kind, it is proportionally greater than the weight, or acts under what is called a mechanical disadvantage. When a weight is sustained by two props, as when two men carry a weight suspended from a pole, one end of which rests on the shoulder of each, the part borne by each man is less as the distance of the weight from him is greater. Thus, if the pole is 10 feet long, and a weight of 500 pounds is sus- pended 2 feet from A and 8 feet from B, then A's part will be to B's as 8 to 2, or as 4 to 1 ; so that A will support 400 lbs. and B 100. 91. When levers are not straight, but more or less crooked; a similar principle of equilibrium holds good, the distance of the weight or power from the fulcrum being es- timated by the length of a perpendicular drawn from the fulcrum to the line of direction in which the power acts. Thus in figure 35, ABC is a crooked lever in which the How many kinds of levers are there ? How is the falcrum situated in the first — in the second — in the third ? Case where the power is at a greater distance from the falcrum than the weight. Case where the weight is farther off than the power. Case of a weight on a pole borne by two men. Howia th^ same principle of equilibrium applied when the lever is not straight 1 MACHINERY. 73 power and weight act in the directions of the lines BS and AS. Now the distances from the fulcrum being measured Fig. 35. by the perpendiculars CM and CN, the general law of equi- librium holds, viz. that the power is to the weight, as the distance of the weight from the fulcrum is to the distance of the power from the fulcrum. 92. A compound lever consists of several simple levers combined together. In a compound lever, the power and the. weight balance each other., when the prodiict of the power multiplied into all the arms on the next side to it, is equal to the product of the weight into ail the arms next to the weight. c Fig. 36. G 'a A B D A i:| IIP ""'i ™ Thus in figure 36, the product of PxACxBFxDG= WxGExFDxCB. Suppose, for example, the longer arms of the lever are severally twice the length of the shorter, and that the weight to be raised equals 400 pounds ; what power Give an example of a heivt lever. What is a eomptmnd lever f When do the power and -weight balance each other ? 7 74 MECHANICS. must we apply? 1 X ' X 1 X400=2x2x2X50. Hence, 50 lbs. applied at P would balance 400 lbs. at W. 93. EXAMPLES. 1. Upon the extremities of a straight lever, are hung two weights, A and B, the former weighing 15 and the latter 60 pounds ; how much farther is A from the fulcrum than B ? By figure 31, AC : CB : : 60 : 15 ; but 60 : 1.5 : : 4 : 1 ; there- fore, the smaller weight is four times as far from the fulcrum as the larger. 2. One end of a lever is 44 feet, and the other 5 feet ; what power must I apply to the longer end to balance a weight at the shorter end of 500 lbs. ? 5 V '500 44 : 5 : : 500 : -^^ =56 lbs. IS-i^r oz. Ans. 3. In a compound lever, (Fig. 36,) the lengths of the long- er arms are 5, 10, 16 feet, respectively, and of the shorter, 1, 2, 3 feet ; what power applied to the longer side, will be re- quired to balance a weight of 100 pounds 1 5x10x16: 1X2X3:; 100: fib. Ans. 4. Wishing to lift from its bed a rock weighing 1000 lbs., I take a handspike 6 feet long, and applying the shorter end to the rock, rest it on a fulcrum at the distance of 1^ feet from the rock ; how much force must I exert at the end of the longer arm to raise the rock? Ans. 333-^ lbs.* 5. A lever of the second order is 20 feet long : at what distance from the fulcrum must a weight of 112 lbs. be placed, so that it may be supported by a power able to sus- tain 50 lbs. acting at the extremity of the lever ? Ans. 8 feet and 1 1^ inches. 6. In a compound lever, the three shorter arms are, re- spectively, 1, 2, 4 feet ; the three longer arms 9, 11, 12 ; the power applied at the end of the longer arm is 3 pounds : what weight will it raise? Ans. 445-^ lbs. 94. The principle of the lever has a most extensive ap- plication in the arts, and the forms under which it occurs aru' very various. \Ve may contemplate it as having equal oi unequal arras. The balance affords the most common example of a level with equal arms. The necessity of arriving at the weight ' This force would just balance the weight ; any additional force would raise it. Balance — what sort of a lever is it ? MACHINERY. 75 of bodies with the greatest degree of accuracy in pecuniary transactions, and more especially in delicate scientific re- searches, as those of chemical analysis, has induced men of science, and artists, to bestow great and united attention upon the construction of this instrument, until they have brought it to an astonishing degree of perfection. The principal parts of the balance are the beam G-H, (Fig. 37.) the points of suspension Gr and H, and the fulcrum E. In order to construct a perfect balance, the most important particulars to be attended to, are the length of the arms, that is, of the beam ; the situation of the center of grav- ity of the whole instrument, with respect to the fulcrum or center of motion ; and the position of the point of sus- pension. Fis:. 37. ().j The sensibility of the balance is increased by increas- mg ttis lengths of the arms ; but unless the arms, when long, ate at the same time of considerable weight, they will not have ihe requisite strength, but will be liable to bend ; and an mcrease of weight, adds to the amount of friction on the center of motion. It is not common, therefore, to make Why has so much pains been taken to malte it accurate? Describo it from the figure. What particulars are especially to be attended to in its coutruction? How is the sensibility of the balance affected by increasing the lengths of the arms ? 76 MECHANICS. the arms of a very delicate balance more than nine inches in length ; and, for the purpose of uniting lightness with strength, the beam is composed of two hollow cones placed base to base, as in Fig. 37. (2.) The center of gravity of the instrument, must be a little below the center of motion. For if the beam is bal- anced on its center of gravity, it will remain at rest in every position, whereas it must be at rest, only when in a hori- zontal position. If the center of gravity is above the center of motion, the position is too unstable, and on the least dis- turbance of the equilibrium, the beam will be liable to upset. Finally if the center of gravity is too far below the center of motion, the equilibrium will be too stable Hence, in very delicate balances, the center of motion is placed a little above the center of gravity. (3.) X\\e, points of suspension xawsX be in the same right line with the center of motion. For since when weights are added to the scales, the effect is the same as though they were concentrated in the points of suspension ; and were those points above the center of motion, the center of gravity would be liable to be shifted above the center of motion, when the beam would upset; and if the same points were below the center of motion, unless the weights added were large, the center of gravity would be too low, and the equi- librium too stable. 95. In order to prevent friction as much as possible, the fulcrum is made of hardened steel, and shaped into a trian- gular prism, or knife edge, smootMy rounded, and turning on a plane of agate or steel, or some other very hard and polished substance. It is only by a nice attention to all these particulars that artists have been able to give to the balance so great a sen- sibilitj'. Some balances have been made to turn with the 1000th part of a grain. By loading the beam the sensibility of the instrument is diminished (Art. 94,) ; it is customary therefore, to estimate its power by finding what part of the weight with which it is loaded it takes to turn it. Thus, if when loaded with 7,000 grains, it will turn with one grain, its power is — oVr. A balance constructed by Kamsden, a How long are the arms of the most delicate balances ? What is the situ- ation of the center of gravity 1 Why is not the beam balanced on its center of gravity? What is the effect of placing the center of gravity above the center of motion ? or of placing it too low ? How are the points of suspen- sion situated t Of what is the fulcrum made ? Give an example of the ex- treme delicacy of some balances. MACHINERY. 77 celebrated English artist, for the Koyal Society, turned with the ten millionth part of the weight. Delicate balances are usually covered with a glass case to prevent agitation from the air, and to secure them from injury. Figure 37, repre- sents an instrument of this kind made for the Royal Institu- tion of Great Britain. 96. The bent lever balance is represented in figure 38. The weight C acts as though it were concentrated in the point D, and the weight in the scale acts at K ; hence an equilibrium will take place, when the article weighed has to G the same ratio as DB has to BK. Now every increase of weight added to the scales causes C to rise on the arc F G, and D to recede from B. Hence the different posi- tions of C, according as different weights are added to the scale, may be easily determined, and the cor- responding numbers marked on the scale F G. 97. It is essential to an accurate balance, that the iwt- arms should be precisely equal in length. The false bal- ance, which is sometimes used with a design to defraud, has its arms unequal. The dealer turns such an instrument to his account both in buying and selling. In buying, he puts his weights on the longer side, for then it takes more than an equivalent to balance them ; and in selling, he puts his weights on the shorter side, because less than an equivalent will produce an equilibrium. The fraud may be detected by making the weights and the merchandise change places. The true weight may be dete mined from such a balance, by putting the article whose wt ght is to be determined, into one scale, and counterpoising it with sand, shot, or any con- venient substance, in the other scale, and then, removing the article, and finding the exact weight of the counterpoise. It is evident that the weight of the merchandise will be the same as that of the weights employed to balance its counter- poise. 98. The steelyard is a lever having unequal arms, in Describe the bent lever balance. How are the arms of the false balance 1 How does the dealer use it so aa to defraud ? How may the fraud be de- teistedt 7. 78 MECHANICS. which the same body is made to indicate different weights, by placing it at different distances from the fulcrum. A pair of steelyards Fig. 39. has usually two graduated sides for determining smaller or great- er weights. It will be seen that on the greater side, the weight is placed nearer the fulcrum. Con- sequently, the weight indicated by the counterpoise, when at a given distance Irom the fulcrum, will be proportionally greater. This instrument is very convenient because it requires but one weight. The pressure on the fulcrum, excepting that of the apparatus it- self, is only that of the article weighed, whereas in the balance, the fulcrum sustains a double weight. But the balance is susceptible of more sensibility than the steelyard, because the subdivisions of its weights can be effected with a greater degree of precision than the subdivision of the arm of a steelyard. 99. The spring steelyard is a very convenient instrument for weighing where the subdivisions of weights are large. It depends on the elasticity of a spiral steel spring, to compress or extend which requires a force proportioned to the degree of compression or extension. The manner of ap plying it will be' easily understood from the rep- resentation in figure 40. After continued use, especially when loaded with heavy weights, the elasticity of the spring is liable to be impaired and the accuracy of the instrument diminished. When made, however, in the best manner spring steelyards retain their accuracy for a long time. Fig. 40. The steelyard defined — point out the diiference between the greater and the lesser side, and show upon what principle they respectively act. \Vhat advantages has the steelyard over the balance? What advantage has -the balance over the steelyard ? Describe the spring steelyai'd. On what prin- ciple does it depend ? MACHINERY. 79 . lOO. In Pig. 41, is represented a vertical section of a large Weighing Machine, such as is used for loads of hay, cotton, or other heavy merchandise. AB, a section of the platform, resting loosely on a frame. ON, DN, levers of the second kind, having their fulcrums ftt C, 1), and resting on a bar at N. W, W. pins which press upward against the platform, when the levers are raised. EF, a lever likewise of the second kind, having its ful- crum at E, and connected by a perpendicular arm, with the beam of a pair of steelyards at G-. Pour levers are usually employed, proceeding from the four corners of an immovable frame, or having their fulcrums firmly set in masonry. The levers all rest on the common support at N. Suppose a load of merchandise is placed on the platform to be weighed. By the steelyards, we ascertain that the weight exerted at G is 100 pounds which force is that exert- ted at P to raise the lever EF. Supposing, for convenience of computation, that the levers have their longer ten times the length of their shorter arms, then 100 pounds at F bal- ances a force of 1000 pounds at N. This force is still further multiplied by the four levers so as to become 10.000 pounds, which is the weight of the load, including that of the platform. If the platform rested on a single lever this would of course sustain a weight of 1 0,000 pounds ; but as the levers severally sustain the same part of the weight, each one bears only one fourth of the load, or 2,500 pounds. Describe the weighing machine represented in figure 41. Show how a weight of 2,500 lbs. may be weighed by a weight of 100 lbs. 80 MECHANICS. 1 1 . When a weight is supported by a lever which rests on two props, the pressure upon both fulcrums is equal to the whole weight. This principle is sometimes applied in ascer- taining the weight of a body too heavy for the steelyards. The body is suspended immovably near the center of a pole, and the steelyards are applied to each end of the pole sepa- rately, the other end meanwhile resting on its fulcrum. The two weights being added together, make the entire weight of the body. If the body is suspended exactly in the center of the pole, it will be sufficient to obtain the weight of one end and double it. The weight of the lever should, in both cases, be subtracted from the entire weight. Since when a weight is suspended between two props, the part sustained by each prop is inversely as tJie distance of the. iveigM from it, it follows that a load borne on a pole, between two bearers, is distributed in this ratio. As the effort of the bearers and the direction of the weight are al- ways parallel, it makes no difference whether the pole is par- allel to the horizon or inclined to it. Whether the bearers ascend or descend, or move on a level plane, the weight will be shared between them in the same constant ratio. 102. Hu.ndsjnkes and cioivbars are familiar examples of levers of the first kind. A hammer affords an example of the bent lever ; and shears, pliers, nutcrackers, and all similar instruments are double levers ; that is. they consist of two levers united. A pair of shears with long handles, like those used by tinners, exhibit very strikingly the in- crease of power gained by bringing the weight, or substance acted on. nearer to the fulcrum. The jaws of animals exhibit a similar property. An oar applied to a boat rowed by hand, a wheelbarrow, and a door shut by the hand applied to the edge remote from the hinges, severally furnish instan- ces of levers of the second kind, where the weight is between the fulcrum and the power. The crane is a lever of the second kind, which is much used when great weights are transported for a short distance, as heavy boxes of merchandise from a vessel to the wharf, or great masses of stone from the quarry to a car or boat How can we ascertain the weight of a body too heavy for the steelj'ards ? How when the body is suspended from the center of the pole ? When a load is boi-ie on a pole resting on the shoulders of two men, how is the part which each bears related to his distance from the ■weight ? Give examples of levers of tue first kind. Example of the bent lever, of double levers. What is the cause of the great power of the tinner's shears? Give examples of levers of the second kind. What is the crane ? MACHINERY. 81 A.a example of the crane, on a small scale, is seen in the ap- ptiiatus of a kitchen fire-place. 103> When one raises a ladder from the ground by one of the lower rounds, the ladder becomes a lever of the third kind, the power being applied between the weight and the prop. Since, in all the mechanical powers, the power and weight have equal momenta, and since, in the third kind of lever, the weight has more velocity than the power, the power is as much greater than the weight, as the velocity with which it moves is less. The difficulty experienced in raising a ladder from the ground by taking hold of the low- est round, or of shutting a door by applying the hand to the side next to the hinges, shows the mechanical disadvan- tage under which a lever of this kind acts. Yet it is very useful in cases where it is required to give great velocity to the body moved. Slieep shears consist of two levers of this kind united. Here the whole force required is so small, that to save it is of no consequence, while so soft and flexible a substance as wool requires the shears to be moved with con- siderable velocity. A pair of tongs is composed in the same manner ; and therefore it is only a small weight that we can lift with them, especially when the legs are long. 104. One of the most remarkable applications of the third kind of lever, is in the hones of animals. These are levers, the joints are the fulcrums, and the muscles are the power. The muscles are endowed with a strong power of contraction, by which they are made to pull upon a tendon or cord, which is inserted in the bone near the fulcrum. Thus, the fore-arm moves on the joint near the elbow as a fulcrum, a little below which is inserted a tendon, connected with a muscle near the shoulder which gives it motion. The arrangement may be well represented by attaching a small cord to one of the legs of a pair of tongs, near the joint. It will require a considerable force to lift the leg by pulling at the string, especially if the string be pulled in a direction nearly parallel with the leg, as it ought to be, since the ten- don which lifts the fore-arm acts in such a direction with re- spect to the arm. The muscles therefore act, in moving the bones, under a double mechanical disadvantage, their force being applied both obliquely and very near the fulcrum. The force which the muscles of the arm exert m raising a Examples of levers of the third kind. To which kind of lever do the hones of animals belong V In what does the force reside which raises a weighs held in the hand ? Wliat is the fulcrum ? Under what mechanical disadva> tage does the arm act 7 82 MECHANICS. weight held in the palm of the hand, is enormouS; as will ba comprehended from the following illustration. Let AB rep- Fig. 42. resent the fore-arm, movmg on the elbow-joint at A, and having the tendon inserted at C, which we will suppose to be one hundred times nearer to A than B is to A. Conse- quently, a weight of 1 lb. at B, would require a force at 0, acting directly upwards of 100 lbs. But the force of the tendon does not act directly vpwards in the direction of CD, but very obliquely; as in the direction of CE, of which the part EA, only can contribute to support the weight. Sup- pose this part to equal -(^oth of the whole force CE. and it follows that the muscular force exerted to raise a weight of 1 lb. in the palm of the hand, would, were it to act without any mechanical disadvantage, be sufficient to raise a weight of 1000 lbs. Yet Dr. Young informs us. that a few years ago there was a person at Oxford, who could hold his arm extended for half a minute, with half a hundred weight hanging to his little finger. But by giving to the muscle the position it has, the great- est possible compactness of structure is obtained, while by making it act so neE.r the fulcrum, what is lost in force, is gained in velocity ; and while the power acts through a small space, the hands are moved quickly through a great distance. In consequence of the dominion which man can gain over the stronger animals, and especially over the great powers of Nature, he has little occasion to exert great strength with his naked hands: the celerity of their move- ments is to him a far more important endowment. How is '.his disadvantage compensated 1 MACHINERY. 83 Fig. 43. CHAPTEK IX. MACHINERY CONTINUED.— OF WHEEL "WORK. 105. When a lever is applied to rai-se a weight, or to overcome a resistance, the space throug-h which it acts at one time is smaL, and the work must be accomplished by a suc- cession of short and intermitting efforts. The common lever is, therefore, used only in cases where weights are required to be raised through small spaces. When a continuous motion is to be produced, as in raising ore from a mine, or in weighing the anchor of a vessel, some contrivance must be adopted to remove the intermitting action of the lever, and render it continual. The wheel and axle, in its various forms, fully answers this pur- pose. It may be considered as a revolving lever. Thus in figure 43, LM is an axle resting upon two sup- ports. D and E ; NAO is a wheel connected with the axle ; W is the weight, which may be balanced by a weight hung to the circumference of the wheel, as w. In the wheel and axle, the law of equilibrium is as follows : The power is to tlie weigliX as the diameter of the axle %s to the diameter of the wheel. If the diameter of the wheel is ten times that of the axle, a power of one pound will balance a weight of ten. In numerous forms of the wheel and axle, the weight is applied by a rope coiled upon the axle; but the manner in which the power is applied is very various, and not often by means of a rope. The circumference of a wheel sometimes carries projecting pins to which the hand is applied to turn the machine. An instance of this occurs in the wheel used in the steering of a vessel. In the common windlass, the To what uses is tlie common lever restricted ? What advantage has the wheel and axle over it ? Describe the wheel and axle from the figure. What is the law of- equilibrium in the wheel and axle t To wh^t is t||e weight iMually attached t 84 MECHANICS. power is applied by means of a winch which corresponds to the radius of a wheel. The axis is sometimes placed in a vertical position and Fig. 44. turned by levers moving horizontal ly. The capstan of a ship (Fig. 44 ) is an example oi this. Levers an swering to the radii of a wheel are in- serted in holes mor- tised in the axis, and turned by several men working together. In some cases, as in the treadmill, the wheel is turned by the weight of animals walking on the circumference, with a motion like that of ascending a steep hill. 106. In the compound wheel and axle, the power is to the weight, as the product of the diameters of all the smaller wheels, is to the product of tJie diameters of all the larger wheels. Thus in Fig. 45, the power being applied to the winch PQ, acts upon the small wheel A, which acts upon the large wheel B, this upon C, and so on. Now if the diameters of the three smaller wheels, in- cluding that of the axle, be severally one fourth those of the larger wheels, (of which the diameter of the wheel de- scribed by the winch PQ, that is, twice PQ, must be con- sidered as one,) then the power will be to the weight as lXlXl;4x4x4, that is, as 1 to 64 ; and a force of ten pounds applied at P will balance a weight of 640 pounds applied at W. 107. It is sometimes desirable to make a variable power produce a constant force. This may be done by making its Specify the different ways in -which the power ia applied. How in the windlass ? How in the capstan ? How in the treadmill ? What is the law of equilibrium in the compound wheel an4 ^le? Explain by figiire 4S MACHINERY. 85 velocity increase as its intensity diminishes. We have an example of this in the reciprocal action between the main spring and fusee of a watch. (Fig-. 46.) The main spring is coiled up in the box A, and is connected with Fig. 46. the fusee B by a chain. When the watch is first wound up, the spring acts with its greatest in- tensity, but then as the wheel B turns, it uncoils with the least velocity ; but on account of the varying diameters of the wheels of the fusee, as the intensity of the spring is diminished, its eflfect is continually increased by acting on a larger wheel. In a similar manner a varying weight may be moved by a constant power. 1 08. EXAMPLES. Ex. 1. The diameter of a wheel is 4-J- feet, and that of its axis 1-J- feet: what power will be required to balance a weight of 100 lbs.? 4i : H : : 100 ; ^,^^^=27 lbs. 12f oz. Ans. Ex. 2. What must be the diameter of a wheel by which a weight of 100 lbs. suspended by a rope going round an axle whose diameter is 1 foot, is balanced by a power of 12 lbs. ? 12 lbs. : 100 lbs. : : 1 : -^iiy^^^Si feet. Ans. Ex. 3. A power of 3 lbs. acts upon a wheel whose diam- eter is six feet ; what weight will balance it upon an axle of 5 inches diameter ? 'Ans. A3^ lbs. Ex. 4. A power of 5 lbs. balances a, weight of 150 lbs. by means of a wheel 10 feet in diameter: what is the diameter of the axle ? Ans. 4 inches. Ex. 5. Four wheels, A, B, C, D, whose diameters are 5, 4, 3, 2 feet respectively, are put in motion by a power of 10 lbs. applied at the circumference of the wheel A ; the wheels act upon each other by means of three smaller wheels, the diameter of each of which is 8 inches ; the last wheel D, turns an axle whose diameter is six inches ; what weight may be sustained by a rope going over the axle ? Ans. "1, 100 lbs. COMMUNICATION OF MOTION BY WHEEL WORK. 109. Motion maybe transmitted by means of wheel How do we make a variable power produce a constant force 1 How «x. emplified in a watch ! 8 86 MECHANICS. work in several different methods, the principal of which are, the friction of the circumference of one wheel, upon that of another — the friction of a band — and the action of teeth. One wheel is sometimes made to turn another, by the mere friction of tlie two circumferences. If the surfaces of both were perfectly smooth, so that all friction were removed, it is obvious that either would slide over the surface of the other, without communicating motion to it. But on the other hand, if there were any asperities,however small, upon their surfaces, they would become mutually inserted among each other, and neither the wheel nor axle could move with- out causing the asperities on its edge to encounter those which project from the surface of the other ; and thus both wheel and axle would move at the same time. Hence, if the sur- faces of the wheel and axle are by any means made rough, and pressed together with sufficient force, the motion of either will turn the other, provided the load or resistance be not greater than the force necessary to break off these small pro- jections which produce friction. In some cases, where great power is not required, motion is communicated in this way through a train of wheel work, by rendering the surfaces of the wheel and axle rough, either by facing them with buff leather, or with wood cut across the grain. .The communication of motion between wheels and axles by friction has the advantage of great smoothness and evenness, and of proceeding with little noise ; but this method can be used only in cases where the resistance is not very considerable, and therefore it is seldom adopted in works on a large scale. Dr. Gregory mentions an instance of a saw mill at Southampton, where the wheels act upon each other, by the contact of the end grain of the wood. The machine- ry makes very little noise and wears well, having been used not less than twenty years. 110. Wheel work is extensively moved by ihe. friction of a band. When a round cord is used, any degree of fric- tion may be produced, by letting the cord run in a sharp groove at the edge of the v/heel. When a strap or flat band is used, its -friction may be increased by increasing its width. The surface at the circumference of a wheel which carries a flat band, should not be exactly cylindrical, but a little con- What are the several methods of communicating motion hy means of wheel work? Explain the method by the friction of the surface. What are the advantages of this method ? Describe tlie method of turning wheels by the friction of a band. MAenraERY. 87 vex, in which case if the band inclines to slip off at either side, it returns again by the tightening^ of its inner edge, as may be seen in a turner's lathe. When wheels are con- nected in the shortest manner by a band, they move in the same direction ; if the band be crossed, they Fig. 4r. will move in opposite directions. (Fig. 47.) Wheels are sometimes turned by chains instead of straps or bands, and are then called ragwlieeh. The chains lay hold upon pins, or enter into notch- es, in the circumference of the wheels, so as to cause them to turn sim- ultaneously. They are used when it is necessary that the velocities should be uni- form, and where great resistance is to be overcome, as in locomotive steam engines, chain water wheels, &c. 111. But the most common mode of moving wheel work, is by means of teeth cut in the circumference of the wheels. The wheels of necessity turn in opposite directions. The connection of one toothed wheel with another is called ^ear- ing. In the formation of teeth, very minute attention must be given to their figure, in order that motion may be com- municated from one wheel to another, without rubbing or jarring. If the teeth are ill matched, as in figure 48, when the tooth A comes into contact with B, it acts obliquely upon it, and as it moves, the corner of B slides upon the plane surface of A in such a manner as to produce much friction, and to grind away the side of A, and the end of B. As they approach the position CD, they sustain a jolt the moment their surfaces come into full contact ; and after passing the position CD, the same scraping and grinding effect is produced in the opposite direction, until by the rev. Fig. 48. frSri What are rag wheels? What is gearing? W^hat attention is to be given to the figure of teeth ? Explain the inconveniences of badly constructed teeth as represented in figure 48. 88 MECHANICS. olution of the wheels the teeth become disengaged. To avoid these evils, the surfaces of the teeth are frequently curved so as to roll on each, other with as little friction, and with as uniform force and velocity as possible. (Fig 49.) Much pains and skill have been bestowed on this subject by mathematicians, with the view of ascertaining the kinda of curves which fulfil these purposes best. REGULATION OF VELOCITY BY WHEEL WORK. 1 1 2> Wheel work serves the Fig. 49. purpose, not only of forming a con- venient communication ol motion between the power and the weight, but also of regulating its velocity. Thus, when the connection is formed by means of a band, as in figure " ^n r^ ^^ 46, the velocity of the wheel B, that / / \_\ yA carries the weight or sustains the r~\®/— 7 f — ' pressure, maybe altered at pleasure, ^\Jll_y ^ by altering the ratio between the /^ ■(T^ diameters of the two wheels. If the 11 Vj diameters are equal, the wheels will revolve with equal velocity ; if A remains the same, while the diameter of B is diminished, the velocity of B will be increased in the same ratio ; or if B remains the same, while the diameter of A is changed, the velocity of B will be changed in the same manner. We set familiar examples of the application of this principle in the common spinning wheel, and the turner's lathe. In the spinning wheel, a band passes round a large wheel and a small one called a spool, having the spindle for its axis ; and in consequence of the great disparity in the size of the wheels, a great velocity is given to the spindle by a comparatively slow revolution of the wheel. In a turner's apparatus, ma- chinery for spinning cotton, and the like, a large hollow cyl inder, or drum, is fixed horizontally, which is kept revolving by the moving power, and from which, motion is conveyed by bands to lathes, spindles, &c., to which any required ve- locity is given, by altering the diameter of the small wheel that is connected with them and turns them. Sometimes a How are these evils obviated ? Second object of wheel work, to regulate velocity — explain how this is done. How exemplified in the spinning wheel and the turner's lathe. What is a dram ? Use of a drum of conicd form. MACHINERY. 89 change of velocity is effected by making the drum of a coni- cal shape, and then the velocity imparted to the lathe or spindle, will be greater or less, according as the band pro- ceeds from the larger or smaller part of the drum. 1 1 3« A more exact method of regulating the velocity of motion, is by means of wheels and pinions. An example of this kind, is seen in Pig. 50, where A, ^'S- ="• B.C, are three wheels, and a, b, c, are the cor- responding pinions. As the leaves of the pinions successively pass between the teeth -pf the wheel, they must be equal and similar to them ; and since magnitudes have the same ratio to each other as their like parts, it follows that the number of teeth in a wheel, and of leaves in the pinion that acts upon it, express the ratio of the circumfer- ence or radius of the wheel to that of the pinion. Hence, in an equilibrium, the power multiplied by the product of the numbers expressing the amount of teeth in all the wheels respectively, is equal to the weight multiplied by the pro- duct of the several numbers denoting the leaves in each of the pinions. Itis farther evident, that the velocity of a wheel and that 'oiMBU)inion connected with its circumference, will be in- fSPI^s the number of teeth in each. Thus in Fig 50, if the pinion a has 10 teeth, and the wheel B has 100, a will move ten times as fast as B. For the same reason b will move ten times as fast as C, so that, in this arrangement, the power moves with 100 times the velocity of the weight. By varying the ratio between the number of teeth in the pinion, and the number of teeth* in the wheel with which it is connected, we may vary the velocity of any wheel at pleasure. 1 1 4. A familiar instance of this is afforded in the mech- anism of a common clock. A pendulum by falling gains a Show how velocity is regulated by wheels and pinions. Show how velocity 7S regulated by means of the pendalam. 8* 90 MECHANICS, Fiff. 51. quantity of motion sufficient to carry it on the other side to the same height as that from which it fell ; and were it not for the resistance of the air and the impediments, a pendulum when once set in motion would continue to vi- brate by its own inertia and would thus afford, without the aid of any machinery, an exact measure of time. But in order to continue its vibrations, some small force must be applied to it to compensate for the loss of motion from fric- tion and resistance. This force is applied to the pendulum of clocks by the weight, and an analogous force is supplied to the balance wheel of watches and chron .meters by springs. In Pig. 51. let A B be a wheel having 30 teeth, and let N. M, be a pendulum, connect- ed with the wheel by the pallets., I, K ; and to the axis a, let a weight be hung. It is evident that this weight, were there nothing to arrest it, would descend by the force of gravity with accelerated velocity. It endeuvors thus to descend, and hence exerts the required force on the pallets of the pendulum. For, every time the pendulum performs a double vibration (returning to the same point from which it set out.) a tooth of the wheel escapes.* and the wheel runs down until the next tooth strikes upon the pallet, and thus gives it the impulse which is necessary to keep up the vibrations. _ It would seem therefore that, for beating seconds, only a single wheel is necessary; nor would anymore be ajaao lute- ly indispensable; but in this case the weight would Hijend so fast, as soon to reach the floor, and the clock would re- quire to be wound up again every few minutes. Hence a series of wheels are interposed between the pendulum and the weight, by which the descent of the latter is retarded upon the principle explained in Art. 113, and the descent of the weight is slower in proportion as the series is more ex tensive. In cheap clocks, as some of those made with wooden <5 N * Hence this wheel is called the scapemenU .Why does the pendalum continae to vibrate ? Illustrate by figure 51. How many wheels arc necessary to continue the beating of the penrtulum ? Why are more emploj ed ? What are the disadvantages of a small number of wheels 7 MACHINERY. 9i wheels, the series is short, or the number of wheels employed for retarding the descent of the weight is small, and such clocks require frequent winding up ; but in clocks of finer workmanship, a greater number of wheels is interposed, and such clocks require to be wound up less frequently. Many go eight days, and some are made to go a whole year with out winding. WHEEL CARRIAGES. 115. When a loaded carriage is moving on a horizontal plane, free of obstacles, the resistance to be overcome does not consist of the weight of the load, directly, but of the fric- tion occasioned by the weight. For, since the weight acts in a direction perpendicular to the plane, it cannot oppose the motion of the carriage in a direction parallel to the plane. Nor would increasing the weight, to any extent, make any difference, were it not that we should thus increase the fric- tion, which (as will be explained more fully hereafter) is pro- portioned to the weight. When a carriage wheel is made to slide on the ground, (as when a wheel is locked) the whole amount of the fric- tion is encountered without bringing in to our aid any me- chanical advantage ; but when a wheel turns on its axle, the friction is transferred from the ground to the axle, and each spoke of the wheel successively becomes a lever, turning on the ground as a fulcrum, while the power, or force of the team, is exerted on the end next to the axis. By thus trans- ferring the friction from the ground to the axle, each spoke, in its turn, is made to aid in overcoming that friction. Fig. S2. Thus, in Fig. 52, let C be the axis, CP the line of draught, and E the point where the wheel touches the plane. The force ap- plied in the direction CP, acts on CK at C, and turns it on its fulcrum at R. This is the force by which the wheel is made to ad- vance. But the friction on In wheel carriages, in what consists the resistance ? What is theresista:;ce when the carriage is made to slide on the ground ? Ditto, when a wheel turns SQ its axle ? What office does each spoke perform 1 Explain hy figure 52. 92 MECHANICS the axle at C, re-acts in the opposite direction, having a lever- age equal only to the radius of the axle, while the power which overcomes this, has a leverage equal to the radius of the wheel. Hence, in the wheel, there is a mechanical ad- vantage gained in overcoming the friction, in the ratio of the radius of the wheel to the radius of the axle. Moreover, the axle may be made of such materials, and lubricated with such substances, as to render the actual amount of friction much less than it would be were the wheel made to slide on the ground. But wheels have another important advantage, namely, in overcoming obstacles ; in which case they act on the princi- ple of the bent lever. Thus let A be an obstacle, as a stone for example. From A let fall the perpendiculars AN, AM, upon CR, CP, and conceive MAN to be a bent lever, turning on A as a fulcrum, the power being applied at M in the direction CP, and the weight resting on N (which supports the center of gravity.) Now, the mechanical advantage gained, will be in the ratio of MA to NA. It will therefore be increased (and of course the force necessary to overcome the obstacle be diminished) as the point A is nearer to R ; and the mechanical advan- tage will be lessened as the point A recedes from R. When the obstacle is so large as to make A M only equal to AN, then no mechanical advantage is gained but the whole weight of the load must be lifted by the former ; and when AM becomes less than AN, the wheel involves a mechanical disadvantage, and the difKculty of carrying the wheel over the obstacle becomes very great. It is further obvious that large ivheeh have the mechanical advantage, both as re- gards overcoming the friction, and overcoming obstacles, in a higher degree than small wheels, since these afford a greater leverage than the others on account of the increased length of the spokes. But in practice very large wheels can- not be employed, since they would be either weak or too heavy, and the increased height of the axle would carry the center of gravity too high, and enhance the danger of upsf>t ting. The difficulty of turning might also render unusually large wheels ineligible ; and the axle might be raised so high, as to make the horse draw obliquely downwards and increase the pressure on the ground, whereas the line of draught ought to be so adjusted as to lighten that pressure, especially where the road is soft and yielding. In what ratio is a mechanical advantage gained? Explain the action of wheels in overcoming obstacles. MACHINEKY. 93 When a wheel sinks below the surface, the force is ren- dered strikingly inefficacious from several causes. The ful- crum on which each spoke successively turns gives way, and diminishes greatly the mechanical advantage otherwise gained by transferring the friction from the ground to the axle, as before explained. Likewise the mud or sand into which the wheel has sunk, opposes in front of the wheel an obstacle like that represented at A in Fig. 52, while the ful- crum on which the bent lever turns in the effort to lift the wheel over the obstacle gives way as in the other case, and a great part of the mechanical advantage is lost. From these considerations, it is easy to understand the reason of the superior advantages of hard and smooth roads. 116. The line of draught should not be horizontal, but inclined upwards towards the breast of the horse, in an angle not less than 15 degrees with the horizon. This brings the strain nearly at right angles with the collar, whereas a hori- zontal draught lifts the collar upwards, by which the force is wasted and the animal is choked. The effect of suspending a carriage on springs, is to equal- ize the motion by causing every change to be more gradu- ally communicated to it, and to obviate shocks. Springs are not only useful for the convenience of passengers, but they also diminish the labor of draught; for whenever a wheel strikes a stone, it rises against the pressure of a spring, in many cases without materially disturbing the load ; whereas without the spring, the load, or a part of it, must rise with every jolt of the wheel, and will resist the change of place with a degree of inertia proportionate to the weight, and the suddenness of the percussion. Hence springs are highly useful in baggage wagons and other vehicles used for heavy transportation. A pair of horses draw more advantageously abreast than when one is harnessed before the other. In the latter case, the forward horse, being attached to the ends of the shafts, draws in a line nearly horizontal ; consequently he does not act with his whole force upon the load, and moreover ex pends a part of his force in a vertical pressure on the back of the other horse. What angle should the line of draught makewith the horizon? "WTiatare the disadvantages of having the line of draught horizontal ? Point out the uses of springs in carriages. Why are springs useful in baggage wagons ? Should two horses be harnessed side by side, or one forward of the other ? CHAPTEB X. MACHINERY CONTINUED— THE PULLEY, INCLINED PLANE, SCREW, AND WEDGE. Fig. 53. Fig. 54. THE PULLEY. 1 1 T . A PULLEY is a small grooved wlieel movahle about a pivot, the pivot itself being at tlie same time e'iiher fixed or movable. The fixed pulley is represented in Fig. 53. By it no mechanical advantage is gained, but its use consists in furnishing a convenient mode of changing the direction of the power. Thus, it is far more con- venient to raise a bucket from a well by drawing downwards, as is the case where the rope passes over a fixed pulley above the head, than by drawing upwards, lean- ing over the well. By means of the pul- ley, great facilities are afforded for managing the rigging of a ship. The sails at mast head can be easily raised, while the hands stand upon the deck ; whereas, without the aid of ropes and pulleys, the same force re- moved to the mast head would operate under very great disadvantages. Similar facilities are afforded by this kind of appa- ratus for raising heavy weights, as boxes of merchandise, or heavy blocks of stone in building. Fire escapes sometimes consist merely of a pulley fixed near the window of the apartment, around which a rope may be easily placed, having a basket attached to the end. The man seats himself in the basket, grasping, at the same moment, the rope on the other side of the pulley, and thus he lets himself gradually down. The movable pulley is attended with a mechanical ad- vantage, so that by its aid, a comparatively small power Define the pulley. Is any mechanical advantage gained by the fixed pulley ? What is its use ? Give examples. How are fire escapes constracta^ ? Is any mechanical advantage gained by the movable puUey 1 MACHINERY. 95 may be made to raise great weights. Pig. 55 represents a movable pulley E in connection with a fixed one A. The weight W bears equally Pig. 55. upon the two parts of the rope, and con- sequently that which acts against the power P, sustains only half the weight. An equilibrium will therefore be pro- duced when the power is equal to half the weight. In Fig. 56, blocks of pulleys are rep- resented, in which the weight is dis- tributed over a greater number of parts of the rope; each part therefore sustains a proportionally smaller portion of the load, and yet one of these parts is all that acts immediately against the power. Hence the power will be as much less than the Fig. S6. weight, as the number of parts of the rope is greater than unity. Thus, where there are six parts, three on each side, a power of one pound will balance a weight of six -pounds. This principle is generalized in the following prop- osition : In the pulley an equilibrium is produced, whsn the power ^ is to the weight as one to tiie number of ropes. 118. The ascent of the weight is in all cases retarded in proportion as the efficacy of a given power is increased. Moreover in using any system of movable pulleys, the whole weight of the pulleys themselves, together with the resistance occasioned by the rigidity and friction of the rope, acts against the power, and so far lessens the weight which it is capable of raising. In the more complex system of ^ pulleys, it is estimated, that at least two thirds of the power is expended on the machinery itself On ac- count therefore of the slowness of the motion which the weight receives, and the loss of power from the resistance of the ropes and blocks, such systems of pulleys are seldom employed. It is only in raising vast weights, such as large Describe it by figare 55. Also by figure 5fi. When i,s an equilibriora pro- duced in tbe pulley 1 How is the velocity of the weight affected by increasing the efficacy of the power? Point out the sources of loss or resistance of the pulley. 96 MECHANICS. ships, or great masses of stone from a quarry, that they are ever used. For managing the rigging of a ship, the com- bination usually employed consists of not more than two or three movable pulleys. From its portable form, however, its cheapness, and the facility with which it can be applied, especially in changing or modifying the direction of motion, the pulley is one of the most convenient and useful of the mechanical powers. 119. EXAMPLES. Ex. 1. I wish to raise a block of stone weighing two tons, or 4,480 lbs., but can command a power only equal to 746f lbs. : What number of pulleys shall I require ? 746| ; 4,480 : : 1 : 6 ropes, or 3 movable pulleys, Ans. Since the number of ropes (or parts of the rope,) must be 6, and since each movable pulley has two ropes, as in Fig. 55, therefore the number of movable pulleys must be three; or the block must be analogous to one of those represented in Fig. 56. In this and other similar estimates, no allowance is made for the weight of the pulleys and other parts of the machine- ry which are raised along with the weight. The amount of these must be added to the weight in order to ascertain the power required. Ex. 2. By a system of pulleys containing 6 movable pul- leys, the same string going round the whole, as in Fig. 56, what power will be necessary to sustain a weight of 112 lbs. ? Ans. 9+. THE INCLINED PLANE. Fig. 57. 120. Let Fig. 57 repre- sent an Inclined Plane, whose length is AC, height AB, and base BC ; and let W be a weight drawn up this plane by a power applied at P, and acting parallel to the plane. Then an equilibrium is pro- duced, when the power is to the weight, as the height of tlie plane to its length. Is the combination of pulleys usually employed simple or complex? VThy is the pulley accounted one of the most useful among the mechanical powers J How is the power to the weight ia the Inclined Plane? MACHINERY. 97 The inclined plane becomes a mechanical power in conse- quence of its supporting a part of the weight, and of course leaving a part to be supported by the power. Thus the power has only to encounter ^portion of the force of gravity ftt a time, — a portion which is greater or less, according as the plane is more or less elevated. When a plane is perfect- ly horizontal, it sustains the entire pressure of a body that rests on it ; that is, the pressure on the plane is equal to the whole force of gravity acting on the body. As one end of the plane is elevated, this force is resolved into two, one of which is parallel and the other perpendicular to the plane. In proportion as the plane is more elevated, the part of the force which acts parallel with the plane is increased, until, when the plane becomes perpendicular to the horizon, it no longer sustains any portion of the weight, and the latter de- scends with the whole force of gravity. 121>. The simplest example we have of the application of the Inclined Plane, is that of a plank raised at the hinder end of a cart for the purpose of rolling in heavy articles, as bar- rels or hogsheads. The force required to roll the body on the plank, setting aside friction, is as much less than that required to lift it perpendicularly, as the height of the plane above the ground is less than its length. Every one knows how much the facility of moving heavy loads is increased by such means and how the force required to move them is dimin- ished, by increasing the length of the plane while the height remains the same. Long inclined planes, constructed of plank, are frequently employed in building, especially where high walls are built of large masses of stone, the materials being trundled up the plane on wheelbarrows, or transported on heavy rollers. It is even supposed, that in building the pyramids of Egypt, the huge masses of stone were elevated on an inclined plane. Roads also, except when they are perfectly level, afford examples of this mechanical power. When a horse is drawing a heavy load on a perfectly hori- zontal plane, what is it that occasions such an expenditure of force ? It is not the weight of the load, except so far as that increases the friction ; for gravity, acting in a direction How does the inclined plane become a mechanical power 1 Explain how the inclined {)lane moderates the force of gravity. Example of a plank placed at the hinder end of a cart — ^how mach is the force required to raise the weight diminished by the plank ? Wliat is the effect of lengthening the plane while its height remains the same ? Explain the use of long inclined planes in building. How are the principles of the inclined plane exempli- fied in roads 1 9 98 , MECHANICS. perpendicular to the horizon, can oppose no resistance in th« direction in which the load is moving. The answer is. that the force of the horse is expended chiefly in overcoming fric- tion, and the resistance of the air. But when a horse is drawing a load up a hill he has not only these impediments to encounter, but has also to overcome more or less cf the force of gravity ; that is, he lifts such a part of the load as bears to the whole load the same ratio that the perpendicu- lar height of the hill bears to its length. If the rise is one foot in twenty, he lifts one twentieth of the load, and there- fore encounters so much resistance in addition to the resist- ances which he had to overcome on the horizontal plane. If the ascent were one foot in four, and the load were a ton, the additional force required above what would be necessary on level ground, would be 560 pounds. 1 22. Railways afford another striking exemplification of the principles oif the Inclined Plane. By means of them the irregular surface of a country, however hilly and uneven, is reduced to horizontal levels and inclined planes. Upon a level railroad of the best construction, with carriages of the most perfect finish, one horse is able to draw a load of 22^ tons. Under ordinary circumstances, however, the load does not exceed 16 tons. The resistance to motion, from the causes just mentioned, has been reduced as low as -j^, and may be safely stated at tj-oTi while on the best common road it is never less than -(Vth, and is frequently as great as TjVth. In a boat, on a canal, a horse can draw 30 tons. When horses are employed as the moving power, canals have the advantage over railroads in the transportation of heavy mer- chandise ; but when speed is the object, railroads have a great superiority. But railroads derive their greatest value from the use of steam as the moving power in the locomo- tive. This answers every condition of a perfect force, being capable of being exactly proportionate to the weight to be carried, whether one ton or a thousand tons, and moving with immense speed without ever tiring. In a railroad two things are especially important that the slope should be gen- tle and uniform, and that the curves should be few and grad- ual. Where steep ascents are encountered, an increase of power is required that is useless for the more level -portions of the road, and where frequent and short curves occur, the Howr are the principleB of the inclined plane exemplified in railways ? What load will a horse draw on a railway 7 How are loads drawn up steep ascents t What is the locomotive ? What are its peculiar advantag^es as a moving force 7 MACHINERY. 99 wcles have so little play that in turning, one of the wheels on each axle must drag- or slide, and unless the motion is slackened to a low speed, there is g^reat danger of running off the track. Curves, therefore, where they are unavoida- ble, should be made as gentle as possible.* 1 23. The motion of bodies descending down inclinM vlanes, is subject to the same law of gravity as bodies falling freely ; that is, it is uniformly accelerated. Consequently, here, as in the case of bodies falling without impediment, tlie spaces described are proportioned to the squares of the times, sxiA. to the squares of the. velocities acquired. (Art. 50 — 52.) 124. The velocity acquired in falling down an inclined plane, is the same as that acquired in falling throtigh the perpendicular height of tlie plane. When a plane is but slightly elevated, as in railroads, the acceleration, though constant, is comparatively slow ; but after rolling freely through such a distance as several miles, the motion may become exceedingly rapid. A very remark- able example of the acceleration of bodies descending down inclined planes, occurs at the SUdeof Alpnach in Switzerland. On Mount Pilatus, near Lake Luzerne, is a valuable growth of fir-trees, which, on account of the inaccessible nature of the mountain, had remained for ages uninjured, until within a few years, a German engineer contrived to construct a trough in the form of an inclined plane, by which these frees are made to descend by their own weight, through a space of eight or nine miles from the side of the mountain to the margin of the lake. Although the average declivity is no more than about one foot in seventeen, and the route often circu- itous and sometimes horizontal, yet so great is the accelera- tion, that a tree descends the whole distance in the short space of six minutes. To a spectator standing by the side of the trough, at first is heard on the apprpach of a tree, a roaring noise, becoming louder and louder ; the tree comes in sight at the distance of half a mile, and in an instant af- terwards shoots past with the noise of thunder and the rapid- ity of lightning. When a tree happens to " bolt" from the trough, it cuts the standing trees quite off. * See Renwick*B Practical Mechanics. What are the disadvantages of steep ascents and short carves? When bodies descend inclined planes, at what rate are they accelerated ? How are the spaces proportioned to the times? How does the velocity acquired by falling down an inclined plane compare with that acquired hy falling freely through the same height ? Kelate the circumstances of the Slide of Alpnach. 100 MECHANICS. 125. It takes as much longer for a body to descend down an inclined plane Fig. 58. proportioned to their respective lengths than to fall through its perpen- dicular height, as the length of thfc plane exceeds its height. Thus, in Eig. 58, a body in de- scending successively down the planes AC, AD, AE, would ac- quire in each case the same velocity, being the same as it would acquire by falling down AB ; but the times of describ- ing these several lines would be THE SCREW. 126. When a road, instead of ascending a hiQ directly, winds round it to the summit, so as to lengthen the inclined plane, and thus aid the moving force, the Inclined Plane be- comes a screw. In the same manner a flight of stairs, wind- ing around the sides of a cylindrical tower, either within or without, affords an instance of an inclined plane so modified as to become a screw. These examples show the strong analogy which subsists between these two mechanical powers; or rather,' they show that the screw is a mere modification of the Inclined Plane. This correspondence between the Inclined Plane and the Screw is exhibited in the annexed figure. The distance be'tween the two contig- uous threads of a Fig- 59. screw, corresponds to the height of an inclined plane, and the circumference of the cylinder cor- ( ^K^jllTUI nil II responds to the Aas-e of the same plane ; hence the forces necessary to pro- duce an equilibri- um in the screw, How much longex' does it take for a body to 'descend do'wn an inclined plane than to fall through the perpendicular height of the plane ? Illustrate by figure 58. The Screw — how is its principle exhibited in a road winding around a hill ? Uow by a flight of stairs ? MACHINERY. 101 to the line AB ; the point B will Fig. 60. are the same as in the inclined plane. Thus, let the inclined plane ABC be wrapped round a cylinder, the circumference of whose base is equal then the point A being- placed on A', come round to A', the point C will fall on C, and the line AG will trace out the thread of the screw on the surface of the cylinder as far as C', and may be continued in the same manner. It will be remarked that the power here acts parallel to the base of the inclined plane Thus in fig- ure 60 the power is applied to the handle, which revolves parallel to the base of the screw, or the base of the inclined plane of which the screw is formed. 127. In the screw ^ an equilibrium is pi-odMced when the power is to the weight as the distance between two contigu- ous threads is to the circumference of the base. By inspecting figure 59, it will be seen that " the distance between two contiguous threads," is the height CB of the inclined plane ABC, while " the circumference of the base" is the base AB of the same plane. The law of equilibrium of the screw is therefore the same as in the inclined plane when the power acts in a direction parallel with the base ; in this case the power being to the weight as tlip height of the plane to the base. The power, however, is not always applied directly to the circumferen'ce of the screw, but frequently at the end of a lever inserted into the screw, as in figure 60, and' as in the common cider press. Hence a more general law of equilib- rium is as follows : In the screw, an equilibrium, is produced when the power is to the weight, as the distance between two contiguous threads is to tlie circumfa-ence of tlie circle described in one revolution of the power. 128. The Screw is generally employed where severe pressure is to be exerted through small spaces, and is there- Show how the screw is formed by winding an inclined plane around a cyl- inder. What part of the plane corresponds- to the distance between the threads ? To what line does the power mqve parallel ? What in the law of eqailibrium in the screw ? How is this law analogous to that of the inclined plane ? What is the general expression of the law. when the power acts aX the end of a lever ? For what purpose is the screw used ? 9* 1 02 MECHANICS. fore the agent in most presses. Being subject to great loss from friction, (upon which, however, its chief utility depends, as will be shown hereafter.) it usually exerts but a small power of itself, but derives its principal efficacy from the 'ever, or from wheelwork, with which it is very easily com- bined. Thus in figure 60, were the power applied directly to the screw, the mechanical advantage gained would hard- ly more than compensate for the loss by friction ; but by means of the lever, (which may be lengthened or shortened at pleasure,) the power is greatly increased. The endless screw, is represented in figure 62. It is used in connection with toothed wheels. By means of the endless screw, com- bined with the wheel and axle, a very powerful force may be exerted ; and as the mechanical power of the screw de- pends upon the relative magnitude of the circumference through which the power revolves, and the distance between the threads, it is evident that, to increase the efficacy of the machine, we must either increase the length of the lever by which the power acts, or diminish the distance between the threads. Although, in theory, there is no limit to the increase of the mechanical efficacy by these means, yet prac- tical inconvenience arises from the great spare over which a very long lever traverses. If, on the other hand, the power of the machine is increased by diminishing the distance be- tween the threads, and of course their size, the thread will become too slender to bear a great resistance. The eases in which it is necessary to increase the power of the ma- chine, being those in which the greatest resistances are to be overcome, the object will evidently be defeated, if the means chosen to increase that power deprives the machine of the strength which is necessary to sustain the force^to which it is to be submitted. 1 29. These inconveniences are remedied by Hunter''s Screw, which, while it gives to the machine all the requisite strength and compactness, allows it to have an almost un- limited degree of mechanical efficacy. This screw is com- posed of a smaller and larger thread, the former turning up wards, while the latter turns downwards with a little greater velocity, and consequently the screw, on the whole, advances with the difference between the larger and the smaller Is it commonly employed alone, or in connection with one of the othei mochanical powers? Describe the endless screw. Explain its principle What practical inconvenience arises from the use of a very long lever ? — Alsff fi'om diminishing the distances of the threads too much ? Explain the prin ciple of Hunter's Screw. MACHINERY. 103 Fig. 61. threads ; and since this difference may be small to any ex tent, so the efficacy of the power may be increased indefi- nitely". It will be seen, however, that the motion of such a screw is exceedingly slow. Thus, in figure 61, A descends, while B, playing in a concave screw in A, ascends ; but the distance between the threads of A being greater than the distance between those of B, the screw, on the whole, advances with the difference. Suppose that A has 20 threads in an inch, and B 21 ; then, during one revolution, A will descend through the 20th, while B ascends through the 21st part of an inch. The compound screw, therefore, will advance through a space equal to the differ- ence ; that is, through a space equal to -jV — ^^r =T2Tth of an inch. This small space is, therefore, in effect, the distance between the two contiguous threads ; and the power of the machine is, as usual, expressed by the number of times their distance is contained in the circumference described in one revolution of the power. For example, let the circumference of the circle be one foot ; then 12-^^5-^ — 5040= the weight or resistance, the power being 1 ; or, in other words, the efficacy of the power is increased five thousand and forty times. 130. It is obvious, however, from principles already ex- plained, that the power will in this case move over 5040 times as great a space as the weight. It is on this principle that the screw affords the means of measuring very minute spaces, and hence is derived the Micrometer Screio. The very slow motion which may be imparted to the end of a screw, while the power moves over a space vastly greater, renders it peculiarly adapted to this purpose. For example, suppose a screw to be so cut as to have 50 threads in an inch : then each revolution of the screw will advance its point through the 50th part of an inch, and if that point acted ■ against a thread or wire, it would move it over a graduated space only that distance in a whole revolution of the screw. Now suppose the head of the screw to be a circle an inch in By what is the power of the machine expressed 1 To what use is tho micrometer screw applied ? 104 MECHANICS. diameter, and of course something more than three inches in circumference. The circumference may easily be divided into a hundred equal parts, distinctly visible ; and if a fixed index be applied to it, the hundredth part of a revolution of the screw may be observed, by noting the passage of one division of the head under the index. But the hundredth part of a revolution carries the point of the screw only through the (-[-Jr of 5V=) TiiVotb part of an inch. Such an apparatus is frequently attached to the limbs of graduated instruments for the purposes of astronomical and othei observations ; by which means, a portion of the graduated arc no greater than the 100th part of a second, can be es- timated. In like manner, any other small space may be measured by the aid of the Micrometer Screw. Thus, any aliquot part of a pound, or an ounce, in the steelyards, may be found by adapting the screw to the counterpoise, so as to move it slow- ly over the space between two notches, and at the same time point out, by an index on its head, the exact portion of the space over which it passes. 131. Several of the mechanical powers are frequently combined in the same machine, and great works are some- times accomplished by a comparatively small force, carried over a proportionally greater space. The manner in which this is done is exemplified in the figure annexed to the ful- lowing problem. Fig. 68. Give an example of its use in measuring l-5000th part of an inch ? What other small spaces may be measured by it? What use is made of the endless screjo ? MACHINERY. 105 A shipwngnt wishing- to haul a ship upon the stocks, em- ployed a machine, combining the lever, the screw, the wheel and axle, the pulley, and the inclined plane, as represented in the diagram on page 104. The handle of the winch BC=18 inches. The distance of the threads on CD= 1 inch. The diameter of the wheel ED = 4 feet. The diameter of the axle EF=^1 foot. Gr is a fixed, and H a movable pulley, the number of strings =4. Height of the plane equals half its length. Allowing a man to turn on the handle B with a power equal to 100 lbs., how much force could he exert on the ship? By Art. 127, 100 lbs. exerted at B would become at D, 11309.76 And since the diameter of the wheel is four times that of the axle, X 4 45239.04 Again, this is rendered four-fold by the four strings of the pulley, 4 180956.16 Finally, this is dbubled by the plane, 2 361912.32 Hence, the force exerted on the ship would amount to more than 361,912 lbs., or more than 161^ tons. THE WEDGE. 132. If instead of moving a load on an inclined plane, the plane itself is moved beneath the load, it then becomes a Wedge. Thus, if a perpendicular beam have one end resting upon an inclined plane, (the beam being so secured as to be capable of moving only up and down.) and the plane be drawn under it, the beam will be elevated ; and the power required to effect this will be to that required to raise the beam when applied directly to it, as t/ie height of the plane to its kngth .-—or, considering the plane as a half wedge, the proportion wjU be, as half the back of the wedge to its length. 133. In the, arts and manufactures, wedges are used where an enormous force is to be exerted through a very What different mechanical powers are sometimes combined in the same machine 1 How does the inclined plane become the wedge ? How much less force is required to lift a weight by means of the wedge, than by a force applied directly to it ? In what cases is the wedge used in the arts ! 1 06 MECHANICS. small space. Thus it is resorted to for splitting masses of timber or stone. Ships are raised in docks b)' wedges driver under their keels. The wedge is the principal agent in the oil mill. The seeds from which the oil is to be extracteo are introduced into hair bags, and placed between planes of hard wood. Wedges inserted between the bags are driven I by allowing heavy beams to fall on them. The pressure thus excited is so intense, that the seeds in the bags are formed into a mass nearly as solid as wood. Instances have occurred in which the wedge has been used to restore a tot- tering edifice to its perpendicular position. All cutting and piercing instruments, such as knives, razors, scissors, chisels, nails, pins, needles, awls, &c.. are wedges. The angle of the wedge, m these cases, is more or less acute, according to the purpose to which it is applied. In determining this, two things are to be considered — the mechanical power, which is increased by diminishing the angle of the wedge ; and the strength of the tool, which is always diminished by the same cause. There is, therefore, a practical limit to the increase of the power, and that degree of sharpness only is to be given to the tool, which is consistent with the strength requisite for the purpose to which it is to be applied. In tools intended for cutting wood, the angle is generally about 30° ; for iron it is from 50 to 60 ; and for brass, from 80° to 90 ' Tools which act by pressure may be made more acute than those which are driven by a blow ; and, in general, the softer and more yielding the substance to be divided is. and the less the power required to act upon it, the more acute the wedge may be constructed. 1 34. In many cases the utility of the wedge depends on that which is entirely omitted in the theory, viz., thefrictwn which arises between its surface and the substance which it divides. This is the case when pins, bolts, or nails, are used for binding the parts of structures together ; in which case, were it not for the friction, they would recoil from their pla- ces and fail to produce the desired effect. Even when the wedge is used as a mechanical engine, the presence of fric- tion is absolutely indispensable to its practical utility. The power generally acts by successive blows, and is therefore subject to constant intermission, and but for the friction, the Give examples of its use in spUuiug hard substances — in making oil from seeds — in raising buildings to a perpendicular position, &c. What instru- ments exemplify the wedge ? How is the power of a cutting instrument increased 1 What degree of acuteness is necessary ? How is the friction of the wedge essential to its utility 7 MACHINERY. 107 wedge would recoil between the intervals of the blows with as much force as it had been driven forward, and the object of the labor would be continually frustrated. 135. The following principle is of great importance in relation to all the mechanical powers, and deserving of par- ticular attention. In each of the mechanical powers, and in every machine, thi power and weight balance each other, wheti the power moves as much faster than the weight as its quantity oj matter is less. We can, therefore, make a small power raise a very great weight, by so connecting it with the weight, as to make it move over a very great, while the weight moves over a very small space. By reviewing the several mechanical powers, we shall recognize the operation of this principle in each of them. In levers of the first and second kind, (Figs. 31, 33,) the power being applied at the extremity of the longer arm and farther from the fulcrum than the power, moves over a pro- portionally greater space as the lever turns on its fulcrum ; but in the lever of the third kind. (Fig. 34.) the power being applied nearer the fulcrum than the weight, moves with less velocity than the weight, and consequently acts under a me- chanical disadvantage, and requires to be proportionally greater than the weight. In the wlieel and axle, (Fig. 43,) as both the wheel and its axle revolve in the same time, it is obvious that the power applied at the circumference of the wheel must move as much faster than the weight, as the circumference of the wheel is greater than that of the axle. In the pulley, when the rope merely passes over a fixed pulley, (as in Fig. 53,) the power and weight move over the same space, and no mechanical force is either gained or lost ; but in the movable pulley represented in Fig. 55, the strings that raise the weight are equally shortened., and the power is lengthened by an amount equal to that by which the several parts are shortened ; consequently the power moves as much faster than the weight as the number of ropes is greater than unity. When the number of movable pulleys is great, the great space over which the power must move in order to raise the weight over a comparatively small place, presents a prac- tical inconvenience. (See Fig. 56.) State the comparative velocity of the power and weight in all machincM How can we make a small power raise a great weigbt ? How ia this pri:- ciple exemplified in the lever ? in the wheel and axle ? in the puUev 108 MECHANICS. In the inclined pla,ne, the greater the length of the plane in proportion to its height, the slower will be the perpendic- ular ascent of the weight. For example, if the length of the plane be twice its height, the power must move over twice the space that it would if it rose perpendicularly, and hence the mechanical advantage gained is in the same ratio : that is. the power required is so much less than the weight. In the screw, while the power performs one complete rev olution, the weight is elevated only the distance between tviro contiguous threads. Hence, when the power is applied at the end of a long lever, and the distance between two con- tiguous threads is small, the forward motion of the screw is very slow, while the power traverses a great space. In a combination of the mechanical powers, such as that represented in Fig. 62, we see the same principle very strik- ingly exhibited. Here the power moves 3,619 times as fast as the weight, and the mechanical advantage gained is in the same ratio. Finally, in the wedge, the power of overcoming resistances is proportioned to the acuteness of the wedge ; and the dis- tance to which the parts are separated, that is, the space over which the weight moves, when compared with the space through which the power, (namely, the wedge itself in the direction of the power,) moves, is constantly diminished as the acuteness of the wedge is increased. CHAPTER XI. MACHINERY CONCLUDED. 1 36« Archimedes is said to have boasted to King Hiero that " if he would give him a place to fix has machine, (^roi I7T0I,) he would move the world." Yet there can be no ma chine by the aid of which Archimedes could move the world in any other way, than by moving, himself, over as much more space than that over which he moved the earth, as his weii^ht was less than that of the whole earth. If Archimedes had "sjeived the place he desired, and had also employed wha ■ Tis equally indispensable, a machine which operated !ti {joined plane ■! in the ncrew ? in the wedge ? What did Archimedes boas' 1 what principle could he have moved the world? MACHINERY. 109 free of all resistance, he must have moved with the velocity of a cannon ball, to have shifted the earth only the twenty- seven millionth part of an inch in a million of years. 137. From the foregoing principles it will be inferred, that no momentum, or effective force, is gained by any of the mechanical powers, or by any machine. If a man with his naked hands, can lift to a given height, as one foot, only 150 pounds in one second, it is impossible for him to perform any more labor than this by any mechanical contrivance. On the contrary, when the structure of the machine is compli- cated, there is a loss of force, by employing the machine in- stead of the naked hands, proportioned to the resistance of the parts of the machine itself. It is to be remarked, how- ever, that this doctrine proceeds on the supposition that the useful effect produced, is estimated from the joint product of the /brce, velocity, and time. A convenient method of esti- mating different forces is to draw a heavy weight out of a well, by a rope passing horizontally over a fixed pulley, near the top of the well. Suppose that a man can draw; up a rock weighing 100 lbs., through the space of 50 feet in one minute. He would, of course, be able to draw up ten such masses in ten minutes, weighing in all 1,000 pounds. Now by passing the rope over five pulleys, (allowing nothing for the friction of the pulleys,) he might with the same force lift the whole 1,000 pounds at once ; but it would rise ten times as slowly as the 100 pounds did before, and consequently would be ten minutes in reaching the top. Therefore, in a given time, it appears that the man would raise the same weight through a given space, with or without the aid of machinery. In the former case, the 100 lbs. might have Deen raised during the ten minutes through the space of 500 instead of 50 feet ; but 100x500x10=1000x50x10; so that the labor performed would have been the same in both cases. Let us suppose that P is a power amounting to an ounce, and that W is a weight amounting to 50 ounces, and that P elevates W by means of a machine. In virtue of the property already stated, it follows, that while P moves through 50 feet, W will be moved through 1 foot ; but in moving P through 50 ket,Jifty distinct efforts are made, by each of which, if applied directly, 1 ounce will be moved through 1 foot. How DTOch could he have moved it ? Is any momentnm gained by ma- chinery ? How is the nseful effect estimated ? By what means are different forces estimated ? Example in lifting a rock out of a well. 10 110 MECHANICS. 138. It has long been sought, by some mechanical con trivance, to construct a machine, which would have the powej within itself of generating motion and thus of compensating for the impediments which arise from friction and the re- .distance of the air, and securing Perpetual Motion. The idea of perpetual motion does not imply that a machine wili never wear out ; nor if. when left to itself it were to continue in motion by some external fmxe, as water, wind, or steam until it was worn out, would it be a case of perpetual motion. This term implies that it contains within itself the power of generating motion mdependent of any increase in the force applied. Now that no machine can possess such a power is evident from the inertia of matter, which moves only as it is moved, and from the second law of motion, which establishes an invariable relation between the force impressed and quan- tity of motion produced. Nor can any combination or use of the mechanical powers involve such an effect as perpet- ual motion, since whatever is gained in velocity is lost in the quantity of matter moved ; or if a less power moves a greater weight, it is over a proportionally smaller space ; so that the monientaol the power and the weight are always the same. Hence, all actual attempts to reach such a principle as per- petual motion, (and the attempts have been very numerous, and are still continued.) have proved fruitless, and ended in disappointment. 139> WJiat t/wn, it may be asked, are the advantages gained hy Machinery ? The advantages are still very great, for the following reasons. (1.) By the aid of machinery we. can frequently apply our force to much better purpose. Thus, in lifting a weight out of a well, or in raising ore out of a mine, it is obvious with how much more effect a man can work at the arm of a wind- lass than he could draw directly upon the rope, stooping over the well. So in raising a rock from its bed by means of a handspike or crowbar, we can easily see how much more ef- fectually we can bring our force to bear upon it, than we could do by our naked hands. (2.) By the aid of machinery, a man may be able to per- form works to which his naked strength would be wholly incompetent. Thus, as in the preceding example, one might be able to lift a rock from its bed with a handspike, upon what is meant by perpetual motion ? How is it inconsistent -with the laws of motion ? Result of efforts to produce it ? What are the advantages gained by machinery ? Examples in raising ore from a mine, or in lifting weights out of a well, or a rock from its bed. MACHINERY. I I 1 which he could make no impression with his naked hands ; or, by means of pulleys he might raise a box of merchan- dise from the hold of a ship, which he could not start at all with his unassisted force. In each of these cases, if the u'eight could be divided into small parcels, and if the force could be as advantageously applied without machinery as with it, the labor would be performed as easily in a given time in one way as in the other. But it might not be pos- sible, or at least convenient thus to divide it. Or if instead of dividing it into a number of parcels, the same number of men could act directly upon a weight at once, the aniount of labor which they would all exert in raising the weight without machinery, would be the same as that which the single man before supposed would exert with his machinery. But it might not be convenient to assemble so many hands at a time ; or perhaps such a number could not work advan- tageously together. A farmer has many occasions for lifting or removing great weights when his laborers are not more in number than two or three in all. These must therefore perform the labor of 50 times as many men by being 50 times as long about it. Thus, in the example given on page 105, of a combination of the mechanical powers employed to haul a ship on the stocks, where a single man turning on a winch, with the force of 100 lbs. exerts a force on the ship amounting to 161^ tons, the ship would move as much slow- er than the hand, as 100 lbs. is less than 161-^ tons; and consequently a great length of time would be required for an individual to perform this labor, even supposing no resist- ance were encountered from the machinery itself (3.) Machinery frequently enables a man to exert his whole force in circumstances where, without such aid, he could employ but a part of it. Thus, in winding silk or thread, to turn a single reel might not require one fiftieth part of the force which the laborer was capable of exert- ing. Suitable machinery would enable him to turn fifty spools at once. (4.) But the most striking advantage of machinery is not found in the facilities which it lends to the personal strength of man ; it lies in this, that it affords the means of calling m to his assistance the superior powers of the horse and the ox, of water, of wind, and especially of steam. Here we find Sho^v how a man may perform worka by the aid of machinery to which liia naked strength is unequal? Why is there no gain of force in saeh cases? Show how machinery enables a man to exert his whole force. What is the most striking advantage gained by it 1 1 1 2 MECHANICS. the excellence of mechanical contrivances fully exhibited ; and nowhere else has the inventive genius of man displayed itself to so great advantage. But here, as in all other cases, the various combinations of mechanical powers produce no force ; they only apply it. They form the communication between the moving power and the body moved ; and while the power itself may be incapable of acting except in one direction, we are able, by means of cranks, levers, and toothed wheels, to direct and modify that force to suit our conveni- ence or necessities. Every one may see examples of this in the construction of the most common saw mill or flour mill, turned by water. In a mill for grinding wheat the stones are required to move horizontally, while the action of the water-fall is perpendicular. We therefore receive the whole force on the circumference of a wheel, and transmit it through several intermediate wheels to the revolving stone, where the grinding is performed. So in a saw mill, the water first communicates a rotery motion to the wheel, and this motion is converted by means of a crank into what is called a recip- rocating motion, as that of the saw in its ascent and descent. By means of wheel wrork the velocity of the moving body is increased or diminished at pleasure. In short, machines enable us to form a convenient com- munication between the power and the weight ; to give to the weight any required direction or velocity ; to apply .force to the best advantage ; to vary the circumstances of velocity and time as the amount of our force may require; and to bring to our aid the great moving powers that exist in nature. Our next object, therefore, will be to see by what particular methods these several purposes are accom- plished. REGULATION OF MACHINERY, AND CONTRIVANCES FOR MODI FYING MOTION. 1 40. It is highly important to the successful operation of any machine, that its motion should be regular and uniform. Jolts and irregular movements waste the power, wear upon the machine, and perform the work unevenly. The sources of irregularity are various, but they are chiefly the three following, viz. variations in the power, variations' Show the use of machinery in changing the direction of the force ? Also in regulating its velocity. Enumei-ate the various purposes of machinery. What is essential to the snccessfal operation of a machine! What are th< three sources of irregularity t MACHINERY. 1 1 3 in the weight or resistance, and changes of velocity in parts of the machine itself Thus in the steam engine, the fire may burn with more or less intensity, and produce corres- ponding quantities of the moving power ; the load to be carried (as that of a steamboat) may be much greater at one time than at another, and be subject to sudden changes ; and the motion of the piston, which carries the machinery, ceases altogether at the highest and lowest points, and would move a machine by hitclies, or separate impulses, were there no contrivance connected with it foi keeping up a uniform motion. The kinds of apparatus employed to obviate these diffi- culties, and to secure uniform movements to machines, are, in general, called kegulators. Large machines or engines themselves, in consequence of their inertia, acquire and maintain, to a considerable extent, uniformity of motion. A flour mill, carried by water, when it has acquired a- certain rale of going, will not suddenly change that rate by an alteration in the force of the stream ; and a ship sailing between the opposite forces, arising from the impulse of the wind and the resistance of the water, will move steadily along, notwithstanding the breeze that carries it may fluc- tuate continually. We can see this principle sometimes operating on a smaller scale. A grindstone turned bv a winch moves steadily, although the force applied at o le part of the revolution is much greater than at another. Large grindstones exhibit the advantage of this principle much more than small ones. But in many instances, this natural tendency towards uniform motion is not sufficient, and artificial contrivances are introduced expressly for this purpose. As examples of Eegulators we may especially notice two, the Pendulum and the Fly Wheel. 141. The Pendulum,, by its equal vibrations, communi- cates to delicate machinery a motion extremely regular, and hence its application to the measurement of time. The Fly Wheel affords the most common and effectual method of equalizing motion, especially in heavy kinds of machinery. It consists of a heavy wheel (Fig. 63,; afford- ing as much weight as possible under as small a surface, in order that the inertia may be great while the resistance. from the air is small. It is therefore usually a heavy hoop How exemplified in the steam engine f What general name is given to the kinds of apparatus used to equalize motion ? Why do not large machines 80 much require regulators? How is the pendulum employed to regulate motion ? 10* 114 MECHANICS. Fig. 63. of iron, with thick bars of the same metal. The fly is bal- anced on its axis and so con- nected with the machinery as to turn rapidly around with it; and receiving a constantim- pulse from the moving power, it becomes a magazine or repository of motion. Conse- quently, by its inertia, it is ready to supply any deficiency of power that may arise from the sudden diminution of the moving force, or to check any sudden impulse which may re- sult from an accidental excess of that force. Suppose, for example, the handle of a pump to be connected with a water wheel, and to be carried by it. Here, the power, namely, the water-fall, is constant, while the weight is subject to continual alternations, amounting to a heavy load as the piston is ascending, but opposing scarce- ly any resistance while the piston is descending. The mo- tion, therefore, would vary between nothing and a highly accelerated velocity, and the machinery would be subject to constant strains and jolts. A Fly prevents these alternations and renders the ascent and descent of the piston nearly uni- form. In pile engines or stamping mills, a team of horses is sometimes employed to raise a heavy weight, which, when at a certain elevation, is suddenly disengaged and falls with great force. As the disengagement is instantaneous, the horses would instantly tumble down were not their motion checked by some contrivance which should prevent the ma- chinery from receiving any sudden increase of velocity. This purpose is completely answered by the Ply. 1 42. Beside the use of the Fly Wheel in regulating the action of machinery, it is employed for the purpose of accu- mulating successive exertions of a power so as to produce a much more forcible effect by their aggregation, than could possibly be done by their separate actions. If a small force be repeatedly applied in giving rotation to a Fly Wheel, and be continued until the wheel has acquired a very considera- ble velocity, such a quantity of force will be at length accu- mulated in its circumference, as to overcome resistance and Give a description of the fly wheel, and explain its principle. How is the iiy wheel used for accumulating motion 1 MAOmWERY. 115 jns>J«ce ed'ects utterly disproportionate to the immediate ac- tion ct ihe original force. Thus it would be very easy in a few seconds, by the mere action of a man's arm, to impart to the circumference of a Fly Wheel, a force which would give an mipulse to a musket ball equal to that which it re- ceives from a full charge of powder. 143. The same principle explains the force with which a stone may be projected from a sling. The thong is swung several times around by the arm until a considerable portion of force is accumulated, and then it is projected with all the collected iorce. If a heavy leaden ball be attached to the end of a strong piece of cane or whalebone, it may easily be driven through a board : by taking the end of the rod remote from the ball in ihe hand, and striking the board a smart blow with the end bearing the ball such a velocity may easily be given to ihe ball as will drive it through the •board 1 44. The astonishing effects of a Fly Wheel, as an ac- cumulator of forces, have led some into the error of supposing that such an apparatus zncreases the actual force of a ma- chine. So far from this, smce a Fly cannot act without friction and resistance from the air, a portion of the actual moving force must unavoiaably be lost by the use of this appendage. In cases, however, wnere a Fly is properly ad- justed and applied, this loss ot power is inconsiderable, com- pared with the advantageous distrioution of what remains. As an accumulator of force, a Fiy can never have more force than has been applied to put it in motion. In this respect it is analogous to an elastic spring. In bending a spring, a gradual expenditure of power is necessary. On the recoil, this power is exerted in a much shorter time than that con- sumed in its production, but its total amount is not altered. In this way the Ply Wheel is used. Thus, in mills for roll- ing metal, the water wheel or other moving power is allowed for some time to act upon the Fly alone, no load being placed upon the machine, A force is thus gained which is suffi- cient to roll a large piece of metal, to which, without such means, the mill would be quite inadequate. In the same manner, a force may be gained by the arm of a man acting on a Fly for a few seconds, sufKcient to impress an image on a piece of metal by an instantaneous stroke. Explain the action of a sling. What velocity may be given to a leaden ball attached to the end of a rod ? Does the fly wheel increase the acma. force of a machine V What loss of power does it occasion ? 