UNIVERSITY OF CALIFORNIA. PACIFIC THEOLOGICAL SEMINARY. ^Accession _ * ** " ^ ^ C/05N Class Book Accession LIBRARY GIFT OF ' V, Ramaden's Plate Electrical Machine, (A. D., 1776,) see Sec. 935. FIRST PRINCIPLES OF PHYSICS OK NATURAL PHILOSOPHY, DESIGNED FOR THE 0f BY BENJAMIN SILLIMAN, JR., M.A., M.D. \ PROFESSOR OF GENERAL AND APPLIED CHEMISTRY IN YALE COLLEGE. Kllusttattons. PHILADELPHIA : H. C. PECK & THEO. BLISS. 1859. Entered according to the Act of Congress, in the year 1858, by H. C. PECK & THEO. BLISS, In the Clerk's Office of the District Court of the Eastern District of Pennsylvania. PRINTED BY J. H. BENHAM, NEW HAVEN, CONN. PREFACE. THIS hand-book lias been prepared with a view to give a fair expo- sition of the present condition of the several departments of Physics, and to adapt them to the use of those seminaries of learning in the United States in which this subject is taught, without full mathematical de- monstrations. Accuracy of statement, fullness of illustration, conciseness of expression, and a record of the latest and most reliable progress of science in these departments, have been the leading objects in its pre- paration. Only those who have attempted to harmonize and present in due pro- portion the whole of so vast a subject as this, in a compendious form, can fully appreciate the labor and difficulties which attend it. Without claiming for the present volume any credit more than belongs to a faithful digest and compilation from the best authorities in modern science, it is hoped that it will be found suited to the wants of a large class of both teachers and students. No pains have been wanting to secure accuracy both in fact and mechanical execution. The pubh'shers have spared no expense to illustrate the book with a profusion of wood cuts. Many of these are original designs, or are reduced from larger drawings by photography and others have been selected with care from the best standard authors. It is needless to recapitulate the list of authors whose works have been consulted in the preparation of the text, since the list embraces most of acknowledged repute, both European and American. Whenever it was possible, reference has been had to original memoirs in Journals and Transactions, and in this way many errors current in works of inferior authority have been corrected. With but few exceptions, re- ferences to foreign memoirs have been omitted in the text, as their in- sertion could profit only a very small number of readers, and might seem pedantic. Not so with respect to names of discoverers of important prin- ciples and phenomena. A great number of names of these will be found in the text, in their proper places, and not unfrequently the dates of birth, or death, or both, are given. Every teacher must have observed, in his own experience, that an ab- stract principle is often fixed in the memory by the power of associated .184622 ideas, when it is connected with a date, or item of personal interest, as the attention is awakened by the dramatic, far more than by the di- dactic. Hence it has been thought judicious to introduce numerous im- portant dates in the history of science. The text is printed in two sorts of type, for the convenience of those who wish to review the chief principles of the science, with its laws, omitting the illustrations and matters of secondary importance. Thus there are in fact two books in one. It has not been possible in all cases to carry out this system rigidly, since, from the great pressure of important subjects, some have unavoiably been thrown into small type which are strictly as important as some others in the larger text. The laws are usually stated in italics. It gives me great pleasure to acknowledge many obligations to Prof. CHAELES H. POBTEE, M. A., M. D., of Albany, (some years my assistant,) for Ms constant and most important assistance in the compilation and editing of this book. Pre-occupied as my own time has been, I should not at times have found it possible to proceed without his valuable assistance and ex- cellent judgment. Dr. M. C. WHITE, of this town, has also rendered me important aid, especially in OPTICS, and in the revision of the press. Should this work meet the demands said to exist for such a work as it was designed to be, no care will be wanting to render the succeeding edi- tions entirely free from any errors of the press, or of statement, which may be discovered in this. NEW HAVEN, CONN., Oct. 15th, 1858. TABLE OF CONTENTS. PAGE Introduction. Observation and experi- ment, 1 Inductive philosophy, . . 2 Classification of material bodies, 2 Laws of physics. ... 3 PHYSICS OF PONDERABLE BODIES. General properties of matter. Elements and compounds, 5 Atoms, 5 Laws of combination, . . 10 Essential properties of mat- ter, 12 Nonr-essential properties of matter, 13 Physical forces. Varieties of force, ... 17 Physical states of matter, 21 Modified results of cohesion. Hardness, 23 Malleability, Ductility, . 24 Elasticity, 24 Crystallography. Dynamic and inorganic life, 27 Definition of crystallograph- 29 ic terms, 29 Definition of crystalline forms, 31 Systems of crystallography, 34 Modified forms, .... 38 Goniometers, 47 Crystalline molecules, . . 51 Modes of crystallization, . 52 Amorphism, 57 Dimorphism, 58 1* PAG8 Pseudomorphism. ... 60 Isomorphism, .... 62 Strength of materials. Absolute strength, ... 64 Table of absolute strength, 65 Transverse strength, . . 66 Adhesion of solids. Molecular attraction, . . 69 Statical forces 70 Composition of forces, . 71 Resolution of forces, . . 73 Dynamical forces Variations of motion, . . 75 Composition and resolution of motion, .... 77 Impact of solid bodies. Transfer of force, ... 80 Laws of momentum, . . 81 Ballistic pendulum, . . 85 JSTewton's laws of motion, . 86 Gravitation. Laws of gravitation, . . 87 Astronomical application of the laws of gravitation, 87 Terrestrial gravity, . . 88 Local variations of gravity, 89 Direction of the force of gravity, 91 Estimation of the density of the earth, ... 91 Centre of gravity. Determination of the cen- tre of gravity, ... 93 Centre of gravity in differ- ent figures, . . , . 93 Equilibrium of solids, 95 CONTENTS. PAGE ' Laws of falling bodies. Gravity a source of motion, 97 Velocity of falling bodies, 99 Spaces described by falling bodies, ...._. 99 Table of the laws of falling bodies, 101 Atwood's machine, . ^ . .102 Descent of bodies on incli- ned planes, . . . .104 Descent of bodies in curves, 105 The pendulum. 106 Laws of the oscillation of the pendulum, . . . 108 Physical demonstration of the earth's rotation, 109 Centre of oscillation, . .110 Application of the pendu- lum, Ill Measurement of time, . .112 Projectiles, and central mo- tion. Projectiles, 112 Projection of bodies in dif- ferent directions, . .112 Time of flight of a projectile, 1 14 Angle of elevation, . . .114 Central forces, . . . .115 Illustration of the effects of centrifugal forces, . 117 Eevolution about an axis, 117 Effect of centrifugal force on a yielding mass, 118 Bohnenberger's machine, 119 The gyrascope. . . . 119 Dynamometers. Animal strength, . . .122 Strength of men, . . .122 Horse power machines, . 123 Tables of the strength of men and other animals, 123 Steam power, . . . .124 Theory of machinery. Principle of virtual veloci- ties, 125 Machine, power, weight, 126 Equilibrium and utility of machines, . . . .127 Relation of power to weight, 127 Adaptation of power to weight, 128 Motion of power changed by machines, . . .128 The simple machines. 12 J The lever. Classes of levers, 130 Equilibrium of power and weight, 130 Compound levers, . . . 131 Applications of the lever, 132 The wheel and axle, . . 135 Trains of wheel work, . 137 The pulley, the fixed pulley, 138 Movable pulley, . . . .139 Compound pulley, . . .139 The inclined plane, . . . 140 Applications of power in different directions, . 141 The wedge, applications, 143 The screw, 144 Applications of the screw, 145 Impediments to motion. Passive resistance, . . . 146 Coulomb's apparatus for starting friction, . . 147 Results of Coulomb's exp'ts, 148 Coulomb's apparatus for rolling friction, . . 149 Resultsof Coulomb's exp'ts, 150 Babbage's experiments, . 