116 MECHANICS. 145< We have already explained the mode in which motion is communicated, and its velocity regulated by wlied work. We proceed now to consider a few examples of the more special contrivances by which motion is modified to suit particular purposes, recommending it to the student of mechanics to make himself acquainted with other contrivan- ces of the same nature, by the actual inspection of machine- ry, as opportunity may ofTer. The motion required for a particular purpose may be rec- tilinear, as that of a carriage or bucket drawn out of a well ; or rotary, as in ordinary wheel work ; or reciprocating, as in a saw-mill, or a pendulum. The simplest mode of producing rectilinear motion, is by means of a rope or chain, instances of which are familiar to every one. The simplest mode of changing the direction, is by means of pulleys ; but toothed wheels are also extensive- ly employed for the same purpose. The connection of one toothed wheel with another, is called gearing. When both wheels with their teeth are in the direction of the same plane, it is called spi(r gearing, (Figs. 47, 48, 49 ;) if the teeth, instead of being cut on the circumference in a direc- tion parallel to the axis, are cut obliquely, so that if contin- ued they would pass round the axis like a screw, it is called spiral gearing. (Fig. 64 :) and when wheels are not situated in the same or parallel planes, but form an angle with each other, the wheels themselves are sometimes shaped like frustums of cones, having their teeth cut obliquely, and converging toward the point where the apex of the cone would be situated, and it is then called bevel gearing, (Fig. 65.) Fig. 64. Fig. 65. Fig. 66. Specify the several kinds of motioD, as rectilinear, rotary, and reciproca- ting. What is the simplest mode of producing rectilinear motion ? Ditto of changing the direction ! What is gearing 9 What is spnr gearing 1 What is spiral gearing ? What is bevel gearing ? MACHINERY. 117 Fig. 67. Fig. 68. 1 46. The universal joint consists of two shafts or arms, each terminating in a semicircle, and connected together by means of a cross upon which each semicircle is hinged, (Fig. 66.) When one shaft is turned, either to the right or left, (he other shaft turns in the same direc- tion. The racket wlieel (Fig. 67.) is used to prevent motion in one direction while it permits it in the opposite. The teeth are cut with their faces inclining as in the figure, and a catch is so placed as to stop the wheel in one direction, while it slides over the teeth without obstruction in the opposite direction. 1 47 . The eccentric wheel (Fig. 68,) re- volves about an axis, which is more or less removed from the center, and, consequently, the different portions of the circumference move with ditferent degrees of velocity. Hence, if this wheel is made to act upon a shaft or pinion, as in the figure, it will carry it with a corresponding movement. In orre- ries, such wheels are employed for indica- ting the variable ve'ocities of the heavenly bodies, as they revolve about their centers of motion. 1 48. Reciprocating motion is produced in various ways. The most common method is by means of the crank. In Fig. 69, a shaft AB is urged backwards or forwards, (either vertically or horizontally.) by means of the crank a6, moving on a wheel H, which maybe turned by water or any other power acting at H. By considering the different positions of the crank during the revolution of the wheel, it will be readily seen that the shaft will move up and down like the saw in a saw-mill, or backwards and forwards, a use to which it is applied in polishing plane surfaces, as marble. The motion produced by cranks is easy and gradual, being most rapid in the middle Explain the universal joint. Describe the rachet wheel. Describe the eccentric wheel. How is reciprocating motion produced? Describe the crank. Explain the sort of motion produced by the crank. 113 MECHANICS. of th^ stroke, and graduaLy retarded towards the extremes ; so that shocks and jolts in the moving' machinery are diminished, or wholly prevented by their use. 149. The steam engine, as seen in steamboats, fur- nishes to the student of Mechanics a valuable opportunity of observing; various contrivances for producing, regulating, and modifying motion. Levers and wheels of various kinds and variously connected ; fly wheels and cranks ; circular and reciprocating motions ; and numerous other particulars which appertain to the " elements of machinery," are ther* seen to the greatest advantage CHAPTEE XII. OF THE PENDULUM, OF STRENGTH OF AND OF FRICTION. RIALS, THE PENDULUM. 1 50. The practical application of the Pendulum to three most important objects, namely, the measurement of time, the estimation of the figure of the earth, and as a standard of weights and measures, renders it peculiarly deserving of the attention of the student of Natural Philosophy. A Pcndt/him is a body si/sponded by aright line from any point, and moving freely about that point as a center. The point about which the pendulum re- volves, is called the center of siisjtension. The vibration of a pendulum, is its motion from a state of rest at the high- est point on one side, to the highest point on the other side. The center of oscilla- tion of a pendulum, is such a point that, were all the matter of the pendulum collected in it, the quantity of motion (or momentum) would be equal to the sum of the momenta of all the parts taken separately. Thus, the parts of the pendulum about b, (Fig. 70,) move faster than those about a. and consequently P i" Specify the ose of the steam engine in etudyiwEr the modes of regulating and modifying motion. Define the pendalum. What are its three mo-st im- portant applications ! Define the center of suspension— the vibrations of 8 pendulum — and the center of oscillation. PENDULUM. 119 have more momentum ; but there is a point about which the momenta balance each other, and therefore, in the investiga tions relating to the pendulum, all the parts of which it con- sists may be considered as concentrated in that point, The center of oscillation is below the Sknter of gravity ; for since the parts more remote from the center of suspension have more velocity than the parts that are nearer to it, the quantity of matter below the center of oscillation must be less than the quantity of matter above it. 151. The doctrine of the Pendulum is mainly comprised m the following propositiors. A pendulujn of given length performs its vibrations in equal times, wfiether it vib^-ates in longer or shorter arcs. Upon this property of the pendulum, depends its applica- tion to the measurement of time, as explained in Art. 114. 152« The times of vibration of pendulums of different lengths, are proportioned to the square roots of their lengths. Thus, a pendulum, in order to vibrate half seconds, is only one fourth as long as one that vibrates seconds, for 1 (the time of the longer) ; ^ (time of the shorter) : : %/ 1 : ^\ What must be the length of a pendulum to vibrate quar- ter seconds'? Ans. It must be -fV the length of the seconds pendulum, Jie square root of -(V being i of 1 ; and since the length of a pendulum beating seconds is about 39 inches, that of a pen- , dulum beating quarter seconds is ff =2.44 nearly. Ex. 3. What would be the length of a pendulum that should vibrate once in an hour, the length of the seconds pendulum being 39-iV inches ? Ans. 7997.7 miles, equal to the diameter of the earth, nearly. 153> The times of vibration of the same pendulum on different parts cf the earth's surface, are proportioned to the distances of these poinis from the center oftlie earth. Hence, the pendulum affords the means of measuring the heights of mountains, linA even of ascertaining the figure of the earth itself For, since the times of vibraTions are as the respective distances from the center of the earth, and since How is the center of oscillation .situated with respect to the center of gravity ? How are the times of vibrations of a pendulum of given leng;th ? Ditto of pendulums of ditferent length? How much shorter is a pendulum vibrating quarter seconds than vibrating seconds? What is the len^h of a pendulum that would vibrate once an hour 1 How are the times of vibratiou of the same peadulom, on different parts of the earth ? 120 MECHANICS. the longer the time occupied in one vibration, the smaller the number of vibrations in an hour, consequently the number of vibrations in an hour at the level of the sea would be to the number on the top of a mountain, as the distance of this last point from the ?enter of the earth, to the distance of the general level from the center. For example, a pendulum which vibrated seconds, or 3,600 times an hour, at the level of the sea, was found to vibrate only 3,590 times on the top of a high mountain ; what was the height of the mountain ? 3,590 : 3,600 : : 3,956* : 3,960, or nearly t-^ miles. 154« Again, the pendulum affords us the means of as- certaining tJteJigure of the earth; for by counting the num- ber of vibrations performed at various places on the earth's surface, (at the level of the sea.) we determine the ratio of the respective distances of those points from the center of the earth, those distances being inversely as the number of vibra- tions. Now, if these distances should be all equal to each other, then the earth would be found to be a perfect sphere ; but it is found by actual experiment, that the number of vi- brations increases as we advance from the equator towards the poles, indicating that the polar diameter is less than the equatorial. Example. If a pendulum which beats seconds at the equator, should be found to vibrate 3,613 times in an hour at the pole, how much less is the polar than the equatorial diameter ? 3,613 : 3,600 : : 4,000 : 3,985-s^. This result being subtracted from 4,000, (the equatorial radius,) leaves 14i\ miles, which, being doubled, gives 28-t^ miles, as the difference between the polar and equatorial di- ameters. A more exact determination is 26 miles. 155. A third important application of the pendulum, is, as a standard of linear measures. In order to insure confidence in business transactions, it is essential that the weights and measures employed should be and remain of a certain amount or length, — a condition which cannot be attained otherwise than by adapting them to a fixed and invariable standard. This must have two properties, namely, it must be constant or immutable in itself, and be easily capable of • The diameter of the earth is 7,9U miles. Explain how the pendulom is applied to measure the heights of mountains T also of ascertaining the figure of the earth ? Upon what principle is the pen- dulum adopted as the standard of linear measures ? STRENGTH OF MATERIALS. 121 verijicatio7i These conditions are secured by connecting It with the immutable laws of nature. The standard adopt- ed in France, is a certain aliquot part of the earth's circum- ference, which is called a Tneter ; but a better standard is the pendulum vibrating seconds, because, at any given place, it is of an invariable length, and because, if lost or out of order, another could be easily made. Several nations, therefore, make the length of the pendulum vibrating seconds, the unit of linear measure?, and the square, the unit of superficial measures. In the United States the yard is adopted as the unit, which being made to bear to the seconds pendulum a given ratio, is alike invariable in length. The standard of weight is a cubic foot of water, which being called 1,000 ounces, the value of the ounce, and of course of the pound, and of all other weights becomes determinate. STRENeTH OF MATERIALS. 156. The importance to the architect and the engineer, of ascertaining the form and position of the materials which he employs, in order to secure the greatest degree of strength and stability, at the least expense, has led mathematicians and writers on Mechanics, to devote much attention to this subject. How is the strength of a beam affected by giving to it different shapes and different positions; how must a given quantity of matter be disposed of in order that it may have the greatest possible degree of strength ; and upon what principles depends the stability of columns, roofs, and arches : these, and many similar inquiries, have been objects of pro- found investigation. 1 5 7 • The power of a regular beam, like a stick of tim- ber, to resist fracture when supported horizontally at the two ends, is proportioned to the. depth of the center of gravity below the up- Pig- ''i- per surface. Thus, an oblong beam ^ '^ is much stronger with its narrow than with its broad side upwards, as will be seen by inspecting Pig. 71 ; for the center of gravity being here the center of the stick, its depth EGr is greater when the nar- Strmgtkcf Materials.— VThy has this subject been stadied? What in- qairies does tt suggest ? To what is the strength of a stick of timber, placed horizontally, and resting on its two ends, proportioned 1 Which side of an oblong beam should be uppermost! Explain figure 71. .1 A 1 J ^ C D 122 MECHANICS. row bide is uppermost, than TSg, the depth, when the beam rests on its broad side. Thus, if a joist be 10 inches broad and 2^ thick, it will bear four times more weight when laid an its edge, than when laid fiat-wise. Hence the modern mode of flooring with very thin, but deep pieces of timber. A triangular beam is twice as strong when resting on its broad base, as when resting on its edge. For the center of gravity being f the distance from the vertex to the base, its depth is twice as great when the beam rests on its base as when it rests on its edge. This result of theory, however, has not been confirmed by experiment, but it appears to make no difference in the strength of a triangular beam, whether it rests on its broad base or on its edge. (Ren- wick's Mech. page 178.) These principles apply not only to beams, but to bars, and similar structures of every sort of matter. 158> The strength of any bar in the direction of its 'ength, is propmtional to the area of its transverse section. ' If a number of cords were hanging side by side from the same hook in the ceiling, they would be competent to sustain a weight as much greater than a single cord would sustain, as their number was greater than unity. Fifty cords, all bearing equally, would obviously bear fifty times as great a weight without breaking as a single cord would do. Nor would their power be altered by being placed closely in con- tact with each other so as to constitute one and the same cord. If, in the place of one of these strings, we suppose rows or particles of any kind of matter, the strength of the whole would be in proportion to their number, and this would be measured by the area of a cross section. Hence, the various shapes of bars make no difference in their abso- lute strength, since this depends only on the area of the sec- tion, and must obviously be the same when the area is the same, whatever be the figure. A rope, therefore, or a wire, to which a weight is appended, is as likely to break in one place as in another ; but when the weight of the rope be- comes considerable, and the force is applied perpendicularly, the increase of weight as its length increases, renders it more liable to break in the upper than in the lower parts. How nrnch stronger is a trian^lar beam on its broad base than on its nar row base ? To what is the strength of any bar in the direction of its leugtb proportioned ? State the example of a number of cords suspended from tlie ceiling and supporting weights. Is a rope or wire more liable to break in one place than another! STRENGTH OF MATERIALS. 123 159. The Strength of a beam lying horizontally is m versehj as tJte square of its length. Hence, a beam twice as long as another equal to it in all other respects, has only one fourth the strength. Long beams are weak from their own weight ; and the length may be so increased, that they will break from this cause alone. 160. Tim tendency to fracture on any part of a lurri- zontal beam supported at both ends, is proportional to the product of the distances of that part from the supported ends. In a common stick of timber, therefore, resting horizon- tally, like the joists of a floor, the liability to break is greatest in the middle, and decreases both ways to the ends ; for the product of the two halves is the greatest that can result from any two parts, and the more unequal the parts are, the less is the product. Consequent- ly, a beam, in order to be equally ^^" '^f^ strong throughout must be made tapering, being largest in the center, and growing less and less towards the ends. Exact cacluiation shows, that the true figure of such a beam is that whose section is an ellipse. The timbers which compose the horizontal part of the frame of a house, being usually rectangular parallelopi- peds of uniform dimensions throughout, it is manifest that a considerable portion of the material is wasted ; but in such cases, the attempt to save the material would be at- tended with paramount disadvantages. When, however, the material is expensive, or where lightness is important, as in many kinds of machinery, the foregoing principle may be applied with great advantage. 161. On the foregoing principles. Dr. Gregory makes the following remarks, most of which were originally sug- gested by Galileo, to whom we are indebted for the earliest investigation of these propositions. From the preceding de- duction (says Gregory) it follows, that longer beams and bars must be in greater danger of breaking than less similar ones ; and that, though a less beam may be firm and secure, How is the strength of a horizontal beam proportioned to its length ? "Why are long beams weak ? To what is the tendency of a horizontal beam to break at diiferent points, proportioned? What must be the shape of a beam to be equally strong throughout ? Are beams of this shape used in houses? In what cases are they employed } Which are most liable to break, long beams or short ones ? i 124 MECHANICS. yet a g^reater similar one may be so long^ as necessarily to break by its own weight. Galileo justly concludes, that what appears very firm, and succeeds well, in models may be very weak and unstable, or may even fall to pieces by its weight, when it comes to be executed in large dimensions, according to the model. From the same principles he argues, that there are necessarily limits in the works of nature and art, which they cannot surpass in magnitude ; that im- mensely great ships, palaces, temples, &c., cannot be erect- ed, since their yards, beams, bolts and other parts of theii frame, would fall asunder by their own weight. Were trees of a very enormous magnitude, their branches would, in like manner, fall off Large animals have not strength in propor- tion to their size ; and if there were any land animals much larger than those we know, they could hardly move, and would be perpetually subjected to the most dangerous acci- dents. As to marine animals, indeed, the case is different, as the specific gravity of the water sustains those animals in a great measure ; and in fact, these are known to be some- times vastly larger than the greatest land animals.* It is (says Galileo) impossible for nature to give bones to men, horses, or other animals, so formed as to subsist, and.pro- portionally to perform their ofEces, when such animals should be enlarged to immense heights, unless she uses matter much firmer and more resisting than she commonly does ; or should make bones of a thickness out of all proportion ; whence the appearance and figure of the animal must be monstrous. Hence we naturally join the idea of greater strength and (brce with the grosser proportions, and that of agility with the more delicate ones. The same admirable philosopher likewise remarks, in connection with this sub- ject, that a greater column is in much more danger of being broken by a fall than a similar small one ; that a man is in greater danger from accidents than a child ; that an in- sect can sustain a weight many times greater than itself, whereas, a much larger animal, as a horse, could scarcely carry another horse of his own size. 162. Tlie lateral strengths of two cylinders, of tlie same * Whales in the Northern Regions, are sometimes found sixty feet long, and weighing seventy tons. Are structares stronger or weaker, proportionally, than their small models 7 What would be the consequence were trees much larger tlian they are ? State the case of large land animals and of marine animals. State the comparative liability of a man and a child to receive injury from falling — strength of insects. FEICTIOP* 125 matter, and of equal weight and length, one of which is hoi- hno and the other solid, are to each other as the diameters of their sectimis. The strongest form, therefore, in which a given quantity of matter can be disposed, is that of a hollow cylinder. From this proposition Galileo justly concludes, that Nature in a thousand operations, greatly augments the strength of sub- stances without increasing their weight ; as is manifested in the bones of animals, and the feathers of birds, as well as in most tubes or hollow trunks, which, though light, greatly resist any effort to bend them. Thus, (says he,) if a wheat straw, which supports an ear that is heavier than the whole stalk, were made of the same quantity of matter, but solid, it would bend or break with far greater ease than it now does. And with the same reason, art has observed, and ex- perience confirmed the fact, that a hollow cane, or tube of wood or metal, is much stronger or firmer, than if, while it continues of the same weight and length, it were solid ; as it would then, of consequence, be not so thick. For the same reason, lances, when they are required to be both light and strong, are made hollow. 163« The term Friction, in its usual acceptation, being generally understood, we have already employed it in the foregoing pages ; but we now proceed to inquire more par- ticularly respecting its nature, the laws of its action, and its effects upon machines. In investigating the mathematical principles of mechan- ics, we first proceed on the supposition that the forces in question act without any impediment; that the surfaces which move in contact are perfectly polished and suffer no friction ; that axes and pivots are mathematical lines and points ; that ropes are perfectly flexible ; and, in short, that the power is transmitted through the machine to the work- ing point without sustaining the least loss or diminution. Great simplicity is attained by first bringing the subject to this ideal standard of perfection, and afterwards making suit- able allowances for all those causes which operate in any given case to prevent the perfect action of a machine. What is the strongest form in which a given quantity of matter can be disposed? Examples of such forms in nature and art. Friction. — In the mathematical theory of mechanics, is any allowance made for friction or othel impediments 1 Why are these at first neglected 7 11* 1 26 MECHANICS 164. Surfaces meet with a certain degree of resistance in moving- on each other, in consequence of tJie mutual co- hesion of tlie parts ; a principle which has the greater influ- ence in any given case, in proportion as the surfaces are smooth. But a much greater resistance arises from the asper ities which the surfaces of all bodies have, though in verydif ferent degrees, according to their difl^erent degrees of smooth ness. An extreme case is that of two brushes moving on each other, the hairs of which become interlaced, (especially when the brushes are pressed together.) and oppose a great resistance. Even bodies apparently very smooth, as polished metals, exhibit under the microscope numerous inequalities. Under the solar microscope, the finest needle exhibits a sur- face as rough as the coarsest iron tools do when viewed by the naked eye. To these inequalities of surface, is princi- pally ascribed the friction of bodies when closely in contact; the prominent parts interlock with one another, or meet, and must be broken down before the surfaces can move. Hence, friction is diminished by processes which level these inequal- ities, either by polishing the surface or by covering it with some lubricating substance which fills up the cavities. 165> Forces of this nature, which act by the resistance they occasion to motion, are called passive forces. They pro- duce very different effects in machines when in a state of equilibrium, and in a state of motion. In the one case they assist the power : and in the other case they oppose it. Thus, a weight placed on an inclined plane, will require a less power to support it in consequence of the friction of the plane; and a weight suspended by a rope passing over a pulley vi'ill require a less weight to balance it, on account of the friction of the axle. But the same passive forces operate in just the contrary way when a machine is to be put in mo- tion ; for then a power must be applied, which is sufficient not only to overcome the weight itself, but also the amount of all the resistances. For example, in order to draw a load up an inclined plane, we have to overcome not only the force of gravity by which the load endeavors to descend down the plane, but also the amount of the friction and all the other resistances which impede its motion, although the load would be kept from descending, that is, in a state of equilibrium, by a less force in consequence of these resistances. The What are the sources of friction ? What is there in the nature of the sur- faces of hodies which occasions friction ? How is friction diminished ? What are passive forces ? In what case do they assist the power ? In what case do they oppose it 1 FRICTION. 127 principle is most strikingly observed in the wedge, where the difficulty of making the wedge advance, is greatly in- creased by friction, but the same cause operates to prevent it from recoiling. 166. The forms under which this sort of resistance pre- sents itself are chiefly of two kinds, namely, that of bodies sliding, and of bodies rolling on each other. To the former of these let us first attend. Experiments on the friction of sliding bodies may be made, either by placing them on a table, and observing the weights which they respectively re- quire to drag them along the table, or by placing them on an inclined plane, and observing at what angle the plane must be elevated in order that the body may begin to slide. In the former case, the table is prepared by attaching a vertical pulley to one edge, over which a string is passed, one end being connected to the body in question, and the other end to a pan, like that of a balance, for containing weights. From this simple arrangement, a great variety of particulars may be ascertained respecting the friction of sliding sur- faces. A body shaped like a brick, with a broader and nar- rower side, may be tried on each of its sides separately, and thus it may be seen whether, in a given weight, the extent of surface of contact makes any difference ; the body may be loaded with different weights, and hence may be learned the influence of pressure upon friction ; the body may be tried as soon as it is laid on the table, and after remaining on it for a longer or shorter time; in order to learn whether this cir- cumstance alters the friction ; dif- ferent kinds of bodies may be tried, and the influence of different materials ascertained ; and finally, by dragging the body off the table with different degrees of velocity, the relation of friction to velocity may be investigated. 167. From experiments like the foregoing, endlessly va- ried, the following conclusions have been established : (1.) In a given body, extent of surface makes no differ- ence in regard to friction ; a brick laid on its edge meets with the same resistance from this cause as when laid on its side. Fig. 73. How exemplified in the wedge ? How are experiments on sliding bodies made ? Describe the arrangement with a table and balance. Does extent of surface make any difierence ? 128 MECHANICS. (2.) Friction is proportioned to the pressure. If the pressure of the brick be doubled or trebled by laying weights upon it, the amount of friction will be increased in the same ratio. (3.) Friction is increased by bodies remainuig for some time in contact loith each other. In some cases it does not reach its maximum under four or five days. This principle, therefore, affects slow motions much more than such as sure rapid. In the mutual contact of metals, the friction attains its maximum almost instantaneously. But when metal rubs against wood, or one piece of wood against another, the fric- tion is always increased by resting. (4.) The friction is less between surfaces oi different kinds of matter, than between those of the sarae kind. Copper slides on copper, or brass on brass with greater difficulty than copper on brass ; and it is a general rule never to let two substances of the same hardness move upon each other. To this rule, cast steel is said to form the only exception ; in other cases pivots revolve with less resistance on either hard- er or softer substances than upon those of the same material with themselves. When between the surfaces of wood neat- ly planed, the friction would be equal to one half the press- ure ; and when between two metallic surfaces, it would be equal to one fourth ; between the wood and metal, it would amount to only one fifth the pressure. (5.) Friction is much greater at the first moving of a load, than after it is brought freely into motion. In many instan- ces it is reduced, when a body has attained its final veloci- ty, to less than one half of what it was at first. With regard to different degrees of velocity in moving bodies, it is a gen- eral principle, that ttie friction is tJie same for all velocities ; that a carriage, for example, in travelling from one place to another, would encounter the same resistance from friction, whether it performed the journey in one hour or in ten. The amount of friction, however, is augmented in very slow mo- tions, and greatly diminished in those that are very swift. In this instance, the increase in the one case and the dimi- nution in the other, appears to have some relation to the principle, that the friction of bodies is increased by their re- How is the friction related to the pressure ? How affected by bodies re- maining long in contact? How is the friction between bodies of different &inds ? What substance forms an exception ? Amount of pressure between wood and metal 1 Amount of friction at first moving a load — how much is it reduced when a body has reached its final velocity ? "When a body moves over the same space with different velocities, how is the iiriction ? TTRICTION. 129 maining in contact From some observations of Professor Playfair, made at the Slide of Alpnach, where large fir trees are carried with great velocity down an inclined plane eight miles in length, it would appear, that in the case of very great velocities, friction is not, according to the common doc- trine, either proportioned to the pressure or independent of the velocity ; but that the ratio to the pressure is greatly diminished, and the actual resistance is far less than at com- mon velocities Thus, none but large trees could descend the plane at all ; and when a tree broke into two pieces, the larger part would proceed while the smaller would stop ; and the trees acquired in their descent a rapidity of motion, in- compatible with the supposition that " friction acts as a uni- formly retarding force," which has been considered as an es- tablished principle. The foregoing considerations are in favor of rapid travel- ling, whether on common roads or on railways, since the amount of the resistances is so much less than in slow move- ments ; and accordingly it is said, that the great speed given to stage coaches in England, amounting in some instances to ten or twelve miles per hour, has not been attended with the degree of exhaustion to the teams that would have been anticipated. 168« The laws of friction in rolling bodies are ascer- tained by comparing the forces necessary to roll a cylinder upon a table under various circumstances ; and by similar experiments are found the tnodes in which friction takes place in bodies revolving on an axis. The comparative loss of power which takes place in these three cases, is as fol- lows: Friction of the sliding body is equal to -J- the pressure or 25 per cent. _ Friction of the revolving body 15 per cent. do. rolling do 5 " 169. Friction Wheels, a contrivance by which friction is diminished in the greatest degree possible, owe their effi- cacy in part to the operation of the same principle. Here the axis of a wheel, instead of revolving in a hollow cylin- der, or instead of rubbing against a fixed surface, rests, at each of its extremities, on the circumference of two wheels Relate the facta observed at the Slide of Alpnach. Do the doctrines o' friction favor slow or rapid travelling ? How are the laws of iriction in rotting bodies investigated ? What is the comparative amount of friction in sliding, revolving, and rolling bodies ? What is the construction of friction wheels ! 130 MECHANICS. Fig. 74. placed close by the side of each otner, with their circum- ferences intersecting The axis rests at the point of inter section, and as it revolves, the wheelt revolve with it with the same ve- locity, and thus all friction between them and the axis is prevented, and what remains in the machine in con sequence of the weight of the wheels themselves, is transferred to their axles, and therefore is diminished, in the ratio of the diameter of one of the wheels to that of its axis. This combination may be repeated by several pairs of friction wheels. Bight wheels would contract the friction to the thousandth part. Fig- ure 74 represents the friction wheels usually employed in Atwood's Machine (Fig. 5.) instead of the single wheel in that figure. 170. Other more common methods of diminishing fric- tion are, by rendering the surfaces smooth, by using rollers, and by lubricating the parts in contact. The amount of friction in the several mechanical powers is very different. In the Lever it is very small, especially when the turning edge is of hardened steel and shaped like a knife or prism, and turns upon a hard and smooth basis. The Wheel and Axle, acting upon the same principle as the Lever, occasion but little friction. The stiffness of the cordage, however, and the friction of the gudgeons of the axis, have an effect in most cases equal to about 8 or 10 per cent, of the entire resistance. The Pulley is attended with great loss from this source. It is rarely less than 20 per cent, and often exceeds 60. The Inclined Plane involves but little friction when bodies simply roll on it ; but when heavy bodies rest on axes, as in wheel carriages, the resistance from friction takes place in the same manner as upon plane surfaces. The transportation on inclined planes, as railways, is usually by means of wheels, since the resistance to sliding movements is too great to permit the use of them. The Screw is attend- ed with a great deal of friction. Those with sharp threads have more than those with square threads, and the endless screw has most of all. In both the Screw and the Wedge, How mach wonld eight friction wheels diminish the friction ? What are the methods of diminishing friction ? Specify the comparative amount of Action in the lever, the wheel and axle, the pulley, the inclined plane. FRICTION. 13 1 the friction evidently exceeds the resistance ; otherwise they would not retain their position. 171. Friction is not, therefore, in all cases to be con- sidered as unfavorable to the operation of machinery. It is, in many instances, a highly useful force. Many structures, as those of brick and stone, owe no small part of their stability to the roughness of the materials of which they are composed ; without this resistance, the screw and the wedge would lose their efficacy, and wheels could not ad- vance, nor could animals walk on the ground ; and nails would lose their power of binding separate parts together. The art of polishing surfaces defends on the same cause, and the edges of most cutting instruments are saws, the teeth of which are more or less fine, and act on a similar principle. Even in certain rotary motions, friction becomes a moving force, and urges a body in particular directions contrary to the force of gravity. Specify the comparative amount of friction in the screw and in the wedge, la the friction always to be considered as a loss 1 Bpecify its uses PART 11— HYDROSTATICS. CHAPTEK I. OF FLUIDS AT REST. 172. The principles of Mechanics, demonstrated cand explained in the foregoing pages, are universal in their ap- plication, extending alike to all bodies, whether solid or fluid. But in addition to those properties which fluids have in common with solids, and which bring them under the general laws of Mechanics, they have also properties peculiar to themselves, which give rise to a distinct class of mechan- ical principles, not applicable to solid bodies. These are embraced under the heads of Hydrostatics and Pneumatics, the former division comprising the doctrine of liquids, and .e latter that of aeriform bodies, including vapors and gases. 1 7 3. .A FLUID is a body whose particles inove easily among themselves, and yield to the least force i?npressed, and which when that force is removed, recovers its previous state. Since water, wind, and steam, are the only fluids that are usually employed as mechanical agents, the doctrines of Hy- drostatics and Pneumatics have regard chiefly to them ; but the principles established respecting these, are applicable also to all analogous bodies. It has been usual to denominate liquids and gases respec- tively elastic and non-elastic fluids, on the supposition that water and other liquids are nearly or quite incompressible. An experiment performed by the Florentine academicians, as long ago as 1650, seemed to prov« that w^ater is wholly incompressible. They filled a hollow ball of gold with water, and subjected it to a strong pressure. The water, not Hydrostatics. — To what bodies do the principles of Mechanics apply ? What is said of the peculiar properties of fluids 1 To what new heads do these properties give rise 1 Define a fluid. What fluids are employed as mechanical agents ? Are liquids elastic or non-elastic ? FLUIDS AT REST. . 133 yielding to the compression, oozed through the pores of the gold. Considering the great density and compactness of this metal, the experiment was for a long time held as proving decisively that water is wholly incompressible. Although this experiment shows that water is compressed with great difficulty, yet later experiments have proved, that it is still capable of compression. The most decisive evidence of this point has been recently afforded by the experiments of Mr. Perkins. It has been previously ascertained, that by a press- ure equivalent to that of the atmosphere, or about fifteen pounds to the square inch, water is compressed about one part in twenty-two thousand. Mr. Perkins, by methods to be de- scribed hereafter, applied successive degrees of pressure up to that of two thousand atmospheres, and found the contraction of volume to increase nearly in the ratio of the compressing force. 174. Hydrostatics is that branch of Natural Philoso- phy which treats of the mechanical properties and agencies of LIQUIDS. 1 7 5 • Fluids at rest press equally in all directions. A point in a mass of fluid, taken at any depth, exerts and sustains the same pressure in all directions, upwards, down- wards, or laterally. This is the most remarkable property of fluids, and is what particularly distinguishes them from solids, which press only downwards, or in the direction of gravity. This property naturally results from the freedom of motion that subsists between the particles of fluids ; for if, when a fluid is at rest, the pressure on any given portion were not equal in all directions, that portion would move in the direction in which the resistance was least. But by the supposition it does not move : therefore it is kept at rest by equal and contrary forces acting on all sides. But the most satisfactory evidence of this truth is obtained from experi- ment. On opening an orifice in the side of a vessel of wa- ter, and estimating the force with which the water issues, it is found to be equal to the weight of the incumbent fluid ; and the upward pressure of water at a certain depth is found to sustain the heaviest bodies when exposed to its action alone, the column above the bodies and of course the down- ward pressure being refnoved. 176. A given pressure or blow impressed on anypm tion Mention the experiments of the Florentine academicians. Mention the experiments of Mr. Perkins. What was the result ? Define Hydrostatics. What is the law of pressure of Uuids at rest ? What is the distinguishing property of Haids ? From what property of fluids does this equality of press- ure result ? What experiment proves it ! 12 134 HYDROSTATICS. of a mass of water confined in a vessel, is distributed equally through all parts oftlie mass. A given pressure, as that made by a plug forced inwards upon a square inch of the surface of a fluid confined in a ves- sel, is suddenly communicated to every square inch of the vessel's surface, however large, and to every inch of the sur- face of any body immersed in it. Thus, if I attempt to force a cork into a vessel full of water, the pressure will be felt, not merely by the portion of the water directly in the range of the cork, but by all parts of the mass alike ; and the lia- bility of the bottle to break, supposing it to be of uniform strength throughout. Avill be as great in one place as another ; „._^ and a bottle will break at the point where °' " it happens to be weakest, hovsrever that point may be situated relatively to the place where the cork is applied ; and the effect will be the same whether the stopper be inserted at the top, the bottom, or the side of the vessel. In figure 75, a piston forced down upon the surface of the water in a jar, in- dicates an equality of pressure upon all sides of an inflated bladder B suspended in the center. 177. It is this principle which operates with such aston- ishing effect in the Hydrostatic Press, by means of which a single man can exert a force equal at least to 25,000 lbs., and adequate to crush the hardest substances, or cut in two the largest bars of iron. Its construction is as follows. Fig. 76 represents a press made of the strongest masonry. A is a large and a a small cylinder communicating with each other, and both containing water. PS is a movable piston, press- ing on its upper side a weight W against a strong beam R. In the narrow tube a is a piston s worked by a lever bd, which moves in a fulcrum at c. At i> is a valve opening upwards and admitting water freely from the well below. Now when the piston s is worked, as in a common pump, the water rises into the lube a ; but on depressing s, the water is forced into A, and the whole force acts on S to com press the weight W. Now, since whatever force is applied to any one portion of the fluid, extends alike to every part, therefore the force which is exerted by the pump upon the smaller column, is transmitted unimpaired to every inch of How is the pressure or blow on any part of a confined mass of fluid dis- tribated i GKve examples. Hydrostatic Press — describe it from Fig. 76. FLUIDS AT REST. 135 the larger column, and tends to raise the plank P with a force as much greater, in the aggregate, than that impressed upon the surface of the smaller, as this surface is smaller than that of the larger column ; or (which is the same thing) as the number of square inches in the end of the piston s is less than that of the piston S. The power of such a machine is enormously great ; for, supposing the hand to be ap- plied at the end of the handle, with a force of only ten pounds, and that this handle or lever is so constructed as to multiply that force but five times, the force with which the smaller piston will descend will be equal to 50 lbs. ; and let us suppose that the head of the larger piston contains the smaller 50 times, then the force exerted to raise the press board, will equal 2,500 lbs. A man can indeed easily exert ten times the force supposed, and can therefore exert a force upon the substance under pressure equal to 25,000 lbs. This apparatus is used in pressing books, paper, cloth, hay, cot- ton, and all similar substances ; in extracting oils from seeds or spermaceti ; in uprooting trees ; in testing the strength of ropes, and showing the compressibility of liquids ; and in all cases where it is required to exert an immense force through a small space. ,178. The rationale of the principle of the Hydrostatic Press, will be best understood by recurring to the following Show how the whole force commanioated to the smaller colnmn is transmit- ted to the larger. What amoant of force can a man exert with his naked handst 136 HYDROSTATICS. principles, — that opposite forces are in equilibrium when their momenta are equal ; that a small power may be made to balance a great weight, by making it move, in a given time, over a space as much greater than the larger does, as its weight is smaller ; and that it may be made to overcome that resistance or weight, and give motion to it. if its velo- city is greater than that of the latter in a still higher ratio. Now to apply these principles to the case before us, it is evi- dent that any quantity of water forced out of the smaller into the larger cylinder, must rise in the latter as much slower as the area of the horizontal section is larger. If, for exam- ple, the capacity of the larger cylinder were ten times that of the smaller, then a quantity of water one inch in height, transferred from the smaller to the greater cylinder, would occupy only the height of one tenth of an inch, and conse- quently the depression of the small piston one inch would raise the large one only the tenth of an inch. This case, therefore, resolves itself into that general principle, accord- mg to which a vast force is exerted through a short dis- tance, by moving a small force through a distance much greater. The exertion of a powerful force through a small space, is usually what is required in a press ; and since this force acts with far less loss by friction than the screw, it is proportionally more efficacious and economical. 179. Tlie surface of a fluid at rest is horizontal. The evidence of the truth of this proposition is threefold. First, this result is a natural consequence of the mobility of fluids, since, if any portion is raised above the rest, having nothing to support it, and being acted on by gravity, it must descend in the same manner as a body placed on a perfectly smooth inclined plane. Secondly, whenever a body is fret to move, its center of gravity will descend as low as possible. When, therefore, any portion of a fluid is raised above the general level, the center of gravity of the mass is raised, and it must return before the fluid can be at rest. Thirdly, ex- perience shows that the proposition is true, since fluids, when free to move, always settle themselves with their surfaces parallel to the horizon. It must be understood, however, that the surface of large bodies of water is not, strictly speak- ing, a horizontal level, but is a portion of the convex surface of the earth ; for since the center of gravity of every portion Explain the pnnciple of the Hydrostatic Press. Through how much leas space does the iiaid rise in tlie larger than the smaller tube 1 Why is this force more efficacious and economical than the #crew ? How is the surface of a fluid at rest ! What evidence have we that a fluid at rest is parallel to the horizon ? Are the surfaces at large bodies of water horizontal planes ? FLUIDS AT REST. 137 of the fluid will descend as low as possible, the whole will dispose itself around the center of attraction so as to form a portion of the earth's surface. For small distances, as those occupied by a building or a machine, the curvature is so slight that it may be neglected ; for at the distance of a mile the depression below the tangent drawn at the place of the spectator, is only 7 inches ; but it increases with the square of the distance. Thus at the distance of 10 miles, it is 100 times as great, or 700 inches, equal to 58-^ feet. Upon this principle we shall find that, when raised 30 feet above the earth, as on the top of a house, we can see in every direction about 7 miles ; and on a mountain a mile high, we can see about 95 miles. How far can one see in all directions from the summit of Mont Blanc, say \.5,QlWfeet? Ans. nearly 160 miles 180. A practical application of this principle is made m the art of levelling. The spirit level (Fig. 77,) is the instrument more commonly em- ployed for this pur- ^'S- '''■ pose. This consists of a small cylindrical tube of glass, from two to six inches long, filled with spirits of wine or ether, except a small space, which is occupied by a movable bubble of air. When such a tube is placed horizontally, the bubble of air will remain stationary in the center of the tube, at a fixed mark ; but whenever the tube is inclined, in the least de- gree, the bubble will ascend towards the elevated end. Levels are much used for ad- justing astronomical, survey- ing, and other delicate in- struments. The water level (Fig 78,) s used for determining when two distant points, as P and Q, are on a horizontal level. This is the case when each, wewed from opposite direc- tions, is in a line with the two surfaces A and B. f Ayiiat is the actual figure of the surface 1 WTiat is the deviation from a straight line in 1 00 feet ? How much in a mile ? On what i.s the art of levelling founded ? Describe the spirit level — also the water level. 12* Pig. 78. 138 HYDROSTATIOS. Fig. 79. 181. The jrressure upon any particle of a fluid of uni- form density, is proportioned to its depth below the surface. Thus in Fig. 79, the pressure ex- erted by the fluid at different depths, as X and y. is exactly proportioned to their depth below the surface, so that if y be twice as deep as a;, a body a y would sustain twice as much press ure as at %. This holds good also when the column is inclined, the press- ure on the base AC being the same whether the column is perpendicular or inclined, provided the height above the plane is the same. For although the inclined column is longer than the other, yet the weight of the fluid is partly sustained by the lower side of the vessel, so as exactly to compensate for its greater length. According to Art. 175, the lateral is equal to the down- ward pressure ; and consequently on this principle may easily be estimated the amount of pressure on the sides of any col- umn of water, or on the banks of rivers, canals, &c. At the depth of 8 feet, the pressure on a square foot is equal to the weight of a column of water, whose base is 1 foot and depth 8 feet, and consequently its solid contents 8 cubic feet ; and since 1 cubic foot of water weighs 1000 ounces, or 6-2-i lbs., therefore the weight of the column = 8x62-i=:500 lbs. Hence the pressure on a square foot, at different depths, will be as in the following table. )th in feet. Pressure on a square foot. 8 500 lbs. Depth in 56 feet. Pressure on a square foot. 3500 lbs. 16 1000 64 - 4000 24 1500 72 4500 32 2000 80 5000 40 2500 88 - - 5500 48 - - 3000 96 6000 1 mile, or 5280 feet, 5 miles, 330,000 lbs. 1,650,000 It appears that at the moderate depth of 64 feet, the press- ure of a column of water on the bottom or sides of the What is the pressure on a square foot at the depth of 8 feet in a column of water 1 State the pressure at several different deptlis, as at 32, 48, 56 and 60 feet. Also at the depth of 1 mile, and 5 miles. FLUIDS AT REST. 139 containing pipe, becomes 4 000 lbs. to the square foot; and the pressure on the bottom of the sea, where it is one mile inuiepth, is 330,000 lbs. to the square foot, and where it is five miles deep that pressure is no less than 1,650,000 lbs.* From these considerations we may readily apprehend the cause of the great difhoulty experienced in confining a high column of water ; and hence also may be inferred the im- mense pressure that is exerted on the bottom of the sea. 182. Indications of this vast pressure in deep waters, are manifested by several interesting facts. It has long been known to mariners, that if a common square bottle be let down into the sea, its sides are crushed inwards before it has reached the depth of ten fathoms. If a stronger bottle, (a common junk bottle, for example) be filled with water, corked close, and let down to a certain depth, either the cork will be forced inwards, or if that is secured in its place, the salt water will make its way into the bottle in spite of it, either by compressing the cork, or by forcing in water through it. It was by sinking an apparatus to the depth of 500 fathoms, that Jlr. Perkins first proved the compressi- bility of water, as mentioned in Art. 173. The apparatus consisted of a hollow brass cylinder resembling a small can- non, and furnished with a stopper so contrived as to indicate, when the apparatus was drawn up, how far it had been driven in while at the lowest depth. The same experiments were afterwards repeated on shore, a pressure being applied to the plug, by means of the hydrostatic press, equivalent to 2,000 atmospheres or 30,000 pounds. The increase of pressure in proportion to the depth of the fluid renders it necessary to make the sides of pipes or ma- sonry, in which fluids are to be contained, stronger the deeper they go. The same remark applies to dams, flood-gates, and banks. At the depth of 1,000 fathoms, the compression of water is one twentieth of its bulk, and its specific gravity is in- creased in the same ratio ; so that bodies which sink near the surface of the sea, may float at a certain depth before they reach the bottom. On the other hand, a porous body State examples of ludications of this vast pressure at different depths Case ot a junk bottle— experiments of Mr. Perkins. How great a pressure did Perkms apply by means of the hydrostatic press ? In what parts do cisterns require to be made strongest? What is the compression of water at the depth of 1000 fathoms ? 140 HYDROSTATICS. that is light enough to float near the surface, will have so much water forced into its pores, when it is sunk to a great depth, as never to rise. This is the case with ships that are wrecked in deep water ; the parts of the wreck do not rise to the surface, as they do in shallow water. 183. When a portion, as a square foot, of the lateral sur- face of a column of water, is taken, all parts of it are not equally distant from the surface of the fluid ; and, in this case, the average depth, or (which is the same thing) the depth of the center of gravity, is to be understood according to the following proposition, which applies to every sort of surface, however inclined to the horizon. The pressure of a fluid against any surface, in a direction perpe7idicvlar to it, varies as the area of the surface multi- plied into the depth of its center of gravity below tlie surface of the fluid. Hence, the pressure on the side of the cubical vessel, filled with fluid, is one half the pressure against the bottom ; and the whole pressure against the sides and bottom, is equal to three times the weight of the fluid of the vessel. 184. Fluids rise to tlie same level in tlie opposite arms of a recurved tube. Let ABC, (Fig. 80.) be a recurved tube ; if water be poured into one arm of the tube, it will rise to the same height in the other arm. For, by Art. 181, the pressure upon the lowest part at B, in opposite directions, is proportioned to its depth below the surface of the fluid. Therefore, these depths must be equal ; that is, the heights of the two columns must be equal, in order that the fluid at B may be at rest ; and unless this part is at rest, the other parts of the column cannot be at rest. Moreover, since the equilibrium de- pends on nothing else than the lieights of the respective columns, therefore, the op- posite columns may differ to any degree in quantity, shape, or inclination to the hori- zon. Thus, if vessels and tubes very Case of ships wrecked in deep water. In inclined and extended .surfaces, how is the depth to be estimated ? What is the pressure on the side of a cubical vessel iilled with water 1 What is the whole pressure on the sides and bottom V To what heights do fluids rise in the opposite anas of a re- curved tube ? FLUIDS AT EEST. 141 diverse in shape and capacity, as in Fig. 81, be connected with a common reservoir, and water be poured into any one of them, it will rise to the same level in them all. Fig. 81. The reason of this fact will be farther understood from the application of the principle of Virtual Velocities, (Art. 135 ;) for it will be seen that the velocity of the columns, when in motion, will be as much greater in the smaller than in the larger columns, as the quantity of matter is less ; and hence the opposite momenta will be constantly equal. Hence, water conveyed in aqueducts, or running in natu- ral channels, will rise' just as high as its source. Between the place where the water of an aqueduct is delivered and the spring, the ground may rise into hills and descend into valleys, and the pipes which convey the water may follow all the undulations of the country, and the water will run freely, provided no pipe is laid higher than the level of the spring. Waters running in natural channels in the earth are gov- erned by the same law. The aqueducts constructed by the ancient Eomans were among the most costly ornaments of their arts. Several of them were from thirty to one hundred miles in length, and consisted of vast covered canals, built of stone. They were carried over valleys and level tracts of country upon arcades, which were sometimes of stupendous height and solidity. From the fact that the ancients built aqueducts with so much labor, raising them- to a great height in crossing valleys, instead of availing themselves of the principle under consid- Does the shape of the vessel make any difference 1 How is equality of the height in vessels of varioos figures to be explained 1 How high will water rise in aqueducts 1 Give an account of the aqueducts of the ancient Bomans. 142 HYDROSTATICS. Fig. 83. eration, some have supposed that they were unacquainted with this principle. It appears, nevertheless, that they were acquainted with it, and even understood the use of pipes in conveying water ; but probably the expense of pipes and the difficulty of making them strong enough to resist the press- ure when laid at a considerable depth below the source, pre- vented their general use. '^ 185. "nie pressiire upon the Iwrizontal base of any ves- sel containing a fluid, is equal to tJie weight of a column of tlte fluid, found by multiplying the area of the base into tlie perpendicular height of tlie column, wJiatever be the shape of tlie vessel. This follows from Art. 183, since, here the distance of the center of gravity from the surface of the fluid, is the same as the perpendicular height of the column. With a given base and height, therefore, the pressure is the same, whether the vessel is larger or smaller above, whether its figure is regu- lar or irregular, whether it rises to the given height in a broad open funnel, or is carried up in a slender tube. Hence, any quantity of water, however small, may be rrmde to bal- ance any quantity, however great. This is called the hydrostatic paradox. The experiment is usually performed by means of a water bellows, as is represented in Fig. 8i. When the pipe AD is filled with water, the pressure upon the surface of the bellows, and consequently the force with which it raises the weights laid on it, will be equal to the weight of a cylin- der of water, whose base is the surface of the bellows, and height that of the column AD. Therefore, by making the tube small and the bellows large, the power of a given quantity of water, how- ever small; may be increased indefinitely, The pressure of the column of water in this case corresponds to the force applied by the pistou in the Hydrostatic Press, (Art. 177,) and the explanation according to the principles of virtual velocities, is the same in both cases. Why did they not convey water in pipes? To what i.s the pressure on the horizontal base of any vessel containing a fluid equal ? What is the hydrostatic paradox! How is the experiment performed? Describe the apparatus. SPECIFIC GRAVITY. 143 1 86. In Fig. 83, the pressure on the base CD is the same as thoagh the vessel were filled with water to the level EF. For the upward pressure upon BP or PA is such as just bal- ^'S- st- ances that of the column PGr, as in the hydrostatic paradox. But the downward pressure at BP is just equal to the upward, and is therefore also equivalent to that of a column of water EBPG. It must not be inferred from this, that a given quantity of water will weigh more in one shaped vessel than in another ; for although the pressure on the base CD is increased by the peculiar form of the vessel, and would of itself tend to increase the weight, yet this effect is exactly counterbalanced by the upward pressure exerted on BP, . / SPECIFIC GRAVITY. /\ 187. The Specific Gravity of a body, is its weight com- pared ivith the weight of anoifier body of the same bulk, taken as a standard. Water is the standard for all solids and liquids, and com- mon air for the gases. Therefore, the specific gravity of a solid or a liquid body is the ratio of its weight to the weight of an equal volume of water ; and the specific gravity of an aeriform body, is the ratio of its weight to the weight of an equal volume of air. But a ratio is expressed by a vulgar fraction, whose numerator is the antecedent, and whose de- nominator is the consequent. If, therefore, the weight of a body is made the numerator, and the weight of an equal vol- ume of water the denominator, the value of the fraction, that is, the quotient, will express the specific gravity of the body. Hence, the weight of a body being given, and being made the numerator, every process for finding the specific gravity consists in finding for the denominator the weight of an equal bulk of water or air. The principles upon which the meth- ods of doing this depend, are now to be explained. Can a g:iven quantity of water exert a pressure in a vessel greater than its own weight ? Define Specific Gravity. What substance is the standard for liquids and solids 1 What for bodies in the form of air 1 How i» the specific gravity of a body expressed by a fr»ction ? 144 HYDROSTATICS. Fig. 84. 188. A body immersed in a fluid, loses as rmtch weight as is equal to tlie weight of an equal volume of the fl-Hid. Let EF (Fig. 84,) be a solid body immersed in a vessel of water or any fluid, and suppose it divided into an indefinite num- .ber of perpendicular columns^ reaching to the surface of the fluid, as m n. Novir the up- ward pressure at n is as its depth, and the downward press- ure at o as its depth ; therefore the upward pressure exceeds the downward, by the weight of a column of water equal to n o. The same is true of all the columns, however numerous they may be. that can be drawn parallel to n o; but these col- umns, taken collectively, make up a body of water equal in bulk to the solid. Therefore, the solid is pressed upwards, more than downwards, by the weight of a quantity of watei of the same magnitude, and consequently loses so much of its weight. Hence, the specific gravity of any solid body that will sink in water, is found by the following Rule. — Divide the weight of a body by its loss of weight in water. rig. 85. ExAMPLB. — Wishing to know the specific gravity of a piece of ore which I suspected to contain silver, I first found its weight in a pair of scales to be 560 grains ; and then suspending it from the scale-beam, and weighing it again in water, I found its weight only 425 grains, and consequently it had lost 135 grains. Therefore its specific gravity was 4.1481. 189. When the body whose specific gravity is required is lighter than water, as cork, for example, the object is still to find the weight of an equal bulk of water, since that will constitute the denominator, or divisor, as before. To ascer- tain this, suspend any heavy body, as a mass of lead or glass, m water, and find its weight. Attach to it the lighter body. How much weight does a body lose by being immersed in water ? nias. trate by figure 84. Give the rule for finding the specific gravity of a bodv How do we proceed wlvm the body is lighter than water I SPECIFIC GRAVITY. 145 Now the cork will not only lose all its own weight, but will diminish the weight of the heavy body ; and the weight of an equal bulk of water will be indicated by the whole of what the cork loses, namely, its own weight added to the loss occasioned to the other body. Whence we have the following KuLE. — To find the specific gravity of a body lighter than water. Divide its weight by the sum of its weight added o the loss of weight which it occasions in a heavy body pre- viously balanced in water. Example. — Desirous of finding the specific gravity of a cork weighing 30 grains, I first balanced a bit of lead in water, and then attaching the cork to it, and weighing both together in water, I found that it took 90 grains to restore the lead to its former equilibrium. Therefore, dividing 30 by 90, the specific gravity of the cork was \. A solid which is soluble in water, as a lump of salt, is protected from solution by covering it with oil or a thin coat of bees' wax ; and solids that are very porous and would ab- sorb water, and thus increase their specific gravities, as cer- tain kinds of wood, are first covered with varnish. The spe- cific gravity of solid substances, which are too minutely di- vided to be weighed in water separately, as grains of sand, or shot, may be found by weighing them in a small bucket previously balanced in water. 1 90. The specific gravity of liquids may be ascertained by several different methods. KuLE 1. — Weigh equal volumes of the liquid and of wa- ter, and divide the farmer result by the latter. EuLE 2. — Ascertain the loss of weight of any solid body, first in the liquid and then in water, and divide the former ■ result by the latter. Both these rules obviously depend upon the same princi- ples, as those explained in Art. 187, the weight of the liquid being immediately compared with that of an equal bulk of water; but there is another method, founded on the follow- ing proposition. 191. Two columns of fluids of different specific gravities pressing freely on each other at their bases, balaiice one an- other when their heights are inversely as their specific gravities. Let AB (Fig. 86,) be a recurved tube, and let the height of the column of the fluid B be as much greater than that Give the rule — How do we proceed when the body would be dissolved in water? Give the rule for finding the specific gravity of liquids. When do two fluids of different specific gravities balance each other in a recurved tube ? Illustrate by figure 86. 13 146 HYDKOSTATICS. Fig. 86. of A, as the fluid B is lighter than the fluid A ; the two columns will then be in equilibrium. If the tube be of uniform bore throughout, then the prop- osition is manifestly true, because the quan- tities of matter pressing on each other in op- posite directions will be equal, and will have equal momenta ; but from the peculiar nature of fluids, (Art. 184,) the opposite pressure will be the same, when the heights of the columns are the same whatever may be the shape or capacity of the tube. If we introduce mercury into one arm of the tube, and water into the other, the graduated scale will indicate that the water stands IS-J- times as high as the mercury. Therefore, the specific gravity of mercury is 13-J-. Proof spirit will stand at .923; sweet oil at .915; and their specific gravities are the same, water being 1. 192. If a body floats on a fluid ^ it dis- places as nmch of the fluid as is equal to its own weight. If into a vessel full of water a floating body, as apiece of wood, be introduced, the quantity of water displaced will be found to be exactly equal in weight to the body. Or if the vessll full of water be accurately balanced in a scale, and then removed, and the piece of wood in- troduced, the vessel, on restoring it to the scale, will still remain in equilibrium, the wood exactly com- pensating for the water it displaced. 1 93. An accurate knowledge of the specific gravities of bodies, is of great use for many purposes of science and the arts, and they have therefore been determined with the great- est possible precision. The heaviest of all known substan- ces is platinum, whose specific gravity, in its state of greatest condensation, is 22, water being 1 ; and the lightest of all ponderable bodies is hydrogen gas, whose specific gravity is .069, common air being 1. Since water is 828 times heavier than air, and air is 14-^ times heavier than hydrogen, it fol- lows that platinum is 264,000 times as heavy as hydrogen, and hence a wide range is allowed to the various bodies When a body floats on a flaid, how much of the fluid does it displace 7 How is this fact proved by experiment ? What is the use of detenoining the specific gravity of bodies! What is the heaviest of all known hodiesl What is the lightest? How much heavier is platinum than hydrogen 1 SPECIFIC GRAVITY. 147 which lie between these extremes. The metals, as a class, are the heaviest bodies ; next to these come the metallic ores ; then the precious g-ems ; and finally, minerals in general, animal, liquid and vegetable substances, in order. 1. Metals (not including the bases of the alkalies, as po- tassium and sodium, which are lighter than water) vary in pecific gravity from 6 to 22, arsenic being the lightest and platinum the heaviest. Thus, Platinum . . . . 22.00 Gold . . Quicksilver Lead . . Silver . . Copper 19.25 13.58 11.35 10.47 8.90 Steel Iron Tin Zinc Antimony .... 6.71 Arsenic 6.00 7.84 7.78 7.29 7.00 2. Metallic ores are lighter than the pure metals, but usu- ally above 4. 3. Precious gems are characterized by a high specific gravity, some ranging above 4, but they are generally between 3 and 4, while most stony bodies are between 2 and 3 Thus, Diamond. .... 3.5 I Sapphire 4.2 Topaz 4,0 1 Ruby 4.3 4. Glass ranges from 2-^ to 3. Crown (window) glass 2.5 Bottle glass . . 2.6 Plate glass .... 2.9 Flint 3.3 5. Liquids, in general, lie between f and 2, ether being the lightest, and sulphuric acid the heaviest. Oils are generally a little lighter than water, but a few essential oils are heavier. Ether 0,72 Oil of Cloves . . . 1.04 Alcohol 0.79 Milk 1.03 Proof-spirit . . . 0.92 Vinegar 1.08 Oil of Olives . . . 0.91 Nitric Acid . . . 1.50 Wine 1.00 Sulphuric Acid . . 1.84 6. Woods are generally lighter than water, but a few are hieavier, as Mahogany . . . . 1.06 Oak, 60 years old . 1.17 Dye Woods . . . 1.03 Indian Cedar . . . 1.31 Lignum Vitae . . Ebony . . . . Pomegranate . . Knot 16 years old 1.33 1.33 l.£f5 1.76 194. If we balance in a pair of scales, a tumbler filled with water to a certain mark near the top, and then turning out all the water except a small quantity, introduce any solid What is the heaviest class of bodies? What the next? Name other classes in order. Give the speciiic gravities of various classes of bodieSi as minerals, liquids, &c. 148 HYDROSTATICS. body, (as a tumbler a little less than the first,) so as to raise the water on the sides to the same mark as before, the equi- librium will be restored. Here, the space occupied by the solid immersed, is the same with that before occupied by the water. On the same principle, a ship is floated in a dock with a very small quantity of water, and still rides as freely as on the ocean. By the ascent of the water on the sides, the upward pressure on the bottom is increased, on the same principle as in the Hydrostatic Paradox (Art. 185.) The annexed cut represents a dock of a cubical form, into which a vessel may be floated for the pur- Fig. 87. pose of ascertaining its tonnage. From the known dimensions of the dock, it is easy to ascertain the level of the water corresponding to any number of tons, and to mark a scale on one side accordingly. Suppose that the water, before the vessel is introduced, stands at the level of three tons, and after the vessel is floated in, it stands at fifty tons. Now the weight of the vessel, together with the water, is precisely the same as that of a volume of water would be standing at the same level. Con- sequently, the weight of the vessel and cargo is equal to the rise of the water in the dock, or forty-seven tons. Though, in this case, we cannot say that a quantity of water is dis- placed equal in weight to the solid, (since the whole of the water originally in the vessel may not have been nearly sufficient to fill the space occupied by the ship,) yet the efiect is the same, in regard to the pressure on the water below the ship, and of course on the upward pressure, (Art. 175,) as though the space occupied by the ship below the level of the fluid on its sides, were filled with water. On this prin- ciple, the weight of ^ loaded boat in the lock of a canal is ; easily estimated. Boats are sometimes made of iron instead of wood, their thickness being so much less, that the entire weight of the boat is not greater than when made of wood. The human body, when the lungs are filled with air, is Recite the experiment' with a tumbler of water raised to a certain mark, &c. On what principle is a ship floated into a dock with a small quantity of water? How is the weight of a loaded boat estimated! What is said of iron boats ? SPECIFIC GRAVITY. 149 lighter than water, and but for the difBculty of keeping the lungs constantly inflated, it would naturally float. With a moderate degree of skill, therefore, swimming becomes a very easy process., especially in salt water. When, however, a man plunges, as divers sometimes do, to a great depth, the air in the lungs becomes compressed, and the body does not rise except by muscular effort. The bodies of drowned per- sons rise and float after a few days, in consequence of the in- flation occasioned by putrefaction. Quadrupeds swim much more easily than man, because the motion of the limbs ne- cessary to sustain themselves, nearly coincides with their natural motions in walking, while the body maintains nearly its usual posture. 1 95« If a body is Jield beneath the surface of a fluid, the fnrce with which it will ascend, if it is lighter than the fluid, or with which it vnll descend, if it is heavier, is equal to the difference between its own weight and the weight (f an equal bulk of the fluid. On the foregoing principle is founded the construction of a machine called the Camel, for raising sunken vessels, or for lifting ships over sand banks. Empty hogsheads or boxes sunk by means of weights which are afterwards de- tached, being fixed to a sunken ship, may give it so much buoyancy as to cause it to float. Suppose, for example, a "hundred empty hogsheads were thus attached, what upward force would they exert? * The number of gallons in a hogshead, 63, multiplied by 231, the number of inches in a gallon, gives 14,553 inches ; which, divided by 1,728, gives 8.4 cubic feet in a hogshead. But a cubic foot of water weighs 62^ pounds. Therefore, 62.5x8.4=525 lbs.=weight of a hogshead of water. Now 100 cubic inches of air weigh 30^ grains; there- fore, 100 : 30i : : 14553 : 4438.66=grains of air in a hogs- head ; or (since 437.5 grs. equal an ounce) the number of ounces of air in a hogshead is 10. 14. Hence 525 lbs — 10. 14 oz.=524 lbs. 6 oz. nearly, or 524.375 lbs. for the upward force of an empty hogshead sunk in water ; consequently, the buoyancy of 100 hogsheads is 52437.5 pounds, or almost 23i tons. A similar effect is exhibited in rivers, where the ice is How does the weight of the fanman body compare with that of water 7 Why do the bodies of drowned persons rise? Why do quadrupeds swim more easily than men? With what force will a body held in the water en- deavor to ascend or descend? What is the structure and principle of the Camel ? How are sunken ships raised by means of empty hogsheads ? What is the amount of buoyancy of 100 bogsheads ? 13* 150 HYDROSTATICS. formed upon the stones at their bottom. Ice is specifically lighter than water, and therefore, when it accumulates to a certain degree around the stones, the upward pressure upon the stones exceeds their pressure downwards, and they are brought to the surface, having been sometimes torn up with great force Huge masses of stone appear in many cases to have been floated by the ice adhering to them, and carried to a great distance from the place of their formation. 196. Kocks and stones being only a little more than twice as heavy as water, of course nearly half their weight is sustained while they are immersed in water ; and hence the increased weight which is felt when a large stone is lifted from the bed of a river, as soon as it reaches the sur- face. Large masses of rocks are transported with far great- er facility by torrents, on account of their diminished weight. On the same principle, the limbs feel very heavy on leaving a bath. Life boats have a large quantity of cork mixed in . their structure, or of air-tight vessels of thin copper or tin plate, so that, even when the boats are filled with water, a considerable part still floats above the surface. 197. The magnitudes of bodies may frequently be most conveniently and accurately estimated from the doctrine of specific gravities. Suppose we wish to ascertain the exact number of solid inches contained in a stone of rude and irregu- lar shape, we should find great difiiculty in applying to it any anear measurements ; but if we ascertain its loss of weight in water, we then have the weight of an equal bulk of water, and since 1000 ounces contain 1728 cubic inches, we may easily find how many cubic inches correspond to the weight of water of equal magnitude with the body in question. For example, when we want to find the number of solid inches in a chain, the irregularity of its shape prevents our applying to it any linear measure ; but if we weigh it in water, and subtract this weight from its weight in air, the difference gives us the weight of an equal bulk of water, which we can easily convert into solid inches. Suppose the chain lose 2.34 ounces by being weighed in water, then 1000 oz. : 1728 in : : 2.34 oz, : 4.04 inches. That is, the chain contains a little more than four solid inches. State the effect of ice in raising large rocks. Why does a rock feel so much lighter in the water than out of it ? State the effect on the limbs after bathing. Structure of life boats. How are the magnitudes of bodies estima- ted by means of their speciRc gravities? Example in finding the number of cubic inches in a stone of irregular shape, also in a chain. CHAPTER II. OF LIQUIDS OR NON-ELASTIC FLUIDS IN MOTION. 198. That branch of Natural Philosophy which treats of fluids in motion, is usually denominated Hydraulics. It embraces the phenomena exhibited by water issuing from orifices in reservoirs — projected obliquely or perpendicularly — flowing in pipes, canals, and rivers — oscillating in waves — or opposing a resistance to the progress of solid bodies. 199. If afluid runs through any tube, pipe, or canal, and keeps it constantly full, its velocity, in any part of its course, wiU he inversely as the area of tJie section at thai part. Thus, in a pipe of unequal bore, in difierent parts, it is ob- vious that the same quantity of water must, in a given time, flow through the smaller parts of the tube as through the larger : it must therefore flow proportionally faster. This proposition supposes the fluid to move free of all re- sistance, and hence it can never hold accurately true in prac- tice. In every canal or river, the velocity of the middle of the stream is greater than that of any other part, being less retarded by the friction of the bottom and sides ; and in a tube, the particles near the axis always move most rapidly. It is of consequence to avoid all unnecessary expansions, as well as contractions, in pipes or canals, since there is al- ways a useless expense of force in restoring the velocity which is lost in the wider parts. 200. The phenomena of RrvERs have sometimes been explained on the supposition that rivers are bodies falling freely down inclined planes. But the conclusions deduced from this doctrine, are so at variance with experience, as to be of no value. Were every part of the bed of a river uniform, like a tube, the channel or portion which moves with the greatest velocity, would be in the center of the surface ; but inequalities in the sides and bottom usually throw it out of the center, and incline it to one side or the other. The increased Velocity of a fluid in different parts of a tube of unequal bore. Does the foregoing proposition hold good in practice ? What portion of a stieam moves with the greatest velocity t How is it in a tube ? What is said of all un- necessary expansions and contractions in tubes or canals? On what princi- ples have the phenomena of Rivers been explained ? Do the conclasions of the theory agree with experience ? 152 HyDEOSTATICS. velocity of a stream during a freshet, while the stream is confined within its banks, exhibits something of the accele- ration which belong to bodies falling freely down an in- clined plane. It presents the case of a river flowing upon the top of another river, and consequently meeting with much less resistance than when it runs upon the rough un- even surface of the earth itself. The augmented force of a stream in a freshet, arises from the simultaneous increase of the quantity of water and the velocity. In consequence of the friction of the banks and beds of rivers, and the numer- ous obstacles they meet with in their winding course, their progress is very slow ; whereas, were it not for these imped- iments, it would become immensely great, and its effects would be exceedingly disastrous. A very slight declivity is sufficient for giving the running motion to water. Three inches per mile, in a smooth, straight channel, gives a veloc- ity of about three miles per hour. The Ganges, which gath- ers the waters of the Himalaya Mountains, the loftiest in the world, at the distance of eighteen hundred miles from its mouth, is only eight hundred feet above the level of the sea, — that is, about twice the height of St. Paul's church in Lon- don ; and to fall these eight hundred feet, in its long course, the water requires more than a month. The great river Magdalena, in South America, running for a thousand miles between two ridges of the Andes, falls only five hundred feet in all that distance. 20 1 . Tlie velocity with which a fluid issues from a S7nall orifice in the bottom or side of a vessel, kept constantly full, is equal to that which a heavy body would acquire, by fall- ing from the level of the surface to the level of the (trifice. In the construction of water works, it is customary to con- duct the stream, or such a part of it as is required, into a cubical cistern, and to let it issue from the side of this, near to the bottom, and thus fall upon the main wheel. Instead of admitting the water to the wheel in this manner, it has sometimes been supposed that an advantage might be gained by letting the water fall down a height equal to that of the top of the cistern, perpendicularly upon the top of the wheel, on the supposition that we might thus avail ourselves of the What is the cause of the increased velocity of a river daring a freshet ? Hovi' great a declivity is necessary in order just to give motion to water ? What is the velocity due to a descent of three inches per mile ? How high is the source of the Gang^es ahove the sea — the great river Magdalena ? With what velocity does a fluid issue from the bottom or side of a vessel kept con- stantly full ? PHENOMENA OP RIVEKS. 153 force acquired by the water in falling-. But according to the preceding proposition, the force would be the same whether the water issued from the cistern and thus applied itself to the wheel, or whether it fell upon the wheel from a height equal to that of the surface of the water in the reservoir above the orifice. This is true in theory ; but in practice it would be foufid more advantageous to take the water out of the cistern, since the force of water falling through the air is considerably diminished by the resistance of the air. 202. The quantities of water which issue from orifices of the saine dimensions, in the side of a cistern or column, are proportional to the square roots of their depths below the surface of the fluid. According to the last proposition, the velocities are equal to those acquired by bodies falling freely through the depths of the orifices ; but the velocities acquired by falling bodies are as the square roots of the spaces ; that is. the velocities are proportional to the square roots of the depths ; and since the quantities must evidently vary as the Velocities, there- fore, the quantities discharged by orifices of the same size at different depths are as the square roots of their depths. Accordingly, an orifice sixteen inches from the surface, will discharge twice as much in a given time as one four inches deep : and in order to draw off from a given cistern four times as much as before, we must place the orifice or gate sixteen times as deep. A gate opened in a reservoir at the depth of 64 inches, will discharge only four times fis much as it would at the depth of 4 inches. 303< If a cylindrical or prismatic vessel, of which the horizontal section is everywhere the same, is filled with fluid, and empties itself hy an orifice, the velocity ivith which tlve surface descends, and also the velocity ivith which tfie water issues, is uniformly retarded. The velocity with which the surface descends is propor- tional to that with which the fluid issues from the orifice, and therefore is as the square root of the depth. But the velocities of bodies projected perpendicularly upwards are in the same ratio to their spaces, and therefore a body projected perpendicularly upwards, is in the same relative circumstan- Is it better to let water/aH on a wheel or issue from a cistern at the same depth ? State the proportion between the respective quantities of water that issue from orifices at diiferent depths ? How much more water will an orifice 16 inches below the surface discharge than one only 4 inches? How much more will a gate opened in a reservoir discharge at the depth of 64 inches than at the depth of 4 inches 1 At what rate is the velocity of the surface of § fluid isBuing from an opening in a vessel retarded ? 154 HYDEOSTATICS. ces as the descending surface of the fluid ; and as the pro jected body is uniformlj- retarded, the same is true of the de- scending surface. On this principle is constructed the Clepsydra, or water- clock. Since the descent of the surface is uniformly retard- ed, the spaces which it describes in equal times, reckoning from the bottom, are as the odd numbers, 1, 3,5, 7, &c. ; and if a cylindrical vessel of water be furnished with an orifice at the bottom which will exactly discharge the whole column in twelve hours, and the sides of the vessel be divided into spaces corresponding to the foregoing numbers, the succes- sive heights of the column become measures of time. 204. If we accurately mark the time in which a cylin- drical or prismatic vessel^ whose horizontal section is every- where the same, discharges itself to the level of a given ori- fice, and then draw off for tlve same time, keeping the vessel constantly full, we shall obtain double the quantity of fluid in the latter case as in the former. When the vessel is kept constantly full, the velocity at the orifice (and of course the quantity discharged) continues uni- formly the same as at first ; and since the circumstances of this case are exactly analogous to those of a body projected perpendicularly upwards ; and since, if a body thus projected were to continue to ascend with the first velocity, it would pass over a space twice as great in the same time as when uniformly retarded ; therefore, the truth of the proposition is manifest. 205. A fluid spouting from the side of a vessel, de- scribes the curve of a parabola. The fluid is precisely in the same circumstances as a pro- jectile acted on by the force of projection, (viz. the pressure of the incumbent fluid,) and by the force of gravity. There- fore, according to Art. 68, it describes the curve of a para- bola. As in the case of other projectiles, the proposition holds good, whatever may be the angle of elevation of the jet. 206. When a fluid spouts from the side of a petpen- dicular column, its random or hm'izontaZ distance will be the greatest when it spouts from the center, and it vrill be equal at equal distances from tlie center above and below. Explain the structure of the water-clocV, or Clepsydra. State the case of a fluid discharging itself from a given orifice when the vessel is kept full. What curve does a spouting fluid describe ? From what part of the column must a fluid spout to strike at the greatest horizontal distance ? At what two points will the distances be equal ? LAWS OF SPOUTING FLUIDS. 155 The lower parts of the column being subjected to the strongest pressure, namely, that of the incumbent column, we might suppose that the lower the orifice, the greater would be the random ; but we must recollect, that such a spout would reach the plane sooner than those at a higher elevation. 207. The term Friction is applied to the obstruction occasioned to the passage of fluids in the same manner as it is to solids ; and it exists to such an extent as to become an object of considerable inconvenience in practice. It can be obviated only by making the conveying pipe of much larger dimensions than would otherwise be necessary, so as to allow the free passage of a sufficient quantity of fluid through the center of the pipe, while a ring or hollow cylinder of water is to be considered to be at rest all around it. Other cir- cumstances beside friction likewise tend to diminish the quantity of fluid which would otherwise pass through pipes, — such as the existence of sharp or right-angled turns in them, permitting eddies or currents to be formed, or not pro- viding for the eddies or currents that form naturally, by suit- ing the shape of the pipe to them. It follows, therefore, that whenever a bend or turn is necessary in a water pipe, it should be made in as gradual a curve or sweep as possible ; that the pipe should not only be sufficiently capacious to af- ford the necessary supply, but should be of a uniform bore throughout, and free from all projections or irregularities against which water can strike, and form eddies or reverber- ations, since these will impede the progress of the fluid as effectually as the most solid obstacles. 208« An unexpected facility is gained in the discharge of a fluid from the bottom or side of a vessel, by applying a pipe to the orifice. On account of the friction known to occur in the passage of a fluid through a tube it might be supposed that a simple orifice made in the vessel might be more favorable to the discharge of the fluid than an opening prolonged by a tube ; but it has been found by experiment, that a vessel of tin, with a smooth hole formed in its bottom, did not discharge water as rapidly as another containing the same weight of water, and an orifice of the same dimensions, to which a short pipe was applied. By varying the length How is the term Friction used in hydraulics 1 How is it obviated ? What other circumstances diminish the quantity of fluid which would other wise be discharged by a pipe? How should tliese impediments be guarded against? What facility is gained in the discbarge of a Huid by applying a pipe to the ei A VALVE is a contrivance which permits a flvid to pass 'in one direction, but prevents its passing in the opposite direction. The clapper seen on the under side of a pair of bellows, is a familiar example of a valve. The valve em- Desoribe the air pnmp. Point oat the plate, the barrels, the conducting pipe, the receivers, the gauge. Define a valve — exempUtied in a bellows. MECHANICAL PROPERTIES OP AIR. 171 ployed in the air pump, usually consists merely of a strip of oiled silk, tied over a small orifice. The air, by pressing oz/^ wards from the orifice, raises the silk, opens the valve, and makes its escape ; while by pressing inwards upon the ori- fice, it keeps the strip of silk close to the orifice, and is there- fore prevented from passing in that direction. The piston and cylinder are exemplified in a common syringe. It con- sists of a hollow cylinder, or barrel, to which is fitted a short cylinder called the piston, which is moved up and down the barrel by means of a projecting handle called the piston-rod, and is fitted so closely to the barrel as to be air tight. Sup- pose now that the cylinder is in a perpendicular position, closed below, but open above, and that the piston rests on the bottom. On drawing up the piston, the air above it is lifted out, and the space below it is a vacuum. If a small orifice be made in the bottom of the barrel, then, as the pis- ton is drawn upwards, the air will flow in and no vacuum will be formed ; and as the piston is depressed again, the air is forced back. But by attaching a valve to the orifice, we may admit or exclude the exterhal air at pleasure. If the strip of silk be tied on the outside, then, on drawing up the piston, the air will not follow, but the piston will go up heavily, since it lifts up the entire weight of the column of air that rests upon it, (there being nothing below it to act as a counterpoise.) and if the hand be withdrawn from the piston rod, the piston will descend spontaneously. Again, if the valve be placed on the inside, then the external air will follow the piston as it rises, and no vacuum will be formed. If now the piston could be depressed, the air can- not be expelled, (since the valve closes on the orifice in that direction,) and the piston cannot be forced down to the bottom of the barrel, unless a valve is placed in the piston itself, opening outwards ; in this case, the air of the barrel may be expelled by depressing the piston. 224. We have been thus minute in the description of the construction of valves, and of the cylinder and piston, be- cause when these things are clearly understood, the learner will easily comprehend the principle of the air pump, of the common house pump, of the steam engine, and of every other species of pneumatic apparatus. Let us now return to the air pump. In the barrels, two pistons play up and down, each of How are the valves of the air pump constructed? How does the valve operate ? Describe a piston and cylinder as exemplified in a common syringe. How is a valve applied to it? 172 PNEUMATICS. which is furnished with a valve opening upwards, into the open space, through which the piston rods move. Another valve is placed at the bottom of each barrel, opening mto the barrel The piston rods are indented bars, to which a toothed wheel (concealed in Fig. 92, but seen in Fig. 93,) is adapted which being turned backwards and forwards by means ot the winch G, (Fig. 92,) alternately raises and depresses the two pistons, as is represented in Fig. 93. Suppose now the Fig. 93. receiver to be placed on the plate of the pump, one of the pistons being at the top, and the other at the bottom of the barrel. We turn the winch, the piston rises, and the air of the receiver opens the valve at the bottom of the barrel, and diffuses itself equally through the barrel and the receiver. We turn the winch in the opposite direction, the piston de- scends, compresses the air in the barrel before it, which, as it cannot go back into the receiver, opens the valve in the piston itself, and escapes into the vacant space in which the arm of the piston moves. This process is repeated every time the piston rises and falls ; and it is the same in both barrels, two being employed to accelerate the process of ex- Describe the interior structure of the air pump from figure 93. Show how the exhaustion is effected. MECHANICAL PROPERTIES OF AIR. 173 haustion. The pressure on the descending- also helps to raise the ascending- piston. i 225. By means of this instrument, we may obtain very striking illustrations of the mechanical properties of air. il.) The pressure of the air acts with great force on all ies at the surface of the earth, amounting, as we shall show hereafter, to nearly 15 pounds upon every square inch, or more than 2000 pounds upon a square foot. Upon so large a surface, therefore, as that of the human body, the pressure amounts to no less than 13 or 14 tons ; but being so uniformly distributed within and without, and on all sides, it is, when the air is at rest, scarcely perceptible. In conse- quence of this pressure, the air insinuates itself into all fluids, and fills the pores of all solids except the most dense, as gold or platinum. The pressure of the air diminishes the tendency of fluids to pass into the state of vapor, and of course raises their boiling point. Warm water, at a temperature much below the boiling point, will be set a boiling under the re- ceiver of an air pump, or in a vacuum formed in any other way. Indeed, if it were not for atmospheric pressure, water would require only the moderate heat of 72 instead of 212 degrees of heat to make it boil ; and the more volatile fluids, as alcohol and ether, would hardly be found in nature in the liquid state. Experiments like the following may easily be made with the air pump. 1. If we apply a receiver to the plate of the pump, as rep- resented in figure 93, on working the pump the receiver will be held fast to the plate. 2. The annexed figure represents two hemispheres of brass, closely fitted to each I'ig- sm- other at their edges. When these are put together, they can be pulled asunder with very little force, so long as the pressure of the air acts on the inside as well as on the outside. But now, join the parts together, and screw the ball to the plate of the pump. After exhaustion, on removing it, and attach- ing the handle, represented at the bottom of the figure, the hemispheres will be found What is the amount of the pressare of the atmosphere on every square inch of surface — also on every square foot 1 What is the ■whole amount on the human body 1 Does air penetrate fluid and solid bodies 1 How does the pressure of the atmosphere affect the boiling point of fluids ? If it were not (or this, at what temperature would water boil ? 174 PNEUMATICS. to be pressed so closely together as to require great force to separatejthem. This piece of apparatus is called the Magdeburg Henii- spJieres, having been first exhibited at Magdeburg by Otto Guericke, the inventor of the air pump. Guericke had a pair of hemispheres constructed so large, that sixteen horses, eight on each side, drawing against each other, were unable to pull them asunder. 3. If a square* bottle, mounted with a screw, (as in the preceding figure,) be attached to the plate, on exhausting the air, the sides of the bottle will be crushed inwards, with a loud explosion, and the glass be found broken into mi- nute fragments. In this experiment a handkerchief or towel should be spread over the bottle to prevent injury to the eyes. (2.) The elasticity of the air is such, that the smallest por- tion of it may be expanded beyond any known limits, by re- moving the external pressure. By this means, a bubble may be made to fill a very large space. On the other hand, air has been condensed by pressure, until its density has been greater than that of water, still retaining the elastic invisible state. In consequence of its elasticity, air is set in motion by the least disturbance of its equilibrium, whether by con- densation or rarefaction, thus giving rise to the phenomena of winds. (3.) Air is essential to the support of combustion, and to the respiration of animals ; and finally, it is the principal medium of sound. It may be farther shown that the weight of bodies is diminished by the buoyancy of air, (acting on the same principle as water,) and that light bodies are sustained in it in consequence of its greater specific gravity, while, in a vacuum, bodies of various density, as a guinea and a feather, fall towards the earth with equal velocities.! • This experiment shows how much legs adapted to sustain pressure a flat surfactf Is than a round, since a globular vessel of equal thiclmess would not be broken, t For air pump experiments, see supplement. Describe the Magdeburg hemispheres, and the experiment with them. Also with a square bottle. To what extent may air be dilated and compressed ? How is air set in motion ? What relations has air to combustion, respiration, and sound! How is the weight of bodies aifected by the buoyancy of the air ! MECHANICAL PROPEETIES OF AIR. 175 Fig. 95. ^X THE CONDENSER. 226. The condensation of air is usually effected by means of the Condensing Syringe. This instrument is a cylinder and piston, the cylinder having a valve opening outwards, virhile the piston is without a valve. The princi- ple of its operation will be readily under- stood from the figure. Near the top of the cylinder is a small hole, E, in the side, which is immediately below the piston, when this is drawn up to the top of the cylinder. On forcing down the piston, the air is driven before it, and expelled through the valve at the bottom. By connecting a bottle or other close vessel with the bottom, the air expelled may be driven into that, its return being prevented by the same valve. The piston being drawn up again above the opening in the cylinder, another similar portion of air may be forced into the con- densing bottle ; and thus the process may be continued indefinitely. The Condensing Fountain is a bottle, usually of copper, partly filled with water, upon the surface of which the air is con- densed by means of the condensing syringe. The fluid being thus brought under strong pressure, it tends to issue with great force whenever a pipe, D, that is inserted in the bottle, and extends below the surface of the water, is opened. The celebrated spouting springs of Iceland, called the Geysers, in which water accompanied by large masses of rock, is thrown to the height of 200 feet, arise from pneumatic pressure acting upon the surface of water in the interior of the earth, the aeriform substance, whatever it may be, being produced by volcanic action. The Air- Gun is an instrument in which condensed air is substituted as the moving force, instead of gunpowder. By means of a condensing syringe, air is strongly condensed m a metallic ball, furnished with a valve at the mouth, where it is screwed on the gun below the lock. As the lock jlA Describe the Condensing Syringe from figure 95. Describe the Condensing Fountain. Cause of the Geysers? Define the Air-Gun. Show how the force is applied, and how the gun is discharged. 176 PNEUMATICS. is sprung, it falls upon a plug, and forces it upon the valve, which suddenly opens, and the air rushes into the barrel of the gun, and by its sudden expansion, propels a ball much in the same manner as gunpowder would do in its place. 327. The Diving Bell is an apparatus employed lor ex- ploring the depths of the sea. It was formerly made in the shape of a bell, but is now more commonly made square at the top and bottom, the bottom being a little larger than the top, and the sides slightly diverging from above. The ma- terial is sometimes cast iron, the whole machine being cast in one piece, and made very thick, so that there is no danger either from leakage or fracture. Sometimes the diving bell is made of planks of two thicknesses, with sheet lead be- tween them. In the top of the machine are placed several strong glass lenses for the admission of light, such as are used in the decks of vessels to illuminate the apartments below. The diving bell depends for its efficacy on that quality of air which is common to all material substances, impenetra- bility ; that is, the exclusion of all other bodies from the space it occupies. The principle may be illustrated by de- pressing a tumbler or jar in water, with the mouth down- wards : it will be seen (Art. 221,) that the water will ascend so far as to occupy only a part of the capacity of the vessel, the upper part being occupied by the air. As the diving bell descends in the water, the air enclosed in it is subject to its pressure, (which increases with the depth,) and by virtue of its elasticity, it will become condensed in proportion to this pressure. Thus at the depth of about 34 feet, the hydrostatic pressure will be equal to that of the atmosphere, and consequently, the air being under a pressure equivalent to that of two atmospheres, it will be condensed into half its original volume. As the depth is increased, the space occupied by the air in the bell will be proportionally dimin- ished. Seats are furnished for the workmen, and shelves for tools and various other conveniences. Although at the depth of thirty-four feet, the water would occupy one half the capacity of the vessel, and more or less at different depths ; yet by means of a forcing pump or condensing syringe communicating between the atmosphere above and the ma- chine through a pipe, air may be thrown in so as to exclude Describe the Diving Bell — its shape — material — ^how illuminated. On what quality of the air does it depend ! What will be the pressure of the water on the enclosed air at the depth of thirty-four feet 1 How far will the air be condensed at that depth 1 What accommodations are furnished to the workmen ? How may air be thrown in so as to exclude the water entirely ? THE BAEOMETER. 177 the water entirely. By the same means fresh air may be conveyed to the workmen, the portion of air rendered im- pure by respiration, being at the same time suffered to es cape by opening a stop-cock in the top of the machine. THE BAROMETER. 228. Let us take a glass tube, about three feet in length, closed at one end and open at the other. We fill the tube with quicksilver, and invert it in a vessel of the same fluid. The col- umn of quicksilver falls to a certain height, about 29 or 30 inches, wrhere, after vibrating a few times, it remains at rest. The space in the tube above the quicksilver being void of air or any other substance, it is of course a vacuum, and is usually denominated the Torricellian vacuum, from Torricelli, an Italian philosopher, who first discovered this method of producing a vacuum. Various precautions are necessary, in order to preserve this space free from air or any aeriform substance ; but when these precautions are taken, this vacuum is the most complete of any that we can command. The column of quicksilver is sustained by the pressure of the atmosphere on the open mouth of the tube which is immersed in the same fluid ;* and it must have the same weight with a column of the atmosphere of the same base, otherwise it would not be in equilibrium with it. We hence arrive at an accurate knowledge of the actual weight and pressure of the air, since it is equal to the weight of a column of quicksilver of the same base, thirty inches in length. The weight of such a cylinder of quicksilver is easily • As young learners sometimes find a dilBcalty in conceiving clearly how the press- Bre of the air acts in this case, we subjoin a rema^Ic or two. It must bo recol- ected, that any impulse or pressure exerted on the surface of the fluid in the ves- •el, extends alike to any part of it ; and since the fluids act upwards as well as iownwards, it is plain that the pressure acts in sustaining the column of mercury in the same manner as though ]t were applied directly to the mouth of the tube. How may fresh air be supplied to the workmen ? Show the construction of the barometer ? What is the Torricellian vacuum 1 How does the perfec- tion of this vacuum compare with those formed by other methods ? How la (he column of quicksilver sustained 1 178 PNEUMATICS. ascertained, and it results, that the pressure on every square inch of surface is, as stated in Art. 225, about 15 lbs., or more than 2000 lbs. upon a square foot. Since different fluids balance each othei in opposite columns pressing base to base, when their heights are inversely as their specific gravities, a column of water in the place of the mercury, would stand at the height of about 34 feet. For quicksilver being 13.57 times heavier than water, the latter column must be 13.57 times higher than the other; that is 30x13.57= 407.1 inches=33.925 feet. By observing from day to day the height of the column of quicksilver prepared as above, we shall find that it varies through a space of two or three inches, showmg that the atmosphere does not always exert the same pressure, but that a given column of the air is sometimes lighter and sometimes heavier. This instrument, therefore, enables us to ascertain the relative weight of the air at any given time, and hence its name harometer* For the purpose of indi- cating these variations with minuteness and precision, a graduated scale is attached to the barometer, divided into inches and tenths of an inch, and usually extending from twenty-seven to thirty-one inches, — a space which is more than sufficient to comprehend all the natural variations in the weight of the atmosphere. 229. Since the variations of the barometer correspond to the variations in the weight of the air at the same place, and since these are connected with changes of weather, this in- strument thus becomes a weather glass, and enables us, in certain cases, to foresee changes in the weather. The most uniform indications of the barometer are, that its rise denotes fair, and its fall denotes foul weather, whatever may be its absolute height. Also a sudden and extraordinary descent of the mercury attends, and frequently precedes, a violent loind. The mean pressure of the atmosphere, as indicated by the barometer, is nearly the same at the level of the sea in all parts of the earth, corresponding very nearly to 30 inches * From tSapoi vjeight, and f/erpov measure. What would be the height of a. column of water required to balance the pressure of the atmosphere 1 What changes occur from day to day in the height of the barometer ? How are these variations indicated 1 What indica- tions of changes of weather arc afforded by the barometer ? To what height of the barometer does the mean pressure of the atmosphere in all parts of the world, correspond? THE BAROMETER. 179 of mercury. This feet has been verified by numberless ob- servations, made with the barometer in both hemispheres, from the equatorial to the polar regions. The following results for several places, in different latitudes, corrected for temperature, elevation above the level of the sea, and the influence of the earth's rotation on its axis, are nearly uniform. Latitude. Bar. Premink Calcutta, . . . . 22° 35' . . , . 29.776 Leaden, . . . . 51 31 . . . . 29.827 Edinburgh, . . . 55 56 . . . . 29.835 Melville Island, . . 74 30 . . . . 29.884 But though the mean pressure of the atmosphere is nearly the same, at the level of the sea, over the whole globe, the extent of the variations to which it is liable, is exceedingh/^ different in different parallels of latitude. At the equatorial regions, the range of the barometer is much more limited than within the polar circles ; and in the frigid zones, it is more limited than in the temperate. Within the tropics the fluctuations of the barometer do not much exceed ■}■ of an inch, while beyond this space, they reach to 3 inches. The most extensive variations take place between the lati- tudes of 30 ' and 60°, being the zone in which the annual changes of temperature and humidity possess the widest range. 230. As the air pump enables us to investigate the me- chanical properties of any portion of air, so the barometer enables us to study the properties and relations of the entire body of the air, that is, the atmosphere. By means of these two instruments, the following facts are well established. (1.) The space occupied by any given portion of air, (as 100 grains for example,) is inversely as the pressure. A weight of two atmospheres diminishes the bulk to one half: of three atmospheres, to one third ; and of one hundred at- mospheres, to one hundredth part of its former bulk. (2.) As the density is likewise inversely as the space occupied, therefore, the density is as the pressure. How is the range of the barometer in the equatorial regions 1 how within the polar circles 1 how in the middle latitudes .' What do the air pump and the barometer respectively enable us to investigate V To what is the space occupied by any given portion of air proportioned 1 To what is the density proportioned ? 180 PNEUMATICS. (3.) Since air, when compressed, endeavors to restore itiself, with a force which is equal to that which compresses it, (being when at rest in equilibrium with that force,) there- fore, the elasticity is as the density mid inversely as the space occupied. In this proposition, the temperature is sup- posed to remain uniform. But, the bulk and density of a portion of air remaining the same, the elasticity^ is as tlie temperature. Hence, the elasticity of air may be increased either by compressing- it, or by heating it in a confined state ; and its elasticitj' may be diminished either by lessen- ing the pressure, or by cooling it. The elasticity of springs is known to be frequently impaired by continual action. This is not the case with air. Air has been left for several years very much compressed in suitable vessels, in which there was nothing that could have a chemical action upon it; and afterwards, on removing the unusual pressure, and restoring the same temperature, the air has been found to recover its original bulk, which shows that the continuance of the pressure had not diminished the elasticity of it in the least perceptible degree. CHAPTEE II. OF THE MECHANICAL AGENCIES OF AIR AND STEAM. 231. In consequence of our power of forming a vacuum either by the exhaustion of air or by the condensation of steam, and of directing the force with which these elastic substances rush into a void or press towards it, air and steam become important agents or prime movers, in various kinds of machinery. Many of the most useful machines involve in their construction the principles of both hydraulics and pneu- matics, and therefore we have reserved an account of such machines to the present section. Alsot min How do they became prime movers in machineiy ? •.lEOHANIOAL AGENCIES OP AIR. 181 THE SYPHON. 233. If a tube having two arms, a *'''s- ^''■ .onger and a shorter, is filled with water, and the mouth of the shorter arm is im- mersed in water, the fluid will run out through the longer arm until the whole contents of the vessel are discharged. Such~ a tube is called a syphon. It may- be filled with the fluid, either by suction or by pouring water into it, keeping the two orifices, closed until the shorter arm is immersed. Or, when the syphon is large, each orifice is plugged, and water is poured in through an opening in the top of the bend. The opening being closed, the shorter leg is placed in the cistern, the plugs removed, and the fluid is discharged as usual. The prindpk of the syphon is as follows. The atmosphere presses equally on the mouths of both arms of the tube ; but this pressure on each orifice is diminished by the weight of the column of water in the leg nearest to it ; consequently, more of the atmospheric pressure is overcome by the longer than by the shorter column, and therefore the effective press- ure, (or what remains,) is less at the mouth of the longer than at that of the shorter column, and the fluid runs in that direction in which the resistance is least. All this will be obvious by inspecting the figure. Were the shorter column thirty-four feet in height, it would counterbalance the entire pressure of the atmosphere on the surface of the fluid, and consequently, there would be no force remaining to drive the water forward through the tube. The syphon, therefore, i,an never raise water to a greater height than thirty-four feet, nor quicksilver higher than about thirty inches. It is obvious, also, that the place of delivery, that is, the mouth of the longer arm, must be at a lower level than the surface of the water in the leservoir ; so that this instrument cannot be used for elevating, but only for decanting fluids, or transferring it from one vessel to another. Its chief use is by grocers, in transferring liquors from cask to cask. It is sometimes employed in car- rying water over a hill, or from a well to a- level below the surface of the well. The Syphm — describe it. How may it be filled with fluid 1 State thfc principle of the syphon. To what height can the syphon raise water ? Why not higher 1 To what uses is it applied? 16 182 PNEUMATICS. THE COMMON SUCTION PUMP Fig. 98 m f3 jSi 233. This pump consists of two hollow cylinders, placed one under the other, and com- municating by a valve which opens upwards. The lower cylinder (which has its lower orifice under water) is called the suction ttiie. In the upper cylinder, a piston moves up and down from the bottom to a spout in the side near the top. This cylinder we call the exhausting tube. Suppose, at the commencement of the operation, the piston is at the bottom of the exhausting tube in close contact with the valve. On raising it, the air in the suction tube having nothing to resist its upward pressure, lifts the vafve and expands, so as to fill the void space which would otherwise be left in the lower part of the exhausting tube. By this means, the air in the suction tube is rarefied, and no longer being a counterpoise to the pressure of the atmosphere on the surface of the well, the latter preponderates and forces the water up the tube, until enough has been raised exactly to counterbalance the excess of the elasticity of the external air above that of the tube. As the piston descends, the air below it is prevent- ed from returning into the suction pipe by the valve which closes on its mouth, but escapes through a valve in the piston itself, opening upwards in the same manner as in the barrels of the air pump. The piston being raised again, the column of water ascends still higher, until it makes its way through the valve into the exhausting pipe. Then as the piston descends, the water opens its valve, and gets above the piston, and is lifted to the level of the spout, where it is discharged. The principle of the suction pump may therefore be thus enunciated : The water is raised into the exhausting pipe by the press- ure of the atmosphere^ and thence lifted to the level of the spout by means of tlie piston. Since a column of water thirty-four feet in height, in the suction tube, would counterbalance the entire pressure of the Common Siiction Pump — describe it. What are the two cylinders respec- tively called ! Explain its operation. Enunciate the principle of the pump. MECHANICAL AGENCIES OP AIR. 183 atmosphere on the surface of the well, no force would re- main to urge the column any higher, and therefore the valve at the top of the suction tube must be less than thirty-four feet above the well. It is evident that the same force is expended in raising water by means of the pressure of the atmosphere, as when the force is applied directly. We lift upon the atmosphere, instead of lifting directly upon the column of water. This method of raising water from a well, is frequently more con- venient than by a single bucket, but the expenditure of force is the same in both cases. ■1 tsy E THE FORCING PUMP. 234. A cylinder, ABC, (Fig. 99,) is Vk-39. placed with the lower end C in the reser- voir. It has a fixed valve at V, opening upwards, and a solid piston without a valve, playing air tight in the upper barrel AB. It is connected with another barrel DE by a valve V opening upwards and outwards. The tilbe DE is carried to whatever height it may be necessary to elevate the water. Let us suppose that the solid piston P is in contact with the valve V, and that the wa- ter in the lower barrel is at the same level C with the water in the reservoir. Upon raising the piston, the air in BC will be rarefied, and the water will ascend in BC exactly as in the suction pump. Upon again depressing the piston, the air in PV will be depressed, and it will force open the valve V, and escape through it. The pro- cess, therefore, until water is raised through V into the upper barrel, is precisely the same as for the suction pump ; the valve V taking the place of the piston-valve in that machine. Now let us suppose that water has been elevated through V, and that the space PV is filled with it. Upon depressing the piston, this water, not being permitted to return through V, IS forced through V, and ascends in the tube DE. By continuing the process, water will accumulate in the tube DE, until it acquires the necessary elevation, and is dis- "Hovr high can the suction pamp raise water? Do we gain any force by means of the pomp ? Forcing Pump — describe it. 184 PNEUMATICS. charged. Or, to enunciate the principle of this machine in general terms — In the forcing pump, the piston has no valve, htct. the water being ekvated into the exhausting tvhe, as in the suction pump, it is tJien forced, by tlie descent of the piston, into the ascending pipe through a valve placed in the side atid at the bottom, of the exhausting tube. 23 5> In forcing pumps, since the power is applied by separate impulses, the water would issue in jets, were not some contrivance adopted to equalize its flow from the tube. This purpose is effected by means of an air vessel, in which a portion of condensed air is made the medium of communi- cation. The force imparted by successive blows of the pis- ton is first received by this confined body of air, and this, by its elasticity, reacts on the surface of the water in the air vessel, and forces it out by the conducting pipe or hose. An example of this is afforded in the Fire Engine. The fire engine consists of two forcing pumps, which throw the water into an air vessel, from ^»S- 1""- which it is thrown out of the conducting hose by the elastic pressure of condensed air. — Thus (Pig. 100,) AB, ABare two forcing pumps, whose pis- tons PP are worked by a beam whose fulcrum is at F ; VV are valves which open upwards from a suction tube T, which communicate with a reservoir ; t t are force-pipes, which communicate by valves VV, opening into an air ves- sel M. A tube L is inserted in the top of this vessel, ter minating in a leathern tube or hose, through which the water IS forced by the pressure of the air confined in M, which, in consequence of its elasticity, acts nearly uniformly on the surface of the water, and forces it through the hose in a con- tinual stream. Enunciate its principle. Wliat is tlie use of the air veseel in the forcing pomp ? Describe the Fire Engine. STEAM ENGINE. 185 THE STEAM ENGINE. 236. It belongs to Chemistry to investigate the proper- ties of steam, and to Natural Philosophy to apply it as a mechanical agent. The Steam Engine is the fruit of the lii^hest efforts of both these sciences, and the most valuable Dresent ever made by philosophy to the arts. As it is im- possible clearly to understand the principle and construction of this engine without a knowledge of the properties of steam, on which they depend, we subjoin an account of a few of its leading properties, referring to chemical authors for a more detailed view of this subject The great and peculiar" property of steam, on which its mechanical agencies depend, is its power of creating at one mome^nt a high degree of elastic force, and losing it instan- taneously the next moment. This force, acting on the bot- tom of the piston which moves in the main cylinder, raises it, and fills the space below it with steam. The steam is suddenly condensed, and hence no obstacle is opposed to the descent of the piston, but it is readily forced down again by steam acting from above. This alternate motion of the pis- ton, the rod of which is connected with the working beam, is all that is required in order to communicate motion to all parts of the engine. 237. TJie elastic fmce of steam depends on its tempera- ture and density conjointly ; and the temperature necessary to its production depends upon the pressure incumbent upon the water during its formation. The reason why water boils at the temperature of 212^ is, that at that temperature, the vapor acquires just elasticity sufficient to overcome the atmospheric pressure. Hence, steam produced at the tem- perature of boiling water, has a force equal to the pressure of the atmosphere. When formed at a lower temperature, its elasticity diminishes in a geometrical ratio, and increases in the same ratio when it is formed at a higher temperature. Water boils, or is converted into vapor, at a temperature less than 212°, on high moiyitains, or under the receiver of an air pump, or in other situations where the pressure of the at- mosphere is diminished ; and in a vacuum the boiling point of water is as low as 72 '. Steam Engine. — What part of it belonga to Chemistry, and what to Natural Philosophy ? "What is the peculiar property of steam on which ita mechanical agencies depend? How does the force operate? On what does the elastic force of steam depend? Why does water boil at she temperature of SIS" ? How is the elasticity of steam at low temperatari.B 7 In what situations does water boil at a lower temperature than ZIS" ? 16* 1 86 PNEUMATICS. 238. Heat rapidly augments the elasticity of steam by increasing its density. If we introduce a few grains of wa ter into a flask, and place it over the fire, the water will soon be converted into steam, which will expel the air of the ves- sel and fill its whole capacity. If we now close the orifice of the flask and continue the heat, the steam will increase m elastic force in the same manner as air would do under similar circumstances, which is at a comparatively moderate rate, so that it might be heated red hot without exerting any very violent force. If, however, the vessel is partly filled with water, and the heat is continued as before, then the elastic force is rapidly augmented, and becomes at length so great as to burst almost any vessel that can be provided ; for every new portion of vapor that is raised from the surface of the water, adds to the density of that which was before in the vessel, and proportionally increases its elasticity. In the experiments of Mr. Perkins, a confined portion of steam, not in contact with water, was heated to the temperature of 1400", and still its pressure did not exceed that of five atmospheres ; but, by injecting more water, although the temperature was lessened, the elastic force was gradually increased to one hundred atmospheres. 239. Tlie space into which a given quantity of water is expanded in becoming steam,, depends upmi the tempera- ture, aiid of course upon tlie degree of piressure at which it is formed. Water converted into steam at the temperature of 212°, expands nearly one thousand and seven hundred times ; but at the temperature of 419 \ it expands but thirty-seven times. According to Dr. Thomson, at a temperature not much higher than 500 . steam would not much exceed double the bulk of the water from which it is generated. The ex- pansive force of such steam would be truly formidable. It would, when it issued into the atmosphere, suddenly expand six hundred and fifty times. We do not know at what tem- perature water would become vapor without any increase of volume, but we can estimate that it would then support a col umn of mercury three thousand two hundred and forty three feet (or more than half a mile) high, and would exert a press- ure of nearly twenty thousand pounds on every square inch. In what manner does heat augment the elasticity of steam ? How is the elas- ticity of steam affected when heated in a close vessel over water, and how when heated by itself? Into what space does water expand in becoming steam ! How is this space affected by increasing the pressure ? What would be the space occupied at the temperature of 500 > ? How high a column of mercury would steam support when heated under such a pressure as not to exceed the volume of water 1 STEAM ENGINE. 187 240. The difficulty of understanding the construction and principles of the steam engine, (as is the case also with many other machines where the parts are numerous,) is greatly enhanced by the variety of accidental trappings or appendages that are employed about the machine to perform subordinate offices. As these render the comprehension of the leading principles difficult, when the explanation is at- tempted from the engine itself, so these inferior parts are often so multiplied in diagrams as greatly to obscure the representation. We shall begin our explanation with a dia- gram which presents the naked principles, divested of all unnecessary appendages. The chief parts of the engine are the holler A, the cylinder C, the condenser L, and the air pump M. B is the steam pipe, branching into two arms communicating respectively with the top and bottom of the cylinder ; and K is the eduction jnpe, formed of the two branches which proceed from the top and bottom of the cyl- nder, and communicate between the cylinder and the con- denser. N is a cistern or well of cold water in which the condenser is immersed. Each branch of pipe has its own valve, as F, G, P, Q, which may be opened or closed as the occasion requires. 241. Suppose, first, that all the valves are open, while steam is issuing freely from the boiler. It is easy to see that Explain the constractiou of the steam engine from iigure 101. What are the chief parts 1 1 88 PNEUMATICS. the steam would circulate freely through all parts of the ma- chine, expelling- the air, which would escape through the valve in the piston of the air pump, and thus the mterior spaces would all be filled with steam. This process is called blowing through; it is heard when a steamboat is about set- ting off. Next the valves F and Q are closed, Gr and P re- maining open. The steam now pressing on the cylinder forces it down, and the instant when it begins to descend, the stop cock is opened, admitting cold water, which meets the steam as it rushes from the cylinder, and effectually con- denses it, leaving no force below the piston to oppose its de- scent. Lastly, Gc and P being closed, F and Q are opened, the steam flows in below the piston and rushes from above it into the condenser, by which means the piston is forced up again with the same power as that with which it de- scended. Meanwhile the air pump is playing, and remov- ing the water and air from the condenser, and pouring the water into a reservoir, whence it is conveyed to the boiler to renew the same circuit. 242. Among the different forces which may be em ployed to move machinery, such as animal strength, water, wind, and steam, the last is the most manageable of all, and therefore, for almost every purpose, the most convenient of all powers that are under the control of man. But whether in a given case, we shall employ steam power, or one of the other forces, as water power for example, may depend on the comparative economy of the two forces. A water fall, near at hand, may furnish us with the required power, cheaper than we can produce it artificially from steam. In the ear- lier forms of construction adopted in the steam engine, so much of the steam was wasted by injudicious management, as greatly to diminish the usefulness of this engine, and to render it in most cases a less eligible force for carrying ma- chinery than animal strength or water. The modern im- provements in the steam engine have consisted, mainly, in preventing this waste of steam, and of course in economizing the amount of fuel required to produce the power. Previous to the yea,r 1763, when Watt began his improvements on the steam engine, not less than three fourths of the steam produced in the boiler was wasted. Show how the steam operates in the ascent and descent of the piston ? How does steam compare with other forces in manageableness? How in economy ? What formerly diminished the usefulness of this machine 1 In what have consisted the modern improvements of the steam engine ? What portion of the steam was formerly wasted ? STEAM ENGINE. 189 243. The greatest improvement introduced by Mr. Watt, consisted in performing the condensation in a separate vessel ; whereas the previous method was to admit a jet of cold water into the cylinder (CC) itself, which cooled the whole apparatus ; and when steam was admitted again from the boiler, a great quantity of it was consumed in heating the cooled surface up to the boiling point, which must be done before the steam could have sufficient elastici- ty to move the machinery. Various subordinate contrivan- ces were also employed, with the view of pft)moting conve- nience or economy, the principle of which will be understood from the description of the annexed figure, vrhich represents the steam engine in its most improved state. A. The Boiler, containing a large quantity of water, which is constantly renewed as fast as portions are converted into steam. B. The Steam Pipe, conveying the steam to the cylinder, having a steam cock h to admit or exclude the steam at pleasure. C. The Cylinder, surrounded by the jacket c c, a. space kept constantly supplied with hot steam, in order to keep the cylinder from being cooled by the ex- ternal, air. D. The Eduction Pipe, communicating between the cyl- inder and the condenser. E. The Condenser, with a valve e, called the Injection cock, admitting a jet of cold water, which meets the steam the instant the latter enters the condenser. P. The Air Pump, which is a common suction pump, but is called the air pump because it removes from the condenser, not only the water, but also the air and steam that escapes condensation. GG. The Cold Water Cistern, which surrounds the con- denser and supplies it with cold water, being filled by H. The Cold Water Pump. I. The Hot Well, containing water from the condenser K. The Hot Watep>, Pump, which conveys back the water of condensation from the hot well to the boiler. LL. Levers, which open and shut the valves in the chan- nel between the steam pipe, cylinder, eduction pipe, and condenser ; which levers are raised or depressed In what consisted the great improvement of Watt ? Describe the old method. Give a description of the various parts in order from the iigurea. 190 PNECMATICy: • by projections attached to the piston rod of the con- denser. MM. Apparatus for Parallel Motion. By this contri- vance the piston rod is made to move in a right line, although the end of the vrorking beam moves in the arc of a circle. NN. The Working Beam. Fig. 102. 00. The Governor. This consists of two heavy balls, suspended from a perpendicular shaft, in such a manner as to be capable of falling close to the side of the shaft when at rest, but when made to revolve, they recede from it by the centrifugal force. Now, by connecting the governor with the fly wheel, it is made to partake of the common motion of the en- gine, and the balls will remain at a constant dis- tance from the perpendicular shaft, so long as the motion of the engine is uniform ; but whenever the engine moves faster than usual, the balls will recede STEAM ENGINE. 19. larther from the shaft, and by raising a valve con- nected with the boiler, will let off such a portion of the force as to reduce the speed to the rate required. P. The Crank. This, when the end of the working beam, to which it is attached, descends, turns the fly wheel half round, and when it rises, completes the revolution of the wheel. QQ. The Fly Wheel. The motion of the piston, being communicated first to the working beam, and thence to the crank, is finally received by the fly wheel, which, by its inertia, as explained in Art. 141, ren- ders the force uniform. The main shaft or axis to which the fly wheel is attached, receiving thus a uni- form rotation, motion may be transferred from it to every kind of machinery. 244. The kind of valve chiefly employed in the steam engine, is tha.t called the puppet valve* It resembles the stopper of a decanter, but is more obtuse. All these various appendages of the machine are carried by the engine itself; the air pump is worked by having the piston rod attached to one arm of the working beam, and the valves are opened at the instant required by means of levers, to which also motion is communicated from the same source. 245. Soon after the invention of these engines. Watt found that, in some instances, inconveniences arose from the too rapid motion of the steam piston at the end of its stroke, owing to its being moved with an accelerated motion.^ This was owing to the uniform action of the steam pressure upon It. For on first putting it in motion, at the top of the cylin- der, the motion was comparatively slow ; but from the con- tinuance of the same pressure, the velocity with which the piston descended was continually increasing, until it reached the bottom of the cylinder where it acquired its greatest velocity. To prevent this, and to render the descent as nearly uniform as possible, it was proposed to cut ofi" the steam before the descent was completed, so that the remainder might be effected merely by the expansion of the steam which was admitted to the cyiinder.J To accomplish this * Several examples are seen in the figure, on the right of the cylinder, above and belew. t For since the steam continues to act upon the piston during its descent, its velocity would be constantly increased, Hke that of a ball in the barrel of a gun. ^ Steam engines constiucted on this principle are said to act czpanaivdy. What kind of valve ia used? Describe it! When are steam engines said to act expansively ? 192 PNEUMATICS, he contrived, by means of a pin on the rod of the air pump, to close the upper steam valve wrhen the steam piston had completed one third of its entiredescent, and to keep it closed during the remainder of that descent, and until the piston again reaches the top of the cylinder. By this arrangement the steam pressed the piston with its full force through one third of the descent, and thus put it in motion ;' during the other two thirds of the way, the steam thus admitted acted merely by its expansive force, which became less in exactly the same proportion as the space, given to it by the descent of the piston, increased. Thus, during the last two thirds of.the descent, the piston is urged by a gradually decreasing force, which in practice is found just sufficient to keep up in the piston a uniform velocity. Another advantage gained by this contrivance, independently of the uniformity of motion, was, that two thirds of the fuel was saved ; for in- stead of consuming a cylinder full of steam each descent of the piston, only one third of a cylinder was necessary. 3 46* As an example of a selfWegulating machine, the steatn engine surpasses all other forms of machinery. On this subject, Dr. Arnott has the following remarks. " The steam engine, (says he,) in its present improved state, appears to be a thing almost endowed with intelligence. It regulates, with perfect accuracy and uniformity, the number of its strokes in a given time, and, moreover, counts or re- cords them, to tell how much work it has done, as a clock records the beats of its pendulum. It regulates the supply of water to the boiler, the briskness of the fire, and the quantity of steam admitted to work ; opens and shuts its valves with absolute precision ; oils its joints ; takes out any air which may accidentally enter intd parts where a perfect vacuum is required ; and when anything goes wrong which it cannot of itself rectify, it warns its attendants by ringing a bell. Yet with all these talents and qualities, and even when possessing the power of 600 horses, it is obedient to tlie hand of a child. Its aliment is coal, wood, charcoal, or other combustibles ; but it consumes none while idle. It never tires, and wants no sleep ; it is not subject to any malady when originally well made, and only refuses to work when worn out with age. It is equally active in all climates, and will do work of any kind. It is a water pumper, a How ip Bteam cut off during the descent of the piston 7 By what force is the pistrn moved during the last two tliirds of its descent? How much force was saved by this contriv ance ? What is said of the steam engine as a self- regulating machine 1 Recite Dr. Arnott's remarks on this subject. STEAM ENC;NE. 193 miner, a sailor, a cotton spinner, a weaver, a blacksmith, a miller ; and a small engine in the character of a stearn pony, may be seen dragging after it on a railroad a hundred tons of merchandise, or a regiment of soldiers, with greater speed than that of our fleetest coaches. It is the king of machines, and a permanent realization of the ^wm of eastern fable, whose supernatural powers were occasionally at the command of man." 247. The Locomotive is a form of the steam engine adapted to motion. It is employed chiefly in conveying loads on railways. As it is important to consult for light- ness, and for compactness of structure, steam of a high power is worked, and no condensing apparatus is used. The boiler is traversed horizontally by a great number of stout copper tubes, (one hundred or more,).a.bout two inches in diameter. These serve as flues, through which the flame and smoke from the fire circulate in their passage to the chimney. Their diameter being small, their strength is great, so that they are not liable to burst with high pressure steam, while the water of the boiler, through which they pass, is by this means brought extensively into contact with a heated metallic surface. In figure 103, F is the furnace. Fig. 103. r,f which D is the door at which the fuel is introduced, and N is the grate. The entire space represented by the letters BB is occupied by the boiler. This is traversed by the metallic tubes pP^ open at both ends and serving as flues Locomotive. — Describe it. 17 194 METEOKILO&Y. through which the smoke and hot air pass from the fur nace to the chimney C. The level of the water in the boiler, is indicated by the horizontal dotted line, and the space above this is occupied by the steam. V is a valve worked by the lever L, which opens or closes it at the pleasure of the engineer, who stands on a stage directly in front of the furnace door. On opening V the steam rushes in, following the direction of the arrows, through the steam- pipe SS, and entering the piston box, forces the piston P before it, the steam at the left of P at the same time es- caping into the chimney C. As soon as the piston has reached the limit on the left, the sliding valve carried by the lever N, admits the steam on the left, and permits it to escape on the right into the chimney. By this means, the piston is alternately moved to the right and left ; and, by means of the crank R, motion is thus given to the driving wheels KK, impelling the locomotive forward on the railway. ■^•'^SS^ CHAPTER III. OP METEOROLOGY. 348 • Meteorology is that branch of Natural Philosophy which treats of tlve Atmosphere. In Pneumatics, we learn the properties of elastic fluids in general, on a small scale, and by experiment rather than by observation ; but in Meteorology, we extend our views to one of the great de- partments of nature, and we reason, from the known proper- ties of air and vapor, upon the phenomena and laws of the entire body of air, or the atmosphere. The term was first used by the Grecian philosophers, and denoted what is above the earth* in distinction from what exists on th» surface. 249. Meteorology leads us to consider, first the descrip- tion of the atmosphere itself, including its extent, its weight, its condition at different heights in respect to density and emperature, and the elements that compose it ; secondly, the relation of the atmosphere to water .^ including the manner • From ftETKJjpos, sublimls, high, lofly. Point out the uses of the eeveial parts in Fig. 103. Meteorology. — Define it. How does it differ from Pnenmatica i What was its original meaning as used by the Grecian philosophers ' ATMOSPHERE. 195 in which vapor is raised into the atmosphere, the mode in which it exists there, and the various ways in which it is precipitated in the form of dew, fog, clouds, rain, snow, and hail ; thirdly, the relations of the atmosphere to heat, em- bracing the motions of the atmosphere as exhibited, in a small scale, in artificial draughts and ventilation, and on a large scale, in winds, hurricanes, and tornadoes ; finally, in the relations of the atmosphere to fiery ineteors, as thunder and lightning, aurora-borealis, and shooting stars. EXTEMT, WEIGHT, DENSITY, AND TEMPERATURE OF THE AT- MOSPHERE. 250. The atmosphere is a thin transparent veil envel- oping the earth, and extending to an uncertain height ; probably not less than one hundred miles above it. Phi- losophers have endeavored to measure the height of the atmosphere from the twilight. The last ray of twilight strikes the eye of the spectator when the sun is eighteen degrees below the horizon, being then reflected to the eye from the top of the atmosphere. On this supposition, the height of the place of reflexion may be calculated, and proves to be about forty miles. We have, however, evidence that the atmosphere extends at least 100 miles from the earth, and probably much farther, although it becomes ex- ceedingly rare, at a height even of forty miles. 251. The weight of the entire atmosphere may be easily estimated by means of the barometer ; for, taking the medium height of the barometer at 30 inches, the weight of the atmosphere is equal to that of a sea of quicksilver, covering the whole earth to the depth of two and a half feet. This would add five feet to the diameter of the globe, and the contents of the whole mass of quicksilver, in cubic feet, would be equal to the difference between the solid con- tents of the globe, and those of a sphere having a diameter five feet greater. ' Having given the number of feet of quicksilver,* we have only to multiply that number by the weio-ht of one foot, and we obtain, by calculation, for the * Since quicksilver ia 13.58 times heavier than water, and a cubic foot of water weighs G2.i lbs., couaequuntly 62.5X13.58—8483 lbs. What Bubiects does Meteorology lead us to consider ? Specify the subjects embraced uiider the description of the atmosphere ; under its relations to water ■ to heat ; and tofierv meteors. What is the heigU of the atmosphere S Hovr have philosophers endeavored to measure it ? What is its state at the height of forty miles, and beyond 1 How may the weight ot the whole atmos- phere be estimated 1 19fi METEOROLOGY. "■€ight of the whole atmosphere, more than eleven trillions of pounds, or five thousand biilions of tons. 252. Were the atmosphere of equal density throughout, jt would be easy to determine its height, since opposite columns of different fluids are in equilibrium when their heights are inversely as their specific gravities. (Art. 191.) rherefore, as the specific gravity of air is to that of quick- silver, so is the height of the column of quicksilver to the corresponding height of the column of air that balances it ; and since quicksilver is ten thousand four hundred and forty times as heavy as air. and since the height of a column of quicksilver which balances a column of the atmosphere, is two and a half feet, therefore, ! : 10440 ; : 2.5 : 26,100 feet=5 miles, nearly. But the atmosphere is very far from being throughout of uniform density. Several causes conspire to make its density very unequal. First, the different quantities of superincumbent air at different altitudes, the weight sus- tained growing less and less as we ascend ; secondly, the decreasing attraction of the earth in proportion as the square of the distance from its center increases; and, thirdly, the influence of heat which diminishes the density, and of cold, which increases it. 253> Since the space or volume occupied by a given weight of air is greater as the compressmg force is less, and since that force, so far as depends on the superincumbent mass, is constanly diminishing as we ascend, therefore. The densities of tlie air decrea.se in a geometrical, as tht distajices inc. ease in an arithmetical ratio. By observations on the barometer at different altitudes, aided by calculation, it is ascertained that at the height of seven miles above the earth, the air is only one fourth as dense as it is at the surface. Hence, if we take an arith- metical series increasing by seven, to denote different heights, and a geometrical series whose constant multiplier is one fourth, to denote the corresponding densities we may easily ascertain the density of the air at any proposed elevation. Arithmetical series, 7, 14, 21, 28, 35, 42, 49. Geometrical series, ■}■, tV, -s^-, s+r, -r-;f„-r — i— i J »1 ill) 64) 356) IU21) 409G) Is 3 8 4* What is it in pounds? What would be ita height if it were of the same density throughout ? Specify the three causes which make the atmoepliere of unequal density at difterent elevations. How do the densities of the air decrease as we ascend from the earth ? How many mil«s make the deJisitv one fouj-tb what it was before ? ^ ATMOSPHERE. 197 From this table it appears that at the height of twenty- one miles, the air is sixty-four times as rare as at the surface of the earth ; at the height of forty-nine miles, sixteen thousand three hundred and eighty-four times as rare ; and if we pursue the calculation, we shall find that its rarity at the moderate distance of only one hundred miles, is one thousand million of times greater than at the earth, and, of course, would oppose no sensible resistance to bodies revolving in it. 254. If there were an opening in the interior of the earth, which would permit the air to descend, its density would in- crease in the same manner as it diminishes in the opposite direction. At the depth of about 34 miles, it would be as dense as water ; at the depth of 48 miles, it would be as dense as quicksilver ; and at the depth of about 50 miles, as dense as gold. 25 5« As we ascend from the earth, the tempefoture of the air continually diminishes, until we arrive at a region of frost, the lower limit of which is called the term ol 'perpetual congelation. The height of the term of perpetual congela tion at the equator is almost three miles ; at the parallel of 35^, about two miles; at the latitude of 40\ about a mile and three fourths ; while at the latitude of 80 ', this region approaches very near the earth, and at the pole comes nearly or quite down to the earth. It ought to be particularly remarked, that the different heights decrease very slowly as we recede from the equator, until we rrach the limits of the torrid zone, when they decrease much more rapidly, and most rapidly of all in the middle latitudes from 40 to 45,^ the average difference for every five degrees of latitude from 30 to 60 being 1334 feet, while from the equator to 30 the average is only 509, and from 60 to 80° it is only 891 feet. Important meteorological phenomena depend on this fact. RELATIONS OF THE ATMOSPHERE TO WATER. 256> The atmosphere is composed chiefly of two gases, oxygen and nitrogen, in the proportion of four fifths nitrogen and one fifth oxygen ; but besides these two ingredients, it What is the density at 21, 49, and 100 miles respectively 1 How would the density increase by descending below the surface of the earth 7 How dense at the depth of 34, 48, and 50 miles? What change of temperature does the air sustain as we ascend from the earth? What is meant by the term of perpetnal congelation ? Height of this term at the equator, — at the latitude of 35", 40o, 80 >, and 90 ■ ? What ought to be particularly remarked ? Of what two gases is the atmo&phere composed ? State the proportion of each 7 17' 19S METEOnOLOGY. always contains more or less watery vapor, a minute portion of fixed air or carbonic acid, and various exhalations, which are generally too subtile to be collected in a separate state. By the heat of the sun, the surface of the earth is daily sending into the atmosphere vast quantities of watery vapor which rises not only from seas and lakes, but even from the land, wherever there is any moisture. The vapor thus raised, either mixes with the air and remains invisible, or it rises to the higher and colder regions, and is condensed into clouds. Sometimes accidental causes operate to cool it near the surface of the earth, and then it forms fogs. From the upper regions of the atmosphere, the vapor, when condensed, returns to the earth in the form of dew, and rain, and snow, and hail. 257. The quantity of water which can exist at any moment in a given volume of air. depends on the temper- ature of the air. and when any portion of the atmosphere is charged with as much vapor as it can hold, it is said to be saturated. As the air grows warmer, the amount of vapor required to saturate it increases rapidly doubling for every 27 degrees. Thus a volume of air can contain At 3-2°, the 160th part of its own weight. •' 59^ " 80th " " 86', " 40th " « 113", " 20th " So that, while the temperature increases in arithmetical, the amount of water the air can contain, increases in a geomet- rical progression. Any vapor diffused through the air over and above the amount due to the temperature, does not re- main in the invisible elastic state, but in the state of mist, composing fogs and clouds ; and if any portion of air be cooled down below the point at which all the moisture in it would be saturated, the excess will be condensed, and no more will remain in the invisible elastic state, than just the amount due to that temperature. 258. The teni2xrature at ivhich watery vapor is con densed from the atmosphere is called tl\e dew-point. What other ingredients does the atmoppliere contain? How is watery vapor raised into the atmosphere ? From what sources? What becomes of it? What happens when it is cooled near the surface of the earth ? In what different fornis does it descend from the upper regions? Upon what depends the quantity of water which can exist in the atmosphere? When is the air said to be saturated? How is the amount required to saturate it affected by heating and cooling it ? How many degrees of heat are required to double the amount? What takes place when more vapor is added than is sufficient to saturate the air ? Deiine the dew-point. RELATIONS OP THE ATMOSPTtERE TO WATER. 199 If, at any time, we find that a slight cooling- of the air condenses moisture, then the dew-point is high, showing that the air is nearly saturated with water ; but if a portion of the air requires to be cooled down many degrees before moisture appears, then the dew-point is low, and the air is far from being saturated. Thus, on a sultry summer's day, we frequently observe drops of moisture collect on a tumbler of cold water, because the air that is in contact with the outside of the tumbler being cooled below the dew-point, has all its moisture condensed, which it contains over and above the quantity due to the temperature of the water. At another time, we see no water collected on a tumbler equally cold, because the amount of vapor in the air at that time is so small, that the dew point is below the temperature of the cold surface. We can easily ascertain the dew-point, by putting a thermometer into a tumbler of ice-cold water, and observing at what degree watery vapor begins to be visible on the outside of the vessel. The dew-point affords the means of judging of the comparative dryness or dampness of the air. When a portion of the atmosphere grows warmer without a corresponding increase of vapor, it be- comes very dry; and when it grows colder, the amount of vapor remaining the same, it grows damp. Hot air may contain a large proportion of vapor and yet be very dry. and cold air may be very damp and yet contain but a small pro- portion of watery vapor. With these principles clearly in view, the learner will be able to understand the causes of several familiar phenomena which we will now proceed to explain. L^ 259. Dew is moisture precipitated from the air on sur- yuces colder than itself. It does not fall from the sky, but as the ground becomes at night colder than the air, (as we find by applying the thermometer to both,) the air deposits its moisture upon it just as a film of moisture is found on a tumbler of cold water in a sultry day. Dew does not form on all substances alike that are equally exposed to it. Some substances on the surface of the earth more easily part with their heat than others, and grow colder at night, and these receive the greatest deposit of dew. Deep water, as that of the ocean, does not grow colder in a single night, and When is it said to be liigh and when low? Why does moisture collect on the outside of a vessel of cold water ? Describe the mode of ascertaining the dew-point. How do we judge of the comparative moisture and dryness of the air ? DeKne Dew. Why formed on the surface of the ground at night » Why on dilFercnt substances unequally ? 200 METEOKOLOGY. therefore receives no dew ; and the naked skins of aninmts. being warmer than the air, receive none, although the mois- ture which is constantly exhaled from the animal system itself, as soon as it comes into contact with the colder ail that surrounds the person, may be condensed and moisten the clothes in such a way as to give the appearance of dew. In this manner, also, frost (which is nothing more than frozen dew) collects, in cold weather, on the bodies of domes- tic animals. By a beautiful provision of Providence, dew is always guided with a frugal hand to those objects which are most benefited by it. Green vegetables receive much more than naked sand, equally exposed, and none is squan- dered on the ocean. 260« Fog is ivatery vapor precipitated in the air near the earth. Fogs are formed when the lower portions of the atmosphere are, by any cause, cooled below the dew-point. The vapor may be such as is just rising from the ground, or such as before existed in the air. and meets and mixes with colder air. Thus, in a cold morning, smoke, or condensed vapor, proceeds from various moist substances, as from the breath of animals from a ho'e in the ice of a river, from wells, and from many other sources. In each case, the vapor meets with air colder than itself which, being already saturated, condenses it in the form of mist. A striking ex- ample of fogs is seen over rivers, particularly in a summer morning, marking out their courses for a great distance Here, since the temperature of the water changes but little during the night, while the neighboring land, and of course the air over the land, has become cold, the vapor which rises from the river during the night and meets with cold air, is condensed into a fog. The fogs formed over shoals and sand banks, as the banks of Newfoundland, are deposited from the warm and humid air of the ocean, which is cooled by mixing with the cold air over the banks. 261. Clouds are dependent on the same principle as fogs, consisting of vapor condensed by the cold of the upper regions ; and the mode of cooling, as in the case of fo^s, may be, either by the ascent of vapor into the upper and colder regions of the atmosphere, or by the meeting of op- posite currents of wind of different temperatures, the mois- ture being always precipitated from the warmer ty the Why none on the ocean, or on livins; animals? Define i^o». How formed? Why formed in a cold morning ? Why over rivers ? Why over shoals and the Banks of Newfoundland? How are Clouds formed ? RELATIONS OF THE ATMOSPHERE TO WATER. '201 influence of the cooler portion, which reduces its teinperaiure below the dew-point. The clouds are of four different classes— the cumulus, the stratus, the cirrus and the nimbus. The cutuulus (Fig. 104, a,) is chwacterized by masses of vapor piled on each other, Cumulus, -Fig. 104. Cirrus. as is sometimes seen in forms of much grandeur in a gathering thunder-storm, or in single white clouds that sail through the sky before a north-westerly wind. The stratus (Pig. 105, b.) consists of vapors spread more evenly over the face of the sky, as is seen covering the sky, uniformly, in a cloudy day, or extending in long horizontal layers. The cir- rus (Fig. 104, c,) is so named from its resemblance to carded wool, and consists of a thin veil of long radii sometimes bent into wisps, at a high elevation. The nimbus, (Fig. 105, d,) or rain cloud, is usually seen scudding below the stratus in a rainy day. From the cumulus, the stratus, and the cirrus clouds, three compound clouds are found, each partaking of the characters of two of the simple varieties. Lowest is the cumulostratus, (Fig. 105, e,) which is composed of the stratus Stratus and Nimbus. Si! Fig. 105. Compound Clouds. s te;?-^"? ^^^ E ^B ^s in the main body, but partakes of the cumulus on its borders, being there of a lighter or yellowish hue. and often tufted with small rounded masses. The cirro-stratus (Fig. 105, h.) has likewise the stratus in the principal part, but is fringed or feathery on the margin. The cirro-cumulus (Fig. 105, n,) Name the different clasaea, and describe each kind of cload. 202 METEOROLOGY. exhibits the cumulus cloud broken up in small tufts, giving to the sky a fleecy appearance, at a great elevation. 262. The interest felt in viewing the clouds, is greatly increased by learning their names. They assist us also in foreseeing changes of weather, the appearance of the cu- mulus denoting fair, and that of the nimbus, foul weather. The nimbus is the lowest among the clouds sometimes seeming little else than a fog raised a few hundred feet above its ordinary elevation ; the cumulus is next in order as we ascend ; then comes the stratus, and finally the cirrus. The clouds float at variable heights, from a quarter of a mile to six or eight miles. 263. Rain is water precipitated from the atmosphere in drops. It implies a more sudden and copious condensation of vapor than is necessary to form fog or cloud, such as takes place when a warm and moist portion of air is cooled con- siderably below the dew-point, and the amount of vapor precipitated is so copious as to unite in drops. A mixture of different bodies of air of different temperatures, one cold and the other warm, with its dew-point high, is the usual antecedent and attendant of rain ; and in places where such mixtures do not occur, it seldom or never rains, as in Egypt, where a constant wind blows up the valley of the Nile. On the other hand, great storms of rain are usually attended by the meeting of gusts of winds from opposite quarters, and of very different temperatures. Fig. 106. What pi-actical advantages ariBC from studying the clouds? State their different heights. Define Kmn. When is vapor deposited in rain ? W^=. ciroumstanoes attend the forn/ation of rain ? Wliere does it seldom or Z.^^ r.«n ? By what are great storms (if rain attended ? "i-ver RELATIONS or THE ATMOTHERE TO WATER. 203 264« Siiow is crystalized rain. When the air is near the freezing point, the drops of rain crystalize. as they form, into numerous geometrical figures, of which not less than six hundred varieties have been described by naturalists, although the most common form is the star, consisting of six radii diverging from a common center, and this tendency to divide into six prevails in all the forms. (Fig- 106.) By crystalizing, the watery vapor is purified, arid sxiow water is the purest of all natural waters. By this process, also, the specific gravity of water is diminished, snow flakes being but little heavier than the air, so as to fall lightly upon the earth, and to spread over it a downy covering wonderfully adapted tc confine the heat of the earth, which is its great purpose in the economy of nature. 265< Hail is water precipitated from the atmosphere in the form of ice. When the watery vapor is condensed sud- denly, and in great quantity, by an extraordinary degree of cold, then the vapor which would otherwise be condensed into drops of rain, or crystals of snow, freezes into solid lumpS; which sometimes accumulate, before they reach the earth, into large masses, forming hail-stones of great size. The larger varieties of hail are probably produced by whirl- winds, which hurl a body of very hot and very moist air into the upper regions of the atmosphere where the cold is sufficient to produce sudden congelation, and the hail stones being mechanically buoyed up for a long time by the force of the whirlwind, grow, by the accession of successive layers of ice, into large masses before they finally fall to the ground. Hail-stones are confined, for the most part, to the temperate zones, being seldom witnessed either in the equatorial or the polar regions because it is only in the middle latitudes that the two conditions can meet, namely, a very hot and humid portion of air exposed suddenly to an exceedingly cold medium. In the torrid zone, although the body of hot and humid air may be found, yet the region of congelation is higher than is often reached by whirlwinds; and, in the frigid zone, although the cold medium may be easily found, yet the body of hoi and damp air is wholly wanting. Svvit- Define Snow. Under what circamstanceB is it formed ? How many varieties are there of crystals of snow ? State the most common form 1 Uses of snow in the economy of nature 1 Define Hail. Under what circumstances is it formed? How are large hail-stones produced? To what parts of the earth are hail storms chiefly confine ' ' Why do they prevail chieHy in the temperntji zones ? 204 METEOKOLOGY. zerland and the south of France are peculiarly subject to violent hail storms, for there the hot winds ihat blow from Africa across the Mediterranean, meet with the cold snow- clad peaks of the Alps, and thus present a combmation of circumstances more favorable to the formation of hail-stormg than is found in any other part of the earth. DELATIONS OF THE ATMOSPHERE TO HEAT. 266. Four great subjects arise out of the relations of the atmosphere to heat, — namely, Climate, Ventilation, Winds, and Stoxms. Since also Meteorological Instruments are intimately connected with these subjects it is convenient to consider thom under the same head. It is chiefly by the agencies of heat that air is put in motion. If a portion of air is heated more than the sur- rounding portions, it becomes lighter, rises, and the sur- rounding air flows in to restore the equilibrium ; or, if one part be cooled more than another, it contracts in volume, becomes heavier, and flows off" on all sides until the equilib- rium is restored. Thus the air is set in motion by every change of temperature ; and. as such changes are constantly taking place, in greater or less degrees, the atmosphere is seldom at rest at any one place and never throughout any great extent. These changes of temperature are measured by the Thermometer ; the changes in density, by which the air over a given place becomes sometimes heavier and some- times lighter, are determined by the Barometer ; the degree of dampness in the air is ascertained by the Hygrometer ; the direction of the wind, by the Vane; and the amount of water precipitated from the atmosphere, by the Kain- gage. 267. Thermometers are of various kinds, but that in common use is called from the inventor, Fahrenheit's Ther- mometer, It consists of a small hollow ball called the bulb^ and a fine tube called the stem. The bulb and a part of the stem are filled with quicksilver, which, like other fluids, expands by heat and contracts by cold. When therefore, the air grows warmer, the quicksilver rises in the stem, and sinks again as the air grows colder. Now it is known that while snow is meltino- the water Why in the south of France ? "What subjects ari.so out of the relations of the atmosphere to heat ? What puts air in motion ? How are the changes of temperature, of density, of humidity, and the course of the wind respectively determined? Describe FahrenUeti's thermometer? RELATIONS OF THE ATMOSPHEKE TO HEAT, 205 does not change its temperature until every particle of the snow is melted; and, moreover, that water while boiling constantly remains at the same fixed temperature. If then, we insert the bulb of a thermometer into a vessel of melting snow, the quicksilver will settle to a certain point, and there remain at the same level in the stem until all the snow is liquified; and if we place the thermometer in a vessel of boiling water, the quicksilver will rise to a certain level in the stem and remain there until all the water is boiled away. With a file, or the point of a diamond, we may make a mark on the stem where the metal stands in snow water, and another where it stands in boiling water, and we may divide the part of the stem between these two points into 180 equal spaces, called degrees. We may continue the same divisions on the stem above and below the boiling and freezing points respectively, and thus form the scale of the thermometer. Fahrenheit's scale begins at 32 degrees below the freezing point of water; and, consequently, the boiling is 32+180, or 212 degrees. Instead of marking the divisions of the scale on the stem of the instrument, it is found more convenient to mark those of the same intervals on a strip of ivory, and to attach this to the stem. 268. In the use of the thermometer as a weather-glass, the object is to ascertain the exact temperature of the air, simply, unaffected by any accidental circumstance which might either raise or depress the mercury above the level at which the air alone would cause it to stand. We must, therefore, guard it against either the direct or reflected rays of the sun, and from contact with bodies which are either colder or warmer than the air, such as the walls of a large building, especially when built of brick. A position in a shady place where the air circulates freely, at "a height of about seven feet above the ground, is the most suitable ex- posure. If convenience requires that the instrument should be placed on the wall of the house, (as in the frame of a window,) the effect of the wall in elevating or depressing the mercury should be ascertained by observation, and the correction applied. Finding it convenient to attach my ther- mometer to the outside casement of my bedroom window, I ascertained that, during summer, by the influence of the How can we determine the two fixed points of the scale corresponding to the freezing and the hoiling point of water? Into how many degrees is the epace hetween these two points divided ! How far below the freezing point of water ia the beginning of the scale or ? What is the object when tha thermometer is used as a weather-glass ! How is it to be placed ? 18 205 METEOROLOGY. house, the thermometer stood two degiecs higher in the morning- and four degrees lower in thu afternoon than a thermometer properly exposed, near by. to the influenre of the air alone. I therefore corrected my morning observa- tions by subtracting two degrees, and those of the afternoon by adding four degrees. It is, however, better when prac- ticable to secure a place of exposure that is unexceptionable, than to depend on correcting a place that gives imperfect resuhs. When a register of observations is kept, the times of record may be sunrise for the minimum, and two o'clock P.M. in the winter months, and three o'clock in the summer. The morning and afternoon observations being added together and divided by 2, we obtain the mean for the day. The sum of the daily means, divided by the number of days in the month, give the monthly mean, and the sum of these divided by 12, give the mean of the whole year. Kesults somewhat more accurate are obtained from three daily observations, viz. at nine o'clock morning and evening, and at three o'clock in the afternoon. 269. The Barometer has been already described, and its uses pointed out. (See Art. 228.) It is of all instru- ments the most important to the meteorologist, indicating, as it does, the slightest variations in the pressure of the atmosphere, and with these are connected a large part of all atmospheric phenomena. In all meteorological instruments, but more especially in the barometer, great pains should be taken to procure such as are accurate and reliable ; and this precaution is the more necessary since many of the ther- mometers and barometers sold in the market are not accurate enough for scientific observations. The place of exposure of the barometer may be a hall where the outside doors are frequently opened, and the times of record the same as those of the thermometer. 37 O. The Hygrometer is an instrument for measuring the degree of humidity of the atmosphere. It is made of various forms, but its general principle may be understood from the method of finding the dew-point. (Art. 258.) We pour water into a tumbler in which is inserted a thermom- eter, and adding a little snow or pounded ice to cool it, observe the temperature at which dew begins to form on Describe the times of takings and recording observationa. Barometer, • Its great valae to the meteorologiat ? Care to betaken in order to secure accurate meteorological instruments ? Hygromet&i — How may the general principle be easily illustrated ? CLIMATl. 207 the outside of the tumbler. If a slight cooling of the water below the temperature of the air causes a film of dew to appear, that is, if the dew-point is high, we infer that the air is very damp ; but if the water requires to be cooled very far below the temperature of the air, that is, if the dew- point is low, we infer that the air is very dry. Between these two extremes various degrees of dampness may be indicated and thus this apparatus becomes a simple form of hygrometer. This instrument often affords the means of judging of the probable state of the weather for some time to come. When the hygrometer indicates a low degree of humidity, and remains at nearly a fixed point, dry weather may be expect- ed to continue and increase ; but when the hygrometer denotes that the air is very humid, failing weather soon follows. Moreover, when the hygrometer shows an in- creasing humidity, it is a sign of rain, as a decreasing humidity, is a sign of fair weather. 271. The Eain-gage is an instrument for ascertaining the quantity of water that falls from the sky in the various forms of rain, snow, and hail. The simplest form is a tall tin cylinder, (Fig. 107,) with a funnel-shaped top, having a graduated glass tube communi- ^'S- 1"^- eating with the bottom and rising on the side. The water will stand at the same level in the tube and in the cylinder, and the divisions of the tube may be such as to indicate minute parts of an inch, and thus determine the amount of rain that falls on the area of the funnel, suppose a square foot. It is useful to know the amount of rain that falls annually at any given place, not only in reference to a knowledge of the climate, but also to many practical purposes to which water is applied, such as feeding canals, turning machinery or irrigating land. After an acquaintance with the foregoing meteorolog-ical instruments, we may now pursue our inquiries into the relations of the atmosphere to heat. CLIMATE. 27 2« Climate is the condition of a country with respect to How does it affoi-d the means of foretelling the weather 1 Define the Rain-gage. Why is it important to know the qnantity of rain that falls at any given plat:e ? Define Climate. 208 METEOROLOGY. all the meteorological phenomena. It embraces all that is pe- culiar to that particular region in regard to heat and cold, dampness or dryness of the atmosphere ; dew, fog, rain, snow, or hail j prevailing winds and storms ; thunder and light- ning ; and fiery meteors. Two great causes chiefly control the climate of a country, one depending on its latitude, and the other on its eleva.tion above the level of the sea. In the torrid zone, the direct rays of the sun, and the equality of the days and nights, produce a uniformity of climate unknown in the higher latitudes. Here, in flat and low countries especially, hot weather generally prevails throughout the year, the ther- mometer varying" only through the small range from 60 to 85° In the temperate zone, the peculiarities of climate depend on the obliquity of the sun's rays, (which greatly diminishes the power of his heat.) and the inequality in the length of the days and nights, occasioning a great accumu- lation of heat in the summer, and of cold in the winter. The heat of mid-summer frequently reaches a higher degree than in the torrid zone, — an effect due chiefly to the length of the day and shortness of the nigbt ; and the length of the winter nights conspires with the oblique direction of the sun's rays to cause a great accumulation of cold in the winter. The same causes act with still greater intensity in the frigid zone, although the masses of ice contribute to prevent the great accumulation of heat which might be expected to occur at mid-summer, when the sun is for some time contin- ually above the horizon. 27 3« But the elevation of a country above the general level of the sea has as great an influence over its climate as difference of latitude. As in proceeding from the equator towards the pole, the average temperature of a place for a year becomes one degree less for every degree of latitude, so as we ascend a high mountain, the thermometer falls one degree for every 300 feet ; so that, in climbing a very high mountain, as a peak of the Alps, for example, or of the Andes, we may leave at the base the heat of summer, and pass successively through all the varieties of the season to the extreme cold of winter. The verdure of sprino-, the What particulars does it embrace ? What two caaaea chiefly control the climate of a country? Describe the climate of the torrid zone, and the causes on which it depends. Do the same for the temperate zone, and for tlie firigid zone. How does the relative elevation of a country affect its climate 1 How many feet must we ascend for the thermometer to fall one degree ? Describe the different climates that prevail on tlie same mountain at different elevations. VENTILATION. 209 flowers of summer, the fruits of autumn, and the snows of winter, may be found at different altitudes at the same time. Several other causes, also, greatly modify the climate of a country. Since deep waters, as those of the ocean, do not so readily change their temperature as the land, ihey tend to equalize the temperature of coasts and islands, moderating both the heat of summer ;ind the cold of winter, while the great quantity of heat given out when water is changed to ice or snow, contributes much to temper the severity of a polar winter, as the heat that is absorbed and made to dis- appear, when ice and snow are melting, tends equally to check the heat of the summer's sun. VENTILATION. 274. Ventilation is the art of supplying apartments with pure and wholesome air. The most familiar example we have of the effects of heat in setting air in motion, is in the draught of a chimney. When we kindle a fire in afire-place or stove, it rarefies the air of the chimney, and the denser air from without rushes in to supply the equilibrium, carrying the smoke along with it. Smoke, when cooled, is heavier than air, and tends to descend, and does descend unless borne up by a current of heated air. A hot current of air in a chimney is cooled much more rapidly when the materials of the chimney are damp, than when ihey are dry, and therefore it will 'cool much faster in wet than in dry weather. It is essential to a good draught, that the inside of a chimney should be smooth, for air meets with great resistance in passing over rough substances. Burning a chimney improves the draught, principally by lessening the friction occasioned by the soot. In stoves for burning anthracite coal, it is important to the draught, that no air should get into the chimney except what goes through the fire. On account of the great resist- ance which a thick mass of anthracite opposes to the air, this will not work its way tiirough the coal if it can get into the chimney by any easier route. Hence the pipes which conduct the heated air from a stove to the chimney, should What other caases influence the climate of i place ? Define Ventilation. How is the air set in motion by the draught of a chimney ? Is smoke, when cold, lighter or heavier than air? What makes it ascend in a chimney? Eirect of dampness upon the draught ? Why should a chimney be smooth ! Why does burning ai-chimney improve the draught ? lii stoves for anthracite, why important that no air should enter the chimney except through the fire ? IS* 210 METEOROLOGY. Fiif. 108 be close, especially the joint where the pipe enters the chimney; and care should be taken that there should be no open fire-place or other means of communication, between the external air and the flue with which the stove is con- nected. 27 5. A good illustration of the principles concerned in the draught of a chimney, is seen in the manner in which air circulates in the shaft or pit of a deep mine. Such a rirculiition is kept up briskly, even amounting sometimes to a strong wind, when two shafts or pits of unequal heights are made to communicate with each other by means of a horizontal gallery called a drift. The earth remains nearly at the same temperature summer and winter, while the external air is hotter in summer and colder in winter, than that within the mine. Now were the air within the earth and without of the same density, then the air of the two shafts and of the drift would remain in a state of equi- librium, the longer shaft A being counterbalanced by the shorter shaft B, extending so as to em- brace C, a portion of the external air, to the same height as the column A. But suppose it summer, then the air in A becoming condensed by the in- fluence of the colder earth, is rendered specifically heavier, and overpowers the air in th ■ columns B and C, the latter consisting of air more rarefied than that within the earth. Hence, the air will flow down the longer, and out of the shorter shaft ; and by bringing all parts of the mine into the circulation, the whole interior will be supplied with pure fresh air. Again, suppose it winter ; then the air in the longer shaft being warmer and lighter than the compound column BC, the latter preponderates, and the air flows in the opposite direction, namely, down the shorter and out at the longer shaft. In spring and autumn, when the temperatures of the external air and of the mine are nearly equal, the miners complain much of the suffocating state of the air. 276. It is important both to comfort and health, that the apartments of a dwelling-house, and more especially Show how the draught of a chimney is illustrated by the circulation in mine. Why is it important that dwellings should be well ventilated '! VENTILATION. 21 1 that all crowded rooms, such as churches, Fchool houses, hospitals, and prisons, should be well ventilated. Numerous causes are constantly in operation, and some of them on a very extensive scale, which tend to contaminate the air and render it unwholesome. Of these the most powerful are combustion and respiration. Every fire that is burning-, and every animal that breathes produces a change in the air which renders that portion of it unfit for respiration ; and when we contemplate the vast extent to which these pro- cesses are in operation, we might feel some apprehension lest the atmosphere would become permanently impure, and un- fit for the support of apimal life. But, by'a wise arrange- ment of Providence, counteracting causes are continually at work to restore the air, when contaminated, to its original purit}', so that nothing is required to carry out this benev- olent design but to give a free circulation to the air, and it will purify itself. Such a circulation is given in nature by winds and breezes, which continually diflfuse throughout the atmosphere those portions of air which have imbibed impur- ities, and which thus expose the bad air to the action of those causes which restore its purity. The impurities derived from combustion and respiration are chiefly taken up by the vegetables, and supply an essential portion of their food ; living plants having the remarkable property of appropriating to their own sustenance the impure portions of air contam- inated by the action of burning bodies or by the respiration of animals and giving back to the atmosphere the vital ele- ment of which these processes had deprived it. It is the object of ventilation to imitate nature by discharging from inhabited and crowded rooms the air as fast as it is contam- inated and to supply its place by air that is fresh and pure. The change from the open fire-places used by our fathers, which were themselves powerful ventiators, for close stoves, which withdraw but little air from the apartment, and, of course, occasion the introduction of but little fresh air to supply its place, renders an attention to ventilation peculiarly important. All public buildings, especially, as churches, school-houses, and hospitals, ought to have effectual arrange- ments for an ample supply of pure and wholesome air. 277. In forming the plan of any building designed for human occupancy, three things are worthy of great consid- eration, — how it is to be warmed, — how ventilated, — and "What causes tend to render the air impure ? How are these counteracted 7 How does the vegetable kingdom help to purify the atmosphere ? 2 1 2 METEOH OLOGY. how supplied with an abundance of pure water. At present it falls in our way to consider only how a building is to be furnished with pure and wholesome air. Air is so readily put in motion by every inequality of pressure in different parts, that a good ventilation may be easily secured by an attention to a few simple principles. 1. Since air is instantly contaminated by flowing over impure surfaces cleanliness in and around a dwelling is an indispensable prerequisite to a perfect ventilation. The purest air suffered to pass over ashes or foul dust, or stagnant water, or decaying animal or vegetable substances, will im- mediately imbibe more or less of the unwholesome exhala- tions from any of these sources and become wholly unfit for respiration. A close room, with a floor defiled with dirt and the effects of tobacco, would instantly render the pure air of heaven almost pestilential ; and air used for the sup- ply of air-furnaces, should never be permitted to circulate through cellars or apartments where there are vegetables or other provisions. 2. Stoves, or drums, which merely heat the apartments, without occasioning any change of air. are wholly incom- patible with a good ventilation, and are in the highest degree unsuitable for sleeping rooms and for crowded as- semblies. 3. No stove or furnace ought ever to become, in any part of the outer surface red-hot. or indeed much hotter than boiling water. At a higher temperature than this, the particles of animal and vegetable matter, more or less of which are usually floating in the air, will, on coming in contact with the heated surface, emit a burnt smell both disagreeable and unwholesome. 4. Any contrivance for introducing fresh air from without must have a corresponding opening for the impure air to escape, or else no free circulation can be maintained. The escape flue should also be so situated with respect to the ad- mission pipe, that the air. in passing from one to the other, should traverse all parts of the room. 5. In all school-houses, (and the .same rule applies to various other structures,) where several apartments are to be ventilated, the most effectual and, all things considered, the most economical mode of securing good ventilation, is to construct a brick chimney, in some part of which a fire What three things are important in forming the plan of a dwelling-house 1 State the effect of cleanliness ; of drums ; of heating a stove red-hot. Why should there be a place for the impure air to escape ) / WINDS AND STORMS. 