150 Rigidity of ropes, . . .151 Resistance of fluids, . .151 Actual and theoretical ve- locities, 152 Ballistic curve, . . . .153 Hydrostatics. Elastic and non-elastic flu- ids, ;:< 154 Compressibility of liquids, 154 Equality of pressure, . .156 Downward pressure, . .157 Upward pressure, . . 159 Pressure on the walls, . .159 Total pressure, . . . .160 Table of water pressure at different depths, . .161 Centre of pressure, . . .162 Equilibrium of liquids, . 163 Artesian wells, . . . .164 Hydrostatic paradox, . .165 Hydrostatic press, . . .166 CONTENTS. XI PAGE Levels 168 Archimedes' principle, . 169 Equilibrium of floating bo- dies, 171 Determination of densities, 172 Hydraulics. Pressure of fluids on con- taining vessel, . . .178 Appearance of surface dur- ing a discharge, . . .178 Theorem of Torricelli, . .179 Theoretical and actual flow, 180 Constitution of veins, . .180 Escape of liquids through tubes, 182 Velocity of streams, . .184 Water wheels, .... 185 Capillarity. Laws of the rise and fall of liquids in capillary tubes, 187 Cause of capillarity, . ^ . 187 Influence of curve on capil- lary phenomena, . .188 Laws of the elevation and depression of liquids in capillary tubes, . 189 Ascent of liquids in capil- lary tubes, . . . .190 Law of the equilibrium of liquids between lam- ina;, . . . . . .191 Attraction and repulsion of light floating bodies, . 192 Endosmose. 193 Endosometer, ... 194 Necessary conditions, . 195 Solution for producing en d osmotic action, . 195 Theories of endosmose, 196 Absorption, 196 Gases. The atmospheric air, . .198 Air the type of permanent gases, 199 "Weight of air, .... 200 Atmospheric pressure, . . 201 Measure of atmospheric pressure, 202 PAGE Pressure upon the human body, 203 Construction of barometers, 204 Height of barometric col- umns at different ele- vations, 205 Varieties of mercurial ba- rometers, .... 206 Corrections of barometric heights, 208 Aneroid barometer, . . 209 Bourdon's metallic barom- eter, 210 Variations of the baromet- ric height, .... 210 Relations between baromet- ric changes and the weather, 212 Measure of heights by the barometer, . . . .213 Balloons, ...._.. 214 Construction and filling of balloons, 215 Parachute, 216 Law of Mariotte, . . .217 Manometers, 219 Diffusion of gases, ^ . .220 Illustration of the diffusion of gases, 222 Table of diffusion of gases, 223 Transpiration of gases, . 224 Mixture of gases with li- quids, 225 Absorption of gases by sol- ids, ...... 226 Hydrogen lamp, .... 227 Bellows, 228 Furnace blowers, .... 229 Escape of compressed gases, 229 The syphon, 230 Intermittent springs, . .232 Air-pumps, 233 Vacuum limited, . . . 235 Compression machine, . . 236 Archimedes' screw, . . .236 Chain pumps, 238 Suction pumps, . . . .238 Suction and lifting pumps, 239 Forcing pump, .... 239 Rotary pump, .... 240 Heiro's fountain, .... 241 CONTENTS. PAGE Hydraulic ram, .... 242 Safety tubes, 243 Theory of undulations, 244 Origin of undulations, . 244 Varieties of undulations, 244 Phases of undulations, . . 246 Nodal points, 246 Vibration of solids, Forms of vibration, . . . 247 Laws of the vibration of cords, 248 Vibration of rods, . . .249 Laws of the vibration of planes, 251 Nodal figures, .... 252 Vibration of membranes, 253 Undulations of liquids. Production of waves, . . 254 Progressive undulations, . 255 Stationary waves, . . .256 Reflection of waves, . . 257 Waves from the foci of an ellipse, 257 Waves from the foci of a parabola, ... . 258 Circular waves reflected from a plane, . . . 258 Combination of waves, . 259 Inteference in an ellipse, 260 Undulations of an elastic fluid. Undulations of a sphere of air, 261 Velocity and intensity of aerial waves, . . . 262 Interference of waves of air, 263 Acoustics. Sounding bodies are in vi- bration, 264 Sound is not propagated in a vacuum, .... 265 Sound is propagated in all elastic fluids, . . . 266 Velocity of sound in air, 267 Calculation of distances by sound, 268 Velocity of sound in liquids and solids, . . . .269 Interference of sound, . .270 Refraction of sound, . .271 PAGE . Distance to which sound is propagated, . . .271 Echo, 272 Whispering galleries, . . 274 Speaking tubes and trum- pets, 275 Hearing trumpet. . . . 276 The siren, 277 Sav art's toothed wheels, 278 Music halls, 279 Physical theory of music. Qualities of musical sound, 279 Unison, melody, . . . 280 Musical scale, . . . .280 The sonometer, 281 Number of vibrations cor- responding to each note, 282 Length of sonorous waves, 283 Interval, flats and sharps, 284 Concord and discord, . . 285 Chromatic scale, .... 286 Tuning-fork, 287 Sensibility of the ear, . . 287 Vibration of air contained in tubes. Mouth pipes, 288 Reed pipes 289 Musical instruments, . .290 Bernouilli's laws, . . . .291 Vocal and auditory apparatus. The larynx, 293 The glottis, 294 Mechanism ef the voice, . 294 Range of the human voice, 295 Sounds produced by ani- mals, 296 The external ear, . . .297 The tympanum, .... 298 The labyrinth, . . . .299 Theories of the functions of the auditory parts, . 300 Organs of hearing in the lower animals, . . 301 PHYSICS OF IMPONDERABLE AGENTS. HEAT. General remarks. Definition of terms, . . 302 Nature of heat, .... 303 Sources of heat, .... 304 CONTENTS. PAGE | Measurement o/ temperature, Indications furnished by the thermometer, . 305 Filling thermometer tubes, 306 Fixing standard points, . 307 Different therm, scales, . 308 Gradua'n of thermometers, 310 Tests of a good thermome- ter, '.312 Sensibility and limits of thermometers, . . . 313 Spirit thermometers, . .313 Air thermometers, . . .314 History of the thermometer, 315 Leslie's differential ther- mometer, . . . .315 Rumford's thermoscope, . 316 Maximum and minimum thermometers, . . .316 Metastatic thermometer, .318 Breguet's metallic ther- mometer, . . . .319 Saxton's deep sea therm'r, 320 Pyrometers, 320 Thermo-electric piles, . .324 Expansion. Expansion of solid bodies, 324 Table of the expansion of solids, ... .^ . 327 Force exerted by expansion and contraction, . .328 Phenomena produced by the expansion of solids, 328 Applications of the expan- sion of solids, . . .329 Compensating pendulums, 330 Expansion of liquids, . .333 Force exerted in the expan- sion of liquids, . . . 333 Tables of the expansion of liquids, . . . . .334 Curves of the expansion of liquids, 336 Maximum density of water, '337 Laws of the expansion of gases, 338 Ratio of the expansion of gases by heat, . . .339 Formulse to compute chan- ges of volume in gases, 339 Density of gases, . . . 341 Table of density of gases, 342 PAGE Conduction. Determination of conduc- tibility of solids, . . 343 Table of conductibility of solids, 344 Conductibility of liquids, 346 Conductibility of gases, . 346 Examples of different con- ductibility of solids, . 347 Convection. Convection in liquids, . 350 Currents in the ocean, . . 351 Radiation. Intensity of radiant heat, 352 Universal radiation of heat, 353 Apparent radiation of cold, 354 Reflection of heat, . . .354 Reflective and absorbent power, 355 Emissive power, .... 357 Modifying causes, . . . 357 Applications of radiant heat, 359 Mirrors and reflectors, . . 359 Transmission of radiant heat. Melloni's apparatus, . . 360 Influence of the substance of the screens, . . .361 Influence of the nature of the source, .... 362 Other causes which modify Diathermacy, . . .363 Thermochrosy, .... 364 Applications of diatherma- cy, 364 Analogy between light and heat, 365 Specific heat. Caiorimetry, 366 Determination of specific heat, 367 Specific heat of gases, . .369 Table of specific heats, _ . 869 Decrease of temperature in the atmosphere from elevation, . . . .371 Specific heat in liquid and solid states, .... 371 Liquefaction and solidification. Disappearance of heat du- ring liquefaction, . .372 xiv PAOB Liquefaction and congela- lation gradual, . . .373 Table of latent heat, . .373 Freezing mixtures, . . . 374 Laws of fusion, . . .375 Solution, ...... 376 Laws of solidification, . .876 Change of volume during solidification, . . . 377 Freezing of water, . . .378 Vaporization and condensation. Formation of vapors in a vacuum, . . , . .379 Saturated space, . . .380 Dalton's law of the tension of vapors, . . . .381 Circumstances influencing evaporation, . . . 382 Dew point, ..... 383 Table of boiling points, . 384 Circumstances influencing the boiling point, . . 385 Culinary paradox, . . 386 Hypsometer, ..... 387 Marcet's apparatus, . . . 