213 shall be constantly maintained, or which shall be kept hot by receiving the pipe from a furnace or stove which dis- charges into It the smoke and other heated products of com- bustion. The ventilating flues, which may be opened either at the top or the bottom of a room, (but usually better at the top.) should communicate with this chimney, either opening into the same flue, or what is better, into an ad- jacent flue separated from the chimney by a thin partition 6. The proper temperature of parlors "is from 60 to 70° and of sleeping rooms fiom 50° to 60 If an evaporating dish IS connected with a stove or furnace, it should be care- fully cleansed and supplied with pure water everyday. The dust that settles in an evaporating dish, if sufl^ered to re- main, will cause the water to emit an offensive and un- wholesome effluvium, especially when the water is low.* WINDS AND STORMS. 27 8. We have hitherto contemplated the motions of the atmosphere as they occur chiefly in artificial arrangements, as in the draught of a chimney, or in methods of ventilation ; but nature produces movements on the atmosphere on afar grander scale, in the form of Winds. Rarefaction by heat, and condensation by cold, are the chief causes of winds. The motion of the air, however, producing a wind, may be merely relative, arising from the motion of the spectator. Thus a steamboat, moving at the rate of sixteen miles an hour in a perfect calm, would appear to one on board to be facing a wind moving at the same rate in theopposite direc- tion ; or if, in the diurnal revolution of the earth on its axis, any point of the earth's surface should move faster than the portion of the atmosphere in contact with it, a relative wind in the opposite direction would be the result. The direction of the wind may be modified by various causes, the actual direction being sometimes the resultant of two or more currents which meet from different directions, or of several different forces. 279, Land and sea breezes afford a striking exemplifi- cation of the principle in question. These winds prevail in * Excellent direclions for ventilation may be found in " Baruard^s School-Arch- itecture." What is the most efFectual way of securing a good ventilation ? What is the proper temperature of parlors? also of sleeping rooms? What are the chief causes of winds t Give an instance of a relative wind. How pro- duced by the movement of the air in relation to the diurnal revolution of the earth ? How may the direction of the wind be modified 7 214 METEOROLOGY. most maritime countries, but more especially m the islands of the torrid zone, blowing off from the land at night, and towards the land in the day time. Land being more easily heated and cooled than waler. the air over the land becomes rarefied during the day, ascends, and the surrounding air flows in as into a chimney. At night the air on the land becomes heavier than that on the sea, and the current i? reversed. 280. The trade loinds afford an example of the same causes on a still greater scale. These winds prevail in equatorial regions, extending to nearly 30 degrees on both sides of the equator. When not affected by local causes, they blow constantly at the same place in one and the same direction throughout the year. Their general direction is from noith east to southwest on the north side of the equator and from south-east to north west on the south side of the equator. So constant are they in some parts of the ocean, that ships sailing in the direction in which they blow, after setting their course, have scarcely any occasion to shift a sail for many weeks. The trade winds owe their origin to the combined agency of two causes, first, the movement of (he air on either side of the equator towards the place of greatest rarefaction, (which would be at the equator, where the heat is the most intense ) and, secondly, the westerly tendency arising from the effect of the earth's diurnal rotation on its axis, since they do not instantaneously acquire the greater velocity which the equatorial regions have in consequence of the earth's revolution on its axis. The duration of the trade winds is variously modified in different parts of the world, but always in such a manner that they blow towards the point of greatest rarefaction, and receive a relative motion from the effect of the earth's diurnal rotation. 281. Winds blow with various degrees of velocity, and exhibit the various forms of breezes, high winds, hurricanes, gales, and tornadoes. A velocity of twelve miles an houi makes a strong breeze ; sixty miles, a high wind ; one hundred miles, a hurricane. In some extreme cases, the velocity has been estimated as high as three hundred miles an hour. The force of wind is proportioned to the square of the velocity. Doubling the velocity increases the force fourfold ; tripling it increases it nine-fold, and so on. Describe land and eea breezes, and specify the cause. Do the same witli respect to the trade winds. State the different varieties and velocities of high winds. WINDS AND STORMS. 215 282. It hus been ascertained by experiment that a wind blowingr directly against an obstacle at the rate of 10 miles per hour, strikes it with the force of half a pound to the square foot. A velocity ten times as great, that is. of 100 miles per hour, would strike with the force of 50 pounds to the square foot ; and a velocity of 300 miles per hour, (equal to the most violent hurricane.) would strike the same ob- stacle with a force of 450 pounds to the square foot. Now consider the efTect of these several winds on a perpendicular wall, as that of a house, 30 feet long and 20 feet high, con- taining 600 square feet. The breeze of 10 miles an hour would exert upon the wall only a force of 300 pounds ; that of 100 miles, a force of 30 000 pounds; and that of 300 miles, 270,000 pounds. — a power which hardly any structure could resist. Hence violent gales sweep everything before them. 283> Air, when set in motion either on a small or a great scale, has a strong tendency to a whirling motion, and seldom moves forward in a straight line. The great gales of the ocean, and the small tornadoes of the land, often, if not always, exhibit more or less of a rotary motion, and sometimes appear to spin like a top around a perpendicular axis at the same time that they ad vance forward in some great circuit. Thus the great gales of the Atlantic usually begin to the eastward of the West India Islands and spin- ning like the small whirls we sometimes see among the leaves of autumn, advance towards the American coist, first, in a north-westerly and afterwards in a north-easterly direction, until they have a vast circuit through the northern Atlantic. Their rotary is always greater than their p'"o- g-ressive motion, and becomes more and more rapid towaMs the center of the whirl, near which it sometimes amounts to the highest velocity of a hurricane, while the entire whirl- wind advances at the slow rate of not more than 20 to '^0 miles an hour. With what force to the square foot does a wind of 10 mile.s an hour strike an obstacle 1 Ditto at 100, and at 300 miles per hour ? According to what law does the force increase as the velocity is augmented ? State the eWict of these different velocities on a wall containing 600 square feet. What is slid of the tendency of winds to blow in a circuit T How is it with the Atlantic gales ? How does rotary correspond to the progressive motion in velocitv 8 CHAPTEK IV. I OF ACOUSTICS. X . . 284. Acoustics is t/te science which treats of the nature and laws of sound. In comparing substances which have different properties in respect to sound, as lead and glass, we shall find them distinguished from each other by the degree of vibration which they are capable of receiving, and by the length of time during which they can preserve a vibratory motion ; those substances which are most capable of vibration being most sonorous and those which can longest maintain a state of vibration, also persevering longest in emitting sound. Bodies though of the same substance, differ in these respects according as their form varies ; those forms which are most favorable to the production and continuance of a vibratory motion, being also most favorable to the production and per- manence of sound. Thus, a hollow globe of brass is far less sonorous than the hemispheres which are made by dividing it into two equal parts, since the structure of a globe is such that the parts mutually support each other, like a continued arch, while the form of the hemispheres, which approaches that of a bell, is peculiarly liable to a tremulous vibratory motion. Indeed, when a body sounds pow^erfully, as a large bell, or the lowest string of a harpsichord, we can perceive that it actually vibrates ; and even in cases where the vibration is imperceptible to the naked eye, we may de- tect it by the microscope or by some other artifice. Thus, if we put some water into a glass tumbler or basin and make it sound, by applying the moistened finger, the water will be agitated. If we hold the hand over the pipe of an organ, we shall feel a tremulous motion in the air passing through it. Such experiments may be extended to all solid bodies, by placing upon them pieces of paper, or strewing them with fine sand. Hence, vibrations in the sounding body, are the immediate cause of sound. VIBRATORY MOTION. 285. The importance of the laws of vibratory or un dulatory motion, in its relation especially to sound and ligh* State facts showing the connection between soand and the vibration of the medium. What, in general, is the cause of sound? VIBRATOiiy MOTION. 217 Fig. 109. makes it necessary to introduce here a few of their leading principles. The terms oscillation, vibration, and undulation, are often used interchangeably : but while the term oscilla- tion may be applied to all reciprocating motions, vibration i% more properly restricted to fixed bodies, as a pendulum, or to a string stretched horizontally, and undulation, to motions which are propagated after the manner of waves. Thus a steel spring fixed at one end, vibrates when drawn out of its position from a state of rest. A rope fastened at one end, undulates, when shaken at the other end. A pebble, also, when thrown upon the surface of smooth water, raises un- dulations which spread in all directions from the point of jontact. Although waves are propagated in right lines, yet undulatory motion is to be distinguished from progressive motion. A wave rises and falls in the same place, and does not advance ; but since in falling it raises another wave, and that another, the appearance is that of flowing or progression. But a piece of board thrown on the sea remains constantly at the same place, merely rising and falling without advancing. 286. Such solids as possess elasticity can alone be made to vibrate for any length of time. Blany bodies of this class, as cords and membranes, acquire the requisite elastic force by tension ; others have naturally this property, as rods and plates of metal, glass, and even wood. Bodies of a lineal form, as tense strings and fine wires, are susceptible of three distinct kinds of vibrations, called respectively the trans- verse vibration, the longitudinal vibration, and the vibration of torsion, all of which may be illustrated by the following apparatus. Let AB be a fine brass wire stretched between two points. When drawn out of its fixed position, and let go, it continues to vibrate for some time, exhibiting an example of vibration.s transverse to the axis. On the other hand, if a fine wire be coiled into the form of a helix, as in Fig. 110, and a weight be suspended at its lower end, on raising the weight towards the top, and suffering it to fall, longitudinal vibrations, or those in the direction o*" the Vibratory molkm. — Distinguish between the terms oscillation, vibration, and undnlation. Give an example of vibratory motion ; also of undulatory. How is undulatory distin^nzistied from progressive motion? What class ol substances only can be made to vibrate ? Distinguish between transverse and jongitudinal vibrations, and vibrations of torsion by figures 109, 110. 19 f- ' Bc£ Fig. 110. 218 ACOUSTICS. Fig. 111. axis, are exhibited. If a brass wire be suspended in the place of the helix, and twisted, and then the ball suffered to fall rotary vibrations, or the vibra- tions of torsian will be shown. 387. A simple case of sound produced by vibration, is that afforded by a steel plate, fixed at one end, as in Fig. ill. On drawing the free end of the plate out of a straight line, and letting it go, it vibrates for some time, producing a well-known humming sound. A rope fixed at one end and shaken at the olher, affords a familiar example of undulatory motion ; the un- dulations are transverse, but are propagated, successively, from the free to the fixed end of the rope, as is shown in Fig. 112. Here AB exhibits the first wave, which by falling generates a force which raises a second Fig- 112- wave, AC, which, in like manner, raises a third wave, AD, and thus the undula- tions are propagated through the entire length of the rope. When they reach the fixed end, they are reflected back again, forming an exact counterpart to the first series, each concave part of the returning waves corre- Fig. 113. spending to a convex part of the direct waves, as in Fig. 113, where the full line represents the direct, and the dotted line the reflected undulations. 288. In the vibrations of the elastic spring, (Fig. Ill,) the particles of metal are momentarily displaced, being separated from each other on the convex side, and made to approach each otricr on the concave side ; but in the undu- lations of the rope, (Fig. 113,) there is no real movement of Give examples of the simple production of sound m a spring and in i rope. In which case is there a displacement of the particles ¥ VIBRATORY MOTION. 219 the particles of the rope, from one end to the other, althouffh such IS the appearance, but each portion returns to its state ot rest as soon as it has communicated its motion to the next portion. In vibrations produced by tension, as in Pip- 109, the particles move to and fro in parallel lines, all of which are described in the same time at each vibration of the wire. It is important to remark that all these vibrations are performed in equal times, whether they are performed in longer or m shorter arcs, being-, in this respect, analogous to the pendulum, although the moving force in these cases is elasticity, virhile in a pendulum it is gravity. When a body IS performing a series of undulations, like the rope in Fig. 113, the points intermediate between the rising and the falling wave are at rest ; and these points being those of intersection between the direct and reflected waves^ are called nodal points or nodes. 289. When rods or strings are not uniform in their structures, but thicker or denser in one part than in another, the vibrations of the different parts are not isochronous, and a jarring, discordant sound is produced. Kods do not perform their vibrations in the same plane but in curves. This is shown by fixing a silvered bead to the top of a steel rod and causing it to vibrate as in figure 111. As the rod vibrates, the reflection of light from the metallic bead will render the curvilinear path obvious to the eye. The undulation oi fluids is seen when a pebble is drop- ped on the surface of still water. At the point where the pebble touches the water, a depression takes place ; this produces a corresponding elevation around it ; and this again, by its fall, generates a second depression ; and thus a series of undulations are propagated in circles, continually enlarging in diameter, but diminishing in height, until they become imperceptible. As in the case of the rope, (Fig. 113,) fluid waves when they meet a fixed obstacle are re- flected back, the direct and the reflected waves crossing each other without destroying each others' motions, and forming nodal points in the same manner as the direct and reflected undulations of the rope. 290. Acoustic figures are figures produced by the ar- Describe the vibrations produced by tension in figare 109. How do the times of vibration compare with each other 1 What is meant by nodal points, or Dodes ? What is the effect produced by inequalities in the vibrating body ? Do rods perfoi-m their vibrations in the same plane ? Describe the undula- tions of fluids as produced by a pebble. What is the effect when fluid waves are reflected ? Define Acoustic Jigyres. 220 ACOUSTICS. rangement which particles of sand take on vibratory plates. These figures vary indefinitely with the material and form of the plate, and the manner of vibration. The figures are usually symmetrical, and are often very beautiful in their forms. As specimens, we will take a small square plate of glass, and fastening it horizon- tally at the center by means of a small vise, (Fig. 1 14,) we will strew over it a little fine sand. A violin bow drawn across one corner of the plate will throw the sand into the position represented in Fig. 1 15, a, w^here Fig. 115. a b c d - , I m . ...... the arms of the cross unite the middle points of the parallel sides of the plate. If the bow is drawn across the middle of one side of the square plate, the arms of the square unite in the corners, as b. If the plate be fastened near one of its corners, and the bow be drawn across the middle of one side, the sand will be arranged as in c; and other figures, as d. will be successively developed by different positions of the plate and the bow. These figures indicate the cours^ o{ nodal hnes, which mark the divisions between the vibratory portions into which the plate is divided. 291. Elastic fluids, also, are susceptible of undulatory movements, if the equilibrium of their particles be disturbed. Their undulations resemble those of liquids, but are some what modified by the extreme compressibility and expansi- bility of their particles. Air waves, therefore, difTer from water waves in several particulars. They are the efTect of elasticity, occasioning alternate condensation and rarefac- tion among the particles of air, whereas water waves are caused by gravity ; and air waves are propagated on all sides, forming a sphere of undulations around the point where How produced? Describe several examples from figure Its. What do the nodal lines indicate ! What is said of the undulations of elastic fluids ? In what particulars do air waves differ from water waves f VIBRATORY MOTION. 22 Fig. 116. Aey commence, whiie water waves rise and fall on the surface merely. If the cause which • rated the undulation at first cx)ntinues to operate, there will arise a series of waves withm the first and concentric with it. If waves of air proceedmg from two different points meet together, the waves intersect, but each continues its course freely. At those pomts of intersection, where the velocities of both the particles are m the same direction, the effect is equal to the sum of both ; but when they meet in opposite directions, the effect IS equal to their difference. In the case of equai waves, the effect is doubled when they conspire, but neutralized when they are opposite. When two waves meet from opposite directic)ns and destroy one another, it is called the interference of waves. If two equal sets of waves proceed from A and B, (Fig. 116,) at the points where they mutually intersect, the undu- lating particles will lose all their motion and be at rest. 293. Th^ pitch of musical strings, is found by experience to depend on three circumstances; the length of the string, — its weight or quantity of matter, — and its tension. The tone becomes more acute as we increase the tension, or diminish either the length or the weight. The operation of these several circumstances may be seen in a common violin. The pitch of any one of these strings is raised o/ lowered by turning the screw so as to increase or lessen its tension ; or. the tension remaining the same, higher or lower notes are produced by the same string, by applying the fingers in such a manner as to shorten or lengthen the string which is vibrating-; or, both the tension and the length of the string remaining the same, the pitch is altered by making the string larger or smaller, and thus increasing or dimin- ishing its weight. 393. The vibrations of a string, fixed at both ends, are performed in equal times, whetlier the length of the vihra- tions be greater or smaller. Upon this uniformity in the times of vibration depends What takes place when the caase continues to operate 1 In what case is the effect equal to the sum, and in what case to the difference of the vibra- tions ? Upon what three things does the mich depend f What effect has it to increase the tension — or to sfconea the string— or to increase its nae 7 How are tlie times of the vibrutionn of a siring when fixed at both ends ! 19* 222 AroxTSTics. ihe. uniformity of tone ; for if we employ a string of unequal thickness and consequently one whose vibrations are per- formed in different times, the sound is confused and variable, and any other mode by which we destroy the isochronism, produces a similar effect. The same law has been found to ex-tend to all other cases of musical sounds; and, therefore, we may conclude, that isochronism in tlie vibrations of son- orous bodies, is essential to tlteir producing musical sounds. 294. In ivind instruments, a column of confined air itself is the vibrating body : and here the vibrations are longitudinal instead of lateral, as is the case with strings. That it is really the air which is the sounding body in a flute, organ pipe, or other wind instruments^ appears from the fact, that the materials, thickness, or other peculiarities of the pipe, are of no consequence. A pipe of paper and one of lead, glass, or wood, provided the dimensions are the same, produce, under similar circumstances, exactly the same tone as to pitch If the qualifies of the tones produced by different pipes differ, this is to be attributed to the fric- tion of the air within them, setting, in feeble vibration, their own proper materials. The class of bodies vibrating lon- gitudinally is not only more diversified in its powers than the other classes of sounding bodies, but also more extensive in the range of substances which it comprehends. 295. The different ^iVcA of bodies vibrating longitudi- nally, and free at both extremities, depends on four circum- stances, viz. their elasticity, the temporary rate at which their elasticity is increased by condensation, their length, and their specific gravity, the tone of a body being more acute, according as the elasticity, and the rate of its increase by condensation, are greater, or the length and specific gravity less. The length of the sonorous body is almost exclusively the only one of these circumstances which we have completely in our power ; and with regard to ordinary wind instruments, and all musical instruments where com- mon air is the vibrating body, the length is the circumstance of most importance, since the elasticity, rate of condensa- tion, and specific gravity are then nearly constant quantities. The change of specific gravity, however, to which the air is subject in consequence of changes of temperature, Upon what depends aniformity of tone? To what is isoehronism in the number of vibrations essential ! In wind instruments what is the vibrating body? Does the nature of the material, or its thickness, make any diflerence? State the/oar circumstances on which the pitch of bodies vibi'ating longitu- dinally depends. Which of these can we control ? PROPAOATION or SOUND. 223 materially affects the pitch of wind instruments. The trequency of vibration of a column of air is found to be in- creased about -3-V, by an elevation of 30 Fahrenheit. Thus the tone of an organ has been found to be higher in summer than m winter; and flutes and other wind instruments become gradually more acute as the included air is heated by the breath. 296. If a hell be struck by a clapper on the inside, the bell IS made to vibrate, The base of the bell is a circle ; but It has been found that, by striking any part of the circle on the inside, that part flies out, so that the diameter which passes through this part of the base, will be longer than the other diameters. The base is changed by the blow into the figure of an ellipse, whose longer axis passes through the part against which the clapper is thrown. The elasticity of the bell restores the figure of the base, and again elongates the bell in a direction opposite to the former ; and the two elliptical figures thus alternate with each other, growing smaller and smaller, like the vibrations of a pendulum when the moving force is withdrawn, until the sound dies away. We may be convinced by our senses, that the parts of the bell are in a vibratory motion while it sounds. If we lay the hand gently upon it, we shall feel this tremulous motion, and even be able to stop it ; or if small pieces of paper be put upon the bell, its vibrations will set them 'in motion. We may conceive the bell to be formed of an infinitude of rings, placed one above another, from the base to the highest point. The rings situated nearer to the base, having a greater circumference, tend to perform their vibrations more slowly while the rings nearer to the summit, whose cir- cumferences are smaller, tend to produce vibrations oftener. These sounds will so coalesce as to produce a mixed sound, intermediate between those of the higher and lower rings. \/ PROPAGATION OF SOUND. 297. Air is?^ general, the medium of sound. A bell struck under the receiver of an air pump, gives a feebler and feebler sound, as the exhaustion proceeds, until, when the rarefaction is carried to a certain extent, it emits no sound How much is the frequency of vibration of a column qf air increased by raising the temperature 30^? How exemplified in the organ, flute, &c. I What change of figure does a bell undergo when struck ? What sensation is felt on applying the hand to a bell while ringing? Suppo.'e the bells formed of rings. Propagation of Sound.— What is the ordinary medium of sound 7 Case of a bell under the receiver of an air pump. 224 ACOUSTICS. at all. On the summit of high mountains, where the air is naturally rare, sound ought to be weaker than' at the general level of the earth ; and such is found to be the fact Saussure relates that upon the top of Mont Blanc, the firing of a pistol made a report no louder than that of a child's toy-gun. A fact mentioned by travellers in Alpine countries is explained on this principle. They see distinctly a huntsman on a neighboring eminence, and observe the flashes of his gun, but can scarcely hear the report, even when comparatively near him 298. The agency of air as the medium of sound may be briefly expressed thus : Air receives from sounding bodies vibrations, which it communicates to the origans of hearing. In an open space, and in a serene atmosphere, sound is propagated from the sounding body in all directions. Sounds, even the most powerful, when thus transmitted freely through the air, diminish rapidly in force, as they depart from their sources, and within moderate distances wholly die away. What law this diminution follows, is not yet ascertained ; and is, indeed, in the present state of Acoustics, inc/^pable of determination. Some writers have supposed that sound follows the common law of emanations radiating from a center, and, consequently, that its intensity at different dis- tances from its source varies inversely as the square of the distance ; but we can estimate the force of sounds by the ear alone ; an instrument of comparison whose decisions on this point vary with the bodily state of the observer, and whose scale expresses no definite relation but that of equality. Though sound has in general, at its origin, a tendency to diffuse itself in all directions, it is sometimes more propa- gated in one direction than in others. A cannon seems much louder to those who stand immediately before it, than to those who are placed behind it. The same fact is illustrated by the speaking trumpet; the person to whom the instrument is directed hears distinctly the words spoken through it, while those who are situated a little to one side, hardly perceive any sound. V 299. SouHd is in a great measure intercepted by the in tervention of any solid obstacle between the hearer and the sonorous body. Thus, if while a bell is sounding, houses intervene between us and the bell, we hear it sound but Sound on the top of a high mountain. State the agency of air in the pro. duction of sound. Is the law by which sound increases at a distance, deter mined ? Does it spread equally in all directions ? How is sound afl'ected by the intervention of an obstacle ? PROPAGATION OF SOUND., 225 faintly compared with what we hear after we have turned the corner of the building. From this fact sound would seem to be propagated in straight lines. If however, we speak through a tube, the voice will be wholly confined by the tube, and will follow its windings however tortuous ; hence we infer, that sound is propagated, not in right lines like radiant substances, as heat and light, but in undulatAons after the manner of waves, such as follow when a stone is thrown into still water. 300. Though air is the most common medium of sound, yet it is not the only medium. Various other bodies, both solid and fluid, are excellent conductors of sound ; and the fainter sound of the bell when buildings intervene, as in the case supposed, arises from the fact that sound passes with difficulty from one medium to anothor. If a log of wood is scratched with a pin at one extremity, a person who applies his ear to the other extremity will hear the sound distinctly, and when a long pole of wood is applied at one end to the teeth, the ticking of a watch may be heard at the other end, at a much greater distance, than when there is no medium of communication but the air. The motion of a troop of cavalry is heard at a great distance by applying the ear close to the ground, and it is well known that dogs by this method first discover the approach of a stranger. 301. The VELOCITY of sound is 1130 feet per second. Thus, when a gun is fired at a distance from us, we perceive the flash some time before we hear the report. Thunder follows the lightning at a perceptible interval, although they are known to be contemporaneous events. If a gun be fired at a certain known distance, and we observe the interval between the flash and the report, we may obtain the rate at which sound passes that is, the velocity of sound. The mean of a great number of experiments gives the average velocity of 1130 feet per second. Since, however, the transmission of sound depends on the elasticity of the medium, (Art. 295.) causes which effect the elasticity, likewise affect the velocity of sound. Thus, the velocity is a little greater in warm than in cold air, and consequently is somewhat influenced by climate. 302. Sound moves with a uniform velocity ; that is, it passes over equal spaces in equal times. This important fact Also by passing oat of one medium into another? Is air the only mediinn of sound 1 Examples of the transmission of sound through solid bodies. What is the velocity of sound per second? Is the velocity of sound uniform? 226 ACOtlSTTCS. was first ascertained by Derham, who found that it held good whether the sound was strong- or feeble whether it proceeded from a hammer or a cannon : in short, that neither the strength nor the origin of the sound made any difl^erence. M. Biot caused several airs to be played on a flute at the end of an iron pipe 3120 feet long, and the notes were distinctly heard by him at the other end. without the slightest derange- ment in the order or quality of the sounds. The velocity of sound, however, when transmitted through the air, is slightly influenced by the strength and direction of the ivind. Dr. Derham found that when the wind is blowing in the di- rection of the sound, its velocity must be added to the stand- ard velocity of sound, and must be subtracted from it when opposed to it. A transverse wind does not affect the velocity of sound in the slightest degree. 303. Prom a knowledge of the velocity of sound, the distance of a sounding body may be estimated. Thus if the interval between seeing.a flash of lightning and hearing the thunder, be six seconds, the distance of the cloud is 6x 1130=6780, or 1-j^ miles. The air is a better conduc- tor of sound when humid than token dry. Thus a bell is heard better just before a rain ; and this fact lends some countenance to an opinion of the ancients, that sound is heard better by night than by day. Humboldt was partic- ularly struck with this fact, when he heard the noise of the great cataracts of Oronoco, which he describes as three times greater in the night than in the day. The distance to which sound may be heard, will of course vary with its force, and various o-ther circumstances which are incapable of being reduced to an exact law. Volcanoes, in South America, have sometimes been heard at the distance of three hundred miles ; and naval engagements have been heard at the dis- tance of two hundred miles. The unassisted human voice has been heard from Old to New Gibralter, a distance of ten or twelve miles, the watchword All's Well given at the former place being heard at the latter. Sounds are heard to a much greater distance over water than over land, and farther on smooth than on rough surfaces. 304. Liquids are good conductors of sound. Indeed, sound is conveyed with far greater velocity in water than in Recite the experiment of Biot. What eifect has the wind upon the velocity of sound ? Does a transverse wind aftect it 1 How can the distance of the Bounding body be estimated? How does moisture aftect the conducting power of the air ? To what distance have volcanoes, cannon, and the humaD Ypice been respectively heard ? What is the conducting power of liquids t PROPAGATION OF SOUND. 227 air, and this too in consequence of its greater elasticity ; for since water has been found by Perkins and others, capable of compression and of restoring- itself when the compressincr force is removed, it is to be accounted not only elastic, but as exceeding aeriform bodies in elasticity, in proportion as the force required to compress it is greater. Dr. Franklin having plunged his head below water, caused a person to strike two stones together beneath the surface, and heard the sound distinctly at the distance of more than half a mile. By similar experiments, it has been ascertained, that, though water is a much better conductor of sound than air. yet the sound is greatly enfeebled by passing out of one medium into the other. 305. Solid substances convey sound with various de- grees of facility^ but in general much better than air, and as well if not better than fluids. By placing the ear against a long dry brick wall, and causing a person at a considerable distance to strike it once with a hammer, the sound will be heard tu-ice. because the wall will convey it with greater rapidity than the air, though each will bring it to the ear. The rate at which cast iron conducts sound, was ascertained by M. Biot in the following manner. He availed himself of the laying of a series of iron pipes to convey water to Paris. The pipes were about eight feet in length, and were connected together with small leaden rings. A bell being suspended within the cavity, at one end of the train of pipes, on striking the clapper at the same instant against the side of the bell, and against the inside of the pipe, two dis- tinct sounds successively were heard by an observer sta- tioned at the other extremity. With a train of iron pipes two thousand five hundred and fifty feet, or nearly half a mile in length, the interval between the two sounds was found from a mean of two hundred trials, to be 1.79 seconds. But the transmission of sound through the internal column of air, would have taken 2.2 seconds; which shows that the sound occupied only .41 of a second in passing through the metal. From more direct trials, it was concluded that the exact interval of time, during which the sound performed its passage through the substance of the train of pipes, amount- ed to only the .26 of a second, showing that iron conducts sound about ten times as rapidly as air does. If a string How does water compare in this respect with air? State the experiment of Dr. Franklin upon the aadibility of sounds under water. What is the conducting power of solids? How was the coudaeting power ot cast iron ascertained by Biot 7 828 ACOUSTICS. be tied to a common fire shovel, and the two ends of the string be wound round the fore fingers of each hand, and the fingers be placed in the ears, on striking the bottom of the shovel against an andiron or other solid body, very deep and heavy tones will be heard, and the vibrations of the metal will be clearly perceived. The great power of solid bodies to conduct sound is exom plified in earthqiiakes, which are heard almost simultaneously in very distant parts of the earth. Musical boxes sound much louder when placed on a table or some solid support than when the air affords the only conducting medium. It is easy to ascertain whether a kettle boils, by putting one end of a stick or poker on the lid, and the other end to the ear ; the bubbling of the water, when it boils, appears louder than the rattling of a carriage in the street. A slight blow given to the poker, of which one end is held to the ear, pro- duces a sound which is even painfully loud. 306. A physician of Paris introduced into medical practice an instrument, depending on the power of solid bodies to conduct sound, called the Stethoscope, the object of which is to render audible the actions of the heart and the neighboring organs. It consists of a wooden cylinder, one end of which is applied firmly to the breast, while the other end is brought to the ear. By this means, the pro- cesses that are going on in the organs of respiration, and in the large blood vessels about the heart, may be distinctly heard ; and it is said that the stethoscope, when skilfully used, " becomes the means of ascertaining some diseases in the chest, almost as effectuaUy as if there were convenient windows for visual inspection." REFLEXION OP SOUND. 307. Sounds are reflected by hard bodies, producing the well-known phenomenon called an echo. If a straight line be drawn from the sounding body to the reflecting surface representing the course of the sound before reflexion, and another straight line be drawn from the reflecting surface, in the direction of the sound after reflexion, these two lines will make equal angles with that surface ; that is, when sound is reflected, the angle of reflexion is equal to tJie angle of State the experiment with a fire eliovel. How is the conducting power of the earth exemplHied in eartliquakes ? How to a.scertain when a kettle of water is boihng ? What is the .structure and principle of tlie Stethoscope 7 Reflexion of Sound. — How are the lines of direction of sound before and after retlexioii 1 REFLEXION OF SOUND. 229 incidence. The surfaces of various bodies, solids as well as fluids, have been found capable of reflecting sounds, viz., the sides of hills, houses, rocks, banks of earth, the large trunks of trees, the surface of water, especially at the bottom of a well, and sometimes even the clouds. It is therefore evident, that in an extensive plain, or at sea, where there i,3 no elevated body capable of reflecting sounds, no echo can be heard. It is hence easy to see why the poets, who con- vert Echo into an animated being, place her habitation near mountains, rocks, and woods. An echo is heard when a person stands in a position to hear both the original and the reflected sound ; and the interval will be greater or less ac- cording to the distance of the reflecting surface from the sounding body and from the hearer, and hence the interval may be made a measure of the distance. If the sound of the voice returns to the speaker in two seconds, the distance of the reflecting surface is one thousand one hundred and thirty feet, and in that proportion for other intervals. Thus the breadth of a river may be ascertained when thert. is an echoing rock on the farther shore. A perpendicula\ mountain's side, or lofty cliffs, such as frequently skirt the sea coast, sometimes return an echo of the discharge of artillery, or of a clap of thunder, to the distance of many miles. The number of syllables that can be pronounced in half the interval, will be repeated distinctly ; but a greater number would be blended with the commencement of the echo. 308. The furniture of a room, especially the softer kind, such as curtains or carpets, impairs the qualities of sound by presenting surfaces unfavorable to vibrations. A crowd- ed audience has a similar effect, and increases the difficulty of speaking. Halls for music, or declamation, should be constructed with plain bare walls. Alcoves, recesses, and vaulted ceilings, produce reverberations, which often greatly impair the distinctness of elocution. Indeed, the qualities of a room, in regard to sound, are modified by so many cir- cumstances, that the science of acoustics is worthy of more attention from the architect than- it has generally received. Plane and smooth surfaces reflect sound without dispersing it ; convex surfaces disperse it, and concave surfaces collect What snrfaces have been found capable of reflecting sound 1 Why arn not echoes heard at sea? How must one be situated in order to liear an echo ? How may distances be estimated by echoes ? What effect has the furniture of a room upon the quality of sound ? How do plane, convex, and concave surfaces, respectively reflect sound ? 20 230 ACOUSTICS. it. The concentration of sound by concave surfaces, produ- ces many curious effects both in nature and art. There are remarkable situations where the sound from a cascade is concentrated by the surface of a neighboring cave, so com- pletely, that a person accidentally bringing his ear into the focus is astounded by a deafening noise. Sound issuing from the centre of a circle, is, by reflexion, returned to the centre again, producing a very powerful echo. Such effects are observed in the central parts of a circular hall. An el- liptical apartment conveys sound very perfectly from one focus to the other. A whisper uttered by a person in one focus of such a chamber, will be audible to a person in the other focus, though not heard by persons between. 309. The rolling of thunder has been attributed to echoes among the clouds ; and that such is the case has been ascertained by direct observation on the sound of cannon. Under a perfectly clear sky, the explosion of guns is heard single and sharp, while, when the sky is overcast, or when a large cloud comes overhead, the reports are accompanied by a continued roll, like thunder, and occasionally a double report arises from a single shot. The continued sound of distant thunder, which is sometimes prolonged for many seconds, is not always owing to reverberation, but frequent- ly arises simply from the different distances of the same flash. Although the progress of a flash of lightning through the air were absolutely instantaneous, still, if its path were in a line that would carry it farther from the ear in one place than in another, there would be a corresponding dif- ference in the times at which the sound generated in differ- ent portions of the path, would reach the ear. Herschel observes, that if (as is almost always the case) the flash be zigzag, and composed of broken, rectilinear, and curvilinear portions, some concave, some convex to the ear ; and es- pecially, if the principal trunk separates into many branch- es, each breaking its own way through the air, and each becoming a separate source of thunder, all the varieties of that awful sound are easily accounted for. 3 1 0.. The Sjieaking Trumpet has been supposed by most writers on sound, to owe its peculiar properties to its multiplying sound by numerous reflexions. Hence is How is the sound of a cascade sometimes concentrated ? When sound issues from the center of a circle, how is it reflected? How from the focua of an ellipse? What causes the rolling of thunder? Why is the sound of thunder so much prolonged ? To what does the speaking trumpet owe its power ? REFLEXION OF SOUND. 231 suggested the form of a parabolic conoid, or a tube, the sec- tion of which is a parabola, the place of the mouth being at the focus of a parabola. The vibrations emanating from the mouth would then be reflected into straight lines paral- lel with the axis of the trumpet, and would thus go forward in a col'ected body to a distant point. And. since such a form is also favorable for collecting distinct sounds into one point, the same figure is proposed as most suitable for the Ear Trumpet. But the sound of these instruments may be regarded as merely the longitudinal vibration of a body of air, to which momentum is given in the direction of the axis, not by reflexion from the sides, but by the direct im- pulse of. the mouth. The ancients were acquainted with the speaking trumpet. Alexander the Great is said to have had a horn, by means of which he could give orders to his whole army at once. 3 J 1 . When separate sounds are repeated with a cer- tain degree of frequency, the ear loses the power of dis- tinguishing the intervals, and they appear united in one continued sound. By this means also, sounds, harsh and dissonant in themselves, form a soft and dissonant tone. Any sound whatever, repeated not less than thirty or forty times in a second, excites in the hearer the sensation of a musical note. Nothing is more unlike a musical sound than that of a quill drawn slowly across the teeth of a coarse comb ; but when the quill is applied to the teeth of a wheel whirling at such a rate that 720 teeth pass under the quill in a second, a very soft, clear note is heard. In like man- ner the vibrations of a long harp string, while it is very slack, are separately visible, and the pulses produced by it m the air are separately audible ; but as it is gradually tightened, its vibrations quicken, and the eye soon sees, when it is moving, only a broad shadowy plane ; the dis- tinct sounds which the ear lately perceived, run together, owing to the shortness of the intervals, and are heard as one uniform continued tone, which constitutes the note or sound proper to the string. Nature presents us with numerous examples of a musical sound produced by the rapid succession of an individual sound, not at all musical in itself The hum of winged in- sects, produced by the frequent motion of their wings, the What figure is considered best? To what does the ear trumpel owe its efBcacy? What is the result when separate sounds are repeated with a certain degree of frequency ? Examples in the sound of a quiU and comb, and in a harp string. Examples in nature. 232 AcoTjSTrcs. murmur of a forest, occasioned by the agitation of the leaves and boughs, and the sublime roar of the ocean, constituted of the separate sounds produced by innumerable waves, a/fc familiar examples of the operation of this principle. PHILOSOPHICAL PRINCIPLES 01" MUSIC. 312. Musicalintervah, or sounds differing from each other in pitch by a certain interval, are found by experience to be peculiarly agreeable to the human ear ; a fact for wnjch we can assign no reason, except that such is the constitution of the mind. Birds may sometimes exhibit a fine voice ; but their singing is not musical, having nothing to do with musical intervals. Musical sounds have certain ratios to one another, and are thus brought into the province of mathematics,- because the number of vibrations which produce one musical note, has a constant ratio to the number which produces another musical note. Thus if we diminish the length of a musical string one half we double the number of its vibrations in a given time, and it gives a sound eight notes higher in the scale than that given by the whole string. Therefore, these sounds are represented by the numbers 2 and I, and are said to be in the ratio of 2 to ) . The upper note is said to be the octave of the lower ; and from its great resemblance to the fundamental note, or that afforded by the whole string, it is considered as the commencement of a repetition of the same series ; so that all audible sounds are considered as repetitions of a series contained within the interval of an octave. 3 1 3> A succession of single musical sounds constitutes melody ; the combination of such sounds, at proper inter- vals, forms chords ; and a succession of chords constitutes harmony. Two notes produced by an equal number of vi- brations in a given time, and of course giving the same sound, are said to be in unison. The relation between a note and its octave is, next after that of the unison, the most perfect in nature ; and when the two notes are sounded at the same time, they almost entirely unite. Chords are characterized by frequent coincidences of vibration, while in discords such coincidences are more rare. Thus in the unison, What does expei'ience decide respectins; musical intervals ? Why are masical soands brought into the province of the mathematics ? What is an octave! Explain the terms, melody, chords, harmony, and unison. PHILOSOPHICAL PRINCIPLES OF MUSIC. 233 the vibrations are perfectly isochronous ; in the octave the two coincide at the end of everj' vibration of the longer string, the shorter meanwhile performing just two vibra- tions ; and m the fifth, they coincide at the end of every two vibrations of the longer string, the shorter vibratino- three times m the same period. But in the second, the longer and shorter vibrations can coincide only after eight of the longer and nine of the shorter, and in the seventh, only after eight of the longer and fifteen of the shorter.' Hence the concord is more perfect as the common period is shorter. Musical intervals, therefore, are divided into chords and discards. The octave, the major fifth, the major and minor thirds, the major and minor sixths, are concords, and are pleasing in themselves. The seconds, the sevenths, the minor fifth and major fourths, are discords. The chord consisting of the fundamental note with its third and fifth, and called the harmonic triad, forms the most perfect har- mony, and contains the constituent parts of the most simple and natural melodies. 314. Two sounds may by their meeting produce si- lence. This will be the case when the undulations which cause the sounds are equal and in opposite directions, so as to occasion an interference of the two air-waves (Art 291.) This efTect is known in music by the name of l/eats. We may conceive of cases where the sound waves, being in the same direction, coalesce and augment the sound; and we may also imagine them so to neutralize each other, by meeting from opposite directions, that both waves will be brought to a state of rest, and no undulation will reach the ear. Suppose two strings to be so nearly in unison, that one performs a hundred vibrations while the other performs a hundred and one. Their first few vibrations will conspire and produce a sound wave, such that the effect on the ear will be double. But at the fiftieth vibration one string will be half a vibration in advance of the other, so that the mo- tions of the strings will be at this instant in exactly opposite directions, and consequently the motions of the aerial parti- cles in the two waves will be in opposite directions, and they will therefore interfere and no sound will ensue. The same will be partially the case on each side of the fiftieth, causing In unison, haw are the vibrations 1 — ^how in tlie octave ? — how in the fifth, and the second'/ What notes form chords, and what discords? What fbrina tlie most perfect harmony ? 20* 234 ACOUSTICS. a general delay of sound up to this point, from which it will gradually increase to the hundredth vibration, when one string will have gained one vibration on the other, and the two will again coalesce, giving a double sound. The general effect on the ear resulting froai two such strings, will be an intermitting sound, alternately loud and faint. These alternate augmentations and decays of sound are called beats by musicians. The nearer the strings are in unison, the longer will be the interval between the beats ; and perfect harmony consists in the complete destruction of beats, by tuning the strings in unison or at proper intervals. 3 1 5o The theory of Musical Instruments will be readi- ly understood from the principles already explained. It will be seen that they all' owe their power of producing musical sounds to their susceptibility of vibrations ; that the force or loudness of the sounds they afford depends on the length of the vibrations, and the graveness or acuteness of the sound in other words, the pitch, on their slmoiiess ox frequen- cy ; and that their chords depend, in general, n^on frequen- cy of coincidence hi the vibrations that afford the several sounds of the concord. The nature of stringed instruments may be learned from the violin. Here the strings are of the same length, but differ in weight and tension ; those de- signed to afford the lower notes being heavier and less strained, and those for the higher notes being higher and more tense. The lengths, moreover, are altered by apply- ing the fingers The several strings are usually so adjusted to each other, that is so tancd, that any two contiguous strings make a.ffth. Hence the fourth, or highest stop on one string, brings it into unison with the string above ; and the third stop on any string forms an octave with the open string next below. On account of this power of altering the effective lengths of the strings at pleasure, of developing the harmonic sounds by a skilful application of the fingers, and of varying constantly the degrees of fulness or force in each sound, by a dexterous use of the bow, the violin becomes, in the hands of an accomplished performer, an instrument of great power and compass, while it is capable of greater va riety than any other musical instrument. Tlh.a flute affords an example of wind instruments. Here WheD will two sounds produce silence 7 Explain the nature of beats in mu.sio ? To what do musical instruments owe their power 7 On what does their /o«e or toid/iess depend 7 On ^y bat the pitch 1 On what the cAards / E-tplaiu theric principles from the violin. How is it tuned V PHILOSOPHICAL PEEMCIPLES OF MUSIC. 235 the vibrating body is a column of air, to which different lengths are given by means of the stops which are opened and closed by the fingers. The rapidity of the vibrations, and consequently the pitch, is also changed a whole octave by the management of the breath. 31G. In mixed wind instruments, the vibration or alter- nations of solid bodies are made to co-operate with the vi- brations of a given portion of air. Thus, in the trumpet, and in horns of various kinds, the force of inflation, and per- haps the degree of tension of the lips, determines the num- ber of parts into which the tube is divided, and the harmon- ic which is produced. The hautboy and clarionette have mouth-pieces of diflferent forms, made of reeds or canes ; and the reed pipes of an organ, of various constructions, are fur- nished with an elastic plate of metal, which vibrates in uni- son with the column of air which they contain. An organ generally consists of a number of different series of pipes, so arranged, that, by means of registers, the air proceeding from the bellows may be admitted to supply each series, or excluded from it at pleasure ; and a valve is opened when the proper key is touched, which causes all the pipes belong- ing to the note, in those series of which Uhe registers are open, to sound at once. ^ — - \ Wliat is the vibrating body in the flute ? Explain how its sounds are produced and varied. Explain the theory of mixed wind instruments, aa the trumpet, the hautboy, and the organ. PART IV.— ELECTRICITY. CHAPTEE I. OF THE GENERAL PRINCIPLES OF THE SCIENCE. 317. The term Electricity is used to denote both the unknown cause of electrical phenomena, and the science which treats of electrical phenomena, and their causes. The most general effect by which the presence of elec- tricity is manifested is attraction. Thus, when a glass tube is rubbed with a dry silk or woolen cloth, it acquires the property of atti'acting light bodies, as cotton, feathers, &c. When, by any process, a body is made to give signs of elec- tricity, it is said to be excit.ed. When a body receives the electric fluid from an excited body, it is said to be electrified. Since there is found to be a great difference in bodies in regard to the power of transmitting electricity, all bodies are divided into two classes, conductohs and non-conbuotors. Conductors are bodies through which the electric fluid passes readily ; non-conductars are bodies through n hich the electric fluid either does not pass at all, or but very slowly. The latter bodies are also denominated electrics, because ir is by the friction of bodies of this class, that electricity iy usually excited. An electrified body is said to be insulated. when its connection with other bodies is formed by means of non-conductors, so that its electricity is prevented from escaping. Instruments employed to detect the presence of electricity are denominated electroscopes ; such as are em- ployed to estimate its comparative quantity, are called elec- trometers. This distinction, however, is neglected by some Electricity. — In what two senses is the term used ? By what effect is tin presence of electricity manifested? When is a body said to be excited?— when electriiied? Define conductors and non-conductors. Why are the latter called electrics? When is a body said to be insulated? Define eleo troscopes and electrometers. GENERAL miNCIPLES. 237 Fig. 117. fa A writers, and, to avoid the unnecessary multiplication of terms, it will be neglected in the present treatise, instruments of either kind being called electrometers 318. The Pendulum Electrometer is formed by suspend- ing some light conducting body by some non-conducting substance. Thus, a small ball of tlie pith of elder, hung by a silk thread, constitutes a very convenient instrument for detecting the presence and examining the kind of electricity. Fig. 117, represents a pendulum electrometer, consist- ing of a glass rod fixed in a stand, and bent at the top so as to form a hook. From this hook hangs a thread of raw silk, to the bottom of which is attached a small pith ball, made smooth and round, and weighing only a small part of a grain. The attenuated thread, of silk, unwound from the ball of the silk-worm, forms a very delicate insulator ; but for ordi- nary purposes, a common thread of silk may be untwisted, and a single filament taken for the suspending thread. For the purposes of the learner, it may even be sufficient to sus- pend a ball of cork, or a lock of cotton, or a feather, by a thread of silk. The Gold Leaf Electrometer, represented in Fig. 118, consists of two strips of gold leaf suspended from the metallic cover of a small glass cylinder. By this arrangement, the pieces of gold leaf are insulated ; they are protected from agitation by the air, and electricity is easily conveyed to them by bringing an electrified body into contact with the cover. The approach of an electrified body causes the leaves to separate, or when previously separated, to collapse ac- cording to principles to be explained pres- ently. By the aid of the foregoing instruments, or even by means of the pendulum electrometer alone, we may ascertain the following LEADi.\G FACTS, vvhich are so many fundamental truths in the science of Electricity. 310. Prop. I. Electricity is produced by the friction of all bodies. f c \ How is the pendulum electrometer formed ? Describe the gold leaf elec- trometer. How is electricity produced ? 238 ELECTRICITY. Although friction is the most common, and by far the most extensive means of exciting bodies, yet it is not the only means. Electricity is manifested during the changes of state in bodies, such as liquefaction and congelation, evap- oration and condensation. Some bodies even are excited by mere pressure ; others by the contact or separation of differ- ent surfaces. Most chemical combinations and decomposi- tions are also attended by the evolution of Electricity, which manifests its presence to delicate electrometers. If we rub a piece of amber, sealing wax, or any other resi- nous substance on dry woolen cloth, or fur, or silk, and bring it towards an electrometer, it will give signs of electricity. A glass tube may be excited in a similar manner. More- over, if we bring the excited tube near the face it imparts a sensation resembling that produced by a cobweb. If the tube is strongly excited, it will afford a spark to the knuckle, accompanied by a snapping noise. A sheet of Avhite paper, first dried by the fire and then laid on a table and rubbed with ■India rubber, will become so highly excited as to adhere to the wall of the room, or any other surface to which it is ap- plied. Indeed, friction is so constantly attended by elec- tricity, that in favorable weather the fluid is abundantly in- dicated on brushing our clothes, which thus are made to attract the light downy particles that are floating in the air. 320. Our proposition asserts that electricity is produced by the friction of all bodies, whereas if we hold in the hand a metallic substance, a plate of brass or iron, for example, and subject it to friction, we shall not discover the least sign of electrical excitement. In such cases, however, the elec tricity is prevented from accumulating in consequence of the substance being a. good conductor., and thus conveying the fluid to the hand, which is another good conductor, by which means it is lost as fast as it is excited. But if we insulate a melallic body, or any other conducting substance, then, on being rubbed, it gives signs of electricity, like electrics. 33 !• Pkop. II. Tlie Electricity which is excited from GLASS, and a numerous class of bodies, exhibits different piroperties from that which is excited from ambee., or seal- ing wax, and a class of bodies equally numerous loith tlie otlier. By what means beaide iriction ? Recite the experiments made with a piece of amber, with a j;la.ss tube, and with a sheet of white paper. Are all bodies capable of being electrified by friction ? State the proposition comparing the respective properties of glass and amber. GENERAL PRINCIPLES. 239 The kind of fluid excited from glass and analogous bodies is called viti-eous. aud that from amber and analogous bodies, resinous electricity. The term positive is also used instead of vitreous, and negative instead of resinous In order to understand the applications of the preceding terms vitreous and resinous, positive and^ negative, it is ne- cessary to know something of the two hypotheses upon which these terms are respectively founded. The first hy- pothesis is that proposed by Du Fay. It ascribes all elec- trical phenomena to the agency of two fluids specifically dif- ferent from each other, and pervading all bodies. In unelec- trified bodies, these two fluids exist in combination, and ex- actly neutralize each other. By the separation of the two fluids it is that bodies are electrified, and it is by the re- union of the two fluids, that the electricity is discharged, or bodies cease to be excited. The second hypothesis was pro- posed by Dr. Franklin. It ascribes all electrical phenome- na to the agency of one fluid, which, as in the other case, is supposed to pervade all bodies, being naturally in a state of equilibrium. It is only when this equilibrium is destroyed that bodies become electrified, and it is by the restoration of the equilibrium that the electricity is discharged, or bodies cease to be excited. But a body is electrified when it has either more or less of the fluid than its natural share ; in the former case it is positively, in the latter negatively, electri- fied ; positive electricity, therefore, implies a redundancy, and negative electricity, a deficiency of the fluid. 323« Prop. III. Bodies electrified in different ways attract, and in the same way repel each other. Thus, if an insulated pith ball, (Art. 318,) or a lock of cot- ton, be electrified by touching it with an excited glass tube, it will immediately recede from the tube, and from all other bodies which afford the vitreous electricity, while it will be attracted by excited sealing wax, and by all other bodies which aC!brd the resinous electricity. If a lock of fine long hair be held at one end, and brushed with a dry brush, the separate hairs will become electrified, and will repel each other. In like manner, two insulated pith balls, or any other light bodies, will repel each other when they are elec- Explain the term.s vitreous and resinous, positive and negative. Explain the hypothesis of Du Fay, and that of Franklin. According to Du Fay's hypothesis, what takes place ,when electricity is excited, and what when it ia discharged 7 How do bodies affect each other when electrified the same way, and how when electrified different ways ? State the experiments with a lock of cotton or of hair. 240 ELECTRICITY. trifled the same way. and attract each other when they are electrified different ways. Hence it is easy to determine, whether the Electricity of • forded by a given body is vitreous or resinous ; for, having electrified the electrometer by excited glass, then all those bodies, which, when excited, attract the ball, afford the resi- nous, while all those which repel, the ball, afford the vitreous Electricity. 323. Prop. IV. Tlie two kinds of Electricity are fro- dticed simultaneously ; tlie one kind in the body rubbed,, the otlier in the rubber. For example, if we rub a glass tube with a silk or woolen cloth, the glass becomes positive, and the cloth negative. The foregoing law holds true universally : but the kind of Electricity which each substance acquires, depends upon the substance against which it is rubbed. If we rub dry wool- en cloth against smooth glass, it acquires the resinous, and the glass, the vitreous Electricity ; but if we rub the same cloth against rough glass it becomes positively, while the glass becomes negatively, electrified. The following table contains a number of electric substances, arranged in such a way that when they are rubbed against each other, any substance in the list above another, becomes positively, and any substance below it, negatively electrified. I. Fur of a Cat, 6. Paper, 2. Smooth Glass, 7. Silk, 3. Woolen Cloth, 8. Lac, 4. Feathers, 9. Rough Glass, 5. Wool, 10. Sulphur, The fur of a cat, when rubbed against any of the bodies in the table, always affords the vitreous, and the sulphur al- ways the resinous electricity. Feathers become negative when rubbed against the fur of a cat. smooth glass or wool- en cloth ; but positive when rubbed against wool, paper, silk, lac, rough glass, or sulphur. 334. Prop. V. Electricity passes through some bodies with the greatest facility ; through otlier s viith the greatest apparent difficulty, or scarcely at all ; and others have a conducting power intermediate between the two. How can we determine the kind of electricity produced in a given case 1 How do the electricities of the rubber and the body rubbed compare with each other ? What kind of electricity does the fur of a cat give ? What kind does sulphur give? When do feathers give positive, and when negative! Recite proposition V, respecting the conducting powers of different bodies. GENERAL mmciPLEs. 241 Metals and charcoal, water and all liquids, (oils excepted,) are g-ood conductors. Melted wax and tallow are good con- ductors ; but these bodies while solid conduct very badly. Glass, resins, gums, sealing wax, silk, sulphur, precious stones, oxides, air, and all gases, are non-conductors, or at least very bad conductors. Atmospheric air is a non-con- ductor of the highest class, when perfectly dry ; but it be- comes a conductor, either when moist or when rarefied. The electric fluid easily pervades the vacuum of an air pump, or of the Torricellian tube ; but these are imperfect vacuums ; it is said that Electricity cannot pass through a perfect vacuum. The conducting powers of most bodies are influ- enced by changes of temperature, and also by changes of form. Water, in its natural state, is a good conductor ; but its conducting power is increased by heat and diminished by cold. The same body frequently exhibits great changes in con- ' ducting power by changes of state, or chemical constitution. Thus, green wood is a conductor, dry baked wood a non- conductor ; charcoal a conductor, ashes a non-conductor. It is particularly important to remember that Metals, Water, and all moist substances. Animal substances, as the human body, and the Earth itself, are conductcns ; while the Air, when dry, and all Resinous and Vitreous substances, are non-conductors. These bodies are those which are chiefly concerned in making experiments with electrical appa- ratus. 325. Prop. VI. Insulation is effected in various degrees of perfection, according to the state of the atmosphere, and the nature of the substances employed as insulators. If the air were a conductor, it is not easy to see how the electric fluid could be confined so as to be accumulated. It is, moreover, only when the air is dry that it is capable of insulating well ; hence, in damp, foggy and rainy weath- er, electrical apparatus will not work well, unless the air is dried artificially by operating in a close room highly heated by a stove. Lac, drawn into fine threads, is the most per- fect insulator. Compared with silk thread, such a filament is ten times more elfectual in preventing the loss of the fluid. Fine silk thread, however, when perfectly dry, is among the best insulators : and where great delicacy is re- Ennmerate the best conductors and the best non-condactors. Can elec- tricity pass through a vacuum! What changes in conducting power result from bodies being moist or dry ? Mention the best methods of insulating. 21 242 ELECTRICITY. quired, a single filament of silk, as it comes from the ball of the silk worm, is employed. Its conducting power is somewhat influenced by its color, black being the worst, and a gold yellow the best color for insulating. Glass is much used as an insulator, especially when great strength is re- quired, as in supports to various kinds of electrical appara- tus. Glass, however, is liable to acquire moisture on -its sur- face, in consequence of which its properties as an insulator are materially impaired. This inconvenience is obviated by giving it a thick coat of varnish. Fine hair is a good and convenient substance in some cases of insulation. In some cases, conducting or uninsulating threads are re- quired. Then fine silver wires, or linen threads first steeped in a solution of salt, and dried, are used. 326« The spJiere of communication is the space within which a spark may pass from an electrified body, in any di- rection from it. It is sometimes called the striking dis- tance. The sphere of influence is the space within which the power of attraction of an electrified body extends in every way, beyond the sphere of communication. A glass tube strongly excited will exert an influence upon the gold leaf electrometer at the distance of ten or even twenty feet, al- though a spark could not pass from the tube to the cap of the electrometer at a greater distance than a few inches. 327. The electricity which a body manifests by being brought near to an excited body, without receiving a spark from it, is said to be acquired by Induction. When an insulated conductor, unelectrified, is brought into the neighborhood of an insulated charged conductor, its Electricity undergoes a new arrangement. The end of it next to the excited conductor, assumes a state of electricity opposite 10 that of the excited conductor ; while the farther extremity exhibits the same kind of electricity. Suppose the excited conductor is electrified positively. The end of the insulated conductor next to it becomes negative, and the remoter end, positive ; and intermediate between these two points, there occurs a place where neither positive nor nega- tive electricity can be perceived. This place is called the neutral point. The reason why unelectrified bodies are attracted by ex- cited electrics, is. that they are put into the opposite state Define the sphere of communication — also, the sphere of infiaence. Define indnction. Explain the diflTerence of arrangement in the electricity of an insulated conductor, when brought near a charged conductor. ELECTRICAL APPARATUS. 243 by induction, and then attracted upon the generarprinciple laid down in Prop. III. When they come into the sphere of communication of the excited body, they immediately ac- quire the same kind of electricity, and are repelled. If they come into contact with uninsulated bodies, they lose the electricity they have acquired, and are again put into the opposite state by induction, again attracted and again re- pelled. This process will go on until the electricity of the insulated conductor is all conveyed away. _ The foregoing general principles may be verified with very simple apparatus, such as pith balls, a glass tube, and a stick of sealing weix. But the same facts may be exhibited in a much more striking and impressive manner by the elec- trical machine and its appendages, and our attention will therefore be now turned to the consideration of the subject of electrical apparatus. CHAPTER II. OF ELECTRICAL APPARAT XJS. \ 328« The object of the electrical machine is io accumu- late electricity. It is made of several different forms, but two of these forms are predominant, which it will be suffi- cient for our present purpose to describe ; of these, one is called the Cylinder, the other, the Plate machine. The Cyl- inder Machine is represented in Fig. 119. The principal parts belonging to it, are the cylinder, the frame, the rub- ber, and the prime conductor. The cylinder (A) is of glass, from eight to twelve inches in diameter, and from twelve to twenty-four inches long. It should be perfectly cylindrical, otherwise it will not press the cushion or rubber evenly when turned. It must be as smooth as possible, for rough glass becomes a partial conductor. The cylinder should be so mounted on the frame as to revolve without waddling, for such a motion would prevent its being in uniform contact with the rubber. The frame (BB) is made of wood, which "WTiy are unelectrified bodies attracted by such as are electrified ? Elec '.rical Apparatus. — What is its object ? What are the two usual forms ! Describe the Cyliitier MachiTie — the cylinder, of what made — its size — figure —smoothness, &c. How mounted 7 244 ELECTRICITT. must be close gramed, well seasoned, and baked in an oven, and finally coated with varnish ; the object of all this prepa- ration being: to diminish its conducting powers, and thus prevent its wasting the electricity of the cylinder. The rub- ber (C) consists of a leathern cushion, stuffed with hair like Fig. 119. the padding of a saddle. This is covered with a bkck silk cloth, having a flap which extends from the cushion over the top of the cylinder, to the distance of an inch from the points connected with the prime conductor, to be mentioned presently. The rubber is coated with an amalgam* made of mercury, zinc, and tin, which preparation has been found, by experience, to produce a high degree of electrical excite- • The amalgam recommended by Singer, one of the ablest practical electricians. Is composed of zinc two ounces, of tin one ounce, and of mercury six oimcea. The zinc and tin may be melted together in a ladle, or crucible, and poured into a mortar, previously warmed to prevent the sudden congelation of the melted metals. As suon as they are introduced, they must be rapidly stirred with the pestle, during which process the mercury may be added, and the stirring continued until the amalgam ia cold, when it will be in the form of paste, or fine powder. A little lard is added to give the amalgam the proper consistence ; but if, when applied, it be warmed a little, but a small proportion of lard need be used. In hot weather, less quicksilver Is to be employed. Tlhe frame— o( what made — hovir coated ? The rubber — of what made — how covered — how coated — how insulated? What is the composition of the ELECTRICAL APPARATUS. 245 Fig. 120. ment, when subjected to the friction of glass. The rubber is insulated b}' placing it on a solid glass pillar, and it is made to fit closely to the cylinder by means of a spring, worked by a screw. The prime conductor (D) is usually a hollow brass cylin- der with hemispherical ends. It is mounted on a solid glass pillar, with a broad and heavy foot, made of wood, to keep it steady. The cylinder is perforated with small holes, for the reception of wires (c) with brass knobs. It is important to the construction of an electrical machine, that the work should be smooth and free from points and sharp edges, since these havei a tendency to dissipate the fluid, as will be more fully understood hereafter. For a similar reason the machine should be kept free from dust, the particles of which act like points, arid dissipate the electricity. 329. The Plate Machine (Fig.l20)consists of a circular plate of glass, from eighteen to twen- ty-four inches or more in diame- ter, turning ver- tically on an axis that passes through its cen- ter. The frame IS composed of materials similar to those which compose the frame of the cylindrical ma- chine. This ma- chine is furnished with two pairs of rubbers, attach- ed to the top and bottom of the The vrime amdiictor—ot what made— how monnted— why perforated wilh holes? The^/ofe .AfocAtme— of what does it consist ? How many rob- ban ve used ? 21* 246 ELECTRICITY. plate. The prime conductor consists of a brass cj'linder, pro ceeding from the center in a line with the axis, and having two branches which serve to increase its surface, and at the same time to connect it with the opposite sides of the plate, so as to receive the electricity as it is evolved from each cushion. It is not agreed which of these two machines affords the greatest quantity of electricity from the same surface ; but the cylinder is less expensive than the plate, and less liable to break, and is more convenient for common use. 330. The principles of the electrical machine will be readily comprehended from what has gone before. It differs from the glass tube, only in affording a more convenient and effectual mode of producing friction. By the friction of the glass cylinder or plate against the rubber, electricity is evolved, which is immediately transferred to the prime con- ductor, and may be taken from the latter by the knuckle, or any other conducting substance. If the glass and rubber both remain insulated, the quantity of electricity which they are capable of affording, will soon be exhausted. Hence, a chain or wire is hung to the rubber and suffered to fall upon the table or the floor, which, communicating as it does with the walls of the building, and finally with the earth, supplies an inexhaustible quantity of the fluid to the rubber. In cases where very great quantities of electricity are required, a metallic communication may be formed immediately be- tween the rubber and the ground.* 331. The Hydro-electric Machine is a piece of ap- paratus which affords electricity from steam escaping through • As electrical machineg are expensive, and not always easily procured by the private learner, it may be useful to suggest a mode of fitting up a cheap apparatus. A large tincture bottle may be procured of the apothecary, for the cylinder. A cover of wood may be cemonled to each end, to the center of which, next to the bottom, is screwed a projecting knob for one end of the axis, while the part of the axis to which the handle is attached, is screwed into the center of the cover of wood next to the nozzle. Thus prepared, it may be mounted on such a frame of dry hard wood as every joiner or cabinet maker can construct. A tinner can make the prime conductor, and several other appendages to be described hereafter. Junk bottles or long viala serve well as insulators. Ingenious students of electricity frequently amuse themselves with making machines of this description, some of which have answered nearly every purpose of the most expensive kinds of apparatus. A cement, for electrical purposes, may be made by melting together five ounces of resin, one ounce of beeswax, one otmce of Spanish brown, and a tea spoonful of plaster of Paris, or brick dust. How is the prime conductor constracted 1 What advantage has the cylin- der over the plate machine 1 How does the electrical machine difTer from the glass tube ? How does it afford electricity 1 "Why must the rubber be con- nected, by a conductor, with the ground ? Describe the mode of constructing a cheap electrical apparatus. What may be used for the cylinder ? How mounted? What may he used for the prime conductor, for insulators, &a What is the composition of electrical cement ? ELECTRICAL APPARATUS. 247 a narrow orifice. This source of electricity was first dis- severed in the steam issuinof from the pipe of a locomotive ; and the hydro-electric machine is little else than a small high-pressure boiler furnished with an escape-pipe. While the steam is issuing- forcibly, the boiler becomes strongly negative, and on approaching to it a brass ball, long and vivid sparks will dart towards the ball. By this machine a quantity of electricity is generated in a little time, sufficient for all the purposes of experiment. Some are of opinion that the electricity is excited by the rapid condensation of watery vapor, which is a known source of electricity, while others hold that it is excited merely by the friction of the steam against the sides of the escape-pipe. 332. In order to indicate the degree of excitement in the prime conductor, the Quadrant Electrometer is attached to it, as represented at E, in Fig. 1 19. The electrometer is formed of a semicircle, usually of ivory, divided into degrees and minutes, from to 180,* the graduation beginning at the bottom of the arc. The index consists of a straw. moving on the center of the disk, and carrying at the other extremity, a small pith ball. The perpendicular support is a pillar of brass, or some conducting substance. When this instrument is in a petpendicular position and not electrified, the index hangs by the side of the pillar, perpendicularly to the horizon ; but when the prime conductor is electrified, it imparts the same kind of electricity to the index, repels it, and causes it to rise on the scale towards sHi angle of 90°, Or to a position at right angles with the pillar. An important distinction is to be remarked in the use of the terms intensity and quantity. Intensity refers to the energy with which electricity restores its equilibrium, and is measured by the distance to which it will burst through non-conductors, as the length of the electric spark, or of a flash of lightning. A current of electricity may be great in quantity but low in intensity. 333« When an electrical machine is skilfully fitted up, and works well, on turning it, circles of light surround the cylinder or plate, and brushes or pencils of light emanate copiously from the cushion and other parts of the machine. The circles of light consist of electric sparks, which discharge • Sometimes the division is carried only to ninety degrees, which is all that is necessary. Describe the bydro-electric machine. Describe the quadrant electrometer. What appearances does the machine, when well fitted up, exhibit? 248 ELECTRICITY. themselves between the excited surface and the rubber, their passage being so rapid as to appear like a continued line, like that of a small stick ignited at the end and whirled in the air. The brushes of light arise from the facility with which the fluid escapes from points or thin edges.* In a cylinder machine, the most important circumstance is, that the enclosed air should be always dry. In )rder to insure this, the air which fills it when the ends are closed, should be dry and cold, such as, in our climate, accompanies a north-westerly wind. 334. We proceed to enumerate a few of the effects of electricity as they are exhibited by the electrical machine, confining ourselves, for the present, to those experiments which relate to attraction and repulsion, and the passage of the spark, reserving such as relate to light and heat to future sections. The following effects may be observed with a machine of moderate powers, the rationale of which the learner will readily supply from the propositions given in Arts. 318—3-26. (1.) When the machine is turned, a downy feather, or a lock of cotton held in the hand by a conducting thread.f will be strongly attracted towards the excited surface. (2.) A skein of thread, or lock of fine hair, looped and suspended by the loop from the prime conductor, will exhibit strong repulsions between the threads or hairs. (3.) The quadrant electrometer, being attached to the prime conductor, the conducting powers of different substan- ces may be readily tried. Thus, an iron rod held in the hand, and applied to the prime conductor, will cause the index of the electrometer to fall instantly ; and the same effect will follow the application of any metallic rod. A wooden rod of the same dimensions, will cause the index to descend more slowly ; and a glass rod will hardly move it at all. These ex- periments show that iron is a perfect, and wood an imperfect conductor, and glass a non-conductor. In the same manner the conducting powers of a stick of sealing wax, a roll of silk, or cloth, and of various other bodies may be illustrated. * A cylinder machine will not work well unless the enclosed air be dry. The colder the air that is present when the ends are closed up the better ; for if the air enclosed was originally hot and humid, moisture will be deposited on the inside of the cylinder in certain changes of weather, and the machine will work badly. t The conducting power of linen or cotton thread is improved by mois'tening them with the breath. ^ Experiments. — Describe the experimetit with a feather or locli of cotton— with a skein of thread. Effects of elecuioity ou the conducting powers of bodies 7 ELECTRICAL APPARATUS. 249 (4.) If a pith ball, or feather, or any other light body held by a silk thread, be presented to the prime conductor, it will first be attracted and then repelled, and it cannot again be brought into contact with the electrified conductor until its electricity is discharged by communicating with the finger or some unelectrified conductor. (5.) By placing light bodies between an electrified con- ductor and an uninsulated body, they may be made to move with great rapidity backwards and forwards, from one sur- face^ to the other, being alternately attracted and repelled by the'electrified surface. By this means are performed elec- trical dances, the ringing of bells, and a variety of interest- ing and amusing experiments., (6.) If the rubber be insulated while the machine is turned, the rubber and the glass cylinder, or plate, will be found to be in different electrical states ; an insulated body attracted by the one will be repelled by the other. Bodies are electrified positively by connecting them with the glass, by means of the prime conductor, and negatively by connecting them with the rubber, the latter being insu- lated, and the prime conductor uninsulated. (7.) An electrified body frequently exhibits a tendency to separate into minute parts, these parts being endued with the power of mutual repulsion. Thus a lock of cotton, when electrified, is separated into its minutest fibres Melted sealing wax, when attached by a wire to the prime conduct- or, is divided into filaments so small as to resemble red wool. Water dropping from a capillary syphon tube, on being elec- trified, is made to run out in a great number of exceedingly fine streams. Water spouting from an air fountain is divided into a number of rays, presenting the appearance of a brush. (8.) A portion of electrified air, in consequence of the mutual repulsion between its particles, expands, and when at liberty to escape, becomes rarefied. Thus, a current of air may be set in motion from an electrified point, Or small ball, or be made to issue from the neck of a bottle. Such are some of the leading experiments which may be performed with the common electrical machines, in addition to those which are connected with light and heat, to be more particularly described hereafter. Effects of electricity on attraction and repulsion — on the diiferent states of the machine and rubber ? How are bodies electrified positively — ho-w negatively ? What bodies separate into fibres vi'h^n electrified ? On what principle is a current of air set in motion from an electrified point 7 250 ELECTRICITY. 335. TJie force of electrical attraction or repulsion, at different distances from an electrified body, varies inversely as the square of the distance. Hence electrified bodies exhibit strong attractions and re- pulsions only when very near to each other, and the force decreases rapidly with the distance, being- diminished four times by doubling the distance, and nine times by trebling it. It is worthy of remark, that the foregoing law is the same as gravitation. Electricity resides only at or near the surfaces of bodies. A hollow metallic globe, for example, takes the same charge as a solid globe, of the same dimensions. Bodies of differ- ent figures, however, have the electricity distributed over their surfaces in different manners. Thus, in a conductor of an elongated figure, the electricity is accumulated to- wards the two ends, and more or less withdrawn from the central parts. Fig. 121. Q J Fig. 122. THE LEYDEN JAR. 336. This instrument, which is a very im- portant article of electrical apparatus, consists of a glass jar, coated on both sides with tin foil, except a space on the upper end, withii. two or three inches of the top, which is either left bare, or is covered with a coating of var- nish, or a thin layer of sealing wax. To the mouth of the jar is fitted a cover of hard baked wood, through the center of which passes a perpendicular wire, terminating above in a knob, and below in a fine chain, that rests upon the bottom of the jar. On presenting the knob of the jar near to the prime con- ductor of an electrical machine, while the latter is in operation, a series of sparks pass between the conductor and the jar, which will gradually grow more and more feeble, until they will cease altogether. The jar is then said to be charged. If we now take the discharging rod, (which is a crooked wire, armed at each end with knobs, and How is the force of electrical attraction and repulsion at diiferent distances 7 On what part of bodies does electricity reside ? Is the distribution aifeeted by difference of figures in bodies? How is the electricity accumulated on conductors of an elongated figure ? Ixyden Jar — of what does it consist I Describe it — how charged and discharged. Describe the discharging rod. LEYDEN JAR. 251 msulated by a glass handle, as in Fig-. 122,) and apply one of the knobs to the outer coating of the jar, and bring the other to the knob of the jar; a flash of intense brightness, accompanied by a loud report, immediately ensues. On ap- plying the discharging rod a second time, a feeble spark passes, being the residiMry charge, after which all signs of electricity disappear, and the jar is said to be discharged. If, instead of the discharging rod. we apply one hand to the outside of the charged jar, and bring a knuckle of the other hand to the knob of the jar, a sudden and surprising shock is felt, convulsing the arms, and, when sufficiently powerful, passing through the breast. 337. The Leyden Jar derives its name from the place of its discovery. In the year 1746, while some philosophers of Leyden were performing electrical experiments, one of them happened to hold in one hand a tumbler partly filled with water, to a wire connected with the prime conductor of an electrical machine. When the water was supposed to be sufficiently electrified, he attempted, with the other hand, to detach the wire from the machine ; but as soon as he touched it, he received the electric shock. It was by imita- ting this arrangement, that the Leyden Jar was construct- ed ; for here was a glass cylinder, having- good conductors on both sides, viz., the hand on the outside, and the water on the inside, which were prevented from communicating with each other by the non-conducting power of the glass. A metallic coating, as tin foil or sheet lead, was substituted for the two conductors, and a jar for the glass tumbler, and thus the electrical jar was constructed. Those who first received the electric shock from the Ley- den Jar, gave the most extravagant accounts of its efllects. M. Muschenbrock, a philosopher of Leyden, of much emi- nence, said that " he felt himself struck in his arms, shoul- ders, and breast, so that he lost his breath ; and it was two days before he recovered from the effects of the blow and the terror; adding, that he would not take a second shock for the kingdom of France."' M. Winkler, of Leipsic, testified, that " the first time he tried the Leyden experiment, he found great convulsions by it in his body; and that jt put his blood into great agitation, so that he was afraid of an ar- dent fever, and was obliged to use refrigerating medicines. What sensation is experienced on receiving the charge on the knuckle ? Give the history of the Leyden Jar. What resembhince have the several parts of the jar to the accidental combination which first led to its discovery ? State the accounts at first given of the shock. 252 ELECTRICITY. He also felt a heaviness in his head, as if a stone lay upon it, and twice it gave him a bleeding at the nose." 338. In an age less enlightened than the present, and less familiar with the wonders of philosophy and chemistry, the striking and truly surprising effects of electricity, as ex- hibited by the Leyden Jar, would naturally excite great ad- miration and astonishment. Accordingly, showmen tiav eled with this apparatus through the principal cities of Eu rope, and probably no object of philosophical curiosity ever drew together greater crowds of spectators. It was this as- tonishing experiment (says Dr. Priestley.) that gave eclat to electricity. From this time, it became the subject of gen- eral conversation. Everybody was eager to see, and, not- withstanding the terrible account that was reported of it, to feel the experiment ; and in the same year in which it was discovered, numbers of persons, in almost every country in Europe, got a livelih*od by going about and showing it. All the electricians of Europe, also, were immediately employed in repeating this great experiment, and in attending to the circumstances of it. With similar assiduity and unequalled success, Dr. Franklin betook himself to experiments on the Leyden Jar. He effectually investigated all its properties, by very diversified and ingenious experiments, and gave tht first rational explanation of the cause of its phenomena The following experiments may be easily repeated. 