388 Production of cold by evap- oration, ..... 390 Latent heat of steam, . .391 Force developed during evaporation, . . .392 Condensation of vapors and gases. Distillation, alembics, . . 393 Retorts and receivers, . . 394 Fractional distillation, . . 395 Theory of condensation of gases, ...... 396 Soda water apparatus, . 397 Thilorier's apparatus, . .398 Bianchi's apparatus, . . 399 Liquid and solid carbonic acid gas, ..... 400 Table of the liquefaction and solidification of gases, ...... 401 Variations from Mariotte's law, Density of Vapors. Gay Lussac's method, Dumas' method, .. 402 403 404 PAGE Spheroidal state. Illustration of the spheroi- dal state, .... 405 Temperature of bodies in spheroidal state, . . 406 Rapidity of evaporation, . 407 Spheroids not in contact with heated surface, 407 Causes which produce the spheroidal form, . . 408 Freezing in red hot cruci- bles, ...... 409 Phenomena connected with spheroidal state, . . 409 Steam boiler explosions, . 410 Applications and effects of the spheroidal state, 411 The steam engine. Historical, 411 Worcester's and Savary's engines, 413 Newcomen's engine, . . 414 Watt's improvement, . .415 Low pressure engine, . .416 High pressure engine, . . 417 Steam boilers, . . . .418 Mechanical power of steam, 419 Value of fuel, ... . 420 Ventilation and warming. Draught in chimnies, . . 422 Smoky chimnies, . . . 423 Necessity for ventilation, . 424 Vapor given off from the body, 424 Quantity of air required for ventilation, . . 425 Products of gas illumina- tion, 425 Stone's ventilating shaft, 426 Refrigerators, . . . 427 Emerson's ventilators, . 428 Modes of warming, . 429 Hot-air furnaces, . . . 430 Heating by hot water, 432 Gold's steam heaters, . 433 Automatic boiler, . . 434 Dynamical theory of heat. Motions of the molecules, vaporization, . . . 435 Change in the state or vol- ume of bodies, . . 435 CONTENTS. PAGE Joule's experiments on me- chanical equivalent of heat, 436 Conclusions derived from Joule's experiments, 43*7 OPTICS. General properties of light. Nature of light, .... 439 Theories of light, . . .439 Relation of different bodies to light, ..... 440 Propagation in a homoge- neous medium, . . 441 Velocity of light ... 441 Absorption, dispersion, . 444 Reflection, 444 Refraction, 445 Amount reflected increases with angle of incidence, 446 Intern'l and total reflection, 446 Umbra and penumbra, . . 447 Intensity at different dis- tances, 448 Photometers, 449 Reflection by specula and mir- rors. Mirrors, 449 Specula, 450 Forms of Mirrors, ; . . 45C Reflection from, and images formed by plane mir- rors, 451 Images multiplied by glass mirrors, . . . . ^ 452 Images repeated by incli- ned reflectors, . . . Irregular reflection, . . Foci of concave mirrors, . Secondary axes, .... Convex reflectors, . . . Images formed by concave mirrors, 45! Virtual images, . . . .45' Images formed by convex mirrors, 46 1 Spherical aberration of mir- rors, 46 Refraction in bodies having regular forms. Prisms and lenses, . . .46 453 45 45? 45' 45: PAGE Plane glass, 462 Refraction by prisms, . . 463 Determination of index of refraction, .... 464 Composition of a double convex lens, .... 465 Plano-convex and concave lenses, 467 Rules for determining the foci of lenses, . . . 467 Combined lenses, . . . 468 Optical centre of a lens, . 469 Images formed by lenses, . 469 Sperical aberrati'n of lenses, 470 Aberration of sphericity, . 471 Chromatics. 472 473 Analysis of light, ^ . . Recomposition of light, Complementary colors, . 473 Properties of the solar spectrum, .... 474 Fraunhofer's dark lines, . 475 Intensity of the diff. rays, 476 Kaly chromatics, . . . .477 Chromatic aberration, . .477 Achromatism, . . . .478 Vision. Structure of the human eye, 479 Action of the eye upon light, 481 Inversion of the image form- ed in the eye. Optic axis and angle, . . . 482 Conditions of distinct vision 483 Distance of distinct vision, 485 Aerial perspective, . . . 486 Single vision with two eyes, 487 Near sightedness, long sight- edness, 488 Optical toys. Color blind- ness, 489 Chevreul's chromatic dia- gram, 490 Optical instruments. Magnifying glasses, . . .492 To find magnifying power of a lens, .... 493 The compound microscope, 494 The telescope, . . . .495 Eye-pieces for microscopes and telescopes, . . .496 xvi CONTEFTS. TT i t. PAGE Herschel's and Rosse's re- flecting telescopes, . 493 Achromatic telescopes, . 499 Cambridge telescope, . . 501 Lister's objectives, . . .503 Aberration of glass cover corrected, .... 505 Compound achromatic mi- croscope, 505 Angular aperture, . . .506 Grunow's microscope, . . 507 Magic lantern. Solar mi- croscope, 508 Camera obscura, .... 509 Camera lucida. Photogra- P h 7, 510 Kail way illumination, . .511 Fresnel lens. Sea lights, . 512 Revolving lights, . . . 513 f Telestereoscope, .... 514 Stereoscope, 515 Stereomonoscope, . . .517 Physical optics. Interference of light, . .518 Interference colors of thin plates, 520 Newton's rings. Length of luminous vibrations, . 521 Diffraction, 522 I The rainbow, 523 Fog-bows, halos, coronas, Parhelia, .... 526 Looming. Colors of grooved plates, 527 Fluorescence, 528 Polarization of light. Change produced by polar- ization, , . . . .529 Resolution of vibrations, 530 Polarization by different means, 531 Positive and negative crys- tals, 534 Nicol's single image prism, 535 Polarizing instruments. Co- lored polarization, . 536 Rotatory polarization, . . 637 Colored rings in crystals, 538 Magnetic rotatory polar- ization, 538 . - fABK Atmospheric polarization. The eye a polariscope. Practical applications of polarized light, . 539 MAGNETISM. Properties of Magnets. Lodestones. Artificial mag- nets, 541 Polarity, 542 Magnetic curves. Magnet- ic figures, .... 543 Attraction and repulsion, . 544 Magnetism by contact. Magnetism in non-fer- uginous bodies, . . 545 Magnetic induction. Theoretical considerations, 546 Theory of two fluids, . . 547 Coercive force, .... 548 Terrestrial magnetism. Magnetic needle, . . . 548 Magnetic meridian, . . . 550 Variation chart, .... 551 Variations in the magnetic needle. Dip or incli- nation, 553 Dipping needle, .... 555 Inclination map, .... 556 Magnetic intensity, . . 557 Isodynamic lines. Induc- tive power of earth's magnetism, .... 558 Lines of magnetic force, . 560 Atmospheric magnetism, 561 Production of magnets. Circumstances affecting val- ue of magnets. Mag- nets by touch, . . . 563 Magnets by electro-mag- netism, 565 Compound magnets. To deprive a magnet of its power 566 STATICAL ELECTRICITY. Electrical phenomena. Definitions, 567 xvii Sources of electrical ex- citement. Electrical effects. Attraction and repulsion, .... 568 Positive and negative elec- tricity, 569 Conductors of electricity, 570 Theories of electricity, . 572 Electrical tension, . . .574 "Paths and velocity of elec- tric currents, . . .575 Laws of electrical forces and surface distribution. Coulomb's laws of attrac- tion and repulsion. Torsion electrometer, 575 Demonstration of Cou- lomb's laws, . . . .576 Proof-plane, 577 Electricity resident on sur- faces, 578 Distribution of electricity, 679 Loss of electricity in ex- cited bodies, 580 Induction of electricity. Laws of induction. Induc- tion an act of contigu- ous particles, . . . 582 Attraction and repulsion of light bodies, . . 583 Electrometers, . . . .584 Electrical machines. Electrophorus, .... 585 Cylinder machines. Amal- gam, . . . . . .6 Ramsden's, Hare's machines. Ritchie's double plate machines, . . . .587 Care and management of electrical machines, . 589 Electricity from steam. Other sources of elec- trical excitement, . .590 Theory of the electrical machine, 591 Experimental illustrations of electrical attraction and excitement, . . 592 Accumulated electricity, and its effects. Disguised, or latent electri- city. Condenser of JEpinus, 594 Modes of discharging, . . 596 Volta's electroscope, . . 597 Leydenjar, 598 The electric battery, . .599 The diamond jar, . . . 600 The universal discharger, 601 Electrical light and spark, 602 Positive and negative spark, 604 Effects of electric discharge, 605 Elements united by electri- city. Volta's electri- cal lamp, 606 Mechanical and chemical effects produced by electricity, .... 607 Atmospheric electricity. Franklin's kite, .... 