339* (1.) Tliejar is charged by bringing the knob neai the prime conductor, while the machine is in operation. Ont mode of charging the jar has been already mentioned in Art. 336. It may, however, either be held in the hand, oi placed on the table, or on any conducting support : the only circumstance to be attended to is, tnat the outside shall be uninsulated. A jar, while charging, will sometimes dis- charge itself spontaneously. This effect will be more likely to happen, if the uncoated interval is very clean and dry, and may be prevented altogether, by previously breathing on the uncoated part. (2.) The opposite sides of a charged jar, are in different electrical states, the one positive and the other negative. Thus, if a pith ball, suspended by a silk thread, be applied to the knob, it will first be attracted to it, and then repelled ; but it will now be attracted by the outside coating, until it State facts showiDg the celebrity of the Leyden Jar. Eocpenmcnts. — How is the jar charged ? When is the jar apt to discharge itself spontaneoasly T la what states are the opposite sides of a jar? LEYDEN JAR. 253 becomes electrified in the same way, and then repelled, and so on. (3.) In order to receive the charge, the outside of the jar must he uninsulated. If we attach a string to the knob of the jar, and suspend it in the air, to the prime conductor and put the machine in operation, no charge will be com municated to the jar. The same result will follow, if the jar stands on an insulating stand,* or is insulated in any- other method. An insulated jar, however, may be charged by connecting its knob with the positive conductor, and its outer coating with the rubber. (4.) A second jar may he charged, hy communication with the outside of the first, while the latter is receiving its charge. The charge communicated to the second jar, is of the same kind as that of the first, and nearly of the same degree of intensity, provided the capacity of the two jars be the same. Moreover, if a third, a fourth, or any number of jars, of the same size, be connected in a similar manner, with each other ; namely, having the knob of each in communication with the outside coating of the next preceding, — then all the jars will be charged with the same kind of electricity, but the degree of intensity will decline a little in the successive jars. If the charge be derived, through the prime conduct- or, from the cylinder or plate, as is usually the case, it will be the positive or vitreous electricity. (5.) A jar may he charged negatively, hy receiving the electricity of the ruhher, — the rubber being insulated, and the prime conductor uninsulated. For this purpose, the chain usually attached to the rubber may be transferred to the prime conductor. (6.) When two jars are charged, the one positively and the other negatively, on forming a communication hetween the inside of both, by connecting the two knobs, no discharge will take place, unless the outsides be in conducting commu- nication. Thus, if two jars be charged, the one from the prime conductor and the other from the rubber,! and placed • An insalating stand is any flat support, insulated by a pillar of glass. The pillar is usually a solid cylinder of glass, from six to twelve inches long, varnished so as to protect it from moisture. A junk bottle, surmounted by a circular piece of wood, dry and varnished, makes a very good insulating support. T And both may be thus charged at the same time, by connecting one with the insulated rubber, and the other with the insulated prime conductor, the jars them- selves being uninsulated. Will a jar receive a charge when insulated 1 How to charge a second jar from the first ? If a series of jars be charged from the first, how is the strength of the charge in each ? How to charge a jar negatively ? What is necessary in order that two jars, charged opposite ways, may be discharged? 22 254 ELECTEICITY. Fig. 183. at the distance of a few inches from each other, on insulated supports, on connecting the two knobs by the discharging rod, no discharge will follow ; but, let a wire be laid across the supports, touching the outside of each jar ; then, on ap- plying the discharging rod to the knobs, an explosion will immediately ensue. By means of two jars differ- ently charged, and placed as above, with their outsides in conducting communication, the experiment may be exhibited, which is called the Electrical Spider. It consists of a small piece of cork, so fashioned as to represent the body of a spider, and blackened with ink, having a number of black linen threads drawn through it to represent the legs. This is suspended by a silk thread, half way between the knobs of (he two jars, and vibrates for a long time from one knob to the other, until both jars are discharged. The rationale will be obvious on a little reflection. (7.) The charge of any jar may he divided into definite parts ; that is, the half, the fourth, or any aliquot part of the -charge may be taken. This may be done by connecting the inner and the outer coating of the charged jar, with the inner and outer coating of an unelectrified jar, of the same size and thickness. The respective charges will be meas- ured by the quadrant electrometer, (Fig. 119.) (8.) 27te electricity is accumulated on tlie surface of the glass, and the coatings serve merely as conductors of tlve charge. This is proved by the fact, that when the coatings are movable, so that they can be taken off from the jar after it is charged, neither of them exhibits the least sign of electricity ; while if another pair of coatings is substituted, which have not been electrified, on forming the communica- tion between the inside and outside, the usual discharge takes place, showing that the whole of the charge was re- tained on the glass surfaces of the jar. (9.) Tlie charge of a Leyden Jar may be retained for a Describe the electrical spider. How may the char;^ of a jar be divided t On what part of a jar is the electric Haid accamulated ? LEYDEN JAR. 253 long time. If *he surfaces are well separated from each other, the charge remains for many days and even weeks. The charge is usually dissipated by the motion of particles of dust, or other conducting substances in the atmosphere, from one of the coatings to the other, or by the uncoated in- terval becoming moist, and losing its insulating power ; con- sequently a jar will retain its charge longer in dry than in damp weather. Covering the uncoated part of the jar with a solution of sealing wax in alcohol, or with varnish, pre- vents the deposition of moisture upon it, and consequently tends also materially to prevent the dissipation of its charge. 340. For the purpose of making the theory of the Leyden Jar familiar, we may now recur to the experiments mentioned in Art. 339, and attempt the explanation of them. In the structure of the Jar, we recognize the operation of the principle of indtcction. Here an unelectrified body, (the outer surface,) is brought very near to an electrified body, (the inner surface.) without the possibility of communicating with each other, on account of the non-conducting properties of the glass. The nearer the two surfaces can be brought to each other, the more powerful is the effect of induction, that effect being inversely as the square of the distance. Accordingly, the thinner the jar, the more powerful is the charge it will receive ; but the danger of breaking prevents our employing such as are very thin. To trace the process of charging a jar a little more mi- nutely, let us suppose the jar connected with the prime con- ductor of an electrical machine, from which a spark is com- municated to the inner coating. This, according to the principles of induction, expels a similar quantity of the same fluid from the opposite unelectrified surface, and renders that negative, in the same degree as the inside is positive. Being negative, it increases the attraction of the inner surface for the opposite species of fluid, and another spark is received, which again expels an additional quantity of the same spe- cies of fluid from the outside, and thus the two surfaces con- tinue to act upon each other reciprocally, though with con- stantly diminishing power, until the jar is charged. The reason also is plain, why the outside of the jar must be uninsulated ; since it is only in such case, that the fore- How long may the charg-e of a jar be retained ? How is it u.sualJy disai- pated? How may the waste be prevented? Explain the accumulating power of the jar, on the principle of induction. What effect has the thick UBBB of the jar on this power? Trace the process of charging a jar. 256 ELECTRICITY. going- process of induction can take place t and we readily see why a series of jars may be charged, from the portion of electricity which is expelled from the outside of the first jar. 341. When ajar is charged negatively from the rubber just the. opposite process in all respects takes place, the out side becoming positive by induction, and reacting upon the inside. The case mentioned in Art. 339, (6.) where two jars differently charged, cannot be discharged except their outer surfaces be in conducting communication, will be readily understood ; for it is impossible for the equilibrium to be restored by the union of the electricities on the inside, while the outside remains electrified. If we could suppose this to take place for a moment, and the electricity within to be restored to its natural state, it would again be imme- diately decomposed by the inductive influence of the electri- fied coating without. 342> The phenomena of the Leyden Jar may be equal- ly well explained, by substituting the terms vitreous and resinous instead of positive and negative, on the supposition of two fluids, since the principles of induction apply equally w^ell to both hypotheses. Thus, it is as easy to suppose that the resinous electricity is induced upon the outside by the attraction of the vitreous electricity within, as it is to sup- pose that the outside becomes negative by the loss of a portion of its natural share ; and the necessity of the outer surface being uninsulated, is as apparent in the one case as in the other. CHAPTEE III. OP ELECTRICAL LIGHT, OF THE BATTERY, AND OF THE MECHANICAL AND CHEMICAL AGENCIES OF ELECTRI- CITY. ELECTRICAL LIGHT. 343« Electricallight appears whenever the fluid is dis charged, in cdnsiderable quantity, through a resisting me- dium. "Why must the ontside of a jar be uninsulated before it will receive a charge 1 Explain the process when the jar is charged negatively irom the rubber ? Explain the reason why two jars, diiferently charged cannot be discharged unless the outsides are in conducting communication V Can the facts he explained on either hypothesis ! Electncal Light. — When does electrical light make its appearance ! ELECTRICAL LIGHT. 257 Accordingly, no light is perceived when electricity flows freely through good conductors ; but if such conductors suf- fer' any interruption, as by the intervention of a space of air, or even of an imperfect conductor, then the attendant light becomes manifest. We shall best learn the properties of the electrical spark, by attending to a variety of experiments in which it is exhibited* A glass tube rubbed tviih black silk, which has been smeared with a little electrical amalgam, will yield copious sparks and flashes of light. The tube should be warm, dry, and smooth, and of a size not less than two feet in length, and three fourths of an inch in diameter. The electrical machine, when in vigorous action, affords brilliant circles and streams of light. In order to render the light aflbrded by turning the machine abundar^several practical expedients are necessary. All parts of the machine must be dry and warm, (but not hot.) It is useful to rub very freely the glass plate or cylinder, with an old silk hand- kerchief Black spots or lines that collect on the glass, es- pecially when the amalgam is new, are to be carefully rubbed off; and should dust or down collect on the amalgam of the rubber, this must be removed. The action of the cyl- inder will be increased by the following process : rub a little tallow on the palm of the hand, and applying to the cylinder, turn the machine until the tallow is all taken up by the rubber and. flap. The pores of the flap will then become filled with tallow, it will apply itself more closely to the cylinder, and the supply of electricity will become more cop- ous. A convenient method of recruiting the action of the machine, is to coat a circular disk of pasteboard or leather with amalgam, and to apply it to the glass plate or cylin- der while the machine is turning. If the chain be removed from the rubber to the prime conductor, so that the former shall be insulated and the lat- ter uninsulated, on bringing the ends of the fingers near the rubber, a stream of diluted light will pass between the fin- gers and the rubber. • 344. The electric spark passes, with increased facility, through rarefied air ; and tlm distance to which it will pass * In experiments on electrical light, the room is supposod to be dark. They appear to best a^lvantage in the night. Does it appear in the passage of electricity through good conductors, o thronghbad? How may a glass tube be made to emit light ? How may tl? electrical machine be made to give sparks most freely ? How does tt electric spark pass through rarefied air ? 22* 258 ELECTRICITY. hetween two conductors, is augmented as the rarefaction is made more complete. Instead of the distance of five or six inches, which is the limit of the spark from the prime conductor of an ordin- ary machine in the open air, the spark will pass through the space of five or six feet, in an exhausted receiver If a pointed wire, terminating in a knob above, be intro duced into the top of a tall receiver, and the receiver be placed on the plate of the air pump, on connecting the knob of the wire with the prime conductor, and turning the ma- chine, a brush of light only will appear at the extremity of the wire ; but. on exhausting the air, this brush will enlarge, varying its appearance and becoming more diffused as the air bei^nes more rarefied, until at length the whole receiver is pervroed by a beautiful bluish light, changing its color with the intensity of the transmitted electricity, and produ- cing an effect which, with an air pump of considerable power, is pleasing in the highest degree. When a charged jar is placed under the receiver of an air pump, as the exhaustion proceeds, aluminous current flows over the edge of the jar, between the opposite sides, until the equilibrium is restored. Electric light exhibits a very beau- tiful appearance, as it passes or flows through the Torricel- lian Vacuum* The color is of a very delicate bluish or purple tinge, and the light pervades the entire space. But the most pleasing exhibitions of this kind, are made by forming an artificial atmosphere of vapor in the Torricellian tube. Ether or alcohol, passes into the state of vapor when the pressure of the atmosphere is removed ; and accordingly, on introducing- a drop of one of these fluids into the Torri- cellian vacuum, it immediately evaporates and fills the void. If. now, a strong spark be passed from the prime conductor through this vapor, the spark will exhibit various colors ; in ether, it is an emerald green, or mingled red or green; in alcohol it is red or blue ; but the colors vary somewhat with the distances at which they are seen, and with the tem perature of the vapor. * This Is the vacuum produce^ by means of quicksilver in an inverted glass tube, as in ttie barometer, Art. 228. To what distance will the electric spark pass in an exhausted tube? Relate the experiment of electrifying the receiver of an air pump, while the exhaus- tion is going on. What is the appearance wheu a charged jar is placed « uder the receiver of an air pump ? How does the spark flow through the 1 jrricellian vacuum ? How when made to pass through the vapor of ether alcohol, &^.1 ELECmiCAL LIGHT. 259 ^45. In condensed air, on the contrary, the spark pass- 6* with greater clifBculty than ordinary. In such case also, iti whiteness and brilliancy are augnaented, and its course is jcigzag. These appearances are even exhibited by pass- ing a spark through confined air, of only the ordinary den- sity. The colors of the spark are pleasingly varied by passing it in a condensed form, as in the Leyden Jar, through media of different kinds. The experiment is per- formed by making the given body form a part of the circuit of communication, between the inside and outside of the Leyaen Jar. A ball of ivory in this situation exhibits a beauciiul crimson ; an egg, a similar color, but somewhat lighter ; a mmp of sugar gives a very white light, which re- mains tor some time after the spark has passed ; an^ fluor spar exhibits an emerald green light, or. in some cases, a purple light, winch also continues to glow in the dark for some seconas. i'ne great intensity of the light is shown by the strong illumination which the sparks in the jar com- municate to bodies Slightly transparent. Thus, an e.gg has its transparency gieatly increased ; and if the thumb be placed over the space which separates the two conducting wires that communicate with the two sides of the jar re- spectively, the illumination is so powerful, that the blood vessels, and interior organization of the organ, may be dis- tinctly seen. 346. Metallic conductors, if of sufficient size, transmit electricity without any luminous appearance, provided they are perfectly continuous ; but if they are separated in the slightest degree, a spark will occur at every separation. On this principle, various devices are formed by pasting a nar- row band of tin foil on glass, in the required form, and cut- Pig. 124. o==<) ting it across with a pen-knife where we wish sparks to ap pear. If an interrupted conductor of this kind be pasted round a glass tube, in a spiral direction, and one end of the tube be held in the hand, and the other be presented to an electrified conductor, a brilliant line of light surrounds the "What is the appearance of the spark in condensed air ? What appearance does the spark give when passed through ivory, egg, sugar, and iiuor spar? What facts show the great intensity of the light ? 260 ELECTRICITY. tube, which has been called the spiral tube, or diamond neck- lace. By enclosing the spiral tube in a large cylinder of colored glass, the sapphire, topaz, emerald, and other gems may be imitated Words, flowers, and other complicated forms, are also exhibited nearly in the same manner, by a proper disposition of an interrupted line of metal, on a fiat piece of glass. 347. The light of the electric spark is not a constitttent part of ekctricity, but arises from the sudden compression of the air, or other medium through which it passes. It is well known that air is capable of affording a spark by sudden compression. There is a kind of match con- structed on this principle, in which a small portion of air, contained in a close cylinder, being suddenly compressed by forcing down a piston, yields a spark sufficient to light a quantity of tinder at the bottom of the cylinder. Now it is found by actual experiment, that electricity has the power of condensing air. This fact is shown by means of a small instrument called Kinnersley's Air Tlierinometer. It con- sists of a glass tube, closed air tight at the two V'lg. 125. ends by brass caps, through each of which passes a movable wire, terminated within by a small ball. Through the lower cap is inserted a small glass tube, open at -both extremities, and turned upwards parallel to the cylinder. Into this tube is introduced a quantity of water sufficient to cover the bottom of the cylinder, and of course to rise a little way into the tube. The two balls being set at some distance from each other, and a spark from the Leyden Jar being passed between them, the air within is suddenly rarefied, and the water ascends in the tube, and again descends, when the explosion is xjver. The sudden rarefaction of a portion of air before the electric spark, must cause a sud- den and powerful compression in the portions of air immediately adjacent. The immense velocity of the spark must greatly increase the resistance, and of course the force of compression. This appears to be an adequate cause for the production of the light that accompanies the electric discharge, and hence we I On what principle is electricity made to exhibit words, flowera, fto. T •■hat is the origin of the light which accompanies electricity ? Desoriba What Kinnersley's Air Thermometer. ELECTRIC BATTEE.T. 261 conclude, that light is not inherent in the fluid itself. The greater density and brilliancy of the spark in condensed air, and its feebleness and difFuseness in a rarefied medium, are facts' which accord well with the supposed origin ; and the zigzag form of the spark when long, or when passing through condensed air, is well explained by the same theory. For the electric fluid in its passage through the air, condenses the air before it, and thus meets with a resistance which turns it off laterally ; in this direction it is again condensed, and has its course again changed; and so on. until it reaches the conductor towards which it is aiming. The zigzag form of lightning is accounted for on this principle. Electrical light is found by optical experiments to have precisely the same nature with the light -of the sun, being like this resolved into various colors by the prism, and pos- sessing other properties, to be described under the head of Optics, which identify it with solar light. BATTERY. 348. An Electric Battery consists of a number of Ley- den Jars so combined, that tlie whole inay be either charged or discltarged at once. Very large jars cannot be obtained ; it is rare to find one more than two feet high, by one and a half feet in diameter. Yet some of the mechanical effects of electricity, to be de- scribed hereafter, require a much greater accumulation of the fluid that can be obtained from any single jar. The bat- tery is constructed as follows. Large jars, twelve or four- teen inches high, by five or six inches in diameter, are coat- ed like ordinary Leyden Jars. Twelve of these constitute a battery sufBciently powerful for most purposes, but the power of the battery may be carried to an indefinite extent by increasing the number of jars. When the number is twelve, they are placed four in a row in a box. the bottom of which is coated with tin-foil, by means of which the out- sides of the jars are all in conducting communication. Each jar is separated from the rest by a slight partition of wood. To connect the insides of the jars, their knobs are joined by large brass wires. It is obvious, therefore, that the battery is equivalent to a single jar of enormous size comprehend- ing the same number of square feet. What is the cause of the zigzag form of the spark ? Has electrical light the same nature with solar light ? Battery— Oi what does it consist 1 How constructed 1 How are the jars connected on the inside ? How on the outside I 26il ELECTRICITY. The object of the battery is to accumulate a great quanti- ty of the electric fluid, which is in proportion to the extent of surface ; the intensity, or elastic force, as indicated by the quadrant electrometer, is no greater in the battery wher charged, than in a single charged jar. The battery, like the common jar, is charged by bringing the inside into commu- nication with the prime conductor of an active and powerful electric machine : it is discharged, as usual, by forming a connection between the inside and outside, commonly by means of the discharging rod. 349. The largest machine and battery hitherto con- structed, were made for the Teylerian museum, at Haarlem. The machine consists of two circular plates of glass, each five feet five inches in diameter. The prime conductor con- sists of several pieces, and is supported by three glass pil- lars, nearly five feet in length. The force of two men is required to work the machine ; and when it is required to be put in action for any length of time, four are necessary. At its first construction, nine batteries were applied to it, each having fifteen jars, every one of which contained a square foot of coated glass; so that the grand battery, formed by the combination of all these, contained one hun- dred and thirty-five feet. As examples of the great power of the Teylerian machine, we may mention the following: it charged a Leyden Jar by turning the handle half round, — a charge which the jar would receive and lose by dis- charging itself spontaneously, eighty times in a mmute. A single spark from the conductor melted a considerable length of gold leaf A spark, or zigzag stream of fire, would dart from the prime conductor to a neighboring conductor to the distance of ten feet. A wire three eighths of an inch in diameter, was found to be sufficient to transmit the whole charge of the prime conductor, but the wire would give small sparks to a conductor brought near to it. The sphere of in fluence (Art. 326.) extended to the distance of forty feet, so as sensibly to affect the pith ball electrometer. The spider web sensation (or the peculiar sensation resembling that of the spider's web) which is experienced by holding an exci ted glass tube to the face, was felt by bystanders to the distance of eight feet from the machine. What is the object of the battery? How does the intensity compare with that of a common jar? How is the battery charged and discharged Describe the great machine at Haarlem. What effects were produced by this machine in charging a jar— in melting gold leaf— length of the spark ? How far did the sphere of influence extend ? How far was the spider web sensa- tiou felt 1 EPrECTS OF ELECTRICITY. 263 MECHANICAL EFFECTS OF ELECTRICITV. 350. The sound prodticed by an electric discharge is ascribed to the sudden collapse of tiue air. which Jims been displaced by the passage of the electric fluid. Hence the sound is greater in proportion to the quantity and intensity of the charge. A battery when fully charged, gives a loud explosion. 351. Imperfectly conducting substances, through which a powerful electric charge is passed, are torn asunder with more or less violence. A large Leyden Jar is sufficient for exhibiting some of these mechanical effects : others require the power of the Battery. When the charge is passed through a thick card, or the cover of a book, a hole is torn through it, which pre- sents the rough appearance of a bur on each side By means of the battery, a quire of strong paper may be per- forated in the same manner ; and such is the velocity with which the fluid moves, that if the paper be freely suspend- ed, not the least motion is communicated to it. (See Art. 30.) Pieces of hard wood, of loaf sugar, of stones, and many other brittle non-conductors, are broken, or even torn asun- der with violence, by a powerful charge from the battery. If two wires be introduced into a soft piece of pipe clay, and a strong charge be passed through them, the clay will be curiously expanded in the interval between the wires. The expansion oi fluids by electricity is very remarkable, and productive of some singular results. When the charge is strong, no glass vessel can resist the sudden impulse. Beccaria inserted a drop of water between two wires, in the center of a solid glass ball of two inches diameter ; on pass- ing a shock through the drop of water, the ball was dispersed with great violence. In like manner, by the sudden ex- pansion of a small body of confined air, strongly electrified, explosions may be produced, and bodies that resist its ex- pansion are projected with violence. Even good conductors, when minutely divided, are expanded by electricity. Thus, mercury confined in' a capillary glass tube, will be expanded with a force sufficient to splinter the tube. Wliat is the origin of the sound which accompanies an electrical discharge ? How are imperfect conductors affected by a powerful discharge 1 How are Eieces of hard wood, loaf sugar, stones, &c. affected bjr a charge from the attery? What effects result from the sudden expansion of fluids by the electric charge f Does this effect extend even to good conductors 1 264 ELECTRICITY. CHEMICAL EFFECTS OP ELECTRICITY. 352. By means of Electricity, more or less accumulated, a variety of chemical effects may be produced ; such as the combustion ofinflammalle bodies, the oxidation, fusion, and even coinbustion of metals, the separation of compounds into tlieir elements, or tiie union of elements into compounds. Ether and alcohol may be inflamed by passing the electric spark through them ; nor is the effect diminished by com- municating the spark by means of a piece of ice or any other cold medium. The finger may be conveniently em- ployed to inflame these substances. Phosphorus, resin, and other solid combustible bodies, may be set on fire by the same means ; gunpowder and the fulminating powders may be exploded : and a candle may be lighted. Gold leaf and fine iron wire may be burned by a charge from the battery. Wires of lead, tin, zinc, iron, copper, platinum, silver and gold, when subjected to the charge of a very large battery, burn with explosion and are converted into oxides. The same a.gent, moreover, is capable of reviving those oxides ; that is, restoring them to the state of pure metals. By a similar contrariety of properties, water is decomposed into its gaseous elements, and the same elements are reunited to form water ; and the constituent gases of atmospheric air are, by passing a great number of electric charges through a confined portion of air, converted into nitric acid. MOTIONS OF THE ELECTRIC FLTJID. 353. The velocity of the electric fluid is exceedingly great, but its motion is not instantaneous. Light moves at the rate of 192,000 miles in a second, but according to the experiments of a distinguished English philosopher, Mr. Wheatstone, the electric fluid, in traversing a wire connect- ing the outside and inside of a Leyden Jar, has a velocity of 576,000 miles per second. There is some reason foi believing, however, that the velocity is different in different cases, varying with different degrees of intensity and with the kind of conductor through which it passes ; for, in some recent experiments with voltaic electricity (a form of the State the chemical ^ects produced by electricity. What combustibles may be inflamed ? What substances may be bumed with explosion ? How does electricity act both to decompose and to reunite the elements of bodies ? la the velocity of the electric fluid" piogpressive or instantaneous? MOTIONS OF THE ELECTIirc FLUID. 265 fluid to be described hereafter) the velocity has appeared to be only 28,000 miles per second, and in olhers even as low as 18,000 miles per second. Still, for all ordinary distances on the surface of the earth, its motion may be accounted in- stantaneous. 354. The electric fluid, in its route, selects the best coti- ductors. The Leyden Jar may be discharged with a wire held in the hand, without the insulating handle used in the discharging rod; since metallic wire is a better* conductor than the hand, and the fluid will take its route through that in preference to the hand. But if a wooden discharger be substituted for the wire, the shock -will be felt, since animal substances are better conductors than wood. It is necessary to remark, however, that when the charge is very intense, or the quantity great, as in the battery, then some portion of the fluid will escape from the discharging wire and pass through the hand. In such cases, therefore, it is prudent to make use of the discharging rod. Lightning, in striking a building, usually takes a course which indicates the preference of the fluid for the best con- ductors. 355« The electric fluid, will sometimes take a shorter route through a worse conditctor, in preference to a longer route through a better conductor. The spark will pass through a short space of air, instead of following a small wire thirty or forty feet. The preference of the shorter route is sometimes indicated in taking the electric shock. While one person is receiving the shock from the Leyden Jar, another may grasp his arm without feeling the least effects from the charge. Electricity when concentrated is also prone to divide it- ' self between different conductors when they are near its route, distributing itself among them in quantities corres- ponding to their conducting powers. Thus, when a heavy charge of lightning is descending a rod, some portions of the fluid will leave the rod for other conductors that are near the rod, and that afford a ready passage to the earth. 356. The course of the charge is frequently determined hy the influence of points, either in dissipating or in receiv- ing the fluid. Sharp points connected with the best con- ductors, greatly favor the dispersion of the fluid during its What bodies does the electric fluid select in its route 1 Is such a preference ever manifested by lightning? What preference does the fluid manifest for the ehoitest route? What influence have points on the course of the charge . 23 266 ELECTRICITY. passage, and sharp-pointed conductors determine the charge towards them, from a great distance around. The finest needle, held in the hand towards the knob of one of the jars of a charged battery, will silently discharge it in a few seconds ; and if we apply one hand to the outside of a Leyden Jar, and with the other bring a fine needle to the knob of the Jar, only a comparatively feeble shock will be felt, the charge being rapidly dissipated while the needle is approaching the knob CHAPTEK IV. OF THE EFFECTS OF ELECTRICITY UPON ANIMALS, AND OF THE LAWS OF ELECTRICAL PHENOMENA. 35T< We have already several times incidentally ad- verted to the shock communicated to the animal system, when it is brought into the electric circuit, so that the charge passes through it. We now propose to consider this inter- esting part of the subject more particularly. The electric shock is received, whenever tlie animal system is made a part of the conducting communication between the inside and outside of a charged Leyden Jar. A con- venient method of administering the shock is to place the charged jar on a table, resting immediately on a metallic plate.* or a plate of tin, lead, or copper ; then grasping a metallic rod in each hand, touch one of them to the plate, and the other to the knob of the jar. and a sudden convul- sion of the limbs or the breast will be experienced, more or less violent according to the strength of the charge. The effect is greatly heightened by feelings of dread or appre- hension, and it may be resisted to a considerable degree by voluntary effort. A slight charge affects only the fingers or the wrists ; a stronger charge convulses the large muscles above the armpits ; a still greater charge passes through the • It Is safer to emi)loy such a plate than to bring the conducting rod imme- diately into contact with the outside coating of the jar ; for, in such case, persons unaccustomed to receive the shocic, ore apt to overturn the jar and break it. When is the electric shook received ? What is a convenient method of receiving the shock ? How is the eifect heightened ? Hew do charges of diifereu deorees of intensity affect the system ? EFFECTS OK ANIMALS. 267 breast and becomes in some degree painful. Electricians, however, have frequently ventured upon charges sufBciently powerful to convulse the whole frame. 358. The shock maybe communicated to any number of persons at once. This is usually effected by their joining hands, while the first in the series holds one of the metallic rods, with which he touches the plate, or outside of the jar, and the last in the series holds the other rod, with jvhich he touches the knob of the jar, at which instant the whole num- ber receive the shock at the same moment, and that how- ever extensive the circle of persons may be. The charge of a large battery is sufficient to destroy human life, especially if it be received through the head. By standing on the m- sulating stool, jvhich is a stool with glass feet, a person be- comes an insulated conductor, and may be electrified like any other insulated conductor. A communication being made with the machine, the fluid pervades the system, but excites hardly any sensation except a priclcling of the hair, which at the same time rises and stands erect ; for the hairs being similarly electrified mutually repel each other. 359. While in, this situation, the human system exhibits the same phenomena as the prime conductor when charged ; that is, it attracts light bodies, gives a spark to conductors brought near it, and communicates a slight shock to another person who receives the spark from it. Indeed the same shock is felt by both parties. By means of the insulating stool, the most delicate shocks may be given ; for the charge may be drawn off from any part, by imperfect conductors. Thus a pointed piece of wood will draw off the charge from the eye, in a manner so gentle, as to secure that tender organ against any possibility of in- jury. By a variety of conductors, of different powers, and by points and balls, the sensations may be accommodated, with much delicacy, to the state of the patient, or to the nature of the affected part. 360. The shock may be communicated directly to any in- dividual part of the system, without affecting the other parts, by making that part form a portion of the electric circuit, between the inside and outside of a Leyden Jar. Thus, let How is the shock commanicated to a number of persons at oace ? How would the shock received from a very powerful battery affect the human system ? What are the eflfects of the charge received on the insulated stool 7 What electrical effect does the body exhibit when thus electrified V Describe the mode of giving very gentle shocks. Also the mode of electrifying any particular part, as the arm. 2G8 ELECTRICITY. it be required to electrify an arm. Two directors, (consisting of wires terminating in brass knobs, and insulated by glass handles,) are connected by chains with the knob and the outside coating of a charged jar ; then, on applying one of the directors to the hand, and the other to the naked shoulder, the arm is convulsed. In cases where the patient requires only a moderate shock, the charge is regulated by a con trivance attached to the jar, called Lane^s "^JSliffl Discharging Electrometer, represented Y B ' B ' 5 in 15'ig' 126. S is a stick of solid glass ; I J) B R, two brass knobs, connected by a _^ wire, which slides back and forth in suchf a way that it may be set at any required distance from the knob .of the jar. If we apply one hand to the outside of the jar, and the other to the sliding wire B R. and hold the knob of the jar to an electrical machine while turning, we shall receive a constant succession of shocls. which will be more or less in- tense according as the distance of the knob B from the knob of the jar is greater or less. When B is in contact with the knob of the jar, only the force of a single spark will be felt. 361. Soon after the discovery of the Leyden Jar, com- menced the application of Electricity to Medicine ; and Med- ical Electricity became thenceforth a distinct branch of the science. The first cure said to have been effected by this agent, was upon a paralytic. Electricity shortly became very celebrated for the cure of this disorder, and patients flocked in great numbers to the practitioners of this branch of the profession. As usual, the effects of this new remedy were greatly exaggerated, and it was widely extolled, not only for the cure of palsy, but of all other diseases. It was even pretended that the virtues of the most valuable medicines might be transfused into the system through the medium of electricity, preserving their specific properties in the same manner as when taken by way of the stomach. Prepara- tions of this kind were called Medicated Tubes. Pavati. an Italian, and Winkler, a German, were especially celebrated for this species of practice. The mode was to enclose the Describe Lane's Electrometer. How is it used in giving a succession of shocks of any required strength 1 When was electricity first applied to medicine 1 What was the first cure 1 What pretensions were made respec^ ino; the medicinal virtues of electricity ? Describe the Medicated Tohes. What was the mode of administering medicines by means of them? CAUSE OF ELECTRICAL PHENOMENA. 269 medicines in a glass tabe, then to excite the tube, and with it to electrify the patient. In this way, it was said, the healing virtues of the medicines were communicated to the system in a manner at once efficacious and agreeable. Pretensions so extravagant could not long be sustained, and the natural consequence was that the use of electricity in medicine soon fell into great neglect, and has remained in this situation to the present time. There are, however, certain properties inherent in this agent, which deserve the attention of the enlightened physician, and inspire the hope that, in judicious hands, it may still be auxiliary to the heal- ing art. First, the great activity of this agent, particularly the facility and energy with which it can be made to act upon the nervous system, indicate that it has naturally im- portant relations to medicine. The power of being applied, locally, to any part of the system, renders it a convenient ap- plication in cases where other local remedies cannot be ad- ministered. Secondly, the acknowledged property of elec- tricity to promote the circulation of fluids through capillary tubes, Art. 334, (7,) suggests the probability of its being ef- ficacious in promoting the circulation of the fluids of the animal system, and in increasing the quantity of insensible perspiration. Thirdly, in the history of medical electricity are recorded well attested cures, effected by means of elec- tricity, of such diseases as palsy, rheumatism, gout, indolent tumors, deafness, and a variety of other disorders. CAUSE OF ELECTRICAL PHENOMENA. 363. For the sake of convenience, and for the purpose of avoiding repetition and circumlocution, we have made occasional use of the phrase electric fluid. It may be proper now to inquire whether there are any just grounds for sup- posing such a fluid or fluids to be present in electrical phe- nomena. There are two modes by which the existence of such a fluid may be rendered probable : the first is, by showing that such a supposition is conformable to the analogy of na- ture ; the second is, by proving that the agent of electrical phenomena exhibits the properties of a fluid. What changes occurred in the degrees of reputation of this medicine 7 What properties of electricity lead as to infer medicinal virtues ? What diseases has it been supposed to cure ? Came of Electrical Phenomena. — In what two modes may the existence of such a fluid as the electric be rendered probable ? 23* 270 ELECTRICITY. 363« First; there are somereasons derived from analogy for believing in i/ie existence of an electric fluid. (1.) The reasons in favor of supposing that light and heat are caused by the agency of peculiar fluids, (arguments, however, that we cannot discuss here.) virhich have induced a general be- lief, are, for the most part, equally apJDlicable to electricity. (2.) In the present state of our knowledge, the most subtile of all fluids, indeed the most attenuated form of matter, is hydrogen gas, of which one hundred cubic inches weigh only two and a quarter grains, which is nearly fourteen times lighter than common air. But at no distant period, means had not been devised by mankind for proving the materiality of common air, nor even of identifying the ex- istence of the other gases which now bear so conspicuous a part in experimental philosophy. But as knowledge and experimental researches have advanced, a series of fluids still more subtile than air, have come to light, until we have reached a body nearly fourteen times lighter than air, at which, at present, the series stops. Is it probable, however, that nature stops in her processes of attenuation precisely at the point where, for want of more delicate instruments, or more refined and powerful organs of sensation, our methods of investigation, and powers of discrimination, come to their limit ? An examination of the general analogies of nature will lead us to think otherwise. The subordination which exists among the different classes of bodies that compose the other departments of nature, is endless, or at least indefinite. In the animal creation, for example, beginning with the mammoth or elephant, we descend through numerous tribes to the insect which is barely visible in the sunbeam. Be- fore human ingenuity had devised means of aiding the pow- ers of vision, the naturalist might have fixed this as the limit of the animal creation. But the invention of the microscope has carried the range of human vision immeasurably far- ther ; and at each successive improvement in that instru ment, new tribes of insects or animalcules have been revealed to the eye, still more and more attenuated. A similar sub- ordination might be found in the vegetable kingdom, and in the organic structure of both animals and vegetables. To apply this analogy to the case before us, we begin the series of organic bodies with platinum, and descend through classes of bodies constantly diminishing in density, until we State the argument from anakgy 1 Arguments for the materiality of light and heat applicable to electricity 1 CAUSE OF ELECTRICAL PHENOMENA. 271 come to ether, the lightest of liquids, and on the confines of those bodies which are invisible to the eye, and manifest only by the effects which they produce. By modern dis- coveries the series has been extended to hydrogen, a body 264,000 times lighter than platinum. Here for the present we pause, standing in the same relation with respect to any fluids that may lie beyond, that the ancients stood with re- spect to common air. and all other aeriform fluids. Considerations of this nature lead us to believe that there are, in nature, fluids more subtile than hydrogen ; and such being the fact, we can hardly resist the belief, that Heat, Light, and Electricity, are bodies of this class, — bodies which make themselves known to us by the most palpable and energetic effects, although their own constitution is too subtile and refined for our organs to recognize, or our instru- ments to identify them as material. 364. Secondly, in addition to the foregoing presump- tion in favor of the supposition that electricity is a peculiar fluid, it. exhibits in itself the properties of a fluid. The ra- pidity of its motions, the power of being accumulated, as in the Leyden Jar. its unequal distribution over the surfaces of bodies, its power of being confined to the surfaces of bodies by the pressure of the atmosphere, its attractions and repul- sions, are severally properties which we can hardly ascribe to anything else than an elastic fluid of the greatest tenuity. But granting the presence of an elastic fluid in electrical phenomena, it remains to be determined whether, according to the hypothesis of Franklin, these phenomena are tq be ascribed to the agency of a single fluid, or whether, accord- ing to that of Du Fay, they imply the existence of two dis- tinct fluids. The numerous facts with which the learner has been made acquainted in the preceding pages, will fit him to- appreciate the evidence offered in favor of or against these hypotheses respectively. 365* The principles of each hypothesis have been al- ready explained, (see Art. 321,) and they have been rendered familiar by repeated application. It will be recollected, that they concur in supposing that all bodies are endued with a certain portion of electricity, called their natural share, in which the fluid, whether single or compound, is in a state of perfect equilibrium ; and that in the process of excitation, WhatafethegroandBofpresnmpfionofthe existence of very subtile fluids, lighter than hydrogen gas ?. In what-particulars do tlie two hypollieses con- cur? 272 ELECTRICITY. this equilibrium is destroyed. But here the two views beffin to diverge : the one supposes that this equilibrium is de stroyed in consequence of the separation of two fluids, which . like an acid and an .alkali combining to- form a neutral salt, exactly neutralize each other by mutual saturation, but which, wheii separated, exhibit their individual properties ; the other, that the equilibrium is destroyed, like that of b portion of atmospheric air, by greater or less exhaustion on the one side, or condensation on the other. In the, former case, moreover, the equilibrium is restored by the reunion of the two constituent fluids ; in the latter, lay the movement of the redundant portion to supplythe deficient, as air rushes into the exhausted receiver of an air-pump. It is a remarkable fact, that nearly every electricaP phe- nomenon 'may be perfectly explained in accordance with either hypothesis ; nor is it agreed, that an experimentum crunx* has yet been found. 366. One of the latest advocates of the hypothesis of a single fluid is Mr. Singer, an able practical electrician ; and the most distinguished defender of the doctrine of two fluids is M. Biot. In support of the former doctrine are offered such arguments as the following. (1.) Its gtedXex simplicity. It is supposed to be more conformable to the Newtonian rule of philosophizing, "to ascribe no more causes than are just sufficient to account for the phenomena." The known fru- gality of Nature, in all hfer operations, might lead u."! to sup- pose, that she would not employ two agents to effect a given purpose, when a single agen't would be competent to its pro- duction. This argument, however, cannot be applied, either where one cause is not sufficient to account for the phenom- ena, or where there is direct proof of the existence of more agents than one. (2.) The appearance of a current, circu- lating from the positive to the negative surface, analogous to the passage of air of greater density into a rarefied space. This point is much insisted on by Singer, and numerous ex- amples are brought forward, where the progress of such a current is manifest to the senses. Thus, the flame of a can- * The "experimentum crucis" is apbrase introduced by Lord Bacon, implying a fact which can be explained on one of two opposite hypotheses, and not on the other. The flsfure is derived from a cross set up where two roads meet, to tell the traveller which road to talte. In what do they differ? When, according to each hypothesie, is the eqnili- briurti destroyed? Does each explain all the facts? Whal;isan experimentum crucis!. -State th,e arguments in favor of Franklin's hypothesis. What is in ferred from its simplicity ? Are there any appearance of an electric current ? CAUSE OP ELECTRICAL PHENOMENA. 273 die, brought into the circuit between the inside and outside of a Leyden Jar, is, on the discharge of the jar. bent towards the negative side ; a pith ball, under similar circumstances, moves in the same direction ; when a charged jar is placed under the receiver of an air pump, and the air is exhausted, a luminous cloud flows from the positive to the negative side, in whichever way the jar is electrified. None of these arguments, however, are found to be conclusive, for the me- chanical effects, which are here ascribed to an elastic fluid, that is, the electric fluid, flowing towards the negative side, can all be accounted for, either upon. the principles of attrac- tion and repulsion, common to both hypotheses, or from the mechanical impulse of a, current of air. The electric spark passing instantaneously, or at least with a velocity entirely inappreciable, it is impossible to determine its direction. The fact that bodies negatively electrified repel each other ^ (Art. 322.) is a strong argument against the truth of the hypothesis under consideration. It is not difficult to con- ceive that a self-repellent fluid should communicate the same property to two pith balls in which it resided ; but that the mere deficiency of the fluid should produce the same effect is incredible. This fact drove .3ilpinus, (a celebrated Ger- man electrician, who brought this hypothesis to the test of mathematical demonstration.) to the necessity of supposing that unelectrified matter is self^epellent — a supposition which is not only destitute of proof, but which is inconsistent with the general laws of nature, from which it appears that at- traction and not repulsion exists mutually between all kinds of bodies. In the distribution of electricity upon surfaces differing in shape and dimensions, the fluid is found to ar- range itself in strict accordance with hydrostatic principles, and that too in bodies negatively as well as positively .elec- trified. Now that the privation, or mere absence of a fluid, should exhibit such properties of a present fluid, is incon- ceivable. 367. In favor of the doctrine of two fluids, the following' arguments are urged. (1.) Two opfosile currents ^-ce. su.^- posed to be sometimes indicated. Thus, (Art.oSl.) a card perforated by a strong electric discharge, exhibits burs or protrusions on both sides. The appearance of the electric What preventa us from determining the direction in which electricity moves? What is inferred from tlie fact that bodies negatively electrified repel each other 7 What property has been asserted of unelectrified matter ? State the arguments in favor of the doctrine of two flaids. What indications are there of opposite currents ? 274 ELECTRICITY. spark, passing between two knobs, is supposed by some writers to indicate the meeting of two fluids from opposite parts. When the spark is short, the whole distance between the two knobs through which it passes, is illuminated. But when the spark is long, those portions of it which are nearest to the knobs, are much brighter than the central portions. Near the knobs the color is white, but towards the center of the spark it is purplish. Indeed, if the spark is very long, the middle part of it is not illuminated at all, or only very slightly. Now this imperfectly illuminated part, is obviously the spot where the two electricities unite, and it is in con- sequence of this union, that the light is so imperfect. (2.) The two electricities are characterized by specific differences. The light afforded by the vitreous surface is different from that of the resinous ; when the two opposite portions of the spark meet, as above, the place of meeting is only half the distance from the negative that it is from the positive side ; the bur protruded from the card is larger in the direction of the vitreous than in that of the resinous fluid ; and the two severally produce certain chemical effects in bodies which are peculiar to each. (3.) But the most conclusive argument in favor of two fluids, is the perfect manner in which this supposition accounts for the distribution of electricity on bodies of different dimensions. On the hypothesis that electrical phenomena are owing to the agencies of two fluids, both perfectly incompressible, the particles of which possess perfect inability, and mutually repel each other, while they attract those of tlhe opposite flniid, with forces varying in tlie inverse ratio of the squares of the distances. — on this hy- pothesis, M. Poisson, a celebrated mathematician of France, applied the exhaustless resources of the calculus, to deter- mine^ the various conditions which electricity would assume in distributing itself over spheres, spheroids, and bodies of various figures. The results at which he arrived were such as accord in- a very remarkable degree with experiment, and leave little doubt that the hypothesis on which they were built is true. Nor is any supposition involved in the hy- pothesis itself inconsistent with established facts. (4.) Fi- nally, authority is, at the present day, almost wholly on the side of the doctrine of two fluids,^ — an opinion which has How do the appearances of the spark favor this dootrine ? By what specific differeDce.s are the two electricities characterized ? What inferences are drawn from the mode in which the fluid is distributed ? On which side does authority preponderate ? ATMOSPHERICAL ELECTRICITY. 275 constantly gained new adherents with every new discovery in the science of electrieityj particularly in the department of Galvanism. ' ' CHAPTER V. , OF ATMOSPHERICAL KLECTRIOITY— LIGHTNING RODS- PRECAUTIONS FOR SAFETY DURING THUNDER STORMS. 36 8 • Having learned the laws of Electricity from a greait variety of experiments, the student is now prepared to look upon the works of nature, and to study the phenomena which the same agent produces there on a more extensive scale. The atmosphere is always more or less electrified. This fact is ascertained by several different forms of apparatus. For the lower regidnSj it is sufficient to elevate a metallicrod a few feet in length, pointed at the top, and insulated at the bottom. With the lower extremity is connected an elec- trometer, which indicates the presence and intensity of the electricity. For experiments on the electricity of the upper regions, a kite is employed, not unlike a boy's kite, with the string of which is . intertwined a fine metallic wire. The lower end of the string is insulated by fastening it to a sup- port of glass, or by a cord of silk. The most powerful apparatus ever employed for atmospher- ical electricity, was constructed in France by M. de Romas. He procured a kite seven feet long and three feet wide, and elevated it to the height of five hundred and fifty feet. A cloud coming over, the most striking and powerful electrical phenomena presented themselves. Light straws, that hap- «ned to be on the ground near the string of the kite, began to erect themselves, and to perform a dance between the ap- paratus and the ground, after the manner of dancing images, as exhibited in ordinary electrical experiments. Art. 334, (5.) At length streams of fire began to dart to the ground, some of which were an inch in diameter, and ten feet long, exhibiting the most terrific appearance. Atmospherical Electricity.— 'WhA apparatus Is employed to detect tbo presence of electricity in the atmosphere ? pescribe the apparatus ot Rom^a, — state its effects. 276 ELECTIUCITY. LIGHTNING RODS. ' 369. Dr. Franklin had no sooner satisfied himself of the ijlentity of electricity and lightning, than; with his usual sagacity, he conceived the idea' of applying the knowledge acquired of the'properties" of the electric fluid, so as. to pro- vide- against the dangers of thunder storms. The conducting power of metals, and the influence of pointed bodies, lo collect and transmit- the-fltiid, naturally suggested the striir- ture of the Lightning Rod. The. experiment was fried ana has proved completely successful ; and probably no single application of scientific knowledge ever secured more celeb- rity to its author. ■370. Lightning rods are at present usually constructed of wrought iron, about three fourths of an inch in diameter, but copper is to be preferred where the additional expense is not regarded. The parts may be made separate, but, when the rod is in its place, they, should be put together so as to fit clflsely, and to make a continuous surface, since, the fluid experiences much resistance in passing through links and other interrupted joints. At the -bottom the rod should terminate in two or three branches, going off" in a direction from the building. The depth to which it enters the earth should not be less than five feet; but the necessary depth will depend somewhat on the nature of the soil ; wet soils require a less, and dry soils a greater, degth." In dry sand it must not be less than ten feet; and in such situations, it would be better still to connect, by a convenient conducting communication, the lower end of the rod with a well or spring of water. It is useful to fill up the space around the part of the rod that enters the grodnd, with coarsely powdered charcoal, which at once furnishes a good conductor, and pre- serves the raetal from corrosion. The rod should ascend above the ridge of the building to a height determined by the following principle : that it will protect a space in every direction from it. whose radius is equal to twice its height. Where the building has several chimneys, or other promi^ nences, which may come into competition with the rod, these should be furnished with independent conductors, or with branches connected with the main rod. Metallic roofs and water spouts should either be in good conducting communi- Lightning Rods. — ^Who first suggested their use ? How are lightmng- rods constructed? Materials? How are the parts fitwrt to each other? How terminated at bottom^ How high should the roi* . r Bnd above the top of the building ? Sfti-ETl DURING THUNDER STORMS. 277 cation with the rou,; or be connected with the ground by a separate condu&in^medium. Thus a strip of sheet copper may he dosdy wrapped round tlie rod at some point where the rod meets the metallic roof, the ends of the copper being fastened close^ly to the roof; and water spouts may be made to add to the safety ol a building by letting a metallic rope or other convenient conductor hang from the lower end of the pipe tb the -ground. It is best', when practicable, to attach the rod to me chimney, which needs peculiar protec- tion, both on account of its prominence, and because the products of combustion, smoke, watery vapor, &c. are con- ductors of electricity. For a similar reason a kitchen chim- ney, being that in which the fire is kept during the season .of thunder storms, requires to be especially protected. The rod is terminated above ip. a point, or sometimes in three forks, each of whicn ends in a sharp goint. As these points are liable to have their conducting power impaired by rust, they are protected from corrosion by being covered with gold (eaf; or they may be made of solid silver or platina. Black paint being made of charcoal, forms a better coating for the rod than paints made of other colors, the bases of which are worse conductors. The rod may be attached to the building by wooden stays. Iron stays are sometimes em- ployed, and in most cases they would be safe, since electricity pursues the most direct route; but in case of an extraordinary charge, there is danger that it will divide itself a part passing into the building through the bolt, especially if this ■ terminates in a point. Buildings furnished with lightning rods have occasionally been struck with lightning; but on examination it has generally,. if not always, been found that the structure of the rod was defective ; or that too much space was allotted for it to protect. When the foregoing rules are observed, the^ most entire confidence may be reposed in this rnethod of securing safety in thunder storms. "■ - • PRECAUTIONS FOR SAFETY DURING THUNDER STORMS. 371., The great number of pointed objects that rise above the general level, iii a large city, have the eifect to dissipate the electricity of a thunder cloud, and to prevent its charge irom being concentrated on any single object. Hence How .attached to the bnilding ? What is said of the kitchen chimney ? How is the rod terminated at top 1 Have buildings furnished with lightning rods ever been struck with lightning ? What effect have a great number of high-pointed objects on the liability of a place to be strack? 24 278 ELECTRICITY. damage done by lightning- is less frequent in a populous town, than in solitary buildings. For similar reasons a great number of ships, lying at the docks disarm the light- ning of its power, and thus avert the injury to wliich the form of their masts would otherwise expose them. A soli tary ship on the ocean, unprotected by conductors, would ap- pear to be peculiarly in danger from lightning ; but while the greater number of ships that traverse the ocean are wholly unprotected, accidents of this kind are comparatively raie. The reason probably is, the water being a better con- ductor than wood, the course of the discharge towards the water is not easily diverted, and will not take the mast in its way unless the latter lies almost directly in its course. Barns are peculiarly liable to be struck with lightning, and to be set on fire ; and as this occurs at a season when they are usually filled with hay and grain, the damage is more serious, for the quantity of combustible matter they contain IS such as to render the fire unmanageable. 372. Silk dresses are sometimes worn with the view of protection by means of the insulation they afford. They cannot, however, be deemed very effectual unless they com- pletely envelop the person ; for if the head and the extremi- ties of the limbs be exposed, they will furnish so many ave- nues to the fluid as to render the insulation of the other parts of*the system of little avail. The same remark ap- plies to the supposed security that is obtained by sleeping on a feather bed. Were the person situated vnthin the bed, so as t§ be entirely enveloped by the feathers, they would af- ford some protection ; but if the person be extended on the surface of the bed, in the usual posture, with the head and feet nearly in contact with the bedstead, he would rather lose than gain by the non-conducting properties of the bed ; since being a better conductor than the bed, the charge would pass through him in preference to that. The hori- zontal posture, however, is safer than the erect; and if any advantage on the whole is gained by lying in bed during.a thunder storm, it probably arises from this source. The same principle suggests a reason why men or animals are so frequently struck with lightning, when they take shelter under a tree during a thunder storm. The fluid first strikes the tree, in consequence of its being an elevated and pointed Why is a ship at sea ao seldom struck? Why are barns so apt to be in jnredV Are silli dresses a protection? Is a feather bed a peculiar place ot safety ? What posture is safest ? Why are animals frequently struck under a tree ? SAFETY DURING THUNDER STORMS. 279 object, but it deserts the tree on reaching the level of the man or animal, because the latter is a better conductor than the tree. Tall trees, situated near a dwelling house, furnish a par- tial protection to the building, being both better conductors than the materials of the house, and having the advantage of superior elevation. 373. The protection of chimneys is of particular im- portance, for to these a discharge is frequently determined. When a fire is burning in the chimney, the vapor, smoke, and hot air, which ascend from it, furnish a conducting me- dium for the fluid ; but even when no fire is burning, the soot that lines the interior of a chimney, is a good conduct- or, and facilitates the passage of the discharge. It is quite essential, during a thunder storm, to avoid every considerable mass of water, and even the streamlets that have resulted from a recent shower ; for these are all excellent conductors, and the height of a human being, when connected with them, is very likely to determine the course of an electric discharge. The partial conductors, through which the lightning directs its course, when it enters a building, are usually the appendages of the walls and partitions ; the most secure situation is therefore the middle of the room, and this situation may be rendered still more secure by stan- ding on a glass legged stool, a hair mattress, or even a thick woolen rug. The part of every building least liable to receive injury, is the middle story, as the lightning does not always pass from the clouds to the earth, but is supposed to be oc- casionally discharged from the earth to the clouds. Hence it is absurd to take refuge in a cellar, or in the lowest story of a house ; and many instances are on record in which the basement story has been the only part of the building that has sustained severe injury. Whatever situation be chosen, any approach to the fire-place should be particularly avoid- ed. An open door or window is an unsafe situation, because the lightning is apt to traverse the large timbers that com- pose the frame of the house, and would be determined to wards the animal system on account of its being a better conductor. In a carriage the passenger is safer in the cen- tral part than next to the walls ; but a carriage may be ef- What is the inHuence of tall trees near a dwelling 1 Why is the protection of a chimney peculiarly important 1 Why are we to avoid colleotiona of water ? What parts of a house are safest * What is said of the cellar and of the fire-place, — of an open door or window? lu a can-iage, where is the safest place ? How may a carriage be protected 1 280 ELECTRICITY. fectually protected by attaching to its upper surface met"..ic strips connected with the wheel tire. The fillets of suver plating which are frequently bound round the carriage, may be brought into the conducting circuit. 374. Certain furred animals, particularly the cat, be- come spontaneously electrified. This is more especially ob servable on. cold windy nights, when the state of the air is favorable to insulation. At such times a cat's back will frequently afibrd electrical sparks. Ancient historians men- tion a number of very remarkable occurrences, of good or evil omen, which are due to the electricity of the atmos- phere. Herodotus informs us that the Thracians disarmed the sky of its thunder, by throwing their arms into the air ; and that the Hyperboreans produced the same effect, by launching among the clouds darts armed with points of iron. Caesar, in his commentaries, says, that in the African war, after a tremendous storm, which threw the whole of the Roman army into great disorder, the points of the darts of a great number of the soldiers shone with a spontaneous light. In the month of February, (says he) about the sec- ond watch of the night, there suddenly arose a great cloud, followed by a dreaful storm of hail, and in the same night the points of the darts of the fifth legion appeared on fire. During a dry snow storm, when electricity is evolved in great quantities, and, on account of the dry state of the air, is partially insulated in conducting bodies, similar appear- ances are exhibited. Thus the ears of horses, and vari- ous pointed bodies, emit faint streams of light. These phe- nomena are sometimes exhibited in a most striking manner in a storm at sea, when the masts of a ship, yard arms, and every pointed object are tipped with lightning. CONCLUDING REMARKS. 375. From the energy which electricity displays in our experiments, and much more in thunder storms, there can be no question that it holds an important rank among the ultimate causes of natural phenomena. Its actual agencies, however, are liable to be misinterpreted, and that they have been so in fact, is too manifest from the history of the sci- State facts respecting the electricity of furred animals ? What facts are mentioned by Herodotus and Cresar V Does electricity attend snow storms ? What rank does electricity bold among the causes of natural phenomena ? Have its actual agencies been OTerrated! CONCLUDING REMARKS. 261 ence. After the splendid experiments of the Leyden Jar, and more especially, ,after the identity of electricity with lightning- had been proved, electricians fancied that they had discovered the clue which would conduct them safely through the labyrinth of nature. Everything not before satisfactorily accounted for, was now ascribed to electricity. They saw in it, not only the cause of thunder storms, but of storms in general ; of rain, snow, and hail ; of whirlwinds and water spouts ; of meteors and the aurora borealis ; and finally, of tides- and comets and the motions of-the heavenly bodies. Later electricians have found in the same agent the main spring of animal and' vegetable life,^nd the grand catholicon which cures all diseases. Eecent attempts have been made to establish the very identity of galvanic elec- tricity and. th* nervijus influence, by which the most im- portant functions of animal life are controlled. Among the most important of the agencies of electricity in the economy- of nature, is that which, according to the views of Sir Humphry Davy, it sustains in relation to the chem- ical agencies of bodies. Chemical and electrical attraction he supposes, are. one and the same thing, or at least depend- ent on the same cause, the attraction between the elements of a compound arising solely froin their being naturally in opposite electrical states. But the discussion of this hypoth- esis belongs more appropriately to Galvanism, a branch of our subject which, on account of its peculiarities, especially in the mode of excitation, has been constituted a separate department of science. What different effects have been ascribed to it ? What are Sir Humphry Dayy's views respecting the identity of chemical and electrical attractions ? 24* PART v.— OF MAGNETISM AND ELECTRO MAGNETISM. CHAPTEE I. MAGNETISM. GENERAL PKINCIPLES. 376 Magnettsm i.i tlie science which treats qftkepropet- ties and effects of the tncignet. — The same term is also used to denote the unknown cause of magnetic phenomena ; as when we speak of magnetism as excited, imparted, and so on. Mag'nets are bodies, either natural or artificial, which have the power of attracting iron, and the power, when freely suspended, of taking a direction towards the poles of the earth. The natural magnet is sometimes called the loadstone* It is an oxide of iron of a peculiar character, found occasion- ally in beds of iron ore. Though commonly met with in irregular masses only a few inches in diameter, yet it if sometimes found of a much larger size. One brought frono Moscow to London weighed one hundred and twenty-fivf pounds, and supported more than two hundred pounds ol iron. The attractive powers of the loadstone have been known from a high antiquity, and are mentioned by Homer, Pytha goras and Aristotle. But the directive powers were not known in Europe until the thirteenth century, when they were discovered by a Neapolitan named Flavio; though * Said to be derived fi-uin Itsdan, a Saxon word whicli signifies to guide. Magnetism. — Define magnetism and magnets. What is the loadstone? Which of its powers were known to the ancients ? When were the directive powers discovered t GENERAL PRINCIPLES. 28b some writers have endeavored to trace the history of the compass needle to' a remoter period, and some have strenu- ously maintained that the Chinese were in possession of it many centuries before it was known to Europeans. Magnetism is the most recent of all the physical sciences, and notwithstanding the numerous discoveries achieved in it within a few years, and the remarkable precision with which its laws have been ascertained, yet it is still to be re- garded as a science quite in its infancy, although it is rap- idly progressive. 377. If a magnet be rolled in iron filings, it will attract them to itself This effect takes place especially at two op- posite points, where a much greater quantity of the filings will be collected than in any other part of the body. The twooppositepointsin amagnet, . where its attractive powers ap- '^' pear chiefly to reside, are called its poles. The straight line which joins the poles, is called the a%i&. If a large sewing needle or small bar of steel be rubbed on the loadstone, one extremity on one pole, and the other extremity on the other, the needle or bar will itself become a magnet, capable of exhibiting all the properties of the load- stone. Without staying at present to describe more minutely the process of making artificial magnets, we will suppose ourselves provided with several magnetic needles and bars, and we may proceed with them to study the leading facts of the science of magnetism. By attaching a fine thread to the middle of a needle, and suspending it so as to move freely in a horizontal plane : or by resting it on a point, as is rep- jik_ resented in Fig. 128, we shall have a simple and convenient ap- paratus for numerous experiments. The needle thus suspended will place itself in a direction nearly, though not exactly, north and south. If the needle is drawn-out of the position it assumes when at rest, it will vibrate on either side of that position "What is the present state of this science ? Wliat is the eilect when a magnetic bar is rolled in iron filings ? Define the 'poles and axis of a magnet. How may a steel needle be made a magnet ? How may we suspend a needle for experiment? 284 MAGNETISM. until it finally settles in the same line as before, one pole always turning to the north, and the other towards the south. Hence the two poles are denominated respectively north and south poles. In magnets prepared for expen ments, these poles are marked either by the letters N and S or by a line dra'wn across the magnet near one end which denotes that the adjacent pole is the north pole. 378. By means of the foregoing apparatus we may as certain that the magnet has the following general properties viz. : First, powers of attraction and repulsion. Secondly, the power of communicating magnetism to iron or steel by induction. Thirdly, polarity, or the power of taking a direction to- wards the poles of the earth. Fourthly, the power of inclining itself towards a point below the horizon, usually denominated the dip of the needle. CHAPTER II. OF MAGNETIC ATTRACTION. 379. When either pole of a magnet is brought near to a piece of iron, a mutual attraction takes place between thein. Thus, when the ends of a magnetic bar or needle are dipped into a mass of iron filings, these adhere in a olustor to either pole. A bar of soft iron, or a piece of iron wire, resting on a cork, and floating on the surface of water or quicksilver, may be led in any direction by bring near to it one of the poles of a magnet. This action is moreover recip- rocal, that is, the iron attracts the magnet with the same force that the magnet attracts the iron. If the two bodies be placed on separate corks and floated, they will approach each other with equal momenta ; or if the iron be held fast the magnet will move towards it. Several other metals besides iron, particularly nickel and State the /oMr leading properties of the magnet? Magnetic Attractimi Wliat lakes place when either pole of a magnet is brought near to a piece of iron 1 Is the action reciprocal ? What metals besides iron are susceptible of magnetic attraction 1 MAGNETIC ATTEAOTIJN. 285 cobalt, are susceptible of magnetic attr-action. These metals, however, exist in nature only in comparatively small quan- tities, and therefore by magnetic bodies, are usually intend- ed such as are ferruginous. Even iron, in some of its com- binations with other bodies, loses its magnetic properties ; only a few of the numerous ores of iron are attracted by the magnet. But soft metallic iron, and some of the ores of the same metal, affect the needle even when existing in exceed- ingly small quantities, so that the magnet becomes a very delicate test of the presence of iron. Compass needles are sometimes said to be disturbed by the minute particles of steel left in the dial plate by the dial graver ; and the pro- portion of iron in some minerals may be exactly estimated by the power they exert upon the needle. 380> In tJie action of magnets on each other, poles of the same name repel, those of different names attract each other. Thus, the north pole of one magnet will repel the north pole of the other, and attract its south pole. The south pole of one will repel the south pole of the other, and attract its north pole. These effects, it will be perceived, are analo- gous to those produced by the two species of electricity ; and they equally imply two species of magnetism or two magnetic fluids, (as it is convenient to call them) namely, the northern and the southern ; or, as they are now denom- inated, the boreal and the austral fluids. If we suspend by a fine thread a sewing needle, and approach toward it either pole of a magnetic bar, the needle will rush toward it, and attach itself strongly to the pole. By rubbing the needle on one of the poles of the magnet, it will itself im- ^'«- i^s. bibe the same power of attracting ~ iron, and become a magnet with two poles. If we now bririg one pole of a magnetic bar toward the needle, and then the other pole, we shall find that one attracts and the other repels the needle. Figure 129 represents two large sewing needles magnetized and suspended by fine threads. On ap- proaching the north pole of a magnetic What minute portioDS of iron may be detected by the magnetic needle \ What poles repel and what attract each other ? What names are given to -he two kinds of magnetism ? 286 MAGNETISM. bar to the north pole of the needles, they are forcibly repel- led ; but on applying the south pole of the bar, the north poles of the needles are attracted toward it. 381. By bringing a, magnet vsar to iron or steel, the latter is rendered magnetic by Induction. Thus, let the north pole Fig. 130. ■ of a magnetic bar A, (Pig. ' 130) be brought near to one end of an unmagnet- ized bar of soft iron B : the iron will immediately become itself a magnet, capable of attracting iron filings, having polarity when sus- pended, and possessing the power of communicating the same properties to other pieces of iron. It is, however, only while the iron remains in the vicinity of the magnet, that it is endued with these properties ; for let the magnet be with drawn and it loses at once all the foregoing powers. This, it will be remarked, is asserted o{ soft iron; for steel and hardened iron are differently affected by induced mag- netism. On examining the kind of magnetism induced upon the two ends of the iron bar B, (Fig. 130,) which we may easily do by bringing near it the poles of the needle, (Fig. 128.) we shall find that the nearer end has south, and the remoter end north polarity. This effect also is analogous to that produced by electrical induction. A corresponding effect would have taken place, had the south instead of the north pole of the magnet been presented to the bar of iron ; in \vhich case the nearer end would have exhibited northern, and the remoter end southern polarity. Or, to express this important proposition in general terms. Each jmIh of a magnet induces tlie opposite hind of -polar- ity in tliat end of the iron which is nearest to it, and the same hind in that end which is most remote. 382. TJie power of a magnet is increased by the eoxrtian of its inductive power upon a piece of iron in its neighbor- hood. The end of the piece of iron contiguous to the pole of the magnet, is no sooner endued with the opposite polarity, than Explain liow iron or steel is rendered magnetic by iadnction. What kind of magnetism is induced on the end nearest to the magnet and on the end most remote? How is the power of a magnet influenced by the exertion of the inductive power? MAGNETIC ATTRACTION. 287 it re-acts upon the magnet and increases its intensity, and a series of actions and re-actions take place between the two bodies, similar to what occurs in electrical induction. On this account the powers of a magnet are increased by action, and impaired or even lost by long disuse. By adding from time to time, small pieces of iron to the weight taken up by a magnet, its powers may be augmented greatly beyond their original amount. Hence, the force of attraction of the dissimilar poles of two magn«ts, is greater than the force of repulsion of the similar poles ; because, when the poles are unlike, each contributes to enhance the power of the other but when they are alike, the influence which they recipro- cally .exert, tends to make them unlike, and of course to im- pair their repulsive energies. A strong magnet has the power of reversing the poles of a weak one. Suppose the north pole of the weaker body to be brought in contact with the north pole of the stronger ; the latter will expel north polarity, or the boreal fluid, and attract the austral, a change which in certain cases will be permanent. If the north pole of a magnetic bar be placed upon tii« middle of an iron bar, the two ends of the latter wiJl each have north polarity, while the part of the bar immediately in contact with the magnet receives south polarity ; and if the same north pole be placed on the center of a circular piece of iron, all parts of the circumference will be endued with north polarity Avhile the plate will have a south pole in the center. By cutting the plate into the form of a star, each extremity of the radii becomes a weak north pole when the north pole of a magnet is placed in the center of the star. If an iron bar is placed between the dissimilar poles of the two magnetic bars, both of the magnets will conspire to m- crease the intensity of each pole of the bar, and the magnet- ism imparted to the bar will be considerably stronger than from either magnet alone ; but if the same bar be placed be- tween the two similar poles, the opposite polarity will be im- parted to each end, while the same polarity is given to the center of the bar. Thus, if the bar be placed between the north poles of two magnets, each end of the bar will become a south pole and the center a north pole. When one end of a magnetic bar is applied to the ends of two or more wires How are the powers of a magiiet affected by use and disuse 1 What effect has a strong magnet on the poles of a weak one ? What is the effect when •■iie north pole of a magnet is placed apon the middle of an iron bar ? Also Bvhen placed in the center of a star ? When the iron bar is placed between two dissimilar poles of two magnetic bars ? 288 MAGNETISM. or sewing needles, the latter arrange themselves in radii di verging from the magnetic pole. This effect is in conse-. quenee of their remoter ends becoming endued with similar polarity, and repelling each other. A like effect is observa- ble among the filaments of iron filings that form a tuft on the end of a magnetic bar. 383. The foregoing experiments are sufficient to show that when a piece of iron is attracted by the magnet, it is first converted into a magnet by the inductive influence of the magnetizing body. Each of the iron filings which com- pose the tuft at the pole of a magnetic bar or needle, is it- self a magnet, and in consequence of being such, induces the same quantity in the next particle of iron, and that in the next, and so on to the last. Hence magnetic attraction does not exist, strictly speaking, between a magnet and iron, but only between the opposite poles of magnets ; for the iron must first become a magnet before it is capable of magnetic influence. 384. Soft iron readily acquires magnetism and as readily loses it ; hardened sted acquires it more slowly, but retains it permanently. In the preceding examples, the magnetism acquired by a bar of iron, by the process of .induction, is retained only so long as the magnetizing body acts upon it. Soon after the two bodies are separated the bar loses all magnetic prop-, erties. When a bar of steel is placed very near a strong magnet, the action of the magnet commences immediately upon the end of the bar nearest to it, the north pole, for example, com- municating south polarity to the contiguous extremity of the bar. According to our previous experience, we should ex- pect to find the remote end of the bar of a north pole ; but such is not the immediate result; a sensible time is required before the north polarity is fully imparted to the remote ex- tremity. Indeed, if the bar be a long one, it sometimes hap- pens that the northern polarity never reaches the farthest end, but stops short of it at some intermediate point. This north pole is succeeded by a second south pole, that by an- other north pole, and thus several alternations between the two poles occur before reaching the end of the bar. How do sewing needles arrange themselves around the pole of a magnet 7 How do iron lilings thus arrange themselves ? What change is wrought in each filing! Does magnetic attraction exist between the needle and unmag- netized iron ! State the raspective powers of soft iron and hard steel to re- ceive magnetism ? MAGNETIC ATTRACTION. 289 385. The process of magnetizing a Steel bar or needle is accelerated by any cause which excites a tremulous or vi- bratory motion among the particles of the steel. Striking on the bar with a hammer promotes the process in a remark- able degree, especially if it occasions a ringing sound, whicl^ indicates that the particles are thrown into a vibratory mo- tion. The passage of an electric discharge through a steel baj under the influence of a magnet, produces permanent magnetism. Heat also greatly facilitates the introduction of the magnetic fluid into steel. The greatest possible de- gree of magnetism that can be imparted to a steel bar is com- municated by first heating the steel to redness, and while it is under the influence of a strong magnet, quenching it sud- denly in cold water. A magnet, however, loses its virtues by the same means as, during the process of induction, were used to promote their acquisition. Accordingly, any mechanical concussion or rough usage, impairs or destroys the powers of a magnet. By falling on a hard floor, or by being struck with a ham- mer, it is greatly injured. Heat produces a similar eflfect. A boiling heat weakens, and a red heat totally destroys the power of a needle. On the other hand, cold augments the power of the magnet ; indeed magnets improve with every reduction of temperature hitherto applied to them. 386« If a steel bar, rendered magnetic by indtiction, be divided into any two parts, each part will be a complete mag- net, having two opposite poles. We here meet with a remarkable distinction between mag- netic and electrical induction. When a body, electrified by induction, is divided into two equal parts, the individual electricities alone remain in each part respectively ; but in the case of magnetic induction, although no appearance of polarity be exhibited except at the two ends, yet wherever a fracture is made, the two ends separated by the fracture im- mediately exhibit opposite polarities, each being of an oppo- site name to that of the original pole at the other end of the fragment. If each of the two fragments be again divided into any number of parts, each of these parts is a magnet perfect in itself, having two opposite poles. In magnetism, therefore, there is never, as in electricity. By what means is the process of magnetizing a steel bar accelerated ? What effect has the passage of an electric discharge through a steel bar 7 What is the effect of heat ? By what means does the magnet lose its virtues ? Show the difference between the magnetic and electric induction 1 Is there in magnetism any traiisfer of properties ? 25 290 MAGNETISM. any transfer of properties, but only the excitation of such as were already inherent in the body acted upon. Magnet- ism never passes out of one body into another ; nor can we ' ever obtain a piece of iron or steel that contains exclusively either northern or southern polarity. To explain phenomena like the foregoing, it is assumed that there exist two magnetic fluids, the austral and the bo eal. In ordinary iron these fluids reside in a combined state in which they neutralize each other, and the body ex- hibits no magnetic properties. Each molecule or atom is regarded as a complete magnet in itself, having a north and south pole, and two contiguous atoms as united by opposite poles. Thus let a magnetic bar be composed of parallel rows of particles of which one series only is represented in figure 131, but a thousand ^is- 131- more may be imagined as — - — - - composing the entire bar. By inspecting the figure it will be seen that all the particles are united by their opposite poles except those at the two ends, while these two particles have their respective poles, free and ready to exert their attractions on opposite poles of another magnetic bar as soon as it approaches near them. Or if their terminal particles be applied to iron filings, each will convert a particle of iron into a temporary magnet, and then attract it. Now if we conceive all the rows of particles that form the magnet filled up, then the ends of the bar will consist of innumerable particles, having free magnetism, the one austral and the other boreal, and each end therefore exerting an attractive force in proportion to the number and intensity of the terminal particles. 387. Tim force of attraction, or of repukio7i, exerted upon each other by the poles of two magnets, placed at different distances, varies inversely as the square of tlie distance. This law was ascertained by means of a very delicate ap- paratus, in a manner similar to that adopted in investigating the law of electrical attraction. The same law, therefore, which governs the attraction of gravitation, likewise con- trols electrical and magnetic attractions. It is the most ex- tensive law of the physical world. Nor is this action at a How is the force of attractiou at difierent distances from a magnet ? How was tlie law ascertained ! DIRECTIVE PROPERTIES OF THE MAGNET. 291 distance prevented, or even impaired, by the interposition of other bodies not themselves magnetic. 388. The magnetic povjer of iron resides wholly on tts SURFACE, and is independent of tlie mass. Thus, a hollow globe of iron of a given surface, will have the same effect on the needle as though it were solid throughout. In this fact we again meet with a striking analogy between magnetism and electricity, the same prop- erty having before been shown to belong to the electric fluid. This is one of the most recent discoveries in magnetism, and was made by Professor Barlow at the Military Acade- my at Woolwich, (Eng.) to whose ingenious and assiduous labors are due many of the latest and most important inves- tigations in this science. CHAPTEK III. OF THE DIRECTIVE PROPERTIES OF THK AfAGNET. 