608 Free electricity in the at- mosphere, 609 DYNAMICAL ELECTRICITY. Galvanism, or Voltaism, Discovery of Galvanism, . 610 Volta's discovery, . . .612 The Voltaic battery, . .613 Quantity and intensity, . 615 Electro-positive and elec- tro-negative. Amal- gamation, . . . .616 Batteries with one Jluid. Trough batteries, . . . 617 Hare's calorimotor, . . .618 Smee's battery, .... 619 Batteries with two fluids. Daniell's constant battery, 620 Grove's nitric acid battery, 621 Carbon battery . . . 622 Zamboni and De Luc's piles, 623 Polarity, retarding power, and nomenclature of the Vol- taic pile. Polarity of compound cir- cuit 624 PAGE Retardi'g power of battery, 626 Faraday's nomenclature, 627 Effects of Voltaic pile. . V Voltaic spark and arch, .628 Regulators of electric light, 629 Properties of the electric light, 630 Heat of the Voltaic arch, 631 Chemical effects, electroly- sis, ... 633 Laws of electrolysis and electrolysis of salts, . 635 Electrotype, 636 Metals deposited from solu- tion by presence of an- other metal. Nobili's rings, 638 Physiological effects of the Voltaic pile, . . . 639 Magnetic and electrical effects, 640 Theory of the pile. Volta's contact theory, . 641 Chemical theory, . . .642 Becquerel's laws, . . . 642 Polarization of elements, 643 Theory of Grotthuss for electro - chemical de- compositions, . . . 644 Peschell's molecul'r theory, 645 Electro-dynamics. General laws. (Ersted's discovery, .... 646 Galvanometers, .... 648 Rheostat, 650 Ampere's discoveries and theory, 651 Mutual action of electric currents, , . . . . 652 Helix, or electro-dynamic spiral, 653 De La Rive's floating cur- rent, 654 Directive-action of the earth; magnetizing by the helix, 655 Electro-magnets, .... 657 Musical tones from induced magnetism, . . . .658 PAGE Electro -magnetic motions and mechanical power, 659 Action of magn't on light, 660 Diamagnetism, .... 661 Electric telegraph. History of the telegraph, 663 The earth-circuit, . . . 665 Varieties of electro-tele- egraph's, . . . .666 Morse's recordi'g telegr'ph, 667 House's printing telegraph 668 Electro-chem. telegraph, 669 Submarine telegraphs, the Atlantic cable, . . .670 Electrical clocks, . . . .671 Electro-dynamic induction, and magneto-electricity. Currents induced by other currents, . . . .671 Page's vibrating armature, 674 Currents induced by mag- nets, 675 The earth's magnetism, . 676 Ritchie's Ruhmkorff's in- duction coil, . . . 677 Effects of the induct'n coil, 678 Clarke's magneto-electric apparatus, . . . .680 Other sources of electrical ex- citement. Thermo-electricity. . . .681 Animal electricity, . . . 683 Electrical animals, . . . 684 METEOROLOGY. Climate, seasons, .... 685 Variations of temperature, 686 Isothermal lines, . . .687 Aerial phenomena. Winds 687 Waterspouts, 690 Velocity of winds, . . .691 Aqueous phenomena. Humidity. Hygrometers, 692 Clouds, 695 Rain. Rain-guage, . . . 696 Dew, 697. Frost, . . .698 Snow, 699 CONTENTS. Electrical and luminous phe- Origin of atmospheric elec- tricity, 700 Aurora borealis, . . .701 Disturbance of the magnet- ic needle. Lightning, 703 Thunderstorms, - . . .705 Lightning rods, * . . .706 ERRATA, 707 INDEX, 709 FIRST PRINCIPLES OF NATURAL PHILOSOPHY OR PHYSICS. INTRODUCTION. 1, Our knowledge of the material world is founded upon expe- rience, or the evidence of our senses, and the conviction that the same causes will always produce the same effects, By observation we become acquainted with those changes in the condition and relations of bodies which occur spontaneously in the ordinary course of nature ; but the knowledge thus acquired is meagre and limited when compared with the results of experi- ment. By the use of proper apparatus we can repeat natural phenomena under varied conditions, and, among all the attendant circumstances, we can determine what are accidental, and what are essential to any given effect. In conducting an experiment, we are taught to trace with certainty the connection between dif- ferent phenomena ; to classify effects of the same kind and refer them to their common cause ; in fine, to deduce from many experi- ments the governing principle, or law of nature, in obedience to which they are produced, and to unite both facts and principles into a theory, or comprehensive view of the whole subject. Such theories are a fruitful source of new experiments and new dis- coveries. By a judicious application of their established princi- ples, philosophers have often predicted the results of untried experiments, altogether different from any facts before observed. 