389. If a small needle he placed near one of the poles of a magnet^ ivith its center in the axis of the magnet., it mil take a direction in a line with that axis. Thus, let S N be a large magnetic bar, and s n a. Fig. 133. small needle placed near the north pole of the mag- net with its center in the axis : it will be seen that the action of the pole of the magnet is such as to bring the needle into a line with the magnet. The action of the bar upon the needle, tending to give it this direction, is equal to the sum of its actions upon both poles; while the attraction of the bar upon the whole needle, being only that which the attraction for s, on account of its nearness, exceeds the repulsion of n, must be less than the directive force. 390. If^ the needle be placed at right angles to the bar In what part of a body does magnetic attraction reside ? Directive Proper- ties. — If a small needle, suspended so as to move freely, be placed .near the pole of a magnet, what direction will it take? If a needle be placed at right angles to a magnetic bar, what direction will it ta^ 7 292 MAGNETISM. ivith one of its poles directed towards the center of the bar. it will talce a direction parallel to the bar. By supposing B (Fig. 132,) to be placed as indicated in the above proposition, it will be seen, that the actions of both poles if the magnet would conspire in relation to each pole of the needle, and that these forces can be in equilibrium only when the needle is parallel with the bar. The needle in this situation has a tendency to move towards the mag- net, because ttie attraction being exerted on the nearer and the repulsions on the remoter poles, the sum of the attrac- tions exceeds that of the repulsions. 39 !• Iron flings or other ferruginous bodies, which are free to obey the action of a inagnetic bar., naturally arrange themselves in curve lines, from one pole of tlie magnet to the other. Thus, if we place a I'lg 133 «!lieet of white paper on a magnetic bar, laid on tbe table, and sprinkle iron filings on the paper. the filings will arrange themselves in curves around the poles of the magnet. 392« The magnetic needle, when freely suspended, seldom points directly to the pole oftlie earth,but its deviation from tliat pole is called tlm declination, or the variation of the needle. - A vertical circle drawn through the line in which the needle naturally places itself is called the magnetic meridian. A plane passing at right angles to the magnetic meridian, through the center of the needle, is called its magnetic equator. A line drawn on the surface of the earth passing through the place where the needle points directly to the north pole, and where of course the geographical and mag- netic meridians coincide, is called the line of 'no variation. The North Magnetic Po& was discovered by Commander James Boss, of the British Navy, in 1832. It is situated in the region lying north of Hudson's and west of Baffin's Bay, in Latitude 70' N., Longitude 96^ 30' W. The line of no variation encompasses the globe, but is How do iron filings arrange themselves around a magnetic bar 1 Define or explain what is meant by the declination of the needle, — also by the magnetic meridian, and magnetic equator ? What is the position of the North Mag- netic Pole. — its Latitude and Longitude? DIRECTIVE PROPERTIES OF THE MAGNET. 293 subject to numerous irregularities. Setting out at the mag- netic pole, we may trace it in a direction a little east of south through the British Possessions until it crosses Lake Ontario, the western part of the state of New York, the central part of the state of Pennsylvania, passing a little eastward of Washington City. Thence it pursues a south-easterly course towards the South Polar Regions. Places lying westward of this line have, within certain limits, easterly, and those lying eastward, westerly declinations. Throughout the greater part of the western hemisphere the variation is eastward. The declination of the needle is not constant, but is sub- ject to a small annual change, which carries it to a certain limit on one side of the pole of the earth, when it becomes stationary for a time, and then returns to the pole and pro- ceeds to a certain limit on the other side of it, occupying a period of many years during each variation. 393> Since the variation of the needle must be taken into account in the use of the surveyor's compass, we sub- join the names of a few places in the United States, and the variation belonging to each, and the annual changes of variation. Places. 'Date. Variation. Change. Cambridge, Mass. 1840 9° 18' W. -I-5'.O New Haven, Ct. 1840 6° 10' W. + 4'. 4 Burlington, Vt. 1834 8° 50' W. + 5'. 3 New York City, 1837 5" 40' W. + 3'.6 Philadelphia, 1837 3° 52' W. + 3'.2 Albany, N. Y. 1836 6° 47' W. + 4'.6 Cleaveland, 0. 1838 0° 35' B. — 4'.4 Cincinnati, 0. 1840 4° 46' E. — 3'.1 Detroit, Mich. 1840 2° 00' E. — 4'.0 Alton, 111. 1840 7° 45' E. — 2'.4 Milledgeville, Ga. 1835 4° 40' E. — 2'.3 Mobile, Ala. 1835 7° 12' E. — 1'.5 The sign + denotes that the variation is increasing ; the eign — that it is diminishing. The line of no variation runs near Cleaveland, Ohio, at which place the variation is only 35 minutes. The variation due to any year before or after the given date, may be found by applying the change for one year multiplied by the number of years. Trace tie line of no variation. What is the varation of places lying west- ward and eastward of this line respectively ! Sts. .« the amount of the varia- tions at Cambridge, New Haven, Burlington, &o. 25* 294 MAGNETISM. Thus the variation for 1840 at New Haven being 6° 10' W., and the annual change 5', the variation for 1850 will be 6° 10'+5xl0=7^ 0'. The variation at Cincinnati for 1849, is 4° 46'— 3.1x9=4^ IS'.l. The annual variation in England is 2' 49", by which quantity the needle approaches the pole. The variation of the needle is not, therefore, the same at the same time, in all parts of the earth, but every place has its particular declination. For instance, if we sail from the Straits of Gibraltar to the West Indies, in proportion as we recede from Europe and approach America, the compass will point nearer and nearer due north ; and when we reach a certain part of the Gulf of Mexico, it will point exactly north. But if we sail from Great Britain to the southern coast of Greenland, we shall find the needle deviate farther and far- ther from the north, as we approach Greenland, where the deviation will not be less than 50'- In some parts of Baf- fin's Bay the needle points nearly due west. 394« Beside the anniud variation, the magnetic needle is siibject to daily changes called the diurnaj. variation. The deviation of the horizontal needle from its mean posi- tion is easterly in the morning, and arrives at its maximum about eight o'clock. Thence it returns rapidly to its mean position, which it reaches between nine and ten o'clock, and then its variation becomes westerly, at first increasing rap- idly, so as to reach its maximum at about one o'clock in the afternoon, and then slowly receding during the rest of the day, and arriving at its mean position about ten o'clock at night. 395. A needle first bal- I"ig. 134. anced horizontally on its cen- ter of gravity, and then, mag- netized, no longer retains its level, but its north pole spon- taneously takes a direction to a point below the horizon called the dip op the needle. The Dipping Needle is rep- resented in Pig. 134, where HCA is a graduated circle, HA the horizon, T)d the nee- What is the average annual variation ? What changes of declination do we meet with in going from the Straits of Gihraltar to the West Indies, or from Great Britain to the southern coast of Greenland? How does the needle point in some parts of Baffin's Bay ? State the facts respecting the Diurnal Variation of the needle. Also respecting; the Dip. DIRECTIVE PROPERTIES OP THE MAGNET. 295 die in its inclined position, and ST screws for adjusting the spirit level. The dip of the needle is very different in different parts of the globe, being^ in general, least in the equatorial and greatest in the polar regions. At certain places on the globe the needle has no dip, that is, it becomes perfectly horizontal, and a line uniting all such places is called the magnetic equator of the earth. Again, in the Polar Regions, the dip- ping needle sometimes becomes nearly perpendicular to the horizon. In the middle latitudes, the dip is greater or less, but does not correspond exactly to the latitude. The dip at the city of Washington is 71° 17' and increases as we proceed northward, being at several different places as follows.* St. Louis, 69=31' Cleaveland, (0.) 73M4' Cincinnati, (0.) 70 28 New Haven, 73 26 Philadelphia, 71 56 Cambridge, 74 20 New York, 72 55 Montreal, 76 42 396. The force exerted by the magnetism of the earth varies in different places : its comparative estimate for any given place is called the magnetic intensity /or that place. As in the case of the pendulum in its relation to the force of gravity, the magnetic intensity may be measured by the number of oscillations, which a needle drawn a given num- ber of degrees from its point of rest, performs in a certain time, as a minute for example, the force being as the square of the number of oscillations. In general it is well ascer- tained that the magnetic intensity is least in the equatorial regions, and increases as we advance towards the poles. It is probably at its maximum at the magnetic poles. By as- certaining from actual observation, a number of different places on the surface of the earth where the magnetic inten- sities are equal, and connecting them by a line, it appears that they arrange themselves in a curve around the magnetic pole. These lines are called isodynamic curves. Exten- sive journeys have been undertaken by Humboldt, Sabine * For a more extended list of places with tlie variation and dip, see Professor Loomis on tills subject, in the American Journal of Science, vol. 43d. Where is the Dip least, and where greatest ? AVTiat is the earth's magnetic equator! How is the dipping needle inclined in the Polar Regions? State the amount of dip at Washington, Philadelphia, Jcc. Define Magnetic Inten- ntff. How may it be measured ? In what parts of the earth is the magnetic intensity least ? Where greatest 1 Explain the isodynamic curves. 296 MAGNETISM. Hansteen, and others, to ascertain the points on the surface of the earth where the magnetic intensities are equal, for the purpose of describing these curves. The earliest results indicated the position of the magnetic pole to be in the north-eastern part of Hudson's Bay ; but the directions of these curves presented such anomalies as to suggest the idea of a second magnetic pole in the opposite hemisphere. With a view of ascertaining this point, Professor Hansteen, of Christiana, several years since undertook a journey into Si- beria, at the expense of the king of Sweden, and has fully confirmed the fact, that there exists a second magnetic pole to the north of Siberia, around which the isodynamic curves arrange themselves in regular order. Prom experiments made in deep mines, and in the upper regions of the atmos- phere by aeronauts, it appears that in both these situations, the magnetic intensity is the same as at the corresponding places on the surface of the earth. 397. The effects prodvAxd hy the earth on a magnetic ■needle, correspond to those produced on it by a powerful magnet, and hence the earth itself may he considered as such a magnet. The magnetism of the earth has been supposed by some, to result from a great magnet lying in the central parts of the earth ; by others to be nothing more than the resultant of all the smaller magnetic forces scattered through various parts of the terrestrial sphere ; and by others to be excited on the surface of the earth by the action of the solar rays. The supposition of a great magnet in the interior of the earth, to which all the phenomena of terrestrial magnetism are to be ascribed, is the earliest hypothesis, and is adequate to explain most of the facts of the science. But such a sup- position is inconsistent with the recent discovery of two north poles, implying the existence of four magnetic poles of the earth. The opinion of Biot, that terrestrial magnetism is only the aggregate or resultant of all the individual mag- netic forces residing in different parts of the earth, appears to be no improbable supposition, and accords well with the general doctrine of the composition of forces. Where is the second magnetic pole sitaated 1 How is the magnetic inten- sity of deep mines, and the upper regions of the atmosphere ? What is said of the magnetism of the earth ? How is it supposed to be produced ? How does the supposition that the earth is a magnet accord with the existence of four magnetic poles ? What is Biot's opinion ? DIRECTIVE PROPERTIES OP THE MAGNET. 297 39 8 • Electricity and magnetism are, in some of their properties, remarkably alike, but in others strikingly dis similar. Several of these analogies have been already incidentally mentioned ; but it will be useful to the student to consider them in conupction. Electricity and magnetism agree in the following particulars: (1.) Each consists of two species, the vitreous and resinous electricities, and the austral and boreal magnetisms. (2 ) In both cases, those of the same name repel, and those of opposite names attract each other. (3.) The laws of induction in both are very analogous. (4.) The force, in each, varies inversely as the square of the distance. (5.) The power, in both cases, resides at the surface of bod- ies, and is independent of their mass. But electricity and magnetism are as remarkably unlike in the following particulars. (1.) Electricity is capable of being eicited in all bodies and of being imparted to all : magnetism resides almost exclusively in iron in its different forms, and, with a few exceptions, cannot be excited in any other than ferruginous bodies. (2.) Electricity may be trans- ferred from one body to another ; magnetism is incapable of such transference ; magnets communicate their properties merely by induction, a process in which no portion of the fluid is withdrawn from the magnetizing body. (3.) When a body of elongated figure is electrified by induction, on be- ing divided near the middle, the two parts possess, respec- tively, the kind of electricity only which each had before the separation ; but when a bar of steel or a needle magnetized by induction, is broken into any number of parts, each part has both polarities and becomes a perfect magnet. (4.) The directive properties and the various consequences that result from it, the declination, annual and diurnal variations, the dip, and the different intensities in different parts of the earth, are all peculiar to the magnet, and do not appertain to electrified bodies. METHODS OF MAKING ARTIPICIAL MAGNETS. 399. If the learner has made himself acquainted with the principles expounded in the preceding propositions, he will be qualified to proceed, with interest and intelligence, State the analogies between electricity and magnetism, — also the differen- ces. Metlwd of making Magnets. 298 MAGNETISM. to an explanation of the leading methods practised in the manufacture of artificial magnets. These methods also, by- involving a practical application of those principles, will serve to impress them on the memory and to render the knowledge of them familiar. It will be recollected that magnets are made from other magnets ; that this is done, not by any transference of a portion of the power of the magnetizing body, but by the development of the powers naturally residing in the body to be magnetized ; that this development is effected wholly on the principle of induction ; that the original magnet gains instead of losing by its action on other bodies ; that this power may be induced on iron by the agency of an artificial magnet, or of the loadstone, or of the earth, which is itself a weak magnet, and acts upon the same principles as any other magnet. It must also be kept clearly in mind, that soft iron or steel readily acquires, and as readily loses the magnetism induced upon it, and that hardened iron or steel receives it slowly and with much difficulty, but retains it permanently. As the earth itself may be supposed to have been the original source of magnetism in all other bodies in which it is found, there are methods of magnetizing from the earth without the aid of either the loadstone or an artificial magnet. 400. A needk may he magnetized by bringing the pole of a magnet into close and repeated contact with it. The simplest mode is to lay the needle in a horizontal position, and pass one pole of a magnet over its entire length, repeating the process a number of times, always in the same direction. But a more efl^ectual mode is as follows : Join the opposite poles of two magnets, place them over the cen- ter of the needle, and draw them slowly asunder to the op- posite ends of the needle. Then uniting the magnets as before, lay them again on the center of the needle and repea the process several times. The effect produced by two magnets is much more than double that of one magnet, as may be inferred from Art. 389. But if the needle be of considerable length, several intermediate sets of poles are sometimes developed, as will be seen by applying iron filings. It adds much to the power of the two magnetic bars between which the needle is placed, State the leading: principles to be kept in view in making artiiicial magnets. What is the simplest way of magnetizing a needle ? How does the effect prodaced by two magnets compare with that of one ? Wiiat is said of inter- mediate sets of poles ? DIRECTIVE PROPERTIES OP THE MAGNET. 299 if upon each extremity of the bar most remote from the needle, a mass of soft iron is placed. The iron in this case, acts and re-acts by induction ; and hence, whenever mag- nets are not in use, they require to be connected with iron to prevent the loss of their powers. Pieces of soft iron thus connected with magnets, for the purpose of augmenting their power by induction, are called armatures. Thus A is the armature of the horse-shoe magnet represented in Fig. 136. But it must be recollected that the two species of magnet- ism are not, like those of electricity, separated to a distance from each other, so that one kind may be wholly collected at one end of the bar and the other kind at the other end ; but that the two are separated only at a minute distance, re- maining in the immediate vicinity of each other throughout the whole length of the bar. Hence, in order to give the magnetizing pole its full effect, it becomes necessary to ap- ply it successively to every part of the bar from one end to the other. 401. A more effectual method of magnetizing a needle is the following ; Place two magnetizing bars. A, B, parallel to each other, with their dis- similar poles adjacent; unite the poles at one end by a piece of soft iron R, and ap- ply the poles at the other end to the needle, as is represented in Fig. 135. Upon this prin- ciple, that is, the increased energy with which the two poles act together, is formed what is called the horse-shoe magnet, which derives its name from its peculiar figure, (Fig. 136.) Bars of this form are Fig. 136. converted into magnets upon the same principles as straight ■bars, the magnetizing bar being made to follow the curvature always in the same direction. A very efficacious mode of making horse-shoe magnets is thus described by Professor Barlow. Two horse-shoe bars may be united at their ends, in such a man- What is the effect of placing a mass of soft iron near to the remote ex- tremity of the bar ? Define armatures. Why is it necessary to apply the niag:netiziDg pole to all parts successively ? Describe the horse-shoe magnet What is Barlow's method of making them 1 300 MAGNETISM. ner that the poles which are to be of opposite names shall be in contact. They are then to be rubbed with another strong horse shoe magnet, placing the latter so that its north pole is next to the south pole of one of the new magnets, and consequently its sjputh pole next to the north pole of the same; carrying the movable magnet round and round, always in the same direction. This is esteemed one of the most eligible modes of making powerful magnets. The horse-shoe magnet is itself very convenient for im- parting magnetism to other bodies. Place the poles near the center of the needle ; move them along its surface back- wards and forwards, taking lare to pass over each half of it an equal number of times ; repeat the same operation on the other side ; and the needle will become speedily and effec- tually magnetized. The best mode of making magnetic needles in general, is expressed in the following rule, given as the result of very extensive and accurate experiments, by Capt. Kater. Place the needle in the magnetic ineridian; join the op- posite poles of a pair of bar magnets, {the magnets being in the same line) and lay the magnets so joined, flat upon tlie needle, with their poles upon its center ; then having denoted the distant extremities of the magnets, so that they may form an angle of about two or three degrees with tJie needle, draw them from tlie center of the needle to the extremities, carefully preserving the same inclination ; and having joined the poles of the magnets at a distance from the needle, repeat the operation ten or twelve times on each surface. THE COMPASS. 402. The Compass, (the importance of which to man- kind, has attached to the subject of magnetism its principal value,) is of many different forms, but the chief varieties are the Land compass, the Mariner's compass, the Azimuth com- pass, and the Surveyor's compass. The needle, in all these varieties, is usually a thin ^^^^' ^^' P'^'** °^ ^'^^'' tapering at the extremities ; but a more eligible form has been proposed by Capt. Kater, consisting of four How to magnetize needles with the horse-shoe magnet ? State Kater'a mode of making magnetic needles ? The Com.pass. — Describe the different forms of needles 1 THE COMPASS. 301 narrow strips of steel, united in the form :f a hollow rhom- bus, (Pig. 137.) It is found advantageous to concentrate the powers of the needle as much as possible in the two ex- tremities, and to avoid all inequalities, arising from inter- mediate poles, or from a difference of strength in different parts. The needle is secured at the point of suspension, and furnished with a conical cup of brass which rests on a per- pendicular pin ; and still farther to diminish friction, the point which rests on the extremity of the pin, is made of agate, one of the hardest mineral substances Since, if the needle is magnetized after having been balanced on its cen- ter of gravity, it would no longer remain horizontal, the equipoise is restored by attaching a small weight to the elevated side. The compass, in its simplest form, consists of a long and slender needle, or of a form like the foregoing, enclosed in a suitable box covered with glass. This is all that is essential when it is required merely to know the direction of the meridian, or the north and south points. But, for most purposes, the compass is furnished with a grad- uated circular card, divided into degrees and minutes ; and in the mariner's compass the card is also divided into thirty- two equal parts called rhumbs. The card thus divided is fastened to the needle itself, and turns with it. Thin, slender needles have the greatest directive powers, and are most sensible, since they undergo less friction than those which are heavier ; but due regard to strength requires them to be made of a certain degree of thickness ; an in- crease of length is attended with an increase of directive power; but when the thickness remains the same, the weight, and consequently the friction, increases in the same ratio ; no advantage, therefore, as to directive power, can be obtained by any increase of length. Moreover needles which exceed a very moderate length, are liable to have several sets of poles, a circumstance which is attended with a great diminution of directive force. On this account, short needles, made exceedingly hard, are generally preferable. 403 • The great importance of the mariner's compass, has made its construction an object of much attention, and the best artists have tried their skill upon it. The compass is suspended in its box in such a manner as to remain in a WTiat is essential to the compass ? How is the card graduated ? What kind of needles have the greatest directive power 1 Which are best, long or short needles? 26 302 MAGNETISM. horizontal position, notwithstanding all the motions of the ship. This is effected by means of gimbals. The contriv- ance consists of a hoop, usually of brass, (Fig. 138,) fastened Fig. 138. horizontally to the box by two pivots placed opposite to each other, and constituting the axis on which the hoop turns up and down. At an equal distance from the pivots on each side, that is, at the distance of 90° from each pivot, two other pivots are attached to the ring at right angles to the former, on which the inner box that contains the card is hung. Of course, when it turns on these pivots, its motion is at right angles with that of the hoop. Therefore, all the motions of which the compass box is capable, are performed around two axes which intersect each other at right angles ; consequent- ly, the point of intersection, being in both axes, will' not move at all. But the needle and the attached card rest upon this point, and are connected with the compass box in no other point. Hence they remain constantly horizontal in every position of the box. Describe the manner's compass ? horizontal position? By what means is the needle Kept in a e Kept in CHAPTER IV. ELECTRO-MAGNETISM. 404. It has long been known that an intimate relation exists between electricity and magnetism ; that needles may- be rendered magnetic by passing through them a strong charge of electricity, and that the poles of a compass needle are sometimes reversed, or the powers of the needle entirely destroyed, by a stroke of lightning. But great prominence has of late been given to this subject by the recent discov- eries in Voltaic electricity. In what has already been said under the head of Electricity, we have confined ourselves chiefly to that form of the fluid which is developed by fric- tion. We have now to mention another, and no less inter- esting form under which electricity appears, usually devel- oped by the chemical action of acidulous fluids on metals, and to trace the remarkable relations that exist between the two powers, electricity and magnetism. The production of this form of electricity properly belongs to chemistry, but the application of it as a mechanical power to machinery, as in the electric telegraph, belongs to Natural Philosophy. 405« Electro-magnetism comprehends all those phenom- ena in which electricity calls forth magnetic inf/uences. The most efiectual method of exciting and continuing a current of electricity adapted- to the purposes of electro-mag- netism, is by means of Voltaic apparatus. This develops the fluid, not like the electric machine by friction, but by chemical action excited between certain metals and fluids in a manner soon to be described. Near the beginning of the present century, two Italian philosophers, Galvani and Volta, made known this form of electricity. Galvani having made the first discovery, — this branch of electrical science is called Galvanism. ; and Volta having constructed the first contrivance for accumulating and exhibiting the powers of galvanic electricity, — the ap- paratus employed for this purpose, of whatever form, is called Voltaic apparatus. This distinction, however, is not always observed, but the same apparatus is called Voltaic or Gal- vanic indiscriminately. what relations between electricity and magnetism have long been known 1 By what other method besides friction ia electricity developed ? Define Electro-magnetism. By what apparatus is it excited ? To what does the term Oalvanism properly apply V To what the term Voltaic ? 804 MAGNETISM. Fig. 139. 406. The forms of Yoltaic apparatus in use are very numerous, but the following arrangement will serve as a simple specimen. Let Z represent a plate of zinc, and C a plate of copper, both im- mersed in dilute sulphuric acid, contained in a glass tumbler; and let wires proceed from the ex- tremities of the two plates, as in the figure. On bringing together the ends of the wires, a spark is perceived, and the instant the wires are in contact, a chemical action commences at the zinc surface, positive electricity is gen- erated and flows to the copper, while negative electricity is excited at the copper surface, and flows to the zinc. From the wire connected with the copper pole, is given off positive, and from that connected with the zinc pole, negative electricity. All signs of elec- tricity cease as soon as the wires are separated, but they are instantly renewed when the wires are joined. This alternate closing and breaking the connection of the wires, and thus at one instant forming a communication between the two opposite poles, and the next instant destroying it, is called closing and breaking the circuit. 407. The simple apparatus represented in Fig. 139, is sufficient to illustrate the leading principles of Voltaic ap- paratus, but a more favorable example is afforded in Groves battery, which is at once simple and powerful. The con- taining vessel is a glass tumbler or jar, within which is placed a hollow cylinder of zinc, amalgama- ted with quicksilver, of smaller dimensions than the outside vessel. Inside of this is another cylinder, made of porous earthen ware, and smaller still. A strip of platinum is suspended in the innermost cylinder, sup- ported by an arm of brass, which is fastened to a similar arm proceeding from the zinc cylinder, a piece of ivory being inserted be- tween the two arms, which, being a non- Deecribe the apparatus represented in figure 139. From which pole ia positive, and from which pole is negative electricity given out 1 When do all signs of electricity cease, and when are they renewed ? What is this al. ternate closing and separating the wires called ? Describe Grove's battery Fig. 140. ELECTRO-MAGNETISM. 305 conductor, insulates each from the other. To the top of each arm is attached a binding screw, by means of which a wire may be readily connected with or removed from either pole. Finally the earthen ware cup, which contains the platinum, is filled with strong nitric acid, while the zinc cylinder is filled with sulphuric acid diluted with ten or twelve parts of water. Further, to bring the dilute acid fully in contact with the zinc on both sides, a perpendicular slit is made in the cylinder, which permits the fluid to circulate freely around the zinc. All these parts may severally be recog- nized and pointed out, by an attentive inspection of figure 140, which being an individual member of the battery is called an element of Grove's battery. This form of Voltaic apparatus is much more powerful than that before described, and a very energetic battery may be formed by combining a number (say from 12 to 40) of these single elements, as Leyden jars are combined to form the common electric battery. See Fig. 141. This Fig. 141. form of battery is much used for the electro-magnetic tele- graph. 408. The effects produced by galvanic electricity are partly chemical and partly mechanical. Of the chemical effects, are the decomposition of water and various other compounds ; the production of a most intense heat, which is given off between the poles of a large battery ; and the separation of metals from their solutions, in their pure state, and in such a manner, when desired, as to make them copy pictures with astonishing accuracy. For a knowledge of these interesting properties of galvanic electricity, we must refer the student to works prfifessedly chemical. No What effects of Galvanic electricity are chemical, and what mechanical t 26" 306 MAGNETISM. less interesting and important, however, are those properties of the same agent which belong more appropriately to Nat- ural Philosophy, being of a more m^cJianical nature, such as attractions and repulsions, various magnetic phenomena, and mechanical forces of great energy, forming the basis of a new science denominated electro-dynamics. 409. Let a copper wire, (A B, Fig. 142. ^ Pig 142,) be stretched between two pillars and pass through these to the binding screws G Z ; and parallel to the wire, and above it, let a magnetic needle, N S, be placed, being supported on a point- ed wire W, which may be raised and lowered in its socket. D, at pleasure. Screw the positive wire of a Voltaic jar (Art. 407,) or small battery, to C, and the negative wire to Z, and the positive current will pass from right to left. Instantly on closing the circuit, the magnetic needle will move from its position north and south and point to the west. Lower the wire into the socket, so that the needle may be beneath the conducting wire, and, on closing the circuit, the needle im- mediately turns its north pole towards the east. If instead of the compass needle we employ a needle so balanced on its center of gravity as to be capable of moving freely in a vertical arc like a dipping-needle, on placing this needle parallel to the conducting wire on the west side of it, then, on completing the circuit, the north pole will immediately be elevated, but if placed on the east side of the wire, it will be depressed. Upon attentively considering these facts, it is perceived that they indicate a current of electricity flowing round the wire at right angles to its length. , If a copper wire be stretched between the poles of a battery, iron filings sprinkled on the wire will be attracted to it, and will arrange themselves around it in planes perpendicular to the axis of the wire. But this magnetism lasts only while the current is passing, and the iron filings drop off instantly when the circuit is broken. 410. Dr. Faraday, a distinguished English philosopher, has recently discovered that many bodies, instead of being attracted to the poles of a horse- shoe magnet, are repelled by . What arrangement is made for passing the electric current through a cop- per wire ? What change does this produce on the magnetic needle when placed a^OTJe the wire ? What when placed 6e/ow it? What eiTectB doee the current produce on the dipping-needle ! What do these directions indicate ? ELECTRO-MAGNETISM. 307 Fig. 143. them. Thus ia figure 143, let A B represent a slender thread suspended from the ceiling of a room, and to the lower extremity let a stirrup of copper wire be at- tached, by which stirrup or holder different substances may be conveni- ently suspended, near the poles of a strong electro-magnet, N S. Among different bodies some will be attract- ed towards the poles, and are of course magnetic ; others are repelled and take a position at right angles to the line joining the two poles, and these are called diamagnetic ; and others still receive no motion in either direction, and are therefore called indifferent. Thus, heavy white glass is strongly diamagnetic ; various salts are more or less so ; and the fol- lowing metals are diamagnetic in the order in which they are placed, — bismuth, antimony, zinc, tin, mercury, silver, copper. Many phenomena of electro-magnetism are exhibited by means of the Helix, formed of a wire (usually copper) coiled around a cylinder so as to take the form of a cork- screw. Such a wire may be insulated merely by winding it closely with silk or cotton thread, forming a coated wire similar to that sold under the name of bonnet-wire. Since galvanic electricity is of a low intensity, (Art. 332,) and has consequently little tendency to break through non- conductors, even so slight a non-conductor as silk or cotton thread is sufficient to prevent the electric current from es- caping while traversing the wire.* 411. We will now explain the method of rendering iron magnetic by Induction, — a term which implies that there is no direct communication of electricity to the body, but that it acquires magnetism merely by the electric current passing near it. If we coil such an insulated copper wire around a bar of iron, and connect the two ends of the wire with the two poles of a battery, the iron bar immediately becomes a * In the helix used for the electrio telegraph, the wires are more perfectly in- Bulated by covering the cotton thread with shellac. Diamag-Mtism. — Describe figure 143. When are bodies said to be dia- magnetic! When indifferent 7 Give examples of diamagnetic bodies. Describe the Hdix. What does the term induction Imply? How may a bar of soft iron be rendered "^xagaetic by induction ? 308 MAGNETISM. rig. 144. magnet, but as suddenly loses this power when the Voltaic circuit is broken. The more numerous the coils, the greater is the development of magnetism. A peculiarly eflective arrangement is one rep- resented in Fig. 144. A mass of soft iron entirely destitute of any magnetic properties, is bent into the form of a horse-shoe, or the letter U, and closely wound with insulated copper wire. On connecting the two extremities of the wires N and P, (which communicate with the ends of the helix yfw through cups containing mercury,) with the two poles of a Voltaic battery, the iron instantly becomes endued with astonishing magnetic power. An electro-mag- net constructed by Professor Henry has, in some instances, sustained a weight of 3000 pounds. Enormous as this power is, yet it is instantly lost again on breaking the circuit. 412. The energy with which electro-magnetism maybe made to act for one instant, and the facility with which the action may be entirely destroyed the next, implies a me- chanical force somewhat resembling that of steam, which owes its power in the steam condensing engine to the prop- erty it has of exciting a powerful elastic force one moment and losing all elasticity the next moment, (Art. 236.) The idea, therefore, has been warmly cherished of discovering in electro-magnetism a mechanical force of boundless energy and distinguished above all other forces for convenience, safety, and economy. The individual who has labored with most success in the construction of machines for employing this power as a motive force, is our countryman Dr. Charles Gr. Page. The following cut represents one of the forms of How is the degree of magnetiam affected by increasing tbe number of coils ? Describe Henry's great magnet ? What does this power of suddenly acquiring a great mechanical force and suddenly losing it resemble ? What idea has been oheiisbed with respect to this force ? ELECTRO-MAGNETISM. 309 his electro-magnetic engines. Two electro-magnets of the U form, represented at M N, are firmly secured in a vertical position, the four poles just reaching to the upper surface of Pig. 1»5. the table. The two armatures A A are so arranged as to be brought alternately into contact with the poles of each magnet. This is done by closing and breaking the Voltaic circuit, which is carried through the insulated wires that are coiled around the magnet, and connected with a battery by means of the binding screws S S. When the circuit is closed in connection with M, that magnet attracts the ar- mature A and draws away from N its armature, N not being in communication with the battery. But the next instant, it is brought into communication with the battery, becomes a magnet, attracts the armature, and withdraws it from M. By appropriate contrivances, this reciprocating motion is communicated to the working beam, which gives motion to a crank, and that causes the revolution of a wheel, as is represented in the figure. The mechanisin by which the circuit is opened or closed is called a break. It is rep- resented in the figure at B, and it may easily be conceived, that the revolving wheel may carry a fixture which will al- ternately open and shut the connection with the battery of each set of wires, that communicate between the poles of the magnet and those of the battery. The possibility of em- ploying electro-magnetism as a motive force for driving ma- Deacribe Page's working engine, represented in figure 145. Is the possi- bility of employing electro-magnetism as a force for driving machinery estab- lished? 310 MAGNETISM. chinery, has thus been fully established. But it remains to be seen whether it will prove as convenient and as economi- cal a power as steam. Since, however, it is capable of be- ing generated on any scale, it may be found both convenien and economical in those cases, at least, where the exigen cies would not require so complicated and extensive a moving force as the steam engine. 41 3« But a more wonderful and important agency of electro-magnetism is seen in the Electric Telegraph. Three properties of electricity peculiarly fit it for tele- graphic uses : first, it may be sent to any place, in any re- quired direction, by furnishing a path for it through good conductors ; secondly, it passes from one point on the earth to another, however distant, in a moment of time ; and, thirdly, whatever effects it is capable of exhibiting may be produced at a distant station as well as near at hand, and at the same instant. Galvanic electricity is better adapted to telegraphic purposes than that afforded by friction, be- cause it is easily and cheaply produced so as to supply a continued current ; and, especially, because by its influence, distant motions may be made which serve as signs of ideas, or severally represent letters of the alphabet. The telegraph has been constructed of several different forms, but as that of Morse was the first in which complete success was at- tained, and is, like most great inventions, characterized by a high degree of simplicity, it will be sufficient, for the present purpose, to explain this form of the electric tele- graph. For a general idea of Morse's telegraph, imagine a metal- lic lever, eight or nine inches long, poised upon a fulcrum, the longer end of which is armed with a blunt metallic point, which, when the shorter end is depressed, is brought up forcibly against a strip of paper moving slowly just above it on a roller. The point if brought up hard against the paper will indent it. If kept in contact but an instant, a dot will be made ; if for a longer time, a line, which may be of greater or less length at pleasure. Now it is easy to see that by dots and lines variously combined, the entire alphabet may be represented ; for a single dot (.) may mean a, two dots (..) b, a dot and a line (. — ) c, and so on to the Is it a convenient and an economical force ? Electric Telegraph. Specify the three properties which fit electricity for telegraphic uses? Deecriho Morse's telegraph, iirst in general terms. ELECTRO-MAGNETISM. 3 1 1 end of the alphabet. The alphabet proposed by Professor Morse, arranges the dots and marks differently from the ex- ample here given, but upon the same general principle. Were the lever worked by hand, it is easy to see that an tlphabet of this kind might be written by it. But instead of employing the force of the hand, there is placed under the longer end of the lever, an electro-magnet, which is connected by wires with a small Yoltaic battery, with conveniences for closing or breaking the circuit in an instant. To the end of the lever, which is immediately over the magnet, is attached an armature, which falls upon the poles of the magnet like a small hammer on an anvil. Now the instant the circuit is closed, the horse-shoe bar becomes a magnet and draws down the armature and the shorter end of the lever along with it, at the same time raising the longer end and bringing the point forcibly against the paper, which, by means of clock work, is kept moving along slowly above it on a roller. It is plain from what has been said, that the battery may be a hundred miles from the magnet as well as close at hand, and that the operator may be anywhere along the line of wires that form the communi- cation between the two poles of the battery. All that is necessary is, that the circuit, at some point, should be bro- ken and closed in such a manner as to give the requisite motions to the lever. 414. With the h\egava.g generalidea of the telegraph, let us now see how plain the sub- ject may be rendered by the aid of I'ig- i4fi. diagrams. In figure 146, are seen two bind- ing screws vvith which a resever- ally connected wires that com- municate with the two poles of Grove's battery, (Art. 407.) Every time the button is depressed by the hand of the operator, the circuit is closed, and every time the button is permitted to rise, (as it does of itself by a spring) the circuit is broken. Wher- ever therefore this key is interposed in the circuit, the elec- tric current may be made to flow one instant and to cease the next instant, at the pleasure of the operator. Nor does it make any difference at what point of the circuit the key Describe the construction and use of the key. How is the circuit alter- nately closed and broken ! 312 MAGNETISM. is placed, whether near to the telegraph or a hundred miles off Figure 147, represents the telegraph. At A is seen Fig. 147. the electro-magnet, consisting of a horse-shoe magnet placed perpendicularly, and wound with several thicknesses of in- sulated copper wire, the ends of which form a connection between the poles of the magnet and the binding screws D D, from one of which a wire goes out to the remotest station and returns to the other. The instant the circuit is closed by the Key (Fig. 146,) the electro-magnet becomes endued with a powerful attraction, and forcibly brings down upon the two poles the armature A, and along with it the shorter end of the lever L, the longer end at the same time bring- ing a point on its extremity against a fillet of paper PP, which is reeled off from the wheel S, and carried along uni- formly between rollers. The indentations produced by the point upon the paper, whether dots or lines, indicate the message transmitted by the operator who works the key. The uniform motion is given by clock-work, carried by the weight W, which clock-work is made also to cause a bell B to strike when the operator first touches the key, and it Explain the process of sending a message by the telegraph, from figure 147. What gives motion to the lever? What writes the message ? What is the use of the -looit-work ? Also of the bell ! ANIMAL ELECTRICITY. 313 thus announces that a message is to be sent before the rec- ord on the fillet of paper begins. ANIMAL ELECTRICITY. 41 5. Of the natural agencies of electricity, one of the most remarkable is that exhibited by certain species of fish, especially the Torpedo and the Gymnotus, This peculiar property of the torpedo was known to the ancient natural- ists, and is accurately described by Aristotle and Pliny. Aristotle says that this fish causes or produces a torpor upon those fishes it is about to seize, and having by that means got them into his mouth, it feeds upon them. Pliny says that this fish, if touched by a rod or spear, even at a dis- tance, paralyzes the strongest muscles. The electric organs of these fishes resemble, in their con- struction, the Yoltaic pile, consisting as they do of minute cells filled with gelatinous fluid and abundantly supplied with nerves. In a very large torpedo, one electric organ has been found to consist of 1182 columns, the diameter of each being about one fifth of an inch. Each column is divided by horizontal partitions, consisting of transparent mem- branes, placed over each other at very small distances, and forming numerous interstices, which contain the fluid. The number of partitions contained in a column one inch in length, has been found in some instances not less than one hundred and fifty. By this arrangement, the amount of electrified surface is exceedingly great ; equivalent in one instance to 1064 feet of coated glass. The Gymnotus, or Surinam eel, is found in the rivers of South America. Its Fig. 148. ordinary length is from three to four feet, but it is said to be What fishes have the power of giving electric shocks 7 What ancient vraters have mentioned these ? Describe the electric organs of those fishes. How many columns are there in the torpedo t How is each column divided 1 How great is the extent of surface ? What is said of the Gymnotus t 27 3 1 4 MAGNETISM. sometimes twenty feet long, and to give a shock that is in- stantly fatal. Its electric organs are double, and reach from the head to the tail. Almost every sort of electrical effect has been produced by experiments on these animals, such as the spark ; the development of the two fluids, positive and negative ; shocks ; chemical decompositions ; heat and magnetism. The shock communicated to fishes instantly paralyzes them, so that they become the prey of the Gymnotus. By irrita- ting the animal with one hand, while the other is held at some distance in the water, a shock is received as severe as that of the Leyden Jar. Humboldt, in his travels in South America, describes a method of catching the Gymnotus, by driving wild horses into a lake which abounds with them. The fishes are wearied or exhausted by their efforts against the horses, and then taken ; but such is the violence of the charge which they give, that sometimes the horses are drowned before they can recover from the paralyzing shocks of the eels. "What electrical effects may be produced by experiments with these ani- miils? Describe the method of catching the Gymnotus 1 PART VI,— OPTICS. CHAPTEK I. PRELIMINARY DEFINITIONS AND OBSERVATIONS. 416. Optics is that branch of Natural Philosophy which treats of Light and Vision. More particularly, it is the object of this science to inves- tigate the nature of the agent on which the phenomena of vision depend ; to treat of the motions of light, in respect to its direction, its velocity, and its reflexion from the surfaces of bodies ; to trace its change of direction, and the various other modifications it undergoes by passing through diflfer- ent transparent media ; to explain the phenomena of nature virhich depend upon the properties of light, embracing the doctrine of color ; to trace the relation between light and the structure of the eye, comprehending T;he subject of vision; and finally, to describe the various instruments to which a knowledge of the principles of Optics has given birth, dis- closing many new and wonderful properties of light, and extending the range of human vision, on the one hand, to myriads of objects too minute, and on the other, to number- less worlds too remote, to be seen by the unassisted eye. 417. Luminous bodies are naturally of two kinds, such as shine by their own light, as a lamp or the sun, and such as shine by borrowed light, as the moon, and most of the visible objects in nature. A ray is a line of light ; or it is the line which may be conceived to be described by a particle of light. In a more general sense, the term is applied to denote the smallest Optics. — Define Optics. Enumerate more particularly the objects of this science in regard to the nature and motion of light, to color, to vision, and to optical instruments ? How are laminoas bodies divided into two kinds ? De- 6ne a ray. 316 OPTICS. portion of light which can be separately subjected to ex- periment. A beam is a collection of parallel rays. Kpencil is a collection of converging or diverging rays. A. medium is any space through which light passes. When a space is a perfect void, so as to offer no obstruction to the passage of light, it is said to be &free medium ; when the space inter- cepts a portion only of the light, it constitutes a transparent medium. Transparency, however, may exist in different degrees. When the medium itself is invisible, as portions of air, it is said to be perfectly transparent ; when the me- dium is visible, but objects are seen distinctly through it, as in the clearest specimens of glass and crystals, it is said to be, simply, transparent ; when objects are indistinctly seen through it, it is semi-transparent ; and when a mere glim- mering of light passes through, without representing the figure of objects, it is translucent. Bodies that transmit no light are said to be opake. 418. Rays of light, while they continue in the same unifonn medium, proceed in straight lines. For objects cannot be seen through bent tubes ; the shad- ows of bodies are terminated by straight lines ; and all the conclusions drawn from this supposition, are found by ex- perience to be true. If two bodies with plane surfaces, as two disks of metal, be held between the eye and some luminous point, as a star, on bringing the two planes grad- ually towards each other, the star may be seen through the intervening space until the planes come completely into contact ; but if one of -the surfaces is convex and the other concave, the light is intercepted before the surfaces have met. In consequence of the rectilinear motion of light, it forms angles, triangles, cylinders, cones, &c., and thus its reflex- tions fall within the province of geometry, the principles of which are applied with great effect to the development of the properties and laws of light, after a few fundamental properties are established by experiment. From every point in a luminous object, an inconceivable number of rays of light emanate in every direction, when not prevented by obstacles that intercept it. Thus, from every point in the flame of a candle, as seen by night, light diffuses itself, per- vading an immense sphere, and filling every part of the space Define a beam, a pencil, a medium, a free medium, a transparent medium i When is a body said to be perfectly transparent, transparent, semi-transpar ent, translucent, or opake 1 What is the direction of rays of light ? State the proof that it moves in right lines ? What is said of the number of ray* which emanate from a luminous body t PRELIMINARY DEFINITIONS AND OBSERVATIONS. 317 SO perfectly, that not the mintitest point can be found des- titute of some portion of the rays. Any luminous body of this kind is called a radiant. The pencil of light which proceeds from a radiant, is a cone, the sections of which made by any plane, correspond to the figures called conic sections. If any portion of the pencil be intercepted by a rectilateral figure, that portion constitutes a pyramid of which the 'figure is the base and the luminous point itself is the vertex. 419. Light has a progressive motion of about one hun- dred and ninety-two thousand five hundred miles per second. The estimation of the velocity of light (which may be classed among the greatest achievements of the human mind,) has been effected in two different ways. The first method is by means of the eclipses of Jupiter's satellites. To render this mode intelligible to those who have not studied astronomy, it may be premised, that the planet Jupiter is attended by four moons, which revolve about their primary, as our moon revolves about the earth. These small bodies are observed, by the telescope, to undergo frequent eclipses, by falling into the shadow which the planet casts in a direction opposite to the sun, The exact moment when the satellite passes into the shadow, or comes out of it, as seen by a spectator on the earth, is calculated by astronomers. But sometimes the earth and Jupiter are on the same side, and sometimes on opposite sides of the sun ; consequently, the earth is, in the former case, the whole diameter of its orbit, or about one hundred and ninety millions of miles nearer to Jupiter than in the latter. Now it is found by observation, that an eclipse of one of the satellites is seen about sixteen minutes and a half sooner when the earth is nearest to Jupiter, than when it is most remote from it, and consequently, the light must occupy this time in passing through the diameter of the earth's orbit, and must there- fore travel at the rate of about one hundred and ninety-two thousand miles per second.* Another method of estimating the velocity of light, wholly independent of the preceding, is derived from what is called the aberration of the fi'xed stars. The full explanation of this method must be referred to astronomy ; but it may be understood in general, that ^ 190000000 ,„„„„„ , ijTFTTTTjT— 192000 nearly. 16,5 X 00 With what velocity does light move ? How is its progressive motion proved? Explain the method fi-om observations on Jupiter's satellites, and by the aberration of the fixed stars. 27* 3 1 8 OPTICS. the apparent place of a fixed star is altered from the effect of the motion of its light combined with the motion of the earth in its orbit. It will be remarked, that the place of a luminous object is determined by the direction in which its light meets the eye. But in the case of light coming from the stars, the direction is altered in consequence of the motion of the earth in its orbit, being intermediate between the actual directions of the earth and the light of the star and the velocity of the earth in its orbit being known, that of light may be computed from the proportional part of the effect produced by it in causing the aberration. The ve- locity of light, as deduced from this method, comes out very nearly the same as by the other. Hence it is inferred that the velocity of light is uniform. 420. The intensity of light, at different distances from the radiant, varies inversely as the square of the distance. Thus, if we carry a given surface, as a leaf of paper, to different distances from a candle, at the distance of six feet, the surface will receive only ^ as much light as at the dis- tance of three feet ; at twelve feet, or four times as far as at first, the light will be only Vrth as intense. 421. On this principle, the comparative light afforded by different flames may be determined by what is called i/je ■method of shadows. Desiring to compare the qualities of two kinds of oil. I took two lamps, alike in all respects, and furnished with wicks as nearly equal as possible. One of the lamps I filled with fine sperm oil, and the other with an in- ferior kind called " summer strained" oil. Having lighted the lamps, I placed them on a table opposite to a white wall, and between them and the wall, I set a candlestick contain- ing a long candle, which was a convenient object for form- ing the shadows. I then placed the inferior lamp at such a distance from this object as made a well-defined shadow of the candle on the wall, and finally adjusted the superior lamp so that it threw another shadow of the candle by the side of the former, and, as near as the eye could judge, of the same intensity. On measuring the respective distances of the lamps from the wall, I found the inner one 8, and the outer 9 feet from the wall. Hence I inferred that the illu- minating powers of the two specimens of oil were in the ratio of 81 to 64, or nearly as 5 to 4, and consequently that the better sort of oil gave me one fifth more light than the other. How is the intensity of light at diiferent distances from the radiant? Describe the viethod of shadows. REFLEXION OF LIGHT. 319 Although the intensity of light decreases rapidly as we recede from the radiant, yet the brightness of the object suf- fers little diminution by increase of distance. A candle ap- pears nearly as bright at the distance of a mile as when close to the eye. 422. Whenever the rays of light from the different parts of an ob- ject cross each other before forming the im- age, the image will be inverted. It is mani- fest from figure 1 49, that the light by which the top of the object is rep- resented forms the bottom of the image, and that the light from the bottom of the object forms the top of the image, the two sets of rays crossing each other at the hole in the screen. It is always essential to the distinctness of an image, that the rays which proceed from every point in the object, should be arranged in corresponding points in the image, and should be unaccompanied by light from any other source. Now a screen like that in the figure, when interposed, permits only those rays from any point in the object that are very near togeth- er and nearly parallel to each other, to pass through the open- ing, after which they continue straight forward and form the corresponding point of the image ; while rays coming from any other point in the object cannot fall upon the point occupied by the former pencil, but each finds an appropriate place of its own in the image, and all together make a faith- ful picture of the object. CHAPTER II. OF THE REFLEXION OF LIGHT. 423. Light is said to he reflected when, on impinging upon any surface, it is turned back into the same medium. Instruments employed as reflectors are divided into mir- rors and speculums. The name mirror is applied to reflect- ors made of glass and coated with quicksilver, as common How is the brightness of a light at different distances ? When is light said to be reflected ! Explain the distinction between mirrors and speculums. 320 OPTICS. looking-glasses : the word speculum is applied to a metallic reflector, such as those made of silver, steel, tin, or a pecu- liar alloy called speculum metal. As the light which falls on glass mirrors is intercepted by the glass before it is re- flected from the quicksilver surface, a speculum, or a reflect- or of polished metal, is that supposed to be employed in op- tical experiments, unless the contrary is specified. Such a surface, indeed, is to be understood when the word mirror is used without distinction. The surface of the mirror or speculum may be either plane, concave, or convex, and the reflector is denominated accordingly. A ray of light before reflexion is called the incident ray. The angle made by an incident ray, at the Fig. 150. surface of the reflector, with a perpendicu- lar to that surface, is called the angle of incidence : the angle made by the reflect- ed ray with the same perpendicular is called the angle of reflexion. Thus, in Eig. ) 50, if M N represents the reflecting surface, D C a perpendicular to it at the point C, A C the in- cident, and B C, the reflected ray ; then A C D will be the angle of incidence, and BCD the angle of reflexion. 42 4> Experiments on light are usually conducted in a room which can be made dark with close shutters, one of which is perforated with a circular hole, a few inches in diameter, for admitting a beam of light. This opening is rendered smaller to any required degree by covering it with a piece of board or metallic sheet, having a smaller aper- ture ; and, as the sun may not shine directly into the shut- ter at the time required, a mirror is sometimes attached to the outside of the shutter, so contrived, that by means of adjusting screws, it may be made to turn the rays of the sun into the opening, and to give them a horizontal or any other required direction. The course of the rays is rendered palpable to the eye, by the illuminated particles of dust that are floating in the air. 425« The angles of incidence and reflexion are in the same plane and are equal to ea/:h other. Let a ray of light A C (Fig. 150,) admitted into a dark chamber as above, be incident upon a horizontal speculum What is the angle of incidence and of reflexion ? Explain by the figure How are experiments on light usually conducted ! State the relation between the angles of incidence and reflexion. REFLEXION OF LIGHT. 321 M N at the point C, to which the line G D is perpendicular, and let C B be the reflected ray. Then if the plane surface of a board, or a metallic plate, be made to coincide with the incident ray and the perpendicular, it will be found to coin- cide also with the reflected ray, showing that the three rays are in the same plane. Again, if, from the point C, with the radius C A. a circle be described, on measuring the arcs subtended by the angles of incidence and reflexion, they will be found to be exactly equal to each other. The angles of incidence and reflexion are also equal when the reflexion takes place from a concave or a convex surface ; for the re- flexion being from a point, the curve and tangent plane at that point coincide, and have both the same perpendicular, namely, the radius of the curve. REFLEXION OF LI&HT FROM PLANE MIRRORS. 426. When rays of light are reflected from a plane surface, the reflected rays have the same inclination to one another as their cor- ^'S- 1^'- responding incident rays. ? * ^ ^ When parallel rays, as AB, CD, (Fig. 151,) fall upon a plane mirror, as KS, the reflected rays, BGr, DH, are also par- allel. Morever, when the rays diverge before the reflexion, (Fig. 152,) as KA, KB, they will diverge just as much after reflexion, proceed- ^^s:- isa. ing in the lines AD, BC, which will h b c appear to come from F, a point just as far behind the mirror as E, is be- fore it ; or if DA and CB be consid- ered as two converging rays, they will converge in the same degree after reflexion in the lines AR, BR, and will meet in B, a point just as far before the mirror as the point P, towards which they tended, is behind it. 42 7 • Wlien an object is placed before a plane mirror, the image of it appears at the same distance behind it, of the same magnitude, and equally inclined to it. Let MN, (Fig. 153.) be a plane mirror, and an object be- fore it, the eye being situated at H. Now from every point Rejiexionfrom Plane Mirrors. — How are parallel rays reflected ? Ditto diverging rays? Ditto converging? Explain by the figures. When an object iB placed before a plane mirror^ where is the image situated ? 322 in the object innumerable rays of light are constantly ema nating, which, striking on all parts of the mirror, are reflect- ed off again in various fi;rec- tions. All that is essential to vision is, that a sufficient num- ber of these should be conveyed to the eye. To avoid the confu- sion that arises from the repre- sentation of a great number of lines, we will consider those rays only which flow from the ex- treme parts ot the object; the rays proceeding from the inter- mediate points will of course lie between these. From the point A, then, we may conceive of a vast number of rays of light as proceeding to all parts of the mirror, from which they are reflected again in various directions ; but those only which fall upon the small part of the mirror FGr, namely AF, AG, are conveyed to the eye. These, therefore, are the rays which serve to make the point A visible ; and since they come to the eye as though they diverged from the point a as far behind the mirror as A is before it, the point A will appear as though it were at a. For the same reason the point B will be rendered visible by the rays/H, ^H, which appear to diverge from h, a point as far behind the mirror as B is before it. All the other points in the line AB will take their respective places in the line ah, which will therefore form an exact image or picture of the object, affecting the eye in the same manner as the object would do in its place. It is important to remember, that how many reflexions so- ever light may undergo in passing from the object to the eye, the image will be determined as to position, magnitude, SfC. by the inanner in which the rays finally reach the eye after the last reflexion. 428. When a plane mirror (as a common dressing glass) is turned on its axis, the image revolves twice as fast as the mirror. By turning the mirror through 45°, the image is carried through 90°, so that a mirror set at an angle of 45° with the horizon, represents horizontal objects in a perpendic- ular position, and perpendicular objects on a horizontal level. Explain by the figure. What rays finally determine the plane of the im- age ? "When a plane miiTor revolves on an axis, how much faster than the mirror does the image revolve ? REFLEXION OP LIGHT. 323 429. A common looking-glass furnishes an example of a plane mirror. If we place a lamp before it, rays of light are thrown from the lamp upon every part of the mirror, but we see the lamp by means of those few of the rays only which are reflected to the eye ; all the rest are scattered in various quarters, and do not contribute at all to render the object visible to a spectator at any one point, although they would produce, in like manner, a separate image of the lamp wherever they entered an eye so situated as to receive theui. Were there a hundred people in the room, each would see a separate image, and each in the direction in which the rays come to his own eye. We will suppose M N (Fig. 154,) to be a looking-glass, having a harp placed before it, I'ig- 154. and the eye of the spec- tator at D. Of all the rays that strike on the glass, the spectator will see the image by those only which strike the mir- ror in such a direction, A B, that when reflected from the mirror at the same angle on the other side, they shall enter the eye in the direction B D. The image will appear at C as far behind the mirror as the harp is before it, and it will be seen inverted, because the points which are highest above the mirror will appear lowest in the image, and therefore the object and the image stand base to base. We here learn the reason why objects appear inverted when we see them reflected from water, as the sur- face of a river or lake. 430. When an object is placed between two parallel •plane reflectors^ a row of images is formed in each mirror, appearing in a straight line behind each other to an indefi- nite extent. Let there be two plane reflectors, parallel to each other ; and let an object, a candle for example, be placed between them. An image of the candle will be formed in each mir- ror, as far behind it as the object is before it. Again, each of these images becomes in its turn a new object to the op- Wheu an object is placed between two parallel plane reflectors, what Images are formed ? 324 OPTICS. posite mirror, and forms a corresponding image as far be- hind that mirror as it is itself before it, and thus the images are repeated in a right line until the light becomes too feeble to be visible. Thus, let Fig. 155. AB, CD, (Pig. 155,) be two ^ ^ plane mirrors, and E an ob- ject between them ; two im- ages will be formed of B at g' g' E' and E' ; two more of E' and E' at E" E" ; and thus a succession of images will arise to an indefinite extent ; but since a certain part of the light is lost at every reflexion, each succeeding image is fainter than the preceding. The Endless Gallery is formed on this principle. It consists of a box, in the opposite sides of which are placed two parallel reflectors, and between them a num- ber of images are placed, which are repeated in an endless succession. The experiment may easily be tried by placing two mirrors on the opposite walls of a room, and holding a lamp between them. On the same principle, fancy articles of merchandise in a show-case, and even wares and goods on shelves are sometimes exhibited in numerous repetitiong by being reflected between two parallel mirrors. 43 1» If an object is placed between two plane reflectors INCLINED to each other, the images formed will lie in the cir- cumference of a circle. The common dressing glasses which are mounted on ma- hogany frames, and turn on pivots fixed in the two ends, are convenient for performing this experiment. Two such mir- rors may be placed side by side and a candle set between them. When the mirrors face each other, that is, are par- allel, an indefinite number of images of the candle may be seen in each mirror ; but on turning the mirrors so as to bring their parallel edges at the bottom near each other, while the upper edges are turned outwards, a circular row of images will be observed, the circle continually enlarging as the mirrors are brought nearer to parallelism, and con- tracting more and more as the inclination of the mirrors is increased. 432. The ^a&ifi?osco^e owes to this .principle its power Explain by the figore. What is the principle of the endless gallery? When an object is placed between two plane mirrors inclined to each other, what images are formed ? How may the experiment be performed ? REFLEXION OP LIGHT. 325 of producing' beautiful figures in endless succession and variety. It consists of a short conical-shaped tube, (usually of brass or tin,) containing two mirrors which reach from end to end, forming an angle with each other of 30 or 60 degrees. The larger end of the tube is closed by two cir- cular plater of ground glass, about a quarter of an inch apart, between which are placed a few pieces of glass of dif- ferent colors. The smaller end of the tube is covered, with the exception of a small aperture at the angles where the ends of the mirrors meet, to which the eye is applied. On looking through the tube, the fragments of glass, however irregular they may be, appear arranged in a perfectly sym- metrical figure curiously diversified. On every change of position of the glass pieces, as by a tap of the finger, a new figure is evolved entirely dissimilar to the former. 433* It is found by experiment, that when a pencil of light is incident perpendicularly upon water, only 18 rays out of 1000 are reflected, while the greater part of the re- maining rays are transmitted. As the angle of inclination is increased, the proportion of rays reflected is also rapidly increased, till at an angle of 75°, the reflection is 211 rays; at 85°, 501 ; and at 89°, 692. In glass 25 out of 1000 are reflected at a perpendicular incidence ; and the glass always reflects more light than water, till we reach very great angles of incidence, such as 87^°, when it reflects only 584 rays, while water reflects 614. RErLEXION OF LIGHT FROM CONCAVE MIRRORS. 434. The office of concave reflectors, in general, is to collect rays of light. Hence, when applied to parallel rays, it makes them converge to a focus ; when applied to rays already converging, it makes them converge more ; to diverging rays, it makes them diverge less, or overcomes their divergency so completely as to make them parallel, or even converging. By keeping steadily in mind the proposition that the an- gle which the incident ray makes with a perpendicular to the reflecting surface, is equal to that which the reflected ray makes with the same perpendicular on the other side, Describe the Kaleidoscope. "WTien s pencil of light falls perpendicularly on water, how many rays out of 1000 are reflected I How many from glass 1 Concave Mirrors. — What is the general office of concave mirrors ? How does it affect parallel, diverging, and converging rays respectively? 28 326 OPTICS. the various modes in which light is reflected from a con- cave surface virill be readily understood from the annexed figure. * . Let ccc represent a concave inir- ror, whose center is C, and radius of curvature Cc ; (which radius it must be remembered is always perpendicular to the curve ;) then the various cases will be as fol- lows: Parallel xa.ys, fc,fc, will pass to the other side of the perpendicular and meet in F,* which is half way from the mirror to its center C. Eays diverging from a point more remote than the center, Ac, Ac, making a less angle with the perpendiculars than the parallel rays make, will also make a less angle on the other side of the per- pendiculars, meeting in "a, between the focus and the center. Rays diverging from the center, Cc, Cc, will be reflected back to the center again. If we now pass to the other side of the center, we see that rays which diverge from a point between the center, and the focus, as from a, converge to a point on the other side of the center, as A. Rays diverging from the focus, go out parallel, as cf, cf. Rays that come to the mirror convergirig, as dc, dc, meet in a point between the focus and the mirror, as at D, and when diverging from this point they return in the lines cd, cd, appearing to proceed from a point behind the mirror, as A', which is called the virtual focus. 435. The following experiments, which may be easily repeated, will serve to render familiar the different modes in which images are formed by concave mirrors. (See Fig. 156.) We will suppose a lighted candle to be placed very near * F IB called the focus of parallel rays. Explain from the figare. Where do rays diverging from a point Tnort remote than the center meet? How are rays from the center reflected? — from between the center and the foeux 1 — from the /ocws ? How are convergins; rays reflected t RKPLEXION OP LIGHT. 327 to a concave mirror : — it will form no image before it be- cause the rays go out still diverging, but we see an enlarged image of the candle behind the mirror. As the radiant is withdrawn from the mirror towards the principal focus, the image will rapidly recede on the other side, and grow larger and larger until the radiant reaches the focus, when the image will suddenly disappeeir. On removing the radiant a little farther, the image will be found at a great distance before the mirror and very much enlarged. As the radiant approaches the center, the image approaches it rapidly on the other side of it, constantly diminishing in size until they both meet and coincide in the center. Removing the radiant still farther, the image appears again between the center and the focus, diminished in size, and slowly approaching the focus as the radiant recedes, but it never reaches it, unless when the ra- diant may be considered as at an infinite distance, as in the case of the heavenly bodies. One who looks into a concave mirror sees his own face varied in the following manner. When he holds the reflect- or near to his face, he sees his image distinct^ because the rays come to the eye diverging (which is their natural state with respect to near objects,) and enlarged, because as the rays diverge less than before, the image is thrown back to a greater distance behind the mirror than the object is before it, and the magnitude is proportioned to that distance. As he withdraws the eye, the image grows larger and larger until the eye reaches the focus. From the focus to the cen- ter, no distinct image is seen, because the rays come to the eye converging, a condition incompatible with distinct vis- ion. At the center the eye sees only its own image, since the image is reflected back to the object and coincides with it. Beyond the center, his face will be seen on the other side of the center before the mirror (though habit may lead him to refer it to a point behind it,) and it will be dimin- ished, being nearer to the mirror than the object is, and in- verted, because an inverted image is formed when the rays are brought to a focus, and this becomes the object which is seen by the eye.* • Theae phenomena may be all observed with an ordinary concave shaving glass. Bappose a lighted candle placed before a concave mirror, and state the various appearances at different distances. State the various appearance* when one holds a concave mirror at different distances before his face. 328 OPTICS. 436. Concave mirrors form images of objects, by col- lecting the rays from each Pig. 157. pgjjjt of the object into " corresponding points in the image, unaccompanied by rays from any other quarter. If the object be nearer than the focus, as in figure 157, a magnified image appears behind the mirror, and in its natural position ; but if the object be between the focus and the cen- ter, the image is before the mirror on the other side of the center, larger than the object, and inverted. 437. Concave mirrors, in consequence of the property they have of forming images in the air, were in a less en- lightened age than the present, frequently einployed by showmen for exhibiting surprising appearances. The mir- ror was usually concealed behind the wall, and the object, which might be a skull, a dagger, &c., was placed between it and the wall and strongly illuminated. The rays pro- reeding from the object fell upon the mirror, and were re- flected by it through an opening in the wall, and brought to a focus so as to form an image in the same room with the spectator. If a fine transparent cloud of blue smoke is raised, by means of a chafing dish, around the focus of a large concave mirror, the image of any highly illuminated object will be depicted in the middle of it with great beauty. A dish of fruit thus represented invites the spectator to taste, but the instant he draws out his hand a drawn dagger pre- sents itself 438. Concave mirrors have been used as light-liouse re- flectors, and as burning instruments. When used in light- houses, they are made of copper plated with silver, and they are hammered into a parabolic form, and then polished with the hand. A lamp placed in the focus of the parabola, will have its divergent light thrown, after reflexion, into some- thing like a parallel beam, which will retain its intensity to a great distance. When concave mirrors are used for burn- ing, they are generally made spherical, and regularly ground What use has heen made of concave mirrors by showmen ? By what means may a dish of fruit be strikingly represented ? State the use of con- cave mirrors in light-house reflectors. How are they constructed for burning glasses ? REFLEXION OF LIGHT. 329 and polished upon a tool, like the specula used in telescopes. The most celebrated of these were made by M. Villele, of Lyons, who executed five large ones. One of the best of them, which consisted of copper and tin, was very nearly four feet in diameter, and its focal length thirty-eight inch- es. It melted the metals, as silver and copper, and even some of the more infusible earths. Burning mirrors, how- ever, have sometimes been constructed on a much larger scale by combining a great number of plane mirrors. It is supposed that it was a mirror of this kind which Archi- medes employed in setting fire to the Koman fleet under Marcellus. Athanasius Kircher, who first proved the effi- cacy of a union of plane mirrors, went with his pupil Schein- er to Syracuse, to examine the position of the hostile fleet ; and they were both satisfied that the ships of Marcellus could not have been more than thirty paces distant from Archimedes. Buffon, the celebrated naturalist, constructed a burning apparatus upon this principle which may be easily explained. He combined one hundred and sixty-eight pieces of mirror, six inches by eight, so that he could by a little mechanism connected with each, cause them to reflect the light of the sun upon one spot. Those pieces of glass were selected which gave the smallest image of the sun at two hundred and fifty feet. With one hundred and fifty- four mirrors, he was able to fire combustibles at the distance of two hundred and fifty feet. REFLEXION OF LIGHT FROM CONVEX SURFACES. 439. The oflice of a convex reflector is, in gen- eral, to separate rays of light. Hence, when ap- plied to parallel rays, it makes them diverge, to diverging rays it makes them diverge more, and to converging rays, it makes them converge less, even so much less, sometimes, as to become parallel or diverging. How were the burning mirrors of Archimedes constructed ? How were those of Buffon made ? At what distance could he set fire to combustihies 1 Convex Mirrors. — What is the general oifice of a convex reiieotor ? 28* 330 Ol-T.'CS. Thus, (Fig. 158.) the parallel rays AM, AN, falling upoh the convex mirror MN, are reflected to the other side. of the perpendiculars, CE, CE,into the diverging lines MB, ^ ^ ' ' ' NB, which appear to Pig. 159. come from F behind the mirror, which point is called the virtual focus. In like manner the diverging rays AM, AN, (Fig. 159) are rendered more diverging than be- fore, and appear to come from a point F nearer the mirror than the focus of parallel rays. 440. When an object is placed before a convex mirror, the image of it appears nearer to the surface of the mirror than the object, arid of a less size. Thus, (Fig. 160,) AB is Fig. 160. seen by the eye at ab, and the rays from every point in AB being rendered more divergent by reflex- ion, they will appear to come from a nearer ob- ject ; and since the ex- treme points a and b, are nearer to each other than A, B, the image will be smaller than the object. Convex mirrors exhibit their peculiar properties in the diminished representation which they give of the furniture of a room, as in Fig. 160 ; and as objects sometimes appear more interesting and beautiful in miniature, hence the ap- plication of such mirrors for parlor glasses. Illustrate by the figarea. When an object is placed before a convex mir- ror, where and how large is the image ? Illustrate by the figure. Why are convex mirrors used for parlor glasses ? CHAPTER III. OF THE REFRACTION OF LIGHT, AND OF LENSES AND PRISMS. 441. When light passes out of one medium into another, it is turned out of its course, or refracted, according to the following law : Light, in passing out of a rarer into a denser medium, is refracted towards a perpendicular to that medium ; and in passing out of a denser into a rarer medium it is refracted from, the perpendicular. Thus if aZ> (Fig. 161.) be the surface of a vessel of water, a ray of light AB, passing out of air (a rarer) into water (a denser medium) will not pass in the direction of BC, but will be turned towards the per- pendicular EB, and pass through the water in the line BD ; passing cut of water into air, it will be turned away from the perpendic- ular BF, and pass through the air in the direction of BA. 442. We see an example of the foregoing principle in the bent appearance of an oar in the water, the light of the part immersed (by which it is visible) being turned from the perpendicular, and causing it to appear higher than its true place ; for objects appear in the direction in which the rays of light emanating from ^. ^^^ them finally come to the eye. In the same manner, the bottom of a river ap- pears elevated, and dimin- ishes the apparent depth of the stream. Persons have sometimes been drowned in consequence of venturing into water that appeared, from the apparent el&vation Refraction of Light. — When is light said to be refracted f State the law of refraotioa ? Illustrate by the figure. Give examples of the displacement of objects by means of refraction. 332 OPTICS. Fig. 163. of the bottom, much shallower than it was. The followmg ancient experiment illustrates the same principle. If a small piece of silver be placed in the bottom of a bowl, and the eye be withdrawn until the piece of silver disappears, on fillmg up the bowl with water the silver comes into view, Fig. 162. The Multiplying Glass shows as many images of an ob- ject as there are surfaces, since each surface refracts the light that falls upon it in a different angle from the others ; of course the rays meet the eye in the same number of dif- ferent directions, and the object appears in the direction of each. The candle at A (Fig. 163,) sends rays to each of these surfaces of the glass. Those which fall on it perpendicularly, pass directly through the eye without change of direction, and form one image in its true place at A. But the rays which fall on the two oblique surfaces, have their directions changed both in entering and in leaving the glass, (as will be seen by following the rays in the figure,) so as to meet the eye in the directions of B and 0. Consequently, images of the candle are formed, also, at both these points. A multiplying glass has usually a great many surfaces Fig. 164. " |l" BUipilU Q diamouU. inclined to one another and the number of im- ages it forms is propor- tionally great. 4:4:3< Transparent hodiesdiffer munh among themselves in refracting power. That is, some bodies have the power of changing the direction of light much more than others. Thus, when a ray of light AN, (Fig. 164,) passes into water, it will be turned into the line ND ; if the medium be sulphur, which is denser than Describe the Muttiplying Glass. Do difi'erent bodies refract differently 1 Illustrate by tbe figure. REFRACTION OP LIGHT. 333 water, the direction of the light will be changed more, being refracted farther towards the perpendicular into the line NF ; and if the medium be diamond, the change will be greater still, the refraction being in the line N H. Among different bodies, certain salts of silver and lead,' the diamond, phosphorus, and sulphur, rank highest in re- fracting power ; next come the precious gems, and flint glass, containing a large portion of the oxide of lead, which has a refracting power considerably higher than crown glass, containing less metallic oxide ; to which succeed the aro matic oils. Among transparent solids, fluor spar is distin- guished for its low refracting powers ; but tabasheer, a sub- stance formed from the concreted juice of the Indian bam- boo, is more particularly remarkable for this property. 444. Lenses, on account of their extensive use in the construction of optical instruments, require very particular attention in the study of Optics. They are of several varie- ties, as is shown in the following figure. A double convex lens (A) is a solid formed by two seg- ments of a sphere applied base to base.' Fig. 165. A plano-convex lens (B) is a lens having one of its sides convex and the other plane, being simply a segment of a sphere. A double concave lens (C) is a solid bounded by two con- cave spherical surfaces, which may be either equally or un- equally concave. A plano-concave lens (D) is a lens, one of whose surfaces is plane and the other concave. • Though this is the most common form of the double concave lens, yet it is not esBential that the two segments should be portions of the same sphere : they may be segments of different spheres, in which case the curYatures will be un- equal on the two aides of the lens. What bodies rank highest in refracting power ? What second and third ? What substances are distinguished for low refracting powers ? Lenses. — State the varieties. Define the double convex leofl — a plano-convex a doable concave — a plano-concave. 334 OPTICS. A meniicus (E) is a lens, one of whose surfaces is convex and the other concave, but the concavity being less than the convexity, it takes the form of a crescent, and has the effect of a convex lens, whose convexity is equal to the difference between the sphericities of the two sides. A concavo-convex lens (F) is a lens, one of whose surfaces is convex and the other concave, the concavity exceeding the convexity, and the lens being-, therefore, equivalent to a con- cave lens whose sphericity is equal to the difference be- tween the sphericities of the two sides. A line (M N) passing through the center of a lens perpen- dicular to its opposite surfaces, is called the axis. 4:45« The office of a convex lens is to collect rays of light. When applied to par- allel rays, it makes them con- verge ; to diverging rays it makes them diverge less ; and to converging rays, it makes them converge more. More- over, with regard to diverg- ing rays, the degree of diver- gence may be reduced so much as to render the rays parallel, or even to make them converge, which will depend both on the position of the radiant and on the power of the lens. (See Fig. 166.) On the contrary, the office of a concave lens is to sepa- rate ^Ae ray« o/" /ig-fe. When it is applied to parallel rays, it makes them diverge ; to rays already diverging, it makes them diverge more ; and to converging rays, it makes them converge less, become parallel or even di- verging. (See Fig. 167.) 446. With these general principles in view, we may now advantageously investigate the manner in which ima- ges are formed by means of lenses. 1. If we place a radiant, as a candle, nearer to a lens than Describe a meniscus — a concavo-convex. What is the axis of a lens? What is the office of a convex lens 7 What is the effect on parallel rays ( diverging, and on converging rays ? What is the office of a concave fens lensl REFRACTION OF LIGHT. • 335 its principal focus, then, since the rays go out diverging, no image will be formed on the other side of the lens. 2. If we place the radiant in the focus, the rays will go out parallel, but will still not be collected into a distinct image. 3. If the radiant is removed farther from the lens than its principal focus, then the rays will be collected on the other side of the lens, so as to form a distinct representation of the object. As this last case is particularly important, since it exhib- its the manner in which the images are formed by means of convex lenses, let us examine it with more attention. 447. Bays of light diverging from the several points of any cbject, which is farther from a. convex lens than its iprmcipal focus, wUl he made to converge on the other side of the lens, to points corresponding to those from which they diverged, and will form an image. Let MN (Fig. 168,) be a luminous Fig. 168. object placed before a double convex lens L L. Now every point in the radiant sends forth innu- merable rays in eve- ry direction, part of which fall upon the lens LL. Each pen- cil may be consid- ered as a cone of rays, having for its axis, the straight line which passes through the center of the lens, which line suf- fers no change of direction, while those rays of the pencil which strike upon the extreme part of the lens, form the ex- terior parts of the cone : all the others are of course included between these. It will be sufficient to follow the course of the central and the two extreme rays. Let M L, M C, N L represent such a pencil. The two extreme rays will be col- lected by the lens and made to meet in the axis or central parfin some point on the other side, as at m. For the same reason, every other point in the object will have its corres- ponding point in the image, and all these points of the Formation of Images. — State the effects when a candle is placed neaieJ to a lens than the principal focus — or in the focus — or farther than the focus. State the proposition when rays fall upon a lens diverging from a point be- yond the focus. lUnstrate by the figure. 33(i OPTICS. image taken together, form a true representation of the ob- ject. By inspecting the figure, it will be seen that the axes of all the pencils cross each other in the center of the lens; that the image corresponding to the top of the object is carried to the bottom of the image, while that corresponding to the bottom of the object is the top of the image, and, consequently, that the image is inverted with respect to the object. It will be further seen, that although the individual rays which make up a single pencil are made, on passing through the lens, to converge, yet the axes of all the pencils go out diverging from each other, which carries them farther and farther asunder, the farther they proceed, before they come to a focus. Hence, the farther the image is formed behind the lens, the greater will he its diameter. The diameter of the image will not be altered by changing the area of the lens ; for that diameter will be determined in all cases by the distance between the axes of the two pencils which come from the extremities of the object and cross each other in the center of the lens. The size of the image, however, will be affected by changing the convexity of the lens, while the object remains the same and at the same place. 