1. Upon what is our knowledge of the material world rounded ? How should an experiment be conducted ? What is meant by induc- tive philospliy 1 What is the origin of Inductive Philosophy ? Z INTRODUCTION. When individual experience is enlarged by the experience of other inquirers and other times, and the combined knowledge of many is so arranged as to be comprehended by one, the system becomes a SCIENCE, or philosophy of nature. Because its princi- ples are founded upon a comparison and analysis of facts, a sys- tem of this kind is also called Inductive Philosophy. 2. The origin of inductive philosophy is entirely modern. Galileo (born in 1564) was the first to commence a course of expe- rimental researches ; and Bacon (born in 1561) in his immortal work, Novum Organon, showed that this was the only road to an accurate knowledge of nature. The ancients were ignorant of the principles and methods of inductive science. Their expla- nations of natural phenomena were based on assumed causes, and they are therefore confused and contradictory, and often in di- rect opposition to experience. 3. All material bodies may be distributed into two classes, viz : inanimate, or unorganized ; and animate, or organized. Bodies of the first class, as air, water, minerals, &c., are found in all parts of the earth ; they are not endowed with life ; they have no definite or periodical duration ; and they are acted on only by forces external to themselves. Organized bodies are individuals, made up of many different organs, each of which is adapted to discharge its own proper functions. They are not everywhere the same, but different species belong to different countries. By an innate and peculiar power, called vitality, they change inanimate bodies into their own structure, and thus increase in bulk, and provide a succes- sion of individuals like themselves. After a life of definite dura- tion, they die, and their structures dissolve again into the inani- mate bodies out of which they grew. They are subject to the general laws of matter, but these laws are often modified, and sometimes directly opposed by the action of that unknown power which we call the principle of life. The description of organ- ized bodies constitutes the science of Natural History. 4. To natural philosophy, or physics, belongs the inquiry into those general properties of unorganized bodies which we can see, touch, and weigh ; into the changes which take place among them, the causes of those changes, and their laws. It investi- 3. Into what classes may all material bodies be distributed 1 What is said of unorganized bodies? What of organized ? What is Natural History ? 4. What subjects of inquiry belong to Physics? INTRODUCTION. 3 gates also the properties and laws of certain hypothetical fluids or forces, which are without perceptible weight, and the other pro- perties of ordinary matter ; these fluids or forces produce the phenomena of Heat, Light, Electricity, and Magnetism. The phenomena of Physics have this common characteristic ; they do not result from changes in the nature and constitution of bodies. It is in this that they differ from the phenomena which belong to the domain of chemistry. All the phenomena of Physics are dependent on a limited number of general laws of which they are the necessary conse- quences. However various and complex may be the phenomena, their laws are few, and distinguished for their exceeding simpli- city. All of them may be represented by numbers and alge- braic symbols, and these condensed formula, enable us to conduct investigations with the certainty and precision of pure mathematics. As in geometry, all the properties of figures are deduced from a few axioms and definitions ; so when the general laws of Physics are known, we may deduce from them, by a series of