448. Eays proceeding from any radiant point, which are refracted by the different parts of tlie same lens, do not meet accurately in one focus, but their points of meeting are spread over a ce>-tain space, whose diameter is called the- SPHERICAL ABERRATION (jf the IsnS. Let LL be a pla- ■F>s- 1S9- no-convex lens, on which are incident the parallel rays KL, BL at the extrem- ities, and RL', RL' near the axis ; the axis will proceed on without any change of direction, and the rays which are very near to the axis, being also nearly per- pendicular to the refracting surface, sustain only a slight change of direction, sufficient, however, to collect them into a focus at some distance from the lens in the point F. But What is the relation between the diameter of the image and the distance behind the lens ? Is the diameter of the image affected by altering the area of the lens ? How by altering the convextiy of the lens ? State the prop- osition respecting spherical aberration. Illustrate by the figure. REFRACTION OF LIGHT. 337 the rays E.L, EL, meeting the refracting surface more ob- liquely, are more turned out of their course, and are there- fore collected into a focus in some point nearer to the lens than F, as at/. The intermediate rays refracted by the lens will have their foci between F and/ Continue the lines L/ and L/ till they meet at G- and H, a plane passing through F, perpendicular to the axis. The distance /F is called the longitudinal spherical aberration, and G-H the latitu- dinal spherical aberration. It is obvious that such a lens cannot form a distinct pic- ture of any object in its focus F. If it is exposed to the sun, the central parts of the lens L' m L', whose focus is at F, will form a pretty bright image of the sun at F ; but as the rays of the sun which pdss through the outer part LL of the lens have their foci at points between/ and F, the rays will, after arriving at these points, pass on to the plane G H, and occupy a circle whose diameter is G H ; hence the image of the sun in the focus F will be a bright disk, sur- rounded and rendered indistinct by a broad halo of light growing fainter and fainter from F to G and H. In like manner, every object seen through such a lens, and every image formed by it, will be rendered confused and indistinct by spherical aberration. If we cover up all the exterior portions of the lens, so as to permit only those portions of the rays which lie near the axis to pass through the lens, then the rays all meet at or very near to the point F, and a much more distinct image is formed ; but so much of the light is excluded by this pro- cess, that the brightness of the image is considerably dimin- ished. The dimensions of the image are the same in both cases. 449. The Prism is an important instrument in Optics, especially as it affords the means of decomposing light,"and eniers into the construction of several optical instruments. The triangular prism is the only one employed in experi- ments, and of this nothing more is essential than barely the inclination of two plane transparent surfaces to one another. The optical prism, however, is usually understood to be a piece of solid glass, having two sides constituted of equal parallelograms, and a third side called the base. The line of the intersection of the two sides is called the edge, and the What is the longitvdinal, and what the latitudinal spherical aberration ? What will be the effect of covering the exterior portions of the lens 1 Prism. —What is said of its importance 1 How is the triangular prism constructed ? 29 838 OPTICS angle contained by the sides, the refracting angle of the prism. A straight line passing lengthwise of the prism, through its center of gravity, and parallel to the edge is called the axis. A section made by a plane perpendicular to the axis, is an isosceles triangle. Frequently, the three angles of the prism are made equal to one another, each be- ing 60 .* Figure 170 represents a section of a prism ABC, of which A B is the 6ase, and rig. 170. A C B the refracting angle. D E is a beam of the sun's light falling obliquely on the first surface A C, where one portion is reflected but another portion transmitted. The latter portion instead of proceeding forward directly in the dotted line, and forming an image of the sun at H, is turned upward toward the perpendicular P P, meeting the opposite surface C B in F, where it is again turned upward from the perpendicular P P, in the direction F Gr, elevating the image of the sun from H to G. CHAPTER IV. OF THE SOLAR SPECTRUM, OF THE RAINBOW, AND OF COLORS IN NATURAL OBJECTS. 450. In tracing the course of rays of light through a re- fracting medium, we have thus far supposed them to be ho- • A very convenient priam for common experiments may be constructed as fol • lows : Select two plates of window glass of the best qtiality, or better, Iwo pieces of looking glass from which the silverins: has been removed. Tlie plates may bo five or six inches long and one and a half or two inches broad. They are to be united at their edges at an angle of about sixty degrees, and furnished with a tin case, which shall afford the base and the two ends, and a covering for the edge. One of the ends has an orifice with a stopper, for the convenience of filling with a fluid, which may be pure water, or better, a saturated solution of the sugar of lead filtered perfectly clear. Projections may be attached to the two ends to serve as handles or as an axis on which the prism may rest on supports. Instead of the tin case, we may employ a block of hard wood, first formed into a triangular prism, and then dug out so as to admit the plates. Wliat is the refracting: angle ? What is the axis ? Describe the mode of making a cheap prism. Show the effect of a piism by the figure. THE SOLAR SPECTRUM. 339 mogeneous, and to be all affected in the same manner. But in nature the fact is otherwise ; that is, the sun's light con- sists of rays luhich differ in refrangiiility and in color. The glass prism, in consequence of the strong refraction of light which it produces, (see Art. 449.) is well fitted for experiments of this kind. We procure, therefore, a triangu- lar prism of good flint glass, and having darkened a room, admit a sunbeam obliquely through a small round hole in the window shutter. Across this beam, near the shutter, we place the prism, with its edge parallel to the horizon, so as to receive the beam upon one of its sides. The rays, on passing through the prism, will be refracted and thrown up- wards, as will be rendered evident by conceiving perpendic- ulars drawn to the surface of the prism at the points of inci- dence and emergence. If now we receive the refracted rays upon a screen, at some distance, they will form an elongated image, exhibiting the colors of the rainbow, namely, red, orange, yellow, green, blue, indigo, violet, together compo sing ihs prismatic spectrum. (See Fig. 171.) Fig. 171. S, is a sunbeam ; F, a hole in the window shutter; AB C, the prism, having its refracting angle ACB downwards ; Y, a white spot being an image of the sun formed on the floor before the prism is introduced. A pleasing way of exhibiting the separate colors of the spectrum, is to throw the prismatic beam on a distant wall or screen, so as to form a long spectrum, and into this beam, Of what different kinds of rays does the sun's light consist? Describe the mode of forming the prismatic spectrum. Illustrate by the figure. What screen is used to receive the image ? 340 OPTICS. at some convenient distance from the prism, to introduce a concave lens of a size sufficient to cover each of the different colored pencils successively. The lens will cause the rays of the same color to diverge, and to form a circular image on the screen, which will distinguish them very strikingly from the contiguous portions of the spectrum. 451. If rays of the same color in the prismatic beam he insulated from tlie rest, and made to pass through a second prism, they are refracted as usual, (the aiTumnt of refrac- tion being different from the different colored rays^ but they undergo no farther change of color. To perform this experiment, we provide a board, perfora- ted with a small round hole, and mounted on a stand. This screen is placed across the prismatic beam, a little way from the prism, in such a manner as to permit rays of the same color only to pass through the aperture while the other por- tions of the beam are interceptisd. The homogeneous light thus insulated is made to pass through a second prism, and its image is thrown on the wall. The experiment will be more perfect, if the ho;nogeneous pencil be made to pass through a second screen similar to the first, so as to let only the central rays fall upon the second prism. This second refraction produces no change of color. It will be found, however, that, while all other things remain the same, the several images formed of homogeneous rays will occupy dif- ferent positions on the wall, the red being lowest and the violet highest, and the intermediate colors arranged between them in the order of their refrangibilities. (See Fig. 172.) rig. 172. In addition to the parts of the figure enumerated in Fig. 172, DE represents the first screen, which permits only one State the proposition respecting the refraction of rays of the same color niustrate by the figure. THE SOLAR SPECTRUM. 341 sort of rays to pass by a small aperture at Gr, and d e repre- sents a second screen, which permits only the central rays of this pencil to pass by a small hole sX g ; a b c\s the sec- ond prism, and M is the image of the homogeneous light on the wall. 45 2« The light oftJie sun reflected frcrni the first surface vf bodies^ and also the white flames of all combustiiles^ wlieth- er direct or reflected, differ in color and refrangiiility, like the direct light of the sun. The truth stated in this proposition was established by Newton, by experiments with the prism, similar to those detailed in connection with the preceding propositions. 453a Tlie surOs light is compounded of all tlie pris- matic colors mixed in dvs proportion. If we collect by means of a convex lens, the different col- ored pencils in the prismatic beam, just after they have emerged from the prism, (see Fig. 171,) the image formed by the lens will be perfectly white. A concave mirror may be used instead of the lens, the image being thrown on a screen. Or the rays after they have passed the prism may be received on a second prism of the same kind, placed near the first, with its refracting angle in the opposite direction. In this case the second prism restores the light to its usual whiteness. That all the different colors of the spectrum are essential to the composition of white light, may be rendered evident by intercepting a portion of any one of the colors of the spectrum before they have all been re-united, as in the fore- going experiments. Thus, if we introduce a thread or a wire into any part of the prismatic beam between the prism and the lens, the image formed by the lens will be no longer white but discolored. If, instead of the wire, an instrument shaped like a comb with coarse broad teeth, be introduced into the beam, the discoloration of the image is more diver- sified, the colors of the image being thus compounded of the prismatic colors, which are not intercepted by the comb. If the teeth of the comb be passed slowly over the beam, a suc- cession of different colors appears, such as red, yellow, green, blue, and purple ; but if the motion of the comb be rapid, all these different hues become blended into one by the momen- What other kinds of light differ in color and refrangibility like the direct light of the Ban ? Of what is the sun's light compounded 1 How may we restore the colors of the spectrum to the original white ? How does it appear that all the colors of the speotrom are essential to white light! 29* 342 OPTICS. tary continuance of each in the eye, and the sensation is that of white light. 454. For a similar reason, if the colors of the spectrum are painted on a top, in due intensity and proportion, and the top be set to spinning, the sensation will be that of white light. Or the colors of the spectrum may be first laid on a sheet of paper, and this may be pasted on a cylinder of wood, which may be made to revolve on the whirling ta- bles : the result will be the same. Newton tried various experiments with different colored powders, grinding togeth- er such as corresponded as nearly as possible to the colors of the spectrum. By this means he was able to produce, from the mixture of seven different colored powders, a gray- ish white, but could never reach a perfectly clear white, owing to the difficulty of finding powders whose colors cor- responded exactly to those of the spectrum. 455. Several of the colors oftlve spectrum may he pro- duced by the mixture of otlier colors ; as green by tlie union of yellow and blue, orange by red and yellow, ^'C Experi- ments were devised by Newton for thus combining the colors of two contiguous spectrums, transferring, for exam- ple, the blue of one to the yellow of the other, and forming green by their union. On causing this compound green, however, to pass through the prism, it is resolved into its original colors, yellow and blue, whereas the green of the spectrum is not thus resolved by the prism. Hence Newton infers that the green of the spectrum is not a compound but a simple original color, and so of all the rest. 456. The knowledge of the composition of light, and of the properties of the solar spectrum, naturally lead to an inquiry into the subject of colors, as exhibited in the phe- nomena of nature. The bright tints of the rainbow, the splendid hues sometimes exhibited by thin plates, as soap bubbles, and finally the diversified colors in all the king doms of nature, remain to be accounted for. Some of these we proceed to explain, but others are of a nature too intri cate for the present work. State the experiment with a top or a cylinder,— also Newton's experi- ments to produce white light. How may individual colors of the spectrum be formed ? In what respect does the green of the spectrum differ from the compound green? THE KAINBOW. 343 THE RAINBOW." 457. The rainbow, one of the most striking and mag- nificent of the phenomena of nature, was long ago supposea to be owing to some modification which the light of the sun undergoes in passing into drops of rain ; but the complete development of the causes on which it depends, was reserved 'for the genius of Newton, and naturally followed in the train of those discoveries which he made upon the prismatic spectrum. The rainbow, when exhibited in its more perfect forms, consists of two arches, usually seen in the east during a shower of rain, while the sun is shining in the west. These arches are denominated the outer and the inner bow, of which the inner bow is the brighter, but the outer bow is of larger dimensions every way. The succession of colors in the one is directly opposite to that of the other. 458. Drops of rain, though small, are large in compari- son with the minuteness of rays of light, and are to be re- garded as spheres of water, exerting the powers of refraction and reflexion in the same manner as large globes of water would do. It was, in fact, by investigating the manner in which globular glass ve.=sels filled with water modify the solar rays, that the first hints were obtained respecting the cause of the rainbow. In the year 161 1, Antonio de Domi- nis made a considerable advance towards the theory of the rainbow, by suspending a glass globe in the sun's light, when he found, that while he stood with his back to the sun, the colors of ^'^" ^''^ the rainbow were reflected to his eye in succession by the globe, as it was moved higher or lower. Let us, therefore, in the first place, follow the course of a ray of light through a globule of water. Let SA (Pig. 173,) be a small beam of light from the sun, falling upon the surface of a globule of water at * The theory of the Rainbow iB necessarily somewhat intricate, and possibly may prove too difficult fur the young learner, though we shall endeavor to make it as plain as possible. Rainbow. — ^Who first developed its true theory ? Of what does it conEist t How does the succession of colors in one compare with that in the other 7 Slate the experiments of Antoiiio de Dominis. Explain by the figure. 344 OPTICS. A. Agreeably to what is known of the laws of light m passing out of one transparent medium into another, a por- tion of the rays would be reflected at A, and another por- tion would pass into the drop, and be refracted to the far- ther surface at B. The same effect would recur here, and also at D, and at P ; and were the eye situated in either of the lines B C, D E, or F G, it would perceive the prismatic colors, because some of the rays which composed the beam of light that reached the eye would be refracted more than others, and thus the different colors would be made to ap- pear. Or if a screen were so placed as to receive these transmitted rays, a faint spectrum would be formed upon it. Such a progress of a beam of light admitted through the window shutter, and made to fall on a globular vessel of water, may be actually rendered visible by experiment. 459. It may be remarked that but a comparatively small part of the solar rays that shine upon a drop of water, are required in order to produce the mild light of the rain- bow, aided as its light is by the dark ground or cloud on which it is usually projected ; yet, where the number of rays that enter the eye is diminished beyond a certain limit, the light becomes too feeble for distinct vision. It will also be observed, that a considerable portion of light is lost at each successive reflexion that takes place within the drop, so that a certain beam of light conveyed to the eye after two reflexions, will be much more feeble than the same beam after one reflexion. Indeed, so much of the sun's light is dissipated at the first point of reflexion from the interior sur- face, added to what is transmitted at the same point, and of course never reaches the eye of the spectator, that, were it not for a great accumulation which the sun's rays undergo at a particular point on this drop, whence the light is re- flected and conveyed to the eye, the phenomena of the rain- bow would not occur. The manner in which this accumu- lation is effected is now to be explained. 460. Letfzpq (Pig. 174,) be the section of a drop of rain, fp a diameter, ab, ed, &c. parallel rays of the sun's light, falling upon the drop. Now y/' a ray coinciding with the diameter, would suffer no refraction ; and ab. a ray near to y/. would suffer only a very small inclination towards the radius, so as to meet the remoter surface of the drop very near to^; but the rays vrhich lie farther from yf. being in- How large a portion of the light that falls on drops of rain goes to form the rainbow? Explain how an accumulation of light takes place in a certain pai't of the drop. THE RAINBOW. 345 / '^ — ^: ^'■■■■■^ \ / t a r ■■■.... =4* --^-z^ V clined towards the radius in a greater angle, would be more and more refracted as they were farther removed from the diameter. The consequence would be, that after passing a certain limit, the rays that lay above the limit would cross those which lay below it, and Fig. 174. meet the fur- ther surface somewhere be- tween the di- ameter and the ray which pas- sed through the said limit ; that is, all the rays falling on the quadrant f z, would meet the circumference within the arc kp. But when a quantity is approaching its limit, or is beginning to deviate from it, its variations are nearly insensible. Thus, when the sun is at the tropics, being the limits to, which he departs from the equator, he appears for some time to remain at the same point. In the same manner, a great number of the rays which lie contigu- ous to e d, on both sides of it, will meet in very nearly the same point on the concave surface of the drop at k ni. Con- sequently, a greater number of rays will be reflected from that point than from any other in the arc. Moreover, they emerge nearly parallel, and therefore more of them will enter an eye favorably situated, than if they passed out di- verging. On both these accounts, it appears that there is a particular point in a drop of rain, where the rays of the sun's light seem to accumuJute, and are therefore peculiarly fitted to make an impression on the organ of vision. It is found by calculation, that the angle which the incident and emer- gent rays, in such cases, make with each other, is, for the re^ rays, 42 2', and for the wioto rays, 40 17', These are the angles when the rays emerge after two refractions and What angle do the incident and emergent rays make with each other iq the case of the red and the violel rays respectively 1 346 op'rics. one reflexion : in the case of two refractions and two re- flexions, the angles are, for the red rays, 50' 59', and for the violet 54° 9'. 461. Let us next consider what must be the position of the spectator in order that his eye may receive the emergent rays which make the foregoing angle with the incident rays, and which of course are those which cause the phenomena of the rainbow. The spectator must stand with his back to the sun, and a lijie drawn from the sun towards tlie how, so as to pass through his eye, will make the same angle vnth the emergent rays that they malce with tlie incident rays. Thus, let A B Fig. 175. be the incident and GrI the emergent ray, and let the angle which these two rays make with each other be AKI ; and let IT be a ray passing from the sun towards the bow through the eye of the spectator; then, (since the rays of the sun may be regarded as parallel,) AB and IT are parallel, and the alternate angles AKI and KIT, equal. But AKI is the angle made by the incident and emergent rays, and KIT the angle made by^ the emergent ray and a line drawn from the sun towards the bow through the eye of the spectator. 463. When the sun shines upon tlie drops of rain as they are falling, the rays which come from these drops to the What must be the position of the spectator with respeqf to the son 7 Where does a line drawn from the sun, through the eye, pass with respect to the bow f Explain by the figure ? How are the rays refi-aoted and reflect- ed to produce the inner, and how to pi'oduce the outer bow 1 THE RAINBOW. 347 mje of the spectator^ after one reflexion and two refrac- tions, produce the innerinost or primary rainbotv ; and those rays which come to the eye after two reflexions and two REFRACTIONS, produce the outermost or superior rainbow. Let SOC* be a straight line passing- from the center of the sun through the eye of the spectator at towards the bow, and let SR, SV, be in- cident rays, which, after one reflexion and two refractions, are conveyed to the eye at 0, making (Art. 461.) with SOC angles equal to those formed by the incident and emergent rays. If OV makes with SOC an angle of 40 17', and be conceived to revolve around OC, describing the surface of a cone, all the drops of rain on this surface will be precisely in the situation necessary in order that the violet rays, after two refractions and one re- flexion, may emerge parallel and arrive at the eye in 0, and this will not take place in the same manner in any part of the cloud ; so that by means of this species of rays, the spectator will see on the cloud a violet colored arc, of which OC will be the axis, and C the center. He will see, also, an infinity of other concentric arcs exterior to the violet, each one of which will be made up of a single species of rays ; and according as these rays are less refrangible, their areas will be of greater diameter, so that the largest, com- posed of the extreme red, will subtend an angle ROC of 42° 2'. Therefore, the whole width of the colored bow will be 42° 2' — 40 1 7' or 1 ' 45', the red being on the outside and the violet vsrithin. The contrary order of colors will result from two reflex- ions and two refractions. Let SV, SR', be the incident rays, which after two reflexions and two refractions are con- verged to the eye at 0, making (Art. 46 1 ,) with SOC angles equal to those formed by the incident and emergent rays, namely ."iO- 59' and 54 9' and the lines R'O and VO, as * It will be observed that Ihe line SOC is at right angles to the plane of the paper, that is, to the plane of the bows. State the proposition. Of how many degrees is the angle contained by lines drawn from the eye to the center and to the top of the bow '' What i^ the width of the inner and of the outer bow 1 348 OPTICS. before, be conceived to revolve around SOC ; they will seve- rally meet with all the drops, which having twice refracted and twice reflected the extreme red and violet rays, can transmit them to the eye. Between these two arcs there will be others, exhibiting all the intermediate prismaiij colors; and the whole together will form a second bow, whose breadth will be 54 9'— 50 59', or 3° 10. 463. The rays, therefore, which come from a 1 the drops which raalie an angle of 42 ' 2' with a line passing from the sun through the eye (which may be called the axis of vision. ) appear red ; and it is obvious that a collection of rays drawn all around this axis from the eye to drops thus situated would form a cone, of which the drops themselves would constitute the base, and of course would form a circle. The same is true of all the other colors which emerge from drops at angles which are different for different colors but constant for the same color. Hence, t/ie line which passes from the sun through tlte eye of the spectator, passes also to t}ve center of the how, or is the axis of the cone of which the bow itself is the base. If the sun is on the horizon, this axis becomes a horizontal line ; consequently, the center of the arch rests on the opposite horizon, and the bow is a semicircle, of which the highest point has an altitude above the horizon of 42° 2'. If the sun is at this altitude of 42 2' above the horizon, then the center of the bow will have the same de- pression below the opposite horizon, and the same circum- ference, at its highest point, will just reach the horizon. When the sun is between these two points, the elevation of the bow will be the difference between the altitude of the sun and the foregoing angle. 464. When the spectator is on an eminence, as a high mountain, he may see more than half the bow, when the sun is near setting ; for the axis will in that case pass to a point above the opposite horizon. Travellers who have ascended very high mountains, have occasionally observed their shadows projected on the clouds below, with their heads en- circled with rainbows. In this case, the axis passes to a point above the opposite horizon equal to or greater than the semi-diameter of the bow, so that the whole of the circum- ference comes into view ; and the eye of the spectator being What 18 the position of the axis when the sun is in the horizon ? What part of a circle is the bow in this case ? Where is the center ? What is its altitude above the horizon ?■ Explain the formation of rainbows arouiid the heads qf travellers on high mountains? ATMOSPHERIC KEFRACTION. 349 in the axis, the entire bow is projected around that as a cejiter. upon the surface of the clouds. 46 5 • Haloes, or luminous circles around the sun and moon. When the clouds (usually of the form denominated cirro- stratus) pass over the sun or the moon, these luminaries become encircled with one or more colored rings called ha- loes. These sometimes consist of a single ring, or at most of two concentric rings, tinged on the margin with a feeble red ; but, occasionally, there is seen around the sun a much more complex system of rings, variously interlocked, and colored with more or less of the prismatic hues. These ap- pearances are ascribed in general to the separation of the rays of light in passing through crystals of ice or snow in the region of the clouds ; for it is well known that such par- ticles sometimes exist in the region of perpetual congelation, when the temperature of the air near the surface of the earth is too high to permit their existence at a less eleva- tion. The most common form of halo is a circle about 45 ' in breadth ; and it is found on investigation, that crystals of ice of certain known figures, are capable of refracting and reflecting the light of the sun or moon in such a way as to present these appearances. But hardly any explanation has yet been devised, adequate to account for all the varied and complete forms which haloes sometimes assume.* ATMOSPHERIC REFRACTION. 466. The rays of light from any object,in coming through the atmosphere, are bent out of their course as they traverse the successive stiata of the atmosphere, and more and more as they approach nearer to the earth, where the atmospheric strata rapidly increase in density ; and since an object appears in the direction in which the light finally reaches the eye, the effect of this refraction is to make objects appear higher than their actual position. Thus, in figure 177,8 represents a ray of the sun's light coming to the eye at 0, through successive layers * See a good account of this subject in Brocklesby's Meteorology, p. 199. Haloes.— -When do they occur? Their form? To what are they as- cribed / Size of the most common form 1 Atmospheric Refraction. — When is ligh said to undergo atmospheric refraction ? Docribe Fig. 177. 30 350 orTics. of air which bend it out of its course, so as to make it finally meet the eye in the direction S' 0, elevating the apparent place of the sun from S to S'. Peculiar states of the atmosphere sometimes cause the light to undergo unusual refraction, and to form distorted or inverted images of objects. Ships appear elevated into the atmosphere, appearing at one time erect and at another inverted, and this sometimes happens when the ship itself is belovir the horizon, and consequently out of sight. In Egypt, the air is so misty, when the sands are heated by the sun, as to present the phenomenon called mirage, when an extended plane puts on the appearance of a lake, and the vil- lages situated on eminences seem to stand on islands in the lake. A celebrated example of the effects of unusual atmos- pheric refraction occurs ne ir the straits of Messina in Sicily, and is called /n^a morgana. A spectator on an eminence in the city of Keggio, with his back to the sun and his face to the sea, at a certain hour of the day, sees upon the water numberless distinct appearances of architectural structures, as arches, castles, towers, superb palaces with balconies and windows, villages and trees, plains with herds and flocks, armies of men on foot and on horseback, and, in short, all the scenes and objects of the neighboring region and the city. Sometimes, indeed, these sights are seen in the air as well as on the water, though somewhat less distinctly. COLORS OF BODIES. 467. According to the Newtonian theory, the color of s Dody depends on the kind of light which it reflects. A grea' number of bodies are fitted to reflect at once several kinds of rays, and consequently appear under mixed colors. It may even happen that of two bodies which are green, foi example, one may reflect the pure prismatic green, and the other the green which arises from the mixture of yellow and blue. The quality of selection, as it were, in bodies, which varies to infinity, occasions the different kinds of rays to unite in every possible manner and every possible propor- tion ; and hence the inexhaustible variety of shades which nature, as in sport, has diffused over the surfaces of different bodies. When a body absorbs nearly all the light that reaches it, What appearances are produced by tinnsual refraction 7 Describe thp«9 that oc( ar in Egypt and in Sicily. On what does the color of a body de- pend? NATURE OF LIGHT. 351 that body appears black ; it transmits to the eye so few re- flected rays, that it is scarcely perceptible in itself, and its presence and form make no impression on us, unless as it interrupts, in a manner, the brightness of the surrounding space. NATURE OP LIGHT. 468. The phenmnena of light may be explained, either on the supposition that light is a material fluid of extreme subtilty, or that it is produced by the undulations of an in- dependent medium, set in motion by tlie luminous body. Opticians of great eminence have held the opinion,that light does not consist of actual emanations of material particles from the luminous body, but that such a body has merely the property of communicating a series of vibrations to a peculiar fluid that is diffused throughout the universe, which vibrations form the communication between the luminous body and the eye. The medium is conceived to be of ex- treme tenuity and elasticity ; such, indeed, that though fill- ing all space, it offers no appreciable resistance to the mo- tions of the planets and comets, capable of disturbing them in their orbits. It is, moreover, imagined to penetrate all bodies ; but in their interior to exist in a different state of intensity and elasticity from those which belong to it in a disengaged state, and hence the refraction and reflexion of light. Newton, however, and other distinguished philoso- phers, have held that light consists of actual particles of matter sent off from luminous objects to the eye. In the former case, the fluid is only the medium of light, as air is the medium of sound, the vibrations of the medium fol- lowing each other as wave follows wave, with incredible swiftness, and thus conveying the impression from the ra- diant to the eye ; in the latter case, the motion is that of a chain oi particles of luminous matter, moving in right lines with the same astonishing velocity. Thus, when the sun rises, it either sends forth luminous particles, which, enter- ing the eye, occasion the sensation of vision ; or it puts in motion the peculiar fluid which is the medium of light, which motion is propagated from wave to wave till it reaches the eye. It is a strong argument in favor of the materiality of When does a body appear black ? Nature erf Light. — How may the phexiom- ena of light be explained 1 What is the undulatory theory of light as held by some opticians ? What did Newton hold respecting the materiality of light 7 352 OPTICS. light, that it exhibits the property of attraction, one of the most characteristic properties of matter ; and the motion is conformable to the laws which regulate the motions of small bodies under the same circumstances. It also produces cer- tain chemical changes in bodies which belong to none but a material agent. Either hypothesis, however, serves to ex- plain a great part of the optical phenomena ; but the more recent and refined discoveries of the science have favored the theory of undulations, so that authority at present greatly inclines to this view of the nature of light. Thus, as two waves of sound, by their interference, produce silence, (Art. 314,) so two waves of light may interfere in such a manner as to produce darkness, — a fact which indicates a strong anal- ogy betvi^een sound and light in their modes of production. 469. Within a few years great prominence has been given, in treatises, on Optics, to the subject of the Polar- ization of light. Polarization of light is a cliange which light undergoes after certain refractions or reflexions, by which a ray ac- quires polarity, or different properties on different sides. A great manycurious and elegant phenomena of light are developed and explained by the doctrine of polarization ; the subject, however, is for the most part too intricate to be well understood by the class of pupils for whom this work is es- pecially intended, and we deem it more important to them to occupy their attention with subjects more practically use- ful, referring such as may desire to become acquainted with this and other recondite matters connected with the study of Optics, to our larger treatise on Natural Philosophy (Col- lege Philosophy,) and to more elaborate and extended works. CHAPTEK V. OF VISION. 470.. As a preparation for studying the optical struc- ture of the eye, and the laws of vision, it will be useful first to learn in what way images of external objects are formed What facta favor the latter and what the former theory? Vision.—StOLe the proposition respecting the formation of an image of the son in a dark room? VISION. 353 in a dark room, by light admitted through a hole in the win- dow shutter. A beam of light from the sun, entering into a dark room through a small orifice, and striking upon an opposite wall or screen,forms a circular iniage on tlte wall, whatever.is tlic shape of the wifice. We will suppose the orifice to be comparatively large, as an inch in diameter, and of a triangular or of any irregular shape ; the image formed on the wall will still be circular. For, suppose the orifice to be reduced to a very small circu- lar hole, as a pin hole, (which may easily be done by pla- cing over the orifice a metallic plate, as a sheet of lead, pierced by a drill,) then the rays of the sun passing through this small opening would of course be circular. But the large irregular orifice may be considered as made up of such smaller apertures, or the metallic plate may be conceived to be pierced with an indefinite number of pin holes, and the entire image formed upon the wall may be conceived to be made up of an assemblage of all these images of the sun blended with each other, and therefore as bounded by innu- merable curve lines composed of the individual circles. If the screen be brought near to the orifice, however, the image will be of the same figure as the orifice ; for the rays after they have passed the orifice, must have diverged considerably before the sections that form the image shall afford circles so large, that their blended circumferences shall compose a cir- cular figure. (See Fig. 178.) If the plane which receives the image be not parallel to the orifice, the image will be elliptical, being the section of a cone oblique to its axis. Circular images of the sun are sometimes projected on the ground; through the small openings among the leaves of trees. During an eclipse of the sun, these images copy the figure of the eclipse. If there be various orifices near to each other, thre", for example, through which a beam of the sun shines into a why is the ima^e of the sun on the ■wall circular with diiferent shaped orifices ? What shape is the fig:ure when the screen is oblique to the ori- fice? Explain the figures projected on the ground nnrler trees in eoli ses of the sun. 30" 354 OPTICS. dark room, we shall observe at first, at a certain distance, three distinct luminous circles. At a greater distance these three circles begin to be blended, and finally, on enlarging sufRciently, they unite to form a single circle. 471. If., instead of a beam of solar light, toe admit into a dark room., through an opening in the shutter., tlte light eflected from various objects without., an inverted picture of tliese objects vjill he formed on tlie opposite wall. A room fitted for exhibiting such a picture is called a Camera Obscura. From what has been before explained, it will be readily understood, that from every point in the object, innumerable rays of light proceed and fall upon the window shutter. Of these, however, none can enter the aperture except such as are very near to each other, all others diverging too far to enter a small opening. It is essential to the distinctness of the picture, that rays which proceed from every point in the object should be collected into coiTesponding points in the image, and should exist there free from any mixture of rays from any other point; and it is essential to the brightness of the picture, that as many rays as possible should be con- veyed i'rom each point in the object to its corresponding point in the image. To render the picture distinct, there- fore, the opening ia the window shutter must be small, else the pencils of rays from different points will overlap each other, and confuse the picture ; but as the orifice is dimin- ished, the brightness of the picture is impaired, since, in this case, a smaller number of rays is conveyed from the ob- ject to the image. These modifications of the picture according to the size of the aperture, may be easily exhibited by beginning with a circular aperture two or three inches in diameter, and re- ducing its size gradually by covering it with apiece of board or a metallic plate, perforated with holes of different sizes.* ' A small room, ten feet square, for example, having a window opening towards an unobstructed landscape, mny easily be converted into ii camera obscura. The perforation in the shutter must be made equidistant from the sides of the room ; and from the aperture as a center, with a radius equal to the distance of the opposite wall, describe an arc of a circle, upon which as a base a new concave wall is to be constructed, flniahed with stucco. The other walls and ceiling are to be colored a dead black, while the concave wall, for receiving the image, is made aa white as possible. On admitting the light Ihrougli an aperture half an inch in diameter, a beautiful and distinct picture will be formed on the opposite wall. State the propo.'iition vespectinf! the camera obscura. AVhat is essential to the distinctmss of the picture ? What to its brightness 1 Why must the opening in the window shutter be small ? What kind of room is suitable for a camera obscura? How must it be fitted up ? VISION. 355 472. If , instead of passing through the naked orifice, the rays be received on a convex lens, an inch and a half or two inches in diameter, fixed in the window shutter, a very tn-ight and distinct picture of the external landscape xvUl he for mod on a screen placed at tlie focal distance of the lens. The image is brighter and more distinct than when formed without the aid of the lens, first, because the diame- ter of the lens may be so great as to receive and transmit a much larger portion of the rays which proceed from each point of the object, than would be compatible with distinct- ness, if so large a naked aperture were employed ; secondly, because the rays of each pencil are brought more accurately to a separate focus ; and, thirdly, because the picture being formed nearer to the window shutter, it is smaller, and of course the light, being spread over less space, is more intense. A convex lens fixed in a ball, is used for this purpose, Avhich is so attached to the opening in the shutter as to be capable of being turned towards different parts of the land- scape, like the eye-ball in its socket. Such a lens, with its accompanying parts, is called a Scioptic ball In a bright sunny day, when the sun is on the side of the house opposite to the shutter, and of course illuminating the sides of objects which face the window, we may form, either with or without the aid of the scioptic ball, a very striking and beautiful picture of external objects, exhibiting each in its relative situation, of a size and brightness corresponding to its distance, with all the colors and the most delicate motions of the landscape. The name camera obscura, which appropriately belongs to such a chamber, is also extended to certain boxes in which similar pictures are formed, with pe- culiar devices for rendering the image erect instead of in- verted. The structure of these portable camera obscuras, will be described more particularly among other optical in- struments. 473. The eye is a camera obscura, and the analogy existing between its principal parts, and the contrivances employed to form a picture of external objects, as in the pre- ceding experiments, will appear very striking on comparison. The eye consists of three principal chambers, filled State the proposition respecting the formation of the jjicturc bjj the aid of a lens. Why is it brighter and more distinct ? What is the scioptic ball ? rAe Eye. — What are its three principal chambers ? 356 OPTICS. Fig. 179. with media of perfect transparency. The first of these media A, occupying the anterioE chamber, is called the Aqueous Humor, and consists chiefly of pure water. The cell in which the aqueous humor is contained, is bounded on its anterior side, by a strong horny, and delicately transpar ent coat, aa, and is called the cornea. The posterior surface of the chamber A of the aqueous hu- mor, is limited by the Iris cc, which is a kind of circular epake screen, consisting of muscular fibres, by whose contraction or expansion an aper- ture in its center, called the pupil, is diminished or dilated according to the intensity of the light. In very strong lights, the opening of the pupil is greatly contracted, so as not to exceed twelve hundredths of an inch in the human eye, while in feebler illuminations it dilates to an opening not exceeding twenty-five hundredths, or double its former diameter. The use of this is evidently to moderate and equalize the illumination of the image on the retina which might otherwise injure its sensibility. In animals, as the cat, which see well in the dark, the pupil is almost totally closed in the day-time, and reduced to a very narrow line; but in the human eye, the form of ihe aperture is always circular. The contraction of the pupil is involuntary, and takes place by the effect of the stimulus of the light itself; a beautiJul piece of self-adjusting mechanism, the play of which may be easily seen by bringing a candle near to the eye, while directed to its own image in a looking-glass. Im- mediately behind the opening of the Iris, lies the Crystul- ine Lens, B, enclosed in its capsule, which forms the pos- terior boundary of the chamber A. The figure of the crystaline lens is a solid of revolution, having its anterioi surface much less curved than the posterior. The consis- tence of the crystaline is that of hard jelly, and it is purer and more transparent than the finest rock crystal. In the crystaline a very curious and remarkable contriv- ance is adopted, for overcoming or preventing the spherical Desribe the aqueous humor — the iris, and the pupil. What changes does the pupil undergo 1 Describe the crystaline lens. VISION. 357 aberration that (Art. 448.) belongs to lenses of this form, which refract the rays more towards their marginal than near their central parts, and hence do not bring all the rayS belonging to one pencil to the same focus. Here the diffi- culty is obviated by giving to the central portions of the cryst&line a. proportionally greater density, thus increasing its refractive power .'^o as exactly to correspond to that of the other portions of the lens. The posterior chamber C of the eye is filled with the Vit- reous Humor. Its name is derived from its supposed resem- blance to melted glass; it is a clear, gelatinous fluid, very much resembling the white of an egg. Rays of light di- verging from various objects without, or passing through the aqueous humor, (which is a concave convex lens) have their divergency much diminished, or even, in most cases, are rendered converging, and in this state are transmitted through the erystaline, which has precisely such a degree of refractive power as enables it to bring them to a focus at the distance of the retina, which, as a screen, is spread out to receive the image. The retina, as its name imports, is a kind of white net-work, like gauze, formed of inconceivably delicate nerves, all branching from one great nerve 0, called the optic nerve, which enters the eye obliquely at the inner side of the orbit next to the nose The retina lines the whole of the cavity C up to ^^, where the capsule of the erystaline commences. Its nerves are in contact with, or immersed in, the pignmntum, nigrum, a very black velvety .matter, which covers the choroid memh'ane, mm, and whose office is to absorb and stifle all the light which enters the eye as soon as it has done its office of exciting the retina ; thus preventing internal reflexions, and consequent con- fusion of vision. The whole of these humors and mem- branes are contained in a thick tough coat, called the schrotica, which unites with the cornea and forms what is called the wkite of the eye. 474. Such, in general, is the structure by ■whida. paral- lel rays, and those coming from very distant objects, are brought to a focus on the retina. But there are special con- trivances, suited to particular purposes, which are no less evincive of design and skill than the general organization of the eye. Some of the most remarkable of these we pro- How is it so constructed as to prevent spherical aberration ? Describe th i vitreous humor — the retina — the optic nerve. Describe the pigmentum Digram — tlie choroid membrane — the sclerotica. 358 OPTICS. ceed to mention. The cornea, by protruding, collects the rays of light that come to the eye laterally, and guides them into the eye, thus enlarging the range of vision. It answers to an appendage to the microscope, which will hereafter be described under the name oi field glass. The motion of the eye-ball, by means of which the pupil may be turned in different directions, conduces to the same purpose. Hence, notwithstanding the minuteness of the aperture which ad- mits the light (and it must be small, otherwise the image will not be distinct) the eye may take in at once, without moving the head, a horizontal range of 110° and a vertical range of 120 , namely, 50 above, and 70° below a horizon- tal line. 475. As the radiant approaches the lens, the image re- cedes from it on the other side ; and in our experiments on the formation of images, we are obliged either to change the place of the screen every time the distance of the radiant is altered, or to substitute a new lens which will either throw back the image as much as the increased dis- tance of the radiant brings it forward, or which brings the image as much nearer as the altered place of the radiant tends to carry it off How then is the distinctness of the image maintained in the eye, notwithstanding the immense variety in the distances of objects? We can conceive of but two ways in which this can be accomplished ; either by lengthening or shortening the diameter of the eye in the di- rection of its axis, so as to alter the distance of the retina from the cornea and crystaline, or by altering the curvature of the refracting lenses themselves, increasing their convexity for near objects, and lessening it for objects that are more remote. Perhaps both causes may operate, but the effect is believed to be produced chiefly by the latter cause, namely, change of figure in the refracting lenses. On this subject, Sir J. Herschel remarks, that it is the boast of science to have been aide to trace so far the refined contrivance of this most admirable organ ; not its shame to find something still concealed from its scrutiny; for, however anatomists may differ on points of structure, or physiologists dispute on modes of action, there is that in what we do understand of the formation of the eye, so similar, and yet so infinitely superior, to a product of human ingenuity, — such thought, What Bpeciiil contrivance do we observe in the eye ibr particular purpo.'^es ? What is the greatest range of vision^ which the eye can talie in at once V How is the distinctness of the image maintained in regard to objects at different distances? What is said of the perfection of structure ia the eye ? VISION. 359 such care, such refinement, such advantage taken of the properties of natural agents used as mere instruments for accomplishing a given end. as force upon us a conviction of deliberate choice and premeditated design, more strongly, perhaps, than any single contrivance to be found, whether in art or nature, and render its study an object of the deepest nterest. 476. Writers on comparative anatomy express the high- est admiration of the adaptation of the eyes of different ani- mals to the media in which they respectively live, and to the peculiar wants or habits of each. Thus the crystaline lens of the fish is formed with peculiar reference to the refracting properties of water. In the human eye, this lens has a re- fractive power only a little greater than that of water ; but since the light passes out of a much rarer medium, (air,) such a density is sufficient to bring the rays to a focus ; but were the density of the crystaline lens in the eye of the fish no greater than in the human eye, receiving the light from a medium (water) almost as dense as itself, it would "be un- able to give that change of direction to the rays which would be essential to distinct vision. But provision is made for this exigency by giving to the crystaline lens a much great- er density, and of course a higher refracting power, which enables it completely to fulfil its purpose. Animals which have occasion to see in the dark, as the owl and the cat, have the power of opening or closing the pupil to a much greater extent than man. By this means they are enabled in the dark to collect a far greater number of rays of light. But as such an «-xpansion of the pupil would, in broad daylight endanger the safety of eyes of such peculiar delicacy, the iris closes over the aperture and dimin- ishes it with every increase in the intensity of light, a change which is involuntary on the part of the animal. In an.imals, as birds, which pounce upon their prey, the pupil of the eye is elongated perpendicularly, while in those that ruminate, as the ox, it is elongated horizontally ; being, in each case, exactly adapted to the circumstances of the animal. 47 7 . The images of external objects are of course formed inverted on the retina, and may be seen there by dissecting off the posterior coats of the eye of a newly killed animal, as an ox, and exposing the retina and the choroid membrane What peculiarity has the eye of a fish 1 Also of the cat or the owl 1 Whal is the position of the image on the retina 7 How may it be seen in the eye of an ox 'I 360 OPTICS. from behind, like the image on a transparent screen; seen from behind. The appearance is particularly striking and beautiful when the eye is fixed like the scioptic ball in the window shutter of a dark room. It is this image, and this only, which is felt by the nerves of the retina, on which the rays of light act as a stimulus ; and the impressions therein produced are thence conveyed along the optic nerve to the sensorium, in a manner which we must rank at present among the profo under mysteries of physiology, but which appear to differ in no respect from that in which the im- pressions of the other senses are transmitted. Thus, a par- alysis of the optic nerve produces, while it lasts, total blind- ness, though the eye remains open, and the lenses retain their transparency ; and some very curious cases of half blindness have been successfully referred to an affection of one of the nerves without the other. On the other hand, while the nerves retain their sensibility, the degree of per- fection of vision is exactly commensurate to that of the image formed on the retina. In cases o{ cataract, when the crystaline leus loses its transparency, the light is prevent- ed from reaching the retina, or from reaching it in a proper state of regular concentration ; being stopped, confused, and scattered, by the opake or semi-opake portions it encounters in its passage. The image, in consequence, is either alto- gether obliterated, or rendered dim and indistinct. If the opake lens be extracted, the full perception of light returns; but one principal instrument for producing the convergence of the rays being removed, the image, instead of being formed o>i the retina, would be formed considerably behhul it, and the rays being received on it in a state of convergence, be- fore they are brought to a focus, produce no regular picture, and therefore no distinct vision. But if we give to the rays before they enter the eye. a certain degree of convergence, by the application of a convex lens, so as to render the lenses of the eye capable of finally effecting the exact convergence of the rays upon the retina, distinct vision is the immediate result This is the reason why persons who have under- gone the operation for tlie cataract, (which consists either in totally removing, or in putting out of the way. the opake crystaline) wear spectacles unusually convex. Such glass- es perform the office of an artificial crystaline. An imper- What is the effect of a paralysis of the optic nerve f What is the disease called cataract 1 How is cataract remedied t Why do persons that have had the cataract wear very convex glasses ? VISION. 361 fection of vision similar to that produced by the removal of the crystaline, is the ordinary effect of old ag-e, and its rem- edy is the same. In aged persons, the cornea loses some- thing of its convexity, or becomes flatter. The refracting power of the eye is by this means diminished, and a perfect image can no longer be formed on the retina, the point to which the converging rays tend being beyond the retina. The deficient power is supplied by a convex lens, in a pair of spectacles, which are so selected and adapted to the eye, as exactly to compensate for the want of refracting power in the eye itself, and thus the rays are brought to a focus at the retina, where alone a distinct image can be formed. 478. Near-sighted persons have their eyes too convex, forming the image too soon, or before the rays reach the retina. Concave glasses counteract this effect. Rare cases have occurred where the cornea was so very prominent as to render it impossible to apply conveniently a lens sufficiently concave to counteract its action. Such cases would be ac- companied with immediate blindness, but for that happy boldness, justifiable only by the certainty of our knowledge of the true nature and laws of vision, which in such a case has suggested the opening of the eye and removal of the crystaline lens, though in a perfectly sound state. Other defects of eyesight, whose cause has been ascertained to de- pend on mal-conformation of the cornea, or some other parts of the eye, have sometimes been remedied by adapting to them glasses of a peculiar construction, possessing optical properties adapted to the particular defects they were re- quired to remedy. 479. T/ie estimatwn of the VIST AT^CES and magnitudes of objects is not dependent on optical principles alone, but the information afforded by the eye, is taken in connection tvith various circumstances that influence the mind in judging of these particulars. In the first place, we judge, of the distance of an object by the inclination of the optic axes, which is greater for nearer objects and less for objects more remote. But beyond a cer- tain distance, this method is very indeterminate, since great intervals among remote objects would scarcel}' affect the in- clination of these axes. In the second place, we judge of distance by the apparent magnitude of known objects ; as Why does old age require convex glasses? What is the defect of near- sighted persons 1 State the proposition respecting the magnitudes and dis- tances of objects. In what cases is tlie visnal angle a measme of distance ? 31 362 OPTICS. when a ship of large size, or a high mountain appears com paratively small, we refer it to a great distance. We ar»- also frequently deceived in our estimate of distance when we are approaching large objects, as a great city, or a lofty mountain : we fancy they are nearer than they actually are In the third, place, we estimate the distance of ob'ects by the degree of distinctness of the parts, or brightiwss of the colors Thus, a smoky mountain is referred to a great distance ;* s mountain whose sides are precipitous and bare (especially where the rocks have a new and fresh appearance in conse- quence of having been quarried for use) appears nearer than the reality: ves els or steamboats, seen through a mist in the night have sometimes run foul of each other, being sup- posed by the pilots to be much farther off, in consequence of the indistinctness of their appearance. In the fourth place, our estimate of distance is affected by the number of intervening oljjects. Hence, distances upon uneven ground do not appear so great as upon a plain ; for the valleys, riv- ers, and other objects that lie low are many of them lost to the sight. On this principle, the breadth of a river appears less when viewed from one side than from the center; a ship appears nearer than the truth to one unaccustomed to judge of distances on water ; and the horizontal distance of the sky appears much greater than the vertical distance whence the aerial vault does not present the appearance of a hollow hem- isphere, but of such a hemisphere much flattened in the zenith, and spread out at the horizon. 480. A similar variety of circumstances affects our es- timate of the magnitudes of bodies seen at different distan- ces. First, the visual angle, that is, the angle subtended by the object at the eye, determines the size of objects that are near ; but it is scarcely any guide to the dimensions of re- mote objects, since all such objects subtend angles at the eye comparatively very small. Thus, on this principle, a fiy within a few inches of the eye would appear larger than a ship of war at some distance on water. A giant nine feet in height, but thirty feet off, would appear no larger than a * This appearance exhibits the true color of the atmosphere, becoming visible ia consequence of the extent of the stratum, and the diirk ground which the mountain affords upon which to view it. When do we infer that a .argc sliip is at a great distance ? How do we judge of the distance of mountains ? What inHuence liave intervening objects ? Give examples. State the several ways of judging of the magni- tnijes of objects. How far is the visual angle a cnterion I State the examplea of a fly and a ship of war — of a child and a giant. VISION. 363 child three feet high seen at the distance of ten feet. But as this result is not conformable to experience, it is evident that we must have some means of judging of the magnitudes of objects, beside that derived from the visual angle. If the giant were to remove from the distance of ten feet from the eye to that of thirty feet, his image on the retina would be only one third as long as before ; but, on the other hand, the distance is trebled, and the sort of combination that takes place in us of the two impressions, the one of magnitude, the other of distance, is like the constant product of two quanti- ties, of which one increases in the same ratio as the other di- minishes : whence the giant would appear constantly of the same height, at whatever distance from us he was seen. 481* This corrected result, however, we can make only in cases when we are familiar with the actual size of the body. When not thus familiar, we rely too much on the visual angle, and are thus often greatly deceived. A speck on the window, being at the instant supposed to be an ob- ject on a, distant eminence, is magnified in our estimation into a body of extraordinary size ; (as a line half an inch long into a may-pole;) or distant objects supposed to be very near appear to be of an exceedingly diminutive eize. Sec- ondly, the effect of contrast is visible in our estimation of the magnitudes of bodies, a given object appearing much below its ordinary size, when seen by the side of those of very great magnitude. Men quarrying stone at the base of a high mountain, sometimes appear at a little distance like pigmies, partly from the effect of contrast, but more perhaps from the impression which the mountain gives us of their being nearer than they actually are. Thirdly, objects seen at an angle considerably above or below us, as a man on top of a spire, or a river in a deep valley seen from the top of a mountain, appear greatly diminished. In these cases, since there are no intervening objects to aid us in estimating the distance, we estimate it too low. and hence (Art. 479.) the object appears less than the reality. Moreover, being seen obliquely, its apparent dimensions are diminished on this account, the apparent diameter being determined by the line into which the object is projected perpendicular to the axis of vision. Hence, children judge much less accu- rately both of distances and of magnitudes than adults ; and To what bodies does this role apply? What is the effect of contrast? How is the size of objects when above or below us 1 364 blind persons suddenly restored to sight have usually dis- played an utter inability to judge of these particulars. 482. Tlie impression made by liglii remains on ilie, eye for a short time after the light itself is withdrawn. On this principle a stick ignited at the end and whirled in the air, exhibits a luminous circle. The spokes of a wheel, and other parts of machinery in rapid motion ex- hibit continuous surfaces although made up of parts which are separated from each other by large intervals. Light- ning also, and fiery meteors, appear to describe long lines of light merely because their passage through the atmos- phere is so rapid, that the eye does not lose the impression of the first portions until the last are added. The amusing toy called the Thau- ^'S- 180. matrope., depends on the same principle. An example of it is exhib- ited in Pig. 180, which represents a circular card, on one side of which is inscribed a chariot, and on the other the charioteer. To opposite sides of the card are attached strings, by means of which, taken between the thumb and finger of each hand, a rapid revolution is given to the card, bringing the figures on the opposite sides in quick succession before the eye. When the motion is so swift that the eye retains the impression of both, the two appear to be united, or the charioteer appears in his proper place driving the chariot. The Phantasma- scope consists of disks bearing on their margin a variety of figures, which are so related to each other, that each suc- ceeding figure shall afford a continuation of the preceding, and the whole taken together, when put in rapid revolution, shall exhibit a single figure performing some singular or amusing feat. Thus the figure might commence with a player holding a violin, and a bow which he is just begin- ning to draw ; the second view might represent the bow as drawn a little ; the third still more ; and the whole would then exhibit the usual motions of the bow. Give example.? to show that the impression of light remains in the eya D^'dcribe the Ttiaumatrope and Fhauta.smaecope. CHAPTEE VI. OF MICROSCOPES. 483. The Microscope is an optical instrument, designed to aid tlm eye in tJie inspection of minute ejects. Telescopes, on the other hand, assist the eye in the ex- amination of distant bodies. These two instruments have, probably more than any other, extended the boundaries of human thought ; and no small part of the labor which has been bestowed upon the science of optics, has had for its ul- timate object their improvement and perfection. With the hope of making the learner well acquainted with the principles of the miscroscope, we shall begin with those varieties of the instrument which are the most simple in their construction, and successively advance to others of a more complicated structure. 484. The simplest microscope is a double convex lens. This, it is well known, when applied to small objects, as the letters of a book, renders them larger and more distinct. Let us see in what manner these effects are produced. When a.n object is brought nearer and nearer to the eye, we finally reach a point within which vision begins to grow imperfect. That point is called the limit of distinct vision. Its distance from the eye varies a little in different persons, but averages (^for mmute objects) at aboutyiVe inches. If the object be brought nearer than this distance, the rays come to the eye too diverging for the lenses of the eye to bring them to a focus soon enough, that is, so as to make the image fall ex- actly on the retina. Moreover, the rays which proceed from the extreme parts of the object, meet the eye too obliquely to be brought to the same focus with those rays which meet it more directlj', and contribute only to confuse the picture. We may verify these remarks by bringing grad- ually towards the eye a printed page with small letters. When the letters are within two or three inches of the eye, they are blended together, and nothing is seen distinctly. If we now make a pin hole through a piece of paper, (black paper is preferable.) and look at the same letters through this, we find them rendered far more distinct than before at Microscope — Define the microscope. What is said of the utility of the microscope and the telescope V What is the simpi st form of the microscope? Explain the principles on which it acts ? 31* S6G OPTICS. near distances, and larger than ordinary. Their greater distinctness is owing to the exclusion of those oblique rays which, not being brought by the eye to an accurate focus with the central rays, only tend to confuse the picture formed by the latter. As only the central rays of each pencil can enter so small an orifice, the picture is made up, as it were of the aaxs of all the pencils. The increased magnitude of the letters is owing to their being seen nearer than ordinary and thus under a greater angle, an increase of the visua angle having much influence in our estimate of the magni tude of near objects, though it has but little influence in re- gard to remote objects, (Art, 480.) 485. A convex lens acts on much the same principles, only it is still more effectual. It does not exclude the oblique rays, but it diminishes their obliquity so much, as to enable the eye to bring them to a focus, at the distance of the re- tina, and thus makes them contribute to the brightness of the picture. The object is magnified as before, because it is seen nearer, and consequently under a larger angle, so that the eye can distinctly recognize minute portions, which were before invisible because they did not occupy a sufficient space on the retina. The power of a lens to accomplish these purposes, will obviously depend on its refractive power ; and this, (supposing the material on which the lens is made to remain the same.) will depend on its increased sphericity, and diminished focal distance. Lenses of the smallest focal distance, therefore other things being equal, have the great- est magnifying power, and, therefore, sphei-ules or perfect spheres have the highest magnifying powers of all. When the radiant is situated in the focus of a lens, the rays go out parallel. (Art. 446.) When thus received by the eye, they are capable of being brought to a focus by it. and of form- ing a distinct image. Hence, by means of a lens, an object may be seen distinctly when it is exceedingly near to the eye, provided it be situated in the focus of the lens. The magnifying power of a lens, therefore, depends on the ratio between its focal distance and the limit of distinct vision. The latter being five inches, a lens whose focal distance is one inch, by bringing the object five times nearer, magnifies To what is the greater distinctness owing- — to what the greater magnitude when objects are viewed through a pin hole ? How does the convex lens act? What lenses have the greatest magnifying power? Why can an ob- ject be seen so much nearer the eye by the aid of the microscope ? On what does the magnifying power of a lens depend ? What is the smallest focal distance ? MICROSCOPES. 367 its linear dimensions in the same ratio, and its superficial dimensions in the ratio of the square. Thus, in the case supposed, an object would appear five times as long- and broad, and have twenty-five times as great a surface. Len- ses have been made capable of afl^ording a distinct image of very minute objects, when their focal distances were only -j'oth of an inch. In this case the magnifying power would be as ViT : ■''■ which is as 1 to 300 or as 1 to 90000 in surface. 486. When, however, an object is so near to the eye, a very minute space covers the whole field of vision, and it is only the minutest objects, or the smallest parts of a body, that are visible in such microscopes. The extent of parts seen by a microscope is called the f eld of vieic. A micro- scope of small focal distance has a proportionally small field of view. Moreover, since, when the object is so near to the lens, the rays of light strike the lens extremely diverging, only the central rays of each pencil can be brought accu- rately to a focus. The more oblique rays, therefore, must be excluded by covering up all but the central portions of the lens, by which means the brightness of the image is di- minished. The part of a lens through which the light is admitted, is called its aperture. The aperture of a lens of small focal distance and high magnifying powers, must of necessity be smail, and one of the principal difficulties in the use of such microscopes, is the want of sufficient light. Hence, microscopes of different focal distances are required for different purposes. Where we wish to view a large field at once, we must use a lens which has a large field of view, and of course but comparatively small magnifying powers. Such are the glasses used by watchmakers and other artists. Microscopes which magnify but little, but afford a large field of view, are called magnijiers or inagnifying glasses. Such are the large lenses employed for viewing pictures. But for inspecting the minute parts of a small insect, we require* a much higher power; and, the object being very small a ■.arge field of view is not necessary. The only difficulty to be obviated is the want of light ; and this evil is remedied, either by placing the object in the sun, or by condensing upon it a still stronger light, by means of apparatus special- How e^eat is the magnifying power of snob a lens ? Define the field of view. What microscopes have a small iield of view ? Why are microscopes of small focal distance apt to be deficient in light f Define the aperture. What micro.icopes are called magnifying glasses? How is the want of light in blirh magnifiers obviated ? 363 OPTICS. ly adapted to that purpose, which will be described here- after. * 487. Among the most distinguished achievements of philosophical artists, in our own times, has been the formation of microscopes out of the hardest precious gems, especially the diamond axid the sapphire. The diamond seems to unite in itself almost every desirable quality for this purpose. I will be recollected that this substance is distinguished for its high refractive powers ; hence, a given refracting, and of course magnifying, power may be attained with a lens of less curvature, and consequently subject to less spherical aberratwn, than glass lenses of the same power. Indeed, it is estimated, that the indistinctness arising from spherical aberration, is in a diamond lens only -^th as great as in a glass lens of equivalent power The sapphire has analogous properties, as also the garnet; and pure rock crystal (quartz) is much esteemed for refracting lenses ; but some of the pel- lucid gems are unsuitable for this purpose on account of their possessing the property of giving double images. The comparative curvature and thickness of three lenses of the same refracting power, made respectively of diamond, aap- phire, and glass, are exhibited in the following diagramo. Fig. 181. Diamond. Since, also, a diamond lens admits of being made much thinner than a glass lens of the same power, the loss of light by absorption is far less, and the brightness of the image is proportionally augmented. 488. Another distinguished and valuable property of the diamond is, that it combines with a high refractive, a low dispersive power. By dispersive power it will be ob- served, is meant the power of separating the different colored rays ; that is, of decomposing common light into its pris- matic elements. Hence diamond lenses are naturally near- * A convenieDt pocket microscope is sometimes sold in tlie sbopa, consisting of a slide of ivory or horn, two or three inches in length, in which are set three or four lenses of different powers, adapted to various purposes. What is Bald of the diamond and sapphire microscopeB ? What peculiar properties has the diamond for this purpose, in regard to aberration, bright- ness, achromatic quality, &.c. ? MICROSCOPES. 369 ly achromatic, or afford images which are destitute of color. But while these favorable qualities were known to apper- tain to the diamond, which, taken in connection with its great transparency and purity of structure, were observed to fit it admirably for microscopes of great magnifying powers, vet the extreme hardness of the substance seemed to render the difficulty of grinding it into the requisite shape almost insu- perable. This difficulty has, however, within a few years, been completely overcome by Mr. Prichard, an eminent English artist, who has constructed a number of diamond and sapphire microscopes, whose performances have equalled the most sanguine expectations. Yet such improvements have recently been made in op- tical glass, and microscopes of this substance have been executed of such power and excellence as to render unneces- sary any further resort to the precious gems. Several artists of our own country have constructed microscopes that rival the best of foreign manufacture. Those of Spencer of Can- estoga. (N. Y.,) are particularly celebrated. 489« The Perspective Gla'ss, which is used for view- ing pictures, affords another example of the application of the simple microscope. It consists of a large double convex lens fixed in a frame in a vertical position, from the top of which, on the back side, proceeds a plane mirror which is fixed at an angle of 4-5 with the horizon, and of course it makes the same angle with the lens. Pictures to be viewed are placed in an inverted position, (that is, with the top to- wards the spectator,) on a table at the foot of the instrument. The mirror, being set at an angle of 4.5 with the horizon, ren- ders horizontal objects erect. Its office therefore, is merely to give a proper direction to the rays of light from the picture as they enter the lens, causing them, in fact, to come to the lens in the same manner as they would do were the mirror removed and the picture set up in a vertical position, paral- lel to the lens, at a distance from the lens equal to the length of any ray, measured from the picture to the mirror and from the mirror to the lens. (Art. 428.) Again, in order that the image may be erect, it is necessary that the picture should be placed with its top towards the observer ; for since the image of every point in the picture is just as far behind the mirror as the point is before it, those parts of the picture What difficulty attends the manufacture of diamond mioroscnpeB 7 Per- spective glass — describe it. How are the pictures placed ? What Is the otHce of the miiTor, and that of the lens ? 370 which are designed to occupy the highest parts of the image must be farthest from the I'ig- 182. mirror. This will be under- stood from the following di- agram. A A. a convex lens fixed vertically in a frame. B B, a plane mirror ma- king with the horizon an an- gle of 4.5 C, an object placed hori- zontally upon the table, the upper part being towards the observer. The object will be reflect- ed by the mirror into a per- pendicular position, and its rays will, therefore, fall on the lens in the same manner as they would were it actu- ally situated perpendicularly, and no mirror were employed. Consequently, if the distance of C from the lens be equal to the focal distance of the lens, the rays will come to the eye parallel, and a distinct and magnified image will be formed. When the glass is of good quality, and the picture is exe- cuted agreeably to the rules of perspective, the various parts are exhibited in their natural positions, and at their relative distances, so as greatly to improve the view. The greater distinctness of the parts, and more natural distribution of light and shade than what attends the naked view, is owing not only to the increased magnitude and to the greater quan- tity of the light emitted from the picture, which is collected by the lens and conveyed to the eye, but also to the separa- tion of this portion of light from that which proceeds from various other objects. The lens both conveys more of the light of the picture to the eye than would otherwise reach it, and conveys it unmingled with extraneous light. The im- portance of the latter circumstance is manifested even by looking at the picture through an open tube, or through the hand so curved as to form a tube. 490. The microscopes hitherto examined are such as Describe il fi-om the figure. To what is the greater distinctness of parts owing ? Why does it improve the distinctness of a picture to look througn the hand or an open tube ? MICROSCOPES. 371 are designed to be interposed between the eye and the ob- ject to be viewed, the latter being placed in the focus of par- allel rays of the lens, or a little nearer to the lens than that focus, so that the rays of the same pencil may come to the eye either parallel or with so small a degree of divergency, that the lenses of the eye shall be competent to make them converge and form an image on the retina. In this case, as the rays come to the eye in the same manner as rays from larger objects, at a greater distance, seen without the aid of a lens, the position of the object is not changed ; that is. it is seen erect. Single microscopes, however, are also employed to form a magnified image on a wall or screen, which is seen by the eye instead of the object itself. Two celebrated in- struments, the Magic Lantern and the Solar Microscope, magnify their objects in this manner, in the construction of which the principles under review are happily exemplified. 491. From what has been already learned respecting lenses the following points will be readily comprehended, being for the most part a recapitulation of principles ex- plained and demonstrated. If. in a dark room, we place before a convex lens any lu- minous object; as a candle, we shall observe the following phenomena. (See Art. 446.) 1. If the radiant be placed nearer to the lens than its to- cus, since the rays will go out diverging, no image will be formed on the other side of the lens. 2. Even when the radiant is in the focus, so that the rays go out parallel, they never meet in a focus, and of course never form an image.* 3. But when the radiant is farther from the lens than its focus, the rays converge on the other side, those of each pencil proceeding from the same point in the object, being accurately united in one point in the image, and occupymg that point alone, without the interference of rays from any other point. 4. The axes of the rays from the extreme parts of the ob- ject cross each other in the center of the lens. Hence, they form an image inverted with respect to the object ; and, al- * It will be remarked, Ihal when the single microBcope is used as an eye-glass, the eye itself brings the parallel rays to a focus and foriiis the image. Whv do obiects seen through single microscopes appear erect? Mnjic i««te™.-Recapitalate the leading principles essential to an understanding of this instrument, when the radiant is nearer the lens than the focus, in the focus, and farther than the focus. 372 OPTICS. though the rays which make up any individual pencil are made to converge by the lens, yet the axes (which deter- mine the magnitude of the picture) diverge from each other after crossing at the center of the lens, and hence the image is greater in proportion as it is formed at a greater distance from the lens. When the object is only a little farther off from tlie lens than its focus, the image is thrown to a great distance. an 1 is proportionally magnified. (See Fig. 183.) As the object is Pig. 183. separated farther from the lens (which may be effected either by withdrawing the object from the lens or the lens from the object) the image is formed at a less distance, and is of a diameter proportionally less. (See Art. 447.) Suppose now that we employ a magnifier of so small focal distance, that when the object is placed within one tenth of an inch of the lens, the image is formed on the other side upon a screen or wall at the distance of twenty feet ; the object will be magnified in the ratio of -jV to (20x 12 = ) 240 ; that is, the image will be 2.400 times greater than the object in di- ameter, and 5,760,000 times greater in surface. It would seem, therefore, as if nothing more were necessary in order to form magnified images of objects, than a dark room, a convex lens, and a screen or wall for the reception of the picture. It must be remarked, however, that when the light which proceeds from the object is diffused over so great a Where do the axes of the several pencils cvoss each other ? 'WTiy is the image inverted ? Why ia it enlarged ? What is the magnifying power when the distance of the focus is 1-1 inch, and that of the image 20 feet ? MICROSCOPES. 373 space, its intensity must be greatly diminished, so as to be either incapable of affording a picture which shall be visible at all, or at least sufficiently bright for the purposes of dis- tinct vision. This difficulty is remedied by illuminating the object ; and it is for this purpose, that most of the con- trivances employed in the magic lantern and solar micro- scope are designed. 492. The Magic Lantern consists of a large tin canis- ter, either cylindrical or cubical in its figure, having an o])ening near the bottom into virhich air may enter freely to supply the lamp, and a chimney proceeding from the top and bent over so as to prevent the light of the lamp from shining into the room. The lantern has a door in the side which shuts close, the object being throughout to prevent any light from escaping into the room except what attends the picture. The room itself is made as dark as possible ; or, what is better, the experiments are performed by night. In front of the lantern is fixed a large tube, at the open end of which is placed the magnifying lens. In the same tube, at a distance from the lens somewhat greater than the focal distance, the object is introduced, which is usually some fig- ure painted on glass in transparent colors, the other parts of the glass being blackened so that no light can pass throun-h except that which falls on the object and illuminates it, by which means we shall have a luminous image projected on a black ground. For illuminating the object, an argand lamp is placed near the center of the lantern, the light of which is concentrated upon the object in two ways ; first, by means of a thick lens, usually plano-convex, so situated be- tween the lamp and the object that the rays which diverge from the lamp shall be collected and condensed upon the object ; and secondly, by means of a concave reflector situa- ted behind the lamp, which serves a similar purpose. A, the magnifying lens. B, the object introduced through an opening in the tube. C, the condensing lens. D, the lamp. E, the concave mirror. F, the image thrown on the screen, or a white wall, in a dark room. a, a thumb piece, by which the magnifier may be made Why is it necessary to illuminate the object? Describe the Magic Lan- tern, — its different parts. Where is the magnifying lens placed ? Where rht illuminating glass? Describe from the figure. 32 374 OPTICS. to approach to or recede from the object, and thus the image be thrown to a greater or less distance according to the mair- Fig. 184. nitude required. As the image is inverted with respect tr the object it is only necessary to introduce the object itself i^ an inverted position, and the image will be erect. The objects employed in the Magic Lantern are very various, consisting of figures of men and animals ; of carica- tures ; of representations of the passions ; of landscapes ; and of astronomical diagrams. When the last are employed, this apparatus becomes subservient to a useful purpose in teaching astronomy, and is frequently so employed by popu- lar lecturers on that subject. 493. The Solar Microscope does not differ in princi- ple from the Magic Lantern, only the object is illuminated by the concentrated light of the sun instead of that of a lamp. And since a powerful illumination may thus be effect- ed upon minute objects placed before a magnifier of great power, the solar microscope is usually employed to form very enlarged images of the most minute substances, as the smallest insects, the most delicate parts of plants, and other attenuated objects of natural history. For magnifiers, seve- ral of different focal distances are employed, varying from an inch to the -jV or sV of an inch, it being understood, that those of the shortest focus and greatest magnifying powers can be used only for the minutest objects, since, when bodies of a larger size are brought so near a small lens, their light What objects are used for the Magic Lantern? Solar Microsome How does it differ from the Magic Lantern? What is the size of objects usually employed in this instrument '\ What are the usual focal distances of the lenses ? MICROSCOPES. 375 strikes the lens too obliquely to be transmitted through it. The magnifying lens is fixed into the mouth of a tube, ana the object placed near its focus, much in the same manner, as in the magic lantern ; but instead of the body of the lantern (which contains the illuminating apparatus) a mirror about three or four inches wide, and from twelve to eighteen inches long, is attached to the other end of the tube. This mirror is thrust through an opening in the window shutter of a dark room, and the mouth of the tube to which it is fixed is secured firmly to the shutter, so that the mirror is on the outside, and the tube with its lenses is on the inside of the shutter. By means of adjusting screws, the mirror is turned in such a way as to direct the sun's rays into the tube, where they are received by one or more of the lenses, called condensers^ which collect them and concentrate them upon the object which thus becomes highly illuminated, and capable of affording an image sufficiently bright and dis- tinct, though magnified many thousands or even millions of times. It will be observed that the magnitude of the image depends here, as in other cases of the simple micros- cope, upon the ratio between the distances of the object and the image from the center of the magnifier. If, for example, the object be within the tenth of an inch of the lens, and the image be thirty feet, or three hundred and sixty inches from it, then the image will be 360x 10=3600 times as large as the object in diameter, and (3600)'* = 12,960,000 times in surface. With a given lens, the size of the image depends wholly on the distance to which it is thrown ; that is, on the distance of the wall or screen where it is formed.* 494. When the solar microscope is well constructed, it affords the most wonderful results, and greatly enlarges our conceptions of the delicacy, perfection, and subtil ty of the works of nature. In inspecting vegetables, the eye is de- lighted with the regularity and beauty which characterizes the texture and intricate structure of plants and flowers. The most delicate fibres of a leaf, the pores through which * Instead of employing the sun to illuminate objects, tiie intense light produced by the combustiun of a jet of oxygen and hydrogen gases, is now used with great effect. Whence the in.^trumeiit is called the oxy-hydrogcn microscope. The light of the jet is directed on the object by means of a concave speculum. Explain the use of ibe mirror that is attached to the solar microscope — also the condensers. Upon what does the magnitude of the image depend ? Suppose the object to be 1-10 inch from the lens, and the image be formed at the distance of thirtj; feet, what will be the magnifying power 1 What sub- etitute for the sun's light is employed in the oxy-hydrogen microscope ? What appearances are presented under the microscope by vegetables substances y 376 OPTICS. the vegetable fluids circulate, the downy covering- of plants and foliage, as of certain mosses, which is too minute to disclose its figure to the naked eye, — objects of this kind, .when expanded under the solar microscope, astonish and delight us by the symmetry of their structure. Their appro priate colors are not so well exhibited by this instrument, as by some other forms of the microscope to be described here- after. In the animal VrngAovci, the solar microscope extends the range of vision in a manner no less surprising and in- structive. The minutest insects we are acquainted with, are exhibited to us as animals of the largest size, and often of monstrous shapes, from the multiplicity of their parts and apparent disproportion ; and animalcules, or those membcTs of the animal creation which are too minute to be seen at all by the naked eye. are suddenly brought into life in countless numbers. The forms, the motions, and the habits of these beings, are among the most curious revelations of the solar microscope. The circulation of the blood may be seen iu the fins of fishes and other transparent parts of animals, presenting a very curious and interesting spectacle. The crystallization of salts, which may be exhibited while the crystals are forming and arranging themselves, (as many of them do with great precision and symmetry.) is among the finest representations of this instrument. Since the light is transmitted through the objects, it will of course be understood, that only such objects as are t7-ans parent can be employed in the manner already described. In some varieties of the solar microscope, there are special contrivances for exhibiting qpafe objects by means of reflect- ed light. 49 5 • When we form an image of an object with the single microscope, (as is done in the magic lantern and solar microscope,) if that image is not too large, we may obvi- ously apply to it a magnifier as we would to an original object of the same size. This is the principle of the Com- pound Microscope. The Compound Mtcroscope consists of at least two con- vex lenses, one of which, called the object-glass, is used to form an enlarged image of the object, and the other, called the eye-glass, is used to magnify the image still farther. Does this instrument give a good representation of the colors of objects ? Describe the appearances of animal objects, of the circalation of the blood, and of the crystallization of salts. Are the objects usually employed trans- parent or opake ? How may opake objects be illuminated 1 Compmuuk Microscope. — State its principles. Describe its construction. MICROSCOPES 377 Thus, let ab, (Fig. 185,) be the object, being placed a little farther from the object-glass, cd, than the principal focus, the rays of light emanating from 't will be collected on the other side of Fi§:. 185. the lens and form an image, gh, whose diameter is as much larger than that of the object as its distance from the lens is greater. (Art. 447.) Let c/" be the eye-glass, which must be placed at such a distance from the image, that the latter shall be in the focus of par- allel rays ; then the rays proceeding from the image will go out parallel,* and come to the eye, situated behind the elass, in a state favorable for distinct vision. 496. The masmfying power of the Compound Microscope is estimated as follows. First, the diameter of the image will be to that of the object as their respective distances from the lens. Secondly, the imap-e is magnified by the eye-glass according to the principles of the single micro- «cope, (Art. 485.) namely, from the ratio of its focal distance to the limit of distinct vision. Thus, suppose the image is formed at ten times the distance of the object ; it will of course be magnified ten times. Again, suppose the eye-glass has a focal distance of one inch, the limit of distinct vision being five inches ; the image will be farther magnified five times; by both glasses, therefore, the object will be magni- fied fifty times. If the first ratio be that of one to one hun- dred, then the instrument will magnify the linear dimen- Bions five hundred times, and the surface two hundred and fifty thousand times. From this double magnifying pro- cess, it might be supposed that, by means of the compound microscope, it would be easy to attain a much higher magni- * It is to be remarked here and in all similar cases, that it is only the rays of :ach itidwiduai pencil that are parallel : that is, those rays which come from Iho tame point in the object. The rays of different pencils may cross each other /ariously, and the different pencils may converge or diverge among themselves ; itill, if the rays of each pencil be parallel to one another, the vision will be distinct. How is the magnifying power of the compound microscope estimated? How is the diameter of the image to that of the object ? Upon what princi- ple is the image ma^Tiiiied ? Suppose the image has ten times the distance of the object, and the eye-glaj^s has a focal distance of one inch, what will be the whole magnifying power ? 32* 378 OPTICS. fying power than by the single microscope ; but this is not the fact ; for, in the first place, we cannot form an image of a size beyond certain moderate limits, without making it too large for the eye-glass to cover ; or, if an eye-glass of very large field of view be employed, its focal distance must be great, and consequently its magnifying power small. We are, therefore, unable to employ so high a magnifier for our object-glass as we may apply to the naked eye, and we can employ only a microscope of still inferior power for our eye- glass. 497. On account of the necessity of using a large eye- glass to view the magnified -image, compound microscopes require to have the tube which contains the glasses, larger towards the eye-glass than towards the object-glass. Al- though the compound does not possess higher magnifying powers than the simple microscope, yet it commands a much greater field of view. We view the image with the eye glass in the same manner as we view the object with a sin- gle microscope ; but having already a magnified represent- ation of the object, we have no occasion to apply to the eye so high a magnifier, and therefore we may employ one of greater focal distance, which consequently takes in a greater field of view. The field of view is still farther improved in some compound microscopes by interposing a field glass, which is a convex lens introduced between the eye-glass and the place of the image, and near the latter (as a little above gli, Fig. 1 85,) the effect of which is to diminish the di- vergency of the pencils of rays, and thus to bring into the range of the eye-glass those pencils which would otherwise diverge too much to fall within it. It has been before re- marked that the cornea performs a similar office for thecrys- taline lens of the eye. (Art. 474.) 498., The Portable Camera Obscuea, which is used chiefly for delineating landscapes, consists of a wooden box, (answering to the dark chamber, Art. 471,) with which is connected a convex lens, so exposed to the landscape as to receive the rays of light from the various objects in it, and form a picture of them on a screen placed within the box at the focal distance of the lens. Such is a general description Why can we not attain a higher magnifying power by the compound tlian by the single microscope 1 What rays are rendered parallel to each other ? What shape has the tube of a compound microscope ? "Why has it a greater field of view than the single microscope? What is the lield'glassV Describe the Portable Camera Obscura, For what purpose is it used ? MICROSCOPES. 379 of the instrument, of which there are several different forms The foJlowiug diagram represents a convenient form. ABGD, a box usually made of thin pieces of mahogany. ad. a plano-convex lens, this form being preferred because it has less aberration than a double convex. E D, a plane mirror, turning on a hinge at D, and capable of being raised or lowered, so as to admit more or less of the landscape. b c, a. piece of pasteboard, cov- ered with a sheet of fine white pa- per, and bent so as to form a con- cave screen, and placed at the focal distance of the lens. A casting of stucco, of the figure of a concave portion of a sphere, affords the most perfect picture. The rays of light from external objects, falling upon the mirror ED, are conveyed to the lens in the same manner as though they came directly from ex- ternal objects at the same distance behind the mirror. Pass- ing through the lens, they are brought to a focus and form a picture of the landscape on the screen, which may be viewed by an opening in the side of the box at P, and may be copied by a hand introduced into the box by an opening below. Although the image is inverted with respect to the objects, yet as the spectator, in looking into the box, stands with his back to the landscape, the picture appears erect. Another form of the camera obscura is represented in figure 187, where ABC is a cubical box of mahogany or rosewood, with a project- ing part abed in front. At the open end of the tube is inserted a convex lens b c. and a plane mir- ror at ef. The light from an object mn is collected by the lens and made to fall on the mir- Fig. 187. Explain the manner in which the image is formed. Why does not the image appear inverted ? Describe Fig. 187. 380 OPTICS. ror, which, being inclined at an angle of 45 degrees, reflects the horizontal rays perpendicularly, (Art. 428.) and from an image of the object ik on a screen placed at og. hg is the movable lid of the box. This form of the camera obscura is the one usually employed in taking Daguerreotypes. In the place of the object m n, the human face may be sub- stituted ; and instead of the screen og,s. plate coated with a thin surface of silver, and exposed to the fumes of a sub- stance called iodine. On the plate thus prepared the rays of light impress a perfect image of the object, which is ren- dered more distinct and visible by exposing it to the fumes of mercury, and various chemical preparations. CHAPTEK VII. OF TELESCOPES. 499. The Telescope is an optical instrument, designed to aid the eye in vieunng distant objects. The construction of this noblest of instruments in its dif- ferent forms, involves the application of all the leading prin- ciples of the science of Optics. The study of the Telescope is therefore the study of the science, and a distinct enuncia- tion of the principles involved in it. will serve as a recapitu- lation of the most useful principles of Optics. The advantage which the student will derive from reviewing these points, as exemplified in their application, will justify us in bringing up distinctly to view various principles already unfolded. 500. The leading principle of the Telescope may be thus enunciated : By means of either a convex lens, or a concave mirror, an image of the object is formed, which is viewed and magnified icith a microscope. The most general division of the instrument is into Ee- fracting and Keflecting Telescopes ; of which the former produce their image by means of a convex lens, and the latter by means of a concave mirror. The instrument, ac- cording to the uses to which it is applied, receives the farther BKpIain the mode of taking daguen-eotyes. Telescope. — Define the tele- Boope. What is said of the study of it? Enuuciate Us leading principle. What are the two principal kinds ? TELESCOPES. 381 denominations of the Astronomical and the Terrestrial Telescope ; and also Telescopes are named after their seve- ral inventors, Galileo's, Newton's, Gregory's, Herschel's, &c. THE ASTRONOMICAL TELESCOPE. 501. We begin with this variety because it is one of the most simple, and because, in connection with it, we may conveniently study the theory of the instrument at (arge. Let A BCD, (Fig. 188,) represent the tube of the tele- Tig. 188. scope. At the front end, or at the end which is directed to- wards the object, (which we will suppose to be the moon,) is inserted a convex lens, L, which receives the rays of light from the moon, and collects them into the focus at a, forming an image of the moon. The image is viewed by a magni- fier attached to the end B 0. The lens L is called the object-glass, and the microscope in B the eye-glass. We view the image at a distance equal to its focus of parallel rays. Of course, the distance of the two glasses from each other is equal to the sum of their focal distances. See the annexed figure. MN, object-glass. PQ. eye-glass. A'D', AD, A''D", parallel rays from the top of the object. B'D', BD, B"D", " " " center dko. C'D', CD, CD", " « " bottom ditto. ba, inverted image formed in the focus of parallel rays Specify the different eorta of Telescopes. Astronomical Telescope. — De- scribe Fig. 3 88. How many glasses has it ? What is the object-glass, and what the eye-glass T What cilice does each perform 1 Describe by the Bgui-e. 382 6PF, a pencil of rays, proceeding from the top of the image to the eye-glass and rendered parallel. Fig. 189. cKF, a similar pencil from the center. «QP, ditto ^ bottom. F, point where the different pencils cross the axis. 502. In this instrument we observe a striking resem- blance to the Compound Microscope. (Fig. 185.) In the microscope, however, since the object is nearer the lens than the image, the image is greater than the opject ; but in the telescope, since the object is removed to a great distance, the image is formed much nearer to the lens than the object, and is proportionally smaller. Hence, Compound Microscopes have their tubes enlarged in diameter towards the eye-glass, while telescopes have their tubes diminished in that direc- tion. Since the vertical angles at D, subtended on the one side by the object, and on the other by the image, are equal, were the eye situated at the center of the object-glass, it would see the object and the image under the same visual angle, and consequently, both would appear of the same magnitude. Moreover were the eye placed at the same dis- tance from the image on the other side of it, it would be apparently of the same size as before, and therefore of the same apparent diameter as the object. But by means of a microscope, such as the eye-glass in fact is, we ma)' view it at a much nearer distance, and of course magnify it to an) extent, as was fully shown in explaining the principles of the simple microscope. (Art. 485.) Hence the magnifying Point out bow it resembles tbe compound microscope, and liow it differs from it. Wliy have compound microscopes tbeir tubes enlart^ed, and tele- scopes their tubes diminished towards the eye-glass? Were the eye situated at the center of the object-glass, how would it see the object and the image ? Explain how it magnifies. On what ratio does the magnifying power depend ? TELESCOPES. 383 power of the telescope depends on the ratio between the focal distances of the object-glass and the eye-glass. If, as in the figure, the common focus is ten times nearer the eye- glass than to the object-glass, the instrument will magnify ten times; if one hundred times nearer, on6 hundred times; and so in all other cases. Hence we may increase the magnifying power of the instrument, either by employing an object-glass of a very small curvature, which throws its image to a great distance, or an eye-glass of high curvature and small focal distance. Suppose, for example, the object- glass has a focal distance of forty feet, or four hundred and eighty inches, and the eye-glass has a focal distance of one tenth of an inch, then the magnifying power of this instru- ment would be four thousand and eight hundred in diame- ter, and the square of this number in surface. 503. As the sphericity of the eye-glass may be increased indefinitely, and its focal distance diminished to the same extent, it would seem possible to apply very high magnify- ing powers in very short telescopes. For example, suppose the focal distance of the object-glass is twenty-four inches ; by using a microscope of i^o-th of an inch focus, we have a power of two hundred and forty. But it must be kept in mind, that such microscopes command only an exceedingly small field of view, and would, therefore, not enable us to see anything more than a minute portion of an object of any considerable size ; and not sufficient light would be trans- mitted through such an aperture to answer the purpose of vision. Since the image is inverted with respect to the object, and is viewed in this situation by the eye-glass, objects seen through Astronomical Telescopes appear inverted. By the addition of several more lenses, they may be made to appear erect, as will be shown in the description of the Day Glass, or Terrestrial Telescope ; but at every new refraction a cer- tain portion of light is extinguished, a loss which it is impor- tant to avoid in instruments designed to be used at night; while, in regard to celestial objects, it is not essential wheth- er they are seen erect or inverted. The place for the eye to view the image with the best advantage is at F, where the pencils of parallel rays meet. How may we increase the magnifying power ? What would it be, when the object-glass has a focal distance of 40 feet, and the eye-glass a focal dis- tance of 1-10 inch 1 Why can we not apply high magnifiers in very short telescopes ? Are objects seen by astronomical telescopes erect or inverted ? Why is it not made erect by introducing additional lenses ? 384 OPTICS. 504. The difficuhies to be overcome in the construction of a perfect Refracting- Telescope, (some of which are very formidable.) are chiefly the following: 1. Spherical aberra- tion ; 2. Chromatic aberration ; 3. Want of sufficient light ; 4. Want of a field of view sufficiently ample ; 5. Imperfec tions of glass. Each of these particulars we will briefly con- sider. 505. SpJierical aberration, it will be recollected, occasions indistinctness in images formed by lenses, in consequence of the different rays of the same pencil not being all brought to a focus at the same point, those which fall upon the ex- treme parts of the lens being more refracted and coming to a focus sooner than those which are nearer to the axis. (See Art. 448.) The amount of this error is found to depend on two circumstances, namely, the diameter of the lens, or what is technically called its aperture, and its focal distance; in- creasing rapidly as the aperture is increased, and diminish- ing as the focal distance is increased. Small apertures and flat or thin lenses are. tJierefore, most free from spherical aberration. But if we use small apertures we cannot have a strong light, which is a circumstance of the greatest im- portance in astronomical observations, since it is of little consequence to enlarge the dimensions of an object if we have not light enough to render it visible. Indeed, many astro nomical objects, as small stars, are rendered visible by the telescope, not in consequence of any apparent increase or size, but because this instrument collects and conveys to tho eye a much larger beam of light from them than would oth- erwise enter it. While the diameter of the beam which falls, upon the naked eye is only the fraction of an inch, that col- lected by the telescope may be several inches, or even seve- ral feet, according to the size of the instrument. Hence, the advantage of large apertures is obvious. Again, we cannot wholly remedy the error in question, though we may di minish it, by using very flat lenses which have great foca" distances ; but the tendency of this expedient is to rendei the instrument inconveniently long. Other expedients, therefore, become necessary for correcting spherical aberra tion in refracting telescopes. 506. In the eye-glasses, which are liable to the sam« State the difficulties to be overcome. Spherical aberration — what -a it ' On what two circumstances does it depend? WTiat kind of apertures and lenses are most free from it t What inconvenience attends the usa of su<:L apertures ? What is the inconvenience of using very fiat lenses ? TELESCOPES. 385 difficulty, where the lens has a great curvature, as is the cast with such as have high magnifying powders, the aperture ia necessarily reduced very much, by excluding all the light except virhat passes through the central parts of the lens. At least this is the case where glass lenses are used. But the microscopes made of diamond, sapphire, and other gems, have not only high refractive powers, but are less subject to spherical aberration than similar lenses of glass. But although eye pieces, on account of their small size, may sometimes be made of the precious gems, yet this can rarely be the case on account of the great expense attending them. It is obvious also that they cannot be employed for the object lenses. The most successful method of diminish- ing spherical aberration in eye pieces of glass is by a com- bination of plano-convex lenses, by means of which a given refracting power may be attained with far greater distinct- ness than by a single lens of the same power. Thus, when two plano-convex lenses are placed as in Fig. 190, it is found that the image has four times the distinct- ^^S- 19". ness of a double con- vex lens of equivalent power.* Here F is a lens which would bring the parallel rays to a focus and form the image at the distance of Gr ; but E is another similar lens, which receiving them in a converging state, makes them converge more and come to a focus at H. The double convex lens D would do the same, but with much greater spherical aberration. It ap- pears, indeed, that the spherical aberration may be wholly removed by combining a meniscus with a double convex lens of certain curvatures. 507. In object-glasses, which, on account of their small curvatures, are not so subject to error from spherical aber- ration as eye-glasses are, the most advantageous form is that of a double convex lens of unequal curvatures, the radii of <,_ • Tha SciopUc Ball used in the camera obacura, (Art. 472,) Is furmed of two Buch lenses. What advantages have eye pieces made of diamond, sapphire, &n. ? How is spherical aberration diminished in eye pieces of glass? Illustratf by the figure. What is the most advantageous form of object-glasses? 33 386 OPTICS. the opposite surfaces being as one to six and the flat side be- ing- turned towards the parallel rays. In short, it appears that in order to avoid the errors ari- sing from spherical aberration, in large lenses, they must be made as thin as convenience will permit ; that where it is practicable, they may be most advantageously formed of the precious gems, particularly the diamond ; that a piano-con vex lens with its convex side toward the parallel rays has less aberration than a double convex lens of equivalent pow- er ; that two plano-convex lenses may be so combined as to have only one fourth as much aberration as the double lens, and a meniscus may be so united to a double convex lens as wholly to prevent aberration ; and finally, that the aberra- tion may be reduced to a very small error simply by em- ploying a double convex lens whose curvatures on the oppo- site sides are 1 to 6. Since lenses having the curvature of one of the conic sec- tions are free from spherical aberration. Sir Isaac Newton ground an object-glass into the figure of a paraboloid. This was free from the error in question, but involved another still more formidable since it decompcsed the light and gave an image tinged with the colors of the rainbow. On observ- ing this. Sir Isaac pronounced the farther improvement of the refracting telescope to be hopeless and betook himself to exclusive eflbrts for improving the reflecting telescope. But the combined ingenuity of philosophers and artists has nearly overcome this error also. 508. The next difficulty, therefore, to be considered, is that which arises from the separation of the prismatic colors, in consequence of the different refrangibiiity of the different rays, an error which is called Chromatic Aberration. The general principles of Chromatic Aberration, will be readily comprehended by calling to mind, that distinct ima- ges are formed only when the rays of the same pencil which flow from any point in the object are collected into one and the same point in the image, unmixed with rays from any other point ; that the prismatic rays which compose white light have severally different degrees of refrangibiiity, some being more turned out of their course than others, in pass- ing through the same medium ; that, consequently, the dif- ferent colored rays of the same pencil would meet in differ- State the several expedieots for avoiding the errors of spherical aberration. Why may not leupes of a parabolic figure be used ? Chromatic aberration, — Explain what it is. TELESCOPES. 387 ent points, each set of colored rays forming its own image, but all these images becoming blended with one another, would thus compose a confused, colored picture. To illustrate these principles let L L be a lens of crown glass, and RL, RL rays of white light incident Fig. 191. upon it, parallel to its ^ ^ axis Rr. Let the ex- ^ ^°= ' -''* treme violet rays be re- fracted so as to meet the ^ axis in v ; then the ex- treme red will meet the R axis at some point more distant from the lens, as at r. Gv and Cr are the focal dis- tances of the lens for the violet and the red rays respective- ly. The distance vr is the chromatic aberration, and the circle whose diameter is ab, which passes through the focus of the mean refrangible rays at 0, is called the ci/cle of least aberration 509. It is clear from these observations, that the lens will forrri a violet image of the sun at v, a red image at r, and images of the other colors of the spectrum at interme- diate points between r and v ; so that if we place the eye behind these images we shall see a confused image, possess- ing none of that sharpness and distinctness which it would have had if formed only by one kind of rays. The separation of white light into its prismatic colors, is called Dispersion ; and the comparative power of effecting this separation possessed by different media, is called the Dispersive power. The dispersive power is measured by the ratio which, in any case, the separation of the red and violet rays bears to the mean refraction of the compound ray. Thus, if a ray of solar light on passing through a lens, is turned out of its original direction 27°, and the red and vio- let rays are separated from each other 1 ^, then the disper- sive power is said to be ^Vj which is usually expressed in the form of a decimal fraction, .037=^7. 510. Different bodies possess different dispersive powers. The dispersive powers of a few of the most important sub- stances in relation to the subject before us,, are exhibited in the following table. Illustrate by the figure. Define Dispersion, and Dispersive Power. What is meant by saying that the dispersive power is l-27th 7 338 OPTICS. DispDrsive Power. ^^^- Power. OilofCassm. 0.139 Plate Glass, 0.032 Sulphuret of Carbon, 0.130 Sulphuric Acid, 0.031 Oil of Bitter Almonds, 0.079 Alcohol, 0.0-29 Flint Glass, 0.052 Rock Crystal, 0.026 Muriatic Acid, 0.043 Blue Sapphire, 0.026 Diamond, 0.038 Fluor Spar, 0.022 Grown Glass, (green) 0.036 From this table it appears that the transparent substances which have the highest dispersive power, are the oil of cassia and the sulphuret of carbon,* both of which fluids have been made to perform an important service in the con- struction of achromatic telescopes ; that flint glass, as that used for decanters, has a much higher dispersive power than crown glass, or that which is analogous to window glass ; that the diamond has a low dispersive power, but it is ex- ceeded in this by rock crystal, the sapphire, and fluor spar, which last bodies have the least dispersive power of any known substances. 511. With these facts in view, we may now inquire by tohat means tJm ohject-glass of the telescope is rendered achro- matic. If we place behind LL (Fig. 191.) a concave lens GG of the same glass, and having its surfaces ground to the same curvature, such a lens having properties directly opposite to those of the convex lens, will neutralize its effects. Conse- quently, the rays which were separated into their prismatic colors by the convex lens will be reunited by the concave lens, and reproduce white light. But though such a com- bination of the two lenses will correct the color, yet it also destroys the power of the convex lens to form an image, on which its use solely depends. Could we find a concave lens which would correct all the color and yet not destroy this refracting power, the two lenses would evidently form the achromatic combination sought for. Now this is what is actually done : by making the concave lens of a substance which has a higher dispersive jioiver than that of which the convex lens is made, the curvature of the concave lens will * A limpid fluid prepared from sulphur and cliarcual. What bodies have the greatest dispersive powers ? What the least t By what means is the object-glass of the tele.scope rendered achromatic 7 State the combination of two lenses, so as to destrov the chromatic effect but leave u refracting power. TELESCOPES. 389 not need to be so great as that of the convex lens, and of course the two together, constituting the compound lens, will be ec,uivalent in refracting power to a single lens, whose convexity is equal to the difference of their curvatures. The most common combination is that of flint glass with crown glass, the concave lens being made of flint glass, and the convex of crown. By the table in Art. 510, it will be seen that the dispersive power of flint glass is 52, while that of crown glass is 36, which numbers are nearly as 3 to 2, and these numbers, therefore, may be employed for the sake of illustration. Since the power of the concave lens to reunite the prismatic rays is so much greater than that of the con- vex lens to separate them, we shall not require a refractive power to effect this equivalent to that of the convex lens ; that is, a concave lens of less curvature and proportionally greater focal distance, will serve our purpose. Therefore, An achromatic lens is formed by the union of a convex and a concave lens, whose dispersive powers are respectively proportional to their focal distances. 5 1 2. A telescope furnished with an object-glass thus formed, is called an Achromatic Telescope. The spherical aberration being corrected by the methods pointed out in Art. 505, and the chromatic aberration being destroyed in the manner above described, the Refracting Telescope be- comes an instrument of great perfection, and is reckoned among the greatest works of art. Until recently, it was rare to meet with Refracting Telescopes of an aperture of more than from three to five inches ; for we have already seen that the errors of spherical and chromatic aberration increase rapidly, as the size of the aperture is augmented. 513« If it be asked what is the use of a large aperture, since the magnifying power does not depend upon the di- ameter of the object-glass, but upon the ratio between the focal distance of the object-glass and the focal distance of the eye-glass, (Art. 502,) we answer, that the use of a large aperture" is to admit, condense, and finally convey to the eye, a larger beam of light, and thus to render many objects as the smaller stars, or Jupiter's belts, visible, which other- wise would not be so. on account of the feebleness of the light which they transmit to us. Want of light is in fact one of the greatest difficulties that the telescope has to con- Of what substances are the two lenses made ? State the proposition. What is said of the perfection of the achromatic telescope! What is the use of a large aperture ! 33* 390 OPTICS. tend with ; for, in the first place, the object glasses of most telescopes are comparatively small, and are necessarily so on account of the difficulty of procuring suitable glass for those of a larger size ; an-d in the second place, of the light admitted through the object-glass, a great proportion is in- tercepted and wasted in various ways, many instruments being able to save only the central rays without rendering the image indistinct and colored. Thus, when very high magnifiers are applied, (which of course have very small focal distances,) the rays proceed from the focus and fall upon the microscope so obliquely, that only those which pass through the central parts of the lens can be saved, since such as fall upon the marginal parts of the lens are too much effected by spherical and chromatic aberration, to form with the others a distinct and colorless image. 514. Want of Jield of view is another difficulty to be surmounted. When we use an object-glass of short focus with a high magnifier, the microscope must have a focus proportionally short, and of course the field of view will be very limited and the light but feeble. This difiiculty may be obviated by using an object-glass of very great focal distance. If, for example, the focal distance of the object- glass were only 12 inches, in order to attain a magnifying power of 120, we must employ a microscope whose focal distance is only -(Vth of an inch. But if the focal distance of ttie object-glass were 10 feet, or 120 inches, then our microscope might have a focal distance of 1 inch, which would give a larger field, and a stronger light With the view of obviating several of the foregoing difficulties, the earlier astronomers who used the telescope, employed for their object-glasses lenses whose focal lengths were very great. Cassini, a French astronomer, constructed telescopes eighty, one hundred, and one hundred and thirty-six feet long ; and Huygens employed such as were nearly the same length. The latter astronomer dispensed with the tube, fixing his object-glass, contained in a short tube, to the top of a high pole, and forming the image in the air near the level of the eye, which image he viewed with an eye-glass as usual. With telescopes of this description, several of the satellites of Saturn were discovered. What is said of waTii of light? Why are very high magnifiers attended with a want of Mght 7 What is said of watit of fiM 1 What advantage , have very long telescopes ? How long have they sometimes been made ? TELESCOPES. 391 515. But one of the most formidable difficulties hitherto encountered in the construction of large Eefracting Tele- scopes, has arisen from the imperfections of glass. When Dolland (the English artist who first perfected the Achro- matic Telescope,) engaged in the manufacture of his instru- ments, he fortunately had possession of a considerable quantity of very fine glass ; but when that was used up, no more of equal quality could be obtained in England.* On the continent, however, one or two celebrated artists have been more successful. The most distinguished manufac- turer of optical glass was M. Guinand of Switzerland, who died in 1823. He greatly excelled all his predecessors or contemporaries in fabricating large masses of perfectly homogeneous glass. But even he could produce disks of twelve or eighteen inches in diameter in no other way, than by selecting the purest specimens of smaller pieces, and joining them together. In 1805, M. Fraunhofer of Bavaria, a celebrated manufacturer of telescopes, invited G-uinand to become his associate in the manufacture of optical glass ; and from the united efforts of these most ingenious men, pro- ceeded glass of unexampled transparency and purity. Fraun- hofer has recently deceased, but the finest optical glass is still made by his successors, Merz and Mahler. 516< These circumstances we have thought worthy of being recited in order to impress on the mind of the learner the formidable nature, as well as the great number, of the difficulties to be overcome in the construction of a large Achromatic Telescope. Yet they have in several instances, been completely sui naounted. Fraunhofer executed two telescopes with achromatic object-glasses, the one nine inches and nine tenths, and the other twelve inches in di- ameter ; and at the period of his death, he was proposing to undertake one eighteen inches in diameter. That of 9.9 inches aperture was made for the Russian government, for the use of the observatory at Dorpat, where under the di- rection of M. Struve, a distinguished astronomer, it has already achieved several valuable discoveries in astronomy. • Ttie present Mr, Dolland, a successor of the inventor of Achromatic Telescopes, "has Dot been able to obtain a disk of flint glass four inches and a half in diameter, fit for a telescope, within the last ^ve years, or a similar disk of Ave inches diameter Witliia the last ten years." — Faraaiy^ Phil. Trans- 1830, WTiat is said of the imperfections cfglass 1 Wlio has made the best glass ? What is said of Fraunhofer V What is said of the size and quality of the Dorpat telescope ? 392 OPTICS. The object-glass has a focal length of twenty-five feet The concave part of the compound lens is formed of a dense flint glass made by Guinand, and has a greater dispersive power than any obtained before. It is perfectly free from veins and nearly from every impurity. The instrument has four eye-glasses, varying in magnifying power from one hundred and seventy-five to seven hundred.* But still finer refracting telescopes have recently been constructed, especially one for the observatory at Pulkova, near St. Petersburg, and another for the observatory of Harvard College. The latter is probably the finest refractor hitherto constructed. Its aperture (the available diameter of the bbject-glass,) is nearly 15 inches, and its focal length is 22 feet 8 inches. Its highest magnifying power is about 2000. THE TERRESTRIAL OR DAY TELESCOPE. 517. As the Astronomical Telescope represents objects inverted, it requires to be so modified for terrestrial views, that objects may appear erect. This is effected by the ad- dition of two more lenses of similar figure to that of the eyeglass, and of the same focal length. The first of these additional glasses forms a second image of the object invert- ed with respect to the first image and therefore erect with respect to the object. The image is viewed by the second glass as by a simple microscope. Thus, AB, the object- Pig. 192. glass forms an inverted image nm of the object at MM. Instead of viewing this image by the eye placed at L, as in * It ia said that as a general rule Achronmtic Telescopes are priced in the ratio of the cube of the aperture. If a telescope with an objoot^glaud three inches in diameter is valued at five hundred dollars, one of twelve inches would cost sixty- four tiiueB w much, that is thirty-two thousand dollars. What are ita magnifying powers ? . What is said of the great Pulkova and Cambridge Uefraotora ? Day Glass. — How does it represent objects T By wliat means is this effected ? Describe the construction by the figure. TELKSCOPES. 393 the common astronomical telescope, we suffer the pencils of parallel rays to cross each other at L and fall upon a second lens EP (similar in all respects to CD) which collects them into an image m'n' in its focus of parallel rays, which image is viewed by the eye-glass GH in tha same man»er as the object itself would be. As some portion of the light is reflected, and some ab- sorbed and dissipated by passing through these additional lenses, they of course diminish the brightness of the view ; but in the day-time there will usually be light enough for distinct vision after this loss is sustained, while it is more agreeable and convenient to have the objects presented to us in their natural positions than inverted. It will be re- marked that the additional lenses do not magnify, the focal length of each being the same as that of the first eye-glass. Were they rendered smaller for the purpose of magnifying, the field of view and the light would both be impaired, 518. We usually find in telescopes, particularly those designed for terrestrial objects, some contrivance, as a draw tube, by which the eye-glass can he brought near to, or withdrawn from the object-glass. This is to accommodate the instrument to objects at different distances. When it is directed to very near objects, the image is thrown farther back, and therefore in order that it ma,y be in the focus of the eye-glasses (which is essential to distinct vision) the lat- ter must be drawn backward ; but where the object is re- mote, the image is formed nearer to the object glass and then the eyeglass must be moved forward, till its focus of fiarallel rays comes to the place of the image. For a simi- ar reason, near-sighted persons require the. eye-glass to be brought nearer than usual to the object-glass ; for then the image will be nearer to the eye-glass than its focus of par- allel rays, and the rays will meet the eye diverging, a con- dition favorable to eyes naturally too' convex. For a con- trary reason, long-sighted persons, who usually wear convex spectacles, may adjust the telescope to suit their eyes with- out spectacles, by removing the eye-glass farther back than usual. Most terrestrial telescopes contain a greater number of glasses than are represented in Fig. 192. Such a number ■What effect have the additional glasses upon the brightness of the image ? Do these magnify 1 What is the use of the draw tube 1 What is the use of the glasses scmetimea employed in addition to those required to make the image erect? 4 394 _ OPTICS. are used for the purpose of correcting spherical and chromatic aberration, these errors being less in several fiat and thin lenses than in a smaller number of equivalent lenses of greater curvature. "Astronomical telescopes are easily adapted to terrestrial observations, by removing the eyeglass and substituting a tube containing the additional glasses for rendering the view erect. REFLECTING TELESCOPE. 5 1 9« Eeflecting Telescopes differ in principle from those already described only in forming their image -by a concave reflector, instead of a convex object-glass. The most com- mon form of the Reflecting Telescope, is the Gregorian, so called from the inventor, Dr. James Gregory of Scotland. The general principles of this instrument may be explained as follovsfs : In the G-regorian telescope, the light (supposed to come in parallel rays) is first received by a large concave speculum, by which it is brought to a focus and made to form an in- verted image. On the opposite side of this image, and fa- cing the large speculum, is placed a small concave speculum, of great curvature, at such a distance from the image that the rays proceeding from it and falling on the speculum are made to converge to a focus situated a small distance behind the large speculum, passing through a circular aperture in the center of it. This second image is magnified by a mi- croscope as in the Refracting Telescope. This description may now be applied to the annexed figure. Fig. 193. B How may astronomical telescopes be adapted to terrestrial observations ? Rejkcting Telescopes. — How do they form the image? In the Gregoriap telescope, how is tne image formed? State how this, by a second reflexion, is conveyed to the eye ? TELESCOPES. 395 A B D, a large tube of brass, iron, or mahogany to soutain the reflectors. abed, a. smaller tube to receive the second image and the eye-glass. E E, large concave speculum, usually composed of a me- tallic compound called speculum metal. F F, small concave speculum. m n, image formed by the large reflector. n m, image formed by the small reflector. Gr, eye-glass. W Y, a metallic rod having a screw connected with the small reflector, by means ol which this reflector is made to approach the first image or to recede from it. Some of the pencils of rays necessary to form the respect- ive images, are omitted in the figure to prevent confusion. 5 20. From the foregoing construction it is evident, first, that the image viewed by the eye being in the same posi- tion with the object, the latter will appear erect ; secondly, that since the mirrors may be formed of a parabolic figure,* all spherical aberration may be easily prevented ; thirdly, that since light is not decomposed by reflexion, reflecting telescopes are not subject to chromatic aberration ; and, hence, that it is not necessary to lengthen the tube as the aperture is increased, as is the case in refracting telescopes ; (Art. 514,) but since the light will depend, chiefly on the size of the large reflector, a strong light may be obtained with a comparatively short tube. 521. Under the munificent patronage of George III., Sir William Herschel began, in 1785, to construct a tele- scope forty feet long, and in 1789, on the day when it was completed, he discovered with it the sixth satellite of Sat- urn. The great speculum was more ihsxi four feet in diam- eter, and weighed two thousand one hundred and eighteen pounds. Its focal length was forty feet. The tube which contained it was made of sheet iron. . The light afforded by this instrument was astonishingly great. The largest fixed stars, as Sirius, shone in it with the splendor of tfje sun. The reason of this will be obvious when we reflect that it collected and conveyed to the eye, in * An elliptical figure has the same property. Describe from the figure. Does the Gregorian telescope give the image erect or inverted 1 How is spherical snd chromatio aberration prevented 7 Give an account of Herschel's great telescope. When was it made f What was the size and weight of the great specnlain ' 396 OPTICS. place of the small beam that enters the naked organ a beam of light from the star more than four feet in diameter. Hence it was suited to reveal to the eye numberless stars and clusters of stars, which preceding telescopes had failed to exhibit, because they could not collect a sufficient quan- tity of their light. To economize the light to the best ad- vantage, the small mirror employed in the Gregorian tele- scope (see Fig. 193,) was dispensed with, since every suc- cessive reflexion dissipates a considerable portion of the light, and the image was thrown near to the open mouth of the tube, where it was viewed by the eye-glass directly, the observer being seated so as to look into the mouth in front. In order to prevent the head from obstructing too much of the light, the image was formed near one side of the tube. Its greatest magnifying power was six thousand four hun- dred and fifty ; but this was used only for the smallest stars. But Lord Ross, an Irish nobleman, has recently construct- ed a Reflector, (called the Leviathan^ far excelling that of Herschej, having a speculum 6 feet in diameter, and a tube 50 feet long. The peculiar advantage of these huge instruments, is to collect and transmit to the eye a great amount of light. In magnifying power the large Refrac- tors, like the Cambridge telescope, may be sufficient for all purposes ; but where very dim objects are to be seen, a telescope which conveys to the eye a beam of light six feet in diameter has great advantages over one that commands a beam of only 15 inches. It is a fact, however, that mirrors waste much more of the light than lenses, and are liable to become tarnished by time, and blurred by certain states of the atmosphere; so that a Refractor of the largest class is preferable for most astronomical observations and researches to such instruments as the Leviathan telescope of Lord Ross. To what point was the image thrown. What is the size of Lord RosaS telescope 1 What is the peculiar advantage of large Keflectors 1 SUPPLEMENT OLMSTED'S COMPENDIUM. CONTAINING INSTRUCTIONS TO YOUNG EXPERIMENTERS, TOGETHER WITH A COPIO'IS LIST OF EXPERIMENTS TN NATURAL PHILOSOPHY, ACCOMFAinED BY MINUTE DIRECTIONS FOR PERFORMING THEM, NUMEROUS ENGRAVINGS OF AFPARATUa NEW YORK: CLAEK, AUSTIN & SMITH, 8 PAKE BOW AND S ANN-STBEET. SUPPLEMENT. PART I. INSTRUCTIONS TO YOUNG EXPERIMENTERS. Introductory Observations — Selection and care of Apparatus — Stria- tore and Furniture of Work-room — ^Various Processes connect'sd with experimenting. Section 1. — Introductory Observations. Some persons have a natural aptitude for performing philo- sophical experiments — a certain mechanical turn — which enables them to acquire with ease, what others learn only after great efforts and much experience. Still, no one need despair of becoming expert at this business, il he will set himself seriously at work to learn the trade. It is indispensable to any public course of experiments that they should always succeed. Frequent failures will be followed by a loss of confidence in the pupil. He will either doubt the truth of the proposition itself, which it is the object of the experiment to establish, or he will lose some portion of his respect for his teacher. Indeed, there is a singular sense of the ridiculous, which is apt to come over the mind of the pupil when he sees an experiment fail in the hands of his instructor. Hence, the most adroit and experienced lec- turers in experimental philosophy, find it necessary to make thorough preparation for every lecture, and will hardly risk a single experiment in the presence of their audience unless they have immediately before performed it with success in private. When we see the manipulations of a skilful experimenter, and witness his uniform success, the whole appears so easy, and done with so little apparent effort, that the spectator would suppose that he could do the same ; but, if wholly inexperienced, he would, on trial, probably fail in more than half his experiments, and ir none would he exhibit the ease 400 SUPPLEMENT. and grace of the accomplished lecturer. Three qualities, therefore, are essential to experiments exhibited in public instruction — success, neatness, and elegance. Whenever it is practicable, we would advise every one who has it in view to give a public course of instruction in any branch of ex- perimental philosophy, to serve an apprenticeship under a distinguished master. Let him gain admittance behind the scenes, and he will be surprised to find how many nice points of preparation are involved, in order to give to the public exhibition of experiments that ease and elegance which he had perhaps considered as a matter of course. A few weeks passed where he can witness the private prepara- tory experiments of an accomplished teacher, will aid him more than volumes of directions can do. Many teachers, however, are so situated as to be unable to avail themselves of such an opportunity, and others would, perhaps, be induced to repeat, for their own improvement and entertainment, more or less of the interesting experiments in philosophy, if they were supplied with the necessary instructions. It is chiefly for these two classes of readers that the present article is prepared. Instructions like these, in order to be useful, must be minute. General directions will avail little ; and we regret that our limits do not permit us to be more particular than it is pos- sible to be in so small a space. We most earnestly wish that some one would do for Natural Philosophy what Fara- day has done for Chemistry, in his excellent work on " Chemical Manipulation." If our brief directions should prove inadequate to form the accomplished public lecturer in experimental philosophy, we trust they may still be very useful to private learners who, as a recreation both profita- ble and elegant, or as the means of obtaining more complete eatisfaction, may desire to repeat more or less of the experi- ments of which they read, or which they have witnessed in the lecture-room. On learning the private preparation of those experimenters who exhibit, in their public instructions, the highest degree of success and elegance, it will be found that they have be- forehand had distinctly in mind all the circumstances that enter into each experiment. If a lighted taper, for instance, is used in an experiment, they will not have to go to some distant part of the room to find it, and then have to look up a match to light it ; but it will be within their reach, near 4 INSTRUCTIONS TO YOTTNQ EXPERIMKNTERS. 401 the articles in connection with which it is used, and the match that is to kindle it will be close by its side. If in an experi- ment water is employed, the audience will not be kept wait- ing until it is brought from some distant well or spring ; but it will stand within reach of the operator, and in such a ves- sel as is exactly adapted to the use to be made of it. All these devices to render experiments easy and graceful, as well as sure, usually escape the notice of the spectator ; yet they are generally the fruit of much previous preparation and study. Among the innumerable devices by which uni- form success and apparent ease are obtained, a few are very obvious. Such are the following : — Joints must be close, and never leak ; there must be no spilling or slopping ; no break- age ; no burning of fingers or soiling of clothes ; and every thing must come out agreeably to the predictions of the ex- perimenter and the expectations of the audience. We would not, by the foregoing remarks, discourage young teachers from attempting a course of experiments before their pupils, but we would only urge them to makp euch preparation beforehand as will insure success, and add a certain degree of elegance and grace. It is the want of such preparation that has discouraged many teachers in their attempts to perform the experiments indicated in their text-books ; and hence, valuable collections of apparatus have frequently been purchased by academies, which have remained nearly or quite useless, for want of either ability or inclination in the instructors to bring them into common use. The great number of duties and cares that devolve on most preceptors furnishes indeed, oftentimes, another and more satisfactory reason for neglecting the full use of such aoparatus, since they find it impossible to command time for making the necessary preparation for experimental lec- tures. . The leading objects of the present article are, to prescribe rules for the selection, care, and adjustment of philosophical instruments ; to give directions for the structure and furni- ture of a work-room ; and to offer to the young experimentei minute instructions for performing various processes, which enter more or less into every course of experiments. With such preparation, we propose next to present to him a selec tion of experiments, adapted to the present work, and to sug- gest the various devices which may contribute to render them successful and instructive. 34* 402 siTPPLEMENr. Section Z.— Of the Selection, Gore, and Adjustment of Ph- losophical Apparatus. Although no ill-made apparatus is to be purchased mere- ly because it is cheap, yet it may be more or less plain, ac- cording to the sum to be expended. When the sum is small, utility alone is to be consulted, both in the kind and in the quality of apparatus ; but when a large sum can be com- manded, (large in proportion to the wants of the institution,) then elegance may be more regarded, since no ornaments are more appropriate to any literary institution than its phi- losophical apparatus. It is an encouraging fact, that a great number of useful articles of apparatus may be purchased for a very small sum ; and many ingenious devices may be employed to save expense, by adapting ordinary vessels used in housekeeping to the same purposes as apparatus. For such a course of experiments as will be described in the second part of this article, so small a sum as one hundred dollars will, with judicious economy, supply a great number of useful articles of apparatus, avoiding such instruments as are individually expensive. Five hundred dollars will enable us to add some instruments, as Atwood's Machine, of more costly workmanship ; and one thousand dollars will authorize us to consult for completeness and elegance.* Unless some agent can be employed to select a set of ap- paratus, who is very conversant with instruments, the best safe- guard the purchaser can have, will be the reputation of the artist, who should be well known as a skilful workman, and a man of probity. A philosophical instrument maker is sel- dom accomplished in his art, unless he is a man of intelli- gence, and is himself well acquainted with the principles which his instruments are designed to illustrate, and able to operate with them to the best advantage. It is one source of economy to make the same piece of apparatus serve many different purposes, and the value of an instrument is often tested by the number of things it will show. Artists themselves ought to adapt their instruments severally to as many different uses as possible, and thus to increase their utility ; and an artist who in this manner ren- * It win be recollected here that we are speaking of the exigencies of academies, and not of universities. INSTRUCTIONS TO YOTJNG EXPERIMENTERS. 403 ders his instruments uncommonly useful, is peculiarly de- serving of patronage.* But the care and preservation of philosophical instru- ments, is hardly less important than their original execution. In careless or unskilful hands, the finest apparatus will soon lose all its beauty, and more or less of its accuracy and per- fection. Delicate articles should be kept in drawers or un- der glass cases, and when used they should be made per- fectly clean, and be wiped dry before they are restored to their places. Brass instruments, especially, are much in- jured by oil, or even any spe-sies of moisture, and ought never to be restored to their cases unless perfectly dry and clean, and free especially from the effects of handling. The perspiration of the hand is very injurious when suffered to remain on instruments. Even dust not only impairs the beauty of apparatus, but frequently does it permanent injury by insinuating itself into the valves or joints. Great cau- tion, however, must be used in scouring brass apparatus, not to scratch it, and not to get the polishing material into the joints ; and peculiar pains must be taken to avoid injuring delicate optical instruments by scratching the glass, as will be more particularly insisted on in our remarks on optical instruments. In the disposition and arrangement of apparatus, there ig much room for the exercise of taste and ingenuity ; and few ornaments are more appropriate to a public institution of learning, than well-arranged cases of instruments exhibiting superior means of instruction. Section 3. — Of the Construction and Furniture of the Work-room. It will add much to the convenience of the experimenter, to have a small room near his apparatus or lecture-room, where he has facilities for making or mending apparatus, and preparing various kinds of work connected with a course of experiments. Such a room should be well lighted, and » Philosophical instrument makers can be found in most of our arge cities, who are able to supply to order the various articles of ap- paratus essential to perform these experiments. A large portion of our cuts are loaned expressly for this work, by Mr. Joseph M. Wight- man, 33 Cornhill, Boston, who has the corresponding articles always OP hand and whose skill and fidelity may be fully relied on. 404 SUPPLEMENT. furnished with closets for fuel and waste articles, as empty boxes, worn out apparatus, and the like. It should have a work-bench next to the wall, to which should be firmly at- tached a vise. Over it may be a rack for files, gimlets, pliers, shears and scissors, screw-drivers, and hammers. Near by may be a wall with nails and other supports, on which may be hung one or two saws, and various other arti- cles necessary to mechanical operations. A case of small drawers ought to be near at hand, for containing various raw materials used in a course of experiments. It may not be possible, nor is it necessary, to furnish at first every tool or material which belongs to the work-room ; but when any article is found by experience to be frequently in requisition, it should be constantly kept on hand. Although experiments in Natural Philosophy do not so often require the aid of heat as those in Chemistry, yet this universal agent will be called into requisition many times during a course of experiments ; and, although almost any common fire may be made to answer all the purposes of the experimenter, yet he will find it very convenient to have a small furnace for charcoal. Those made of clay, and used m culinary operations, will be suitable for various occasions ; and a small cylinder stove of sheet iron, furnished at the top with a movable lid, with an opening for a tea-kettle, will be found very useful. A lamp-furnace with an alcohol lamp, supplies the neatest and best mode of applying a moderate heat, especially to liquids. In a large town, where there are various artists and me- chanics at hand, it is less necessary for the experimenter to perform the labors of the work-room, and much valuable time is saved by committing the usual repairs of appai-atus to appropriate mechanics ; but, in more retired situations, it often becomes necessary, in conducting a course of philo- sophical experiments, for the operator himself to meiid ana fit all sorts of instruments. He will have occasion, at times, to solder, to cement, to cut and grind glass, to alter common culinary and household vessels, and adapt them to purposes very different from those for which they were intended. He will have occasion even to make various articles of appa- ratus, of forms more or less complicated. In such circum- stances a mechanical turn is of great service to the experi- menter ; but, if he does not possess this by nature, he may by persevering practice acquire a useful share of it. JVe- mSTRTJCTIONS TO YOtlNG EXrERIMENTERS. 405 cessity is the motlier of invention. No one, however, can ever expect to become an expert and accomplished lecturer in experimental philosophy, without much pains in prepara- tion, and an attention to all those minute circumstancea which, although generally unnoticed by t'.ie spectator, are the secret of the success and elegance of the linished ex. uerimenter. Although occasional disorder may be allowed in the work-room, yet, like a well-conducted kitchen, its habitual appearance should be that of neatness and order , a condi- «on which cannot be secured unless the operator adopts the useful maxim taught in the primary schools, " a place for every thing, and every thing in its place." If the laboratory of the philosopher should be casually thrown into confusion, It must not long remain so ; but whenever he returns to it to undertake the preparation of a new series of experiments, it should not present the discouraging aspect of a dirty or disordered apartment, but that neatness and regularity which are so exhilarating to one when about to engage in any course of labors, intellectual as'well as manual. Let us now consider some of those processes which are to be performed in a philosophical work-room in the prepara- tion of a course of experimental lectures, or in private ex- perimental researches. Section 4. — Of various Processes connected with Philo- sophical Experiments. Fitting Cokks. — The cork is an extiemely useful article In philosophical experiments, and several varieties ought al- ways to be at hand, such as large flat, and cylindrical, of various sizes, from the size of the bung of a barrel to the smallest phial corks. The quality, also, should be the best that can be obtained ; the texture fine, soft, and velvety. When a cork requires paring, hold one end between the thumb and finger of the left hand, and resting the other be- tween the knife and thumb of the right hand, turn it slowly round, so as to bring the side against the edge of the knife. By this method a smooth and even surface will be left, pre- serving the cylindrical shape perfect, whereas the effort to reduce the size of a cork by paring it lengthwise, usually leaves it rough and uneven, and wholly unsuited for making a good joint. A fine file may sometimes be advantageously 406 SCP^LEMENT. used in finishing the process. There are several ways of making a perfect cork joint. It will often be sufficient to dip it into water, and roll it on a table under pressure ; or it may be soaked in boiling water ; or it may be boiled in melted beeswax, afterwards holding it with the tongs over a hot fire for a moment ; or, finally, when a moderate heat is to be applied, it may be simply coated with flour paste. The experiments in natural philosophy seldom require joints to be protected by those infusible lutes which are used in cer- tain powerful chemical processes. Corks sometimes require to be perforated, or hored, for ad- mitting tubes. A burning-iron, tapering at the end, is con- venient for doing this. It is heated to a low redness ; the cork is taken between the thumb and finger of the left hand, and the end rested against a perpendicular wall, on a level with the eye. The hot iron is applied to the center of the end next the eye, and inserted to near the middle of the cork. This is then changed, end for end, and bored through. If the cork be previously pierced with an awl, it may not be necessary to change ends with it, as the iron will then follow the direction of the hole. When the iron is very hot, it should be suffered to remain in the cork but a moment, as the cork will be apt to crack if the iron remains too long. A cork thus bored may be finished with a small rat-tail file. Tha hole should be a little less than the tube to be inserted in it, in order to make a close fit ; and it may be necessary still further to apply cement to the joint, especially when it is required to be air-tight. Corks must not be too tapering, for then they do not come in contact with the neck of a bot- tle in a surface of sufficient extent, but merely touch in a ring around the orifice. Cementing. — A good cement, useful for various purposes, may be made by melting together five ounces of resin, one ounce of beeswax, one ounce of Spanish brown, and a tea- spoonful of plaster of Paris, or brick-dust. A tapering pine stick is a convenient instrument for applying it to a joint in the melted state. When a sufficient quantity is laid on, an iron, moderately heated, may be passed over it, which will make it smooth and glossy. In some instances sealing-wax treated in the same manner, answers well for coating a joint, but it is apt to crack, and when an air-tight joint is required, the above cement is preferable. This kind of cement is most used in fitting up electrical apparatus, but is useful for INSTRUCTIONS TO YOUNG EXPEEIMENTEKS. 40'? many other purposes. Plaster of Paris, in the ground state, as sold by the paint-dealers, is a good cement for certain purposes, as, for example, when a brass cap is to be fasten- ed upon the neck of a glass vessel. It is to be roasted in a ladle at a red heat, and when cold, to be made into a paste with water, and applied immediately. Flour Paste is often used, and should be always on hand, in a covered jar or gallipot. To make it free from lumps, and not liable to mould, observe the following directions. To half a pint of cold water add enough wheat flour to make it of the consistence of cream ; stir the mixture well and place it over a steady fire, stirring frequently, until it boils. Finally, stir in a grain of corrosive sublimate, and keep the paste covered when not in use. Gum Arabic, formed into a mucilage by dissolving it in hot water, is convenient for pasting on paper, and for other similar purposes, and a phial of it should be kept in readi- ness. Colored Liquors are used in various experiments where it is important to make a column of fluid distinctly visible at some distance. Tincture of Cochineal, made by steeping one ounce of cochineal (which may be had of the apotheca- ries) in half a pint of alcohol, will serve nearly every pur. pose required in a course of philosophical experiments. In most instances, a few drops of the tincture added to a pint of water will redden it sufficiently ; but where the column is small, as in a small perpendicular tube, the color should be deeper. When a joint is to be air-tight, as in Pneumatic experi- ments, and is not exposed to heat, a strip of wet Madder wound over it, and the ends firmly tied with twine, furnishes an excellent security against leakage. Thus, if a bottle is to be exhausted of air, and we are uncertain whether the joint at. the neck is close ; or if apparatus is connected by tubes passing through corks ; in these and similar cases, no expedient is better than to wind round the joint a wide strip of wet bladder, and to tie the ends above and below the orifice with strong twine. Doubtful joints, under various circun,- stances, are often very conveniently secured by this method. The simple process of tying is not unworthy the attention of the young experimenter, since it is not unusual for impor- tant experiments to fail from the imperfect manner in whicn this is done. Always use twine of sufficient strength, tho 408 SUPPLEMENT. finer the better, provided it be strong enough ; and in tying the final knot, be sure that the whole is not loosened. Glass apparatus' frequently requires to be cut or bent into various forms. By taking advantage of a crack, or by mak- ing a weak place with a three-cornered file, and then apply- ing the burning iron so as to lead the crack in any required direction, broken glass vessels may frequently be converted to useful purposes, and glass plates may be cut up in this manner almost as well as with the diamond. Edges of glass may be brcken dbwn and brought to a level by means of a common door key, applying one of the openings in the key to the edge, and using the handle for a lever. The betiding of glass tubes is an art easily acquired and very useful. It is only to place the tube across a small furnace or dish ol coals, holding the ends in the hands. As soon as the tube grows red, it may be gently and slowly bent to any required angle, taking care so to direct the eye along the two arms of the tube as to keep them both in the same plane. Thick tubes bend more uniformly than thin ones, which are apt to flatten in the place of flexure. A lamp with large flame, if the heat is sufficient, will furnish sometimes a more con- venient mode of applying the heat than a furnace ; but where the flame is small, the heated part of the tube is not apt to be of sufficient extent. Few things contribute more to the convenience of the ex- perimenter, in operations both of the work-room and the lec- ture-room, than a variety of means for supporting apparatus, and placing it at any required level. The simplest kind of supports consist of pieces of thick board about nine inches square, a pile of which should always be at hand. But a tall iron standard, (such as every blacksmith can make,) rest- ing firmly on three legs, furnished with sliding rings of dif- ferent sizes, like those seen in a lamp furnace, is of constant use for supporting apparatus. A sliding table which the writer has had constructed for his own use, is exceedingly convenient. The table itself is a thick circular piece ol wood nine inches in diameter. The center of this is fasten- ed to the end of a wooden sliding cylinder, three feet long, and two inches through. The frame consists of three legs, resting on castors and firmly braced, and fastened at top in a hub, or stout cylindrical piece of wood perforated through the center, so as to permit the sliding cylinder to move up and down in it. A thumb-screw projects from its side, bv SELECT EXPERIMENTS. 40ft means of which the table may be fixed at any require* A piece of apparatus may be placed on this table, ani. elevated into the view of the audience ; and various piece: ot apparatus may be supported in the most convenient man- 'ler. PART II. SELECT EXPERIMENTS, WITH DIRECTIONS FOR PERFORMING THEM. Experiments on the Laws of Motion — Inertia — Centrifugal Force Falling Bodies — Composition of Motion — Projectiles — Pendulum — Center of Gravity — Mechanical Powers — Experiments in Hydro, statics — Pressure of Fluids — Specific Gravity — Experiments in Pneumatics — Experiments in Electricity and Magnetism — Experi- ments in Optics. Many important and interesting experiments can be per- formed with such simple apparatus as may be supposed to be within the reach of every one ; others require more com- plicated and expensive instruments. We shall, therefore, whenever it can be done with advantage, give two classes of experiments, the former of which will, in many cases, be sufficient to illustrate the principle to which they relate, even should the experimenter be unable to command those more expensive instruments, which might afford a more ex- ax;t and more elegant exhibition of the same principle. Section 1. — Experiments on the Laws of Motion. ON INERTIA. 1. The Top. — This toy which amused our early child- hood, may be employed to instruct our later years, by illus- trating, in a very strikmg manner, a number of important principles of motion. That the top will remain at rest until some adequate force « employed to impress a motion, is conformable to all expe- 35 410 SnPPLEMENT. rience and needs no proof; but the second part of the law of inertia, viz., that a body in motion will continue in mc tion until some adequate force stops it, is lieautifully exhib- ited by the continued motion of a top in consequence of the force impressed upon it, without any oliiei present force to sustain it. The heavier the top, other things being equal, the longer it will continue in motion, me inertia being pro- portioned to the quantity of matter ; and the smoother ana harder the plane on which the top spins, the longer it will spin, since the resistance it meets with on the point of sup- port (which resistance is the chief impediment that destroys its motion) will be less. Although the most ordinary top will illustrate the doctrine of inertia, yet the result will be more satisfactory and instructive if the following hints are followed. First, let the top be made of the hardest wood, as hard maple or lignum vitse, and turned with perfect regu- larity ; and for the running point, insert a small bit of large iron wire rounded smooth at the end. Secondly, a table of the hardest wood may be used for the plane, which should ue levelled by applying to it a water or spirit level, in two different directions. A table covered with a smooth sheer of iron (or better with thick glass) and supported on levelling screws, would furnish the most appropriate plane. Finally, two tops, one made of heavy and the other of light wood, but alike in all other respects, may be spun at the same in- stant. The greater length of time which the heavier top will persevere in motion, and the greater resistance it will oppose to a blow or any other impediment, will illustrate other points in the doctrine of inertia. If a light feather, suspended by a string, is brought near the top while spin- ning, it will be carried round with it, showing that the air in immediate contact with a revolving body, partakes of its motion. 2. The Card and Coin. — If we lay a card of pasteboard ^^ across two wine-glasses (as in Fig. 1) and strike the card at A a sudden blow, it will slip from beneath the coins and leave them in the glasses ; if the blow be applied slowly, the ooins will be carried along with the card. This experiment 9\\- ^-^ ^p^^' serve that the filings adhere only to the two ends or poles as in Fig. 59. 3. Magnetism confined to Iron. — If a number of balls of lead be mixed with several of iron, on applying a magnet, the latter will be taken up and the former left. 4. Magnetic Attraction. — Suspend a sewing needle by a fine thread, and observe the manner in which it moves on bringing a magnet toward it, being first gently disturbed, or agitated, then drawn out of its perpendicular position, and finally, rushing to meet the magnet when brought near to it. 5. Fundamental Law. — Rub the point of the suspended needle on the pole of a magnet, and it becomes itself a mag- net ; and now it will be attracted by one of the poles of the magnet and repelled by the other, agreeably to the law that opposite poles attract, and similar poles repel each other. If a strong magnet be brought toward the similar pole of a suspended needle, it will repel it when at some distance, but when brought near the stronger magnet will expel from the weaker the magnetism of the same kind, convert it into a magnet of the opposite kind, and then attract it. The same principle may be illustrat- Fig. 60. Fig. Gl. ed by suspending two needles, both mag- ' 'netized, as in Figs. 60, 61. The north pole of the magnet will cause the simi- lar poles of the needles to recede from each other, while the south pole of the magnet causes them to approach each other. Various toys, such as ships, fish, swans, &c., which are made to move on water by magnetic attractions and re- pulsions, are sold by the instrument, makers, which afford a pleasing illus- tration of the foregoing principles. 6. Directive Property of the Needle. — Rub the two ends of a large sewing needle, or, better, a fine knitting needle, on the opposite poles of a magnet, alternately. Suspend it norizontally by a delicate thread, and it will place itself in the line of the magnetic meridian. SELEOT EXPERIMENTS. 7. Magnetic Needle. — Fig. 62 represents a needle delicately sus- pended on a pivot. Magnetize a sewing needle, and apply each end plternately to the pole of the sus- ponded needle, and it will be as- certained which is the north and 447 Fig. 62. W which the south pole of the sewing needle. Fig. 63. :^Ji^j^l§:giliiM:jMfe^ Fig. 64. 8. Magnetic Curves. — Lay a sheet of white paper on a magnetic bar, (Fig. 63,) and sprinkle or sift on it fine iron filings. They will arrange them- selves as in the diagram. 9. Bip of the Needle. — Sus- pend a knitting needle horizon- tally by its center of gravity. Now magnetize the needle, and it will no longer retain its hori- zontal position, but the north end will incline or dip at a certain angle toward the horizon, as in figure 64. ' Section 5. — Experiments in Optics. Optical experiments require a room which can be dark- ened at pleasure by shutters, or temporary curtains of oil cloth, and which, on one side at least, will admit the sun freely. A white stuccoed wall, opposite to the window at which the sun's light is introduced, affords a favorable sur- face for exhibiting the images formed in various optical ex- periments ; but where such a wall cannot be commanded, a screen may be used, formed of white muslin, stretched on a 448 SDTPLEMEN r. frame. This should be so attached to the frame, that it may be taken off occasionally, and washed and ironed smooth, in which state it renders the images thrown on it much more distinct and delicate than when it is soiled or rough. For certain purposes, as the camera obscura for example, it is an advantage to have the screen fixed to a bent frame, either of wood or of wire, so as to make it con- cave. A circular hole about four inches in diameter is made in the window shutter, about four feet above the floor, to which is fitted by a horizontal groove a sliding board, which may cover the hole completely, or, by means of several circular holes of different sizes, made in the board, may afford oppor- tunity for diminishing the original opening in the shutter at pleasure. As the sun is not always at the proper altitude for afford- ing a suitable beam of light through the shutter, a piece of apparatus called a heliostat is employed to bring in the re- quired beam. This instrument has a mirror about twelve inches long and four broad, which is thrust through the open- ing in the shutter. This is attached to an open tube which is screwed upon the shutter inside. By means of two ad- justing screws, the mirror may be so turned as to reflect the sun's light through the tube, and thus to give it a horizontal direction, whatever may be the altitude of the sun at the time. Such an apparatus is usually attached to the solar microscope, from which it may be borrowed for the ordinary purposes of a heliostat. The heliostat is sometimes furnished with clock-work, by means of which the beam may be kept steadily in a horizontal position, without the necessity of frequently turning the adjusting screws. The tube attached to the heliostat usually introduces a larger beam than that required for optical experiments ; but it may be convenient- ly reduced to any required size, by inserting in the mouth of the tube a wooden stopper perforated in the center by a hole half an inch in diameter, over which, in a groove, slides a small plate of metal or ivory, having several holes of sizes diminishing from that of the stopper. By this arrangement, a beam of light of any required dimensions may be easily introduced. The room being darkened, the heliostat screwed to the shutter, and a small beam of light being introduced, a little sweeping of the floor to raise the dust will rei»der the beam SLLECT EXPERIMENTS. 449 visible, and define its shape and dimensions. It will be seen to be nearly cylindrical, enlarging a little as it departs from the window, and throwing on the opposite wall or screen an image of the sun, somewhat larger than the orifice where it IS admitted. By cutting the beam with a pane of glass (ground glass is Dreferable) or a sheet of white paper, the section will be seen to be a circle when perpendicular to the axis, and an ellipse when oblique to it. By interposing a convex lens, a pencil is formed of rays converging to a focus, and afterwards di- verging ; all which will be rendered strikingly visible to ihe eye, if the fine dust that is floating in the room be sufficiently dense. A cloud of tobacco smoke will serve the same pur- pose. ON REFLEXION AND REFRACTION. 1. Pmeer of different Surfaces. — The tendency of smooth polished surfaces to reflect light, of rough uneven surfaces to scatter it, and of dark opake bodies to absorb it, may be il- lustrated by introducing various substances into the beam at varying angles. A pane of glass (or half a pane) ground on one side by emery powder, or even by sharp sand, fur- nishes convenient surfaces for exhibiting several of these experiments. 2. Quantity of light reflected from a given surface increase's with the inclination. — If a piece of ground glass be placed perpendicularly to the beam of light, hardly any of the light is reflected ; but on inclining the surface the quantity is in creased, until, at a high angle, a perfect image of the sun is reflected on the wall. 3. Angles of incidence and reflexion equal. — Place hori- zontally before the opening in the window shutter a smooth pane of glass, or a plane mirror, and let fall upon it a beam of the sun's light. It will be seen that the incident and re- flected light make equal angles with the pane of glass, as may be more fully proved by measuring the angles with a graduated semicircle or quadrant. In order to make the light, when introduced by the helio- stat, fall upon the pane of glass at a convenient angle, it is an advantage to fix in the shutter a triangular box, covering a space of about eight inches cut out of the shutter. The ander sidp of the box makes an angle with the shutter of 38* 450 SUPPLEMENT. forty-five degrees, through a circular opening in which thi heliostat may be introduced, and thus the light may b*- thrown down so as to make an angle of forty-five degrees with the horizon. 4. Angular velocity of the reflected ray double that of the mirror. — A common table glass, supported on a frame so as to turn on two points, may be placed in the horizontal beam of light. When it is set perpendicular to the rays, it makes the reflected coincide with the incident rays ; on turning i1 forty-five degrees, the reflected beam rises ninety degrees ?and strikes the ceiling overhead ; and on continuing to turn it toward a horizontal position, the reflected beam moves to- ward one hundred and eighty degrees from its first position. 5. Reflexion between two inclined mirrors. — Place on the table two mirrors similar to that in experiment 4, parallel to each other, so that the bottom lines may be turned to or from each other, and between these lines place a lighted lamp ; on setting the mirrors at different angles to one another, it will be seen that the images of the lamp always arrange tliemselves in the circumference of a circle. The images multiply as the mirrors become more nearly parallel, and when entirely parallel the number of images is unlimited. 6. Refraction through Lenses. — A double convex lens laid across the solar beam exhibits a simple case of refraction. Its office being to collect rays of light, consequent- ly it makes parallel rays converge and brings them to a focus. The large mounted lens that accompanies the perspective glass (Fig. 65) may be conveniently used in these experiments, the mirror being removed. 7. Refraction of diverging and converging rays. —Place the mount- ed lens in the solar beam, and make the converging and diverg- ing pencils formed by it visible by dust. Then on applying another lens to each pencil, successively, it will be seen that rays already converging are made to converge more, and Fig. 65. CS:2? SELEGT EXPERIMENTS. 451 that diverging rays are made to diverge less, to become par- allel, or to converge, according to the power of the lens, or to the previous degree of divergency. 8. Concave Mirrors. — A concave mirror presented to the solar beam, will produce effects similar to those of convex lenses, causing parallel rays to converge to a focus, con- verging rays to converge more, and diverging rays to diverge less, to become parallel, or converging. A small concave shaving-glass is sufficient for these experiments. 9. Images hy Concave Mirrors. — Suspend a concave mir. ror in a dark room, and place a lighted lamp, or a small taper, at various distances from it, as indicated by Fig. 114, p. 295. The radiant must be placed a little one side of the axis, and the image received on a muslin screen, or a piece of white paper. The taper may be supported on a movable stand, and then the operator will have nothing to do but to apply the screen at the'place of the image. 10. Images hy convex lenses. — Place the mounted lens on a table in a dark room, and set a lighted lamp at different distances from it. If the radiant is set very near the lens, then an enlarged circle of light will strike the wall or screen on the other side, but no image will be formed ; if the radi- ant be withdrawn to the focus of parallel rays, the circle of light on the wall will copy the dimensions of the lens, but still will form no image ; but on withdrawing the radiant a little further from the lens, an inverted image of the light will appear on the wall, which will be larger in proportion as it is formed at a greater distance from the lens. Remove the radiant further and further from the lens, successively, and the image will be formed nearer and nearer to the lens, constantly diminishing in size as it approaches the lens. 11. Spherical Aberration. — When a lamp is placed behind a convex lens, and the image is thrown on the wall, a halo is commonly formed around the image, especially if the lens is large and thick. If we now cover the lens with a piece of pasteboard, leaving a circular space of one or two inches in the center, the halo will disappear, that is, spherical aber ration will be prevented. It will be remarked that the image is of the same size when the marginal parts of the lens are covered, as when the whole is exposed. In like manner, it will be found that a small lens forms an image as large as a large lens does, though it is less bright. 452 STJPPLEMENT. 12. Concave Lenses. — Apply to the solar beam a concave lens, and the beam will be enlarged, showing that a lens of this description separates rays of light, and consequently makes parallel rays diverge. 13. Convex Mirrors. — A similar effect will be produced by receiving the solar beam on a convex mirror. Hence concave mirrors and convex lenses, and convex mirrors an concave lenses, correspond to each other. ON COLOKS. For experiments on colors, we require a bright unclouded sun, and a dark room. A glass prism may be supported horizontally by a small frame of wood, having grooves or crotches upon which the enfis of the prism may rest, and in which it may turn with friction enough to keep its place at any required angle. It may be better still to form the sup- porting grooves in such a way, that they will hold the prism fast in any position. Fig. 66. y --■'.-' At some time of day, varying according to the situation of the room, a beam of the sun's light may be admitted through a small circular opening in the shutter, so as to fall on a prism at a suitable angle tor forming the prismatic spec- trum. Such a direct beam is better than one introduced by means of the heliostat ; but this apparatus may be used to bring in the solar beam when it cannot be commanded di- rectly. A small, well-defined beam will afford the finesi SELECT EXPERIMENTS. 453 spectrum. A very white stuccoed wall, or a smooth screen, white and clean, is requisite for receiving the image. By turning the prism backwards and forwards on its axis, when resting on its horizontal supports, we may ascertain the ex- act position of the prism which affords the most distinct and brightest spectrum, in which the several colors are distinctly visible, (Fig. 66.) Having thus formed a good spectrum, we may next proceed to perform several experiments with it. 1. Separation of the colors. — Into the prismatic beam in- troduce a small concave lens, (a spectacle glass will answer,) and, commencing with the violet, place the lens successively in each of the seven colors. They will severally form co- lored circles, giving a distinct impression of each of the sep- arate colors. 2. The individual colors no longer capable of separation into different colors. — Take an opake screen, (a board, for exam- ple,) and through the center bore a hole one-fourth of an inch in diameter. Place the board perpendicularly across the prismatic beam, at some distance from the lens, and in- tercept all the colors except one, as the red, which suffer to pass through the screen and fall upon the wall, forming a. small red image. On applying a prism to this individual beam, it will no longer change color, but will form an elon- gated image of the sun, wholly red. 3. The most refrangible rays the most reflexible. — Form the prismatic spectrum as before, on the wall opposite the win- dow, and turn the prism until the rays successively under- go total reflexion. The violet will vanish first, and the others in the order of their respective refrangibilities, to the red. 4. Compositions and decompositions of the prismatic colors. — Make the room as dark as possible, and form a pure bright spectrum, not too much elongated, but presenting each color bright and dense. A few feet from the wall, hold a glass tube obliquely in the prismatic beam, so that the rays may strike it lengthwise of the tube. An exceedingly gorgeous ring or circular zone of prismatic colors will be formed. By varying the angle of inclination of the tube, the diameters of the colored rings will be varied, and other phenomena de- veloped. A syphon glass tube will afford very numerous and strik- ing changes of color, according as different parts of it are pre.sented to the prismatic beam. When the bend forms the 454 , SUPPLEMENT. refracting and reflecting medium, the display of colors is particularly striking. If a glass vessel of uneven figure, as a tall beer glass, whose surface has different flexures in different parts, be half filled with water, on transmitting the prismatic beam through different parts of this medium, an astonishing va- riety of delicate and rich colors are developed.* 5. Formation of white light from the prismatic colors. — Form a neat and well-defined spectrum, and into the pris- matic beam, at a little distance from the prism, introduce a convex lens of the larger sort. By varying the distance of the lens from the prism, the prismatic rays will be brought to a focus, and form, by their union, a perfectly white image. To show that all the rays of the spectrum are necessary to the formation of white light, introduce a wire into the pris- matic beam before it enters the lens, and intercept succes- sively different portions of the rays. When any of the rays on the side of the violet are intercepted, the lighter colors appear in excess ; and when any portion on the side of the red are intercepted, the darker colors predominate. The prismatic beam, collected also by a concave mirror, forms a white image. 6. Colors of natural bodies. — Introduce into the prismatic beam, at some distance from the prism, flowers of different hues, as red, yellow, blue, and white. Each flower will ap- pear brightest in that part of the spectrum which corresponds to its own color, which will enhance its native beauties, but it will, to a certain extent, assume the other colors of the spectrum when subjected to their light. Thus, a yellow flower will appear red in the red part of the spectrum, and blue in the blue part ; but it will appear to the best ad- vantage in its native yellow. White will successively as- sume all the different colors of the spectrum, each impart- ing to it its own peculiar hue. A white rose will appear to be a red, orange, yellow, green or blue, or violet rose, ac- coj-ding to the part of the prismatic beam in which it is placed. 7. Camera Ohscura. — Any room capable of being dark- ened in the day time, may be converted into a camera oh- scura, by admitting the light reflected from external objects • The author is indebted, for his first knowledge of this method ol varying the prismatic colors, to his friend Forrest Sbephard, Esq. SELECT EXPERIMENTS. 455 • through a hole in the window shutter. A westej n exposure in the morning, and an eastern in the afternoon, is necessary, because at those times, respectively, the illuminated sides oi objects on which the sun shines are turned towards the win- dow. First, admit the light through a hole three inches in di- ameter, and observe an obscure representation of external objects painted on the walls. Secondly, contract the open- ing to one inch, and the figures become more distinct and better defined, but less bright. If now the larger orifice be employed, and a convex lens be placed near it, to bring thp rays to a focus, and a screen placed at the focus of the lens, an image of external objscts, both distinct and bright, will be formed on the screen, representing the figures, colors, and motions of the external world, in the same manner as they are painted on the retina of the eye Magic Lantern. — This is a valuable piece of apparatus, and if care is taken to select such slides as are instructive, many interesting and useful views of natural objects may be represented by it. In some cases, however, the figures accompanying the magic lantern are incorrect, particularly astronomical representations, being mere caricatures of the telescopic views of the heavenly bodies. Solar Microscope. — Our limits do not permit us to say more of this instrument than strongly to recommend it, as one capable of affording new and instructive views both of the animal and vegetable kingdoms, at the same time that it illustrates'important optical principles. The images are best thrown on a white stuccoed wall. Common objects, such as a thread of yarn, a sewing needle especially its eye, a pin's head, and the like, and known in sects, as a mosquito, afford striking impressions of the pow- ers of the instrument. The experimenter may frequently be obliged to examine with a small magnifier numerous spe- cimens of vinegar, before he will find one sufficiently stored with eels to be suitable to his purpose. When found, the best way of submitting them to experiment, is to take two narrow strips of window glass, tie them together at one end, and let the other end dip into the vinegar, in a tumbler. A little of the fluid will ascend between the plates by capillary attraction, carrying the animalcules along with it. The salts best adapted for crystallizations, are Muriate of Am- monia and Muriate of Barytes. Each is applied in a very .hin film to a strip of glass or mica, either with the finge 456 SUPPLEMENl. dipped in the solution and passed over the glass, or with a rag of muslin fastened to the end of a wire. The plate o( glass or mica should be warm and dry, and the smaller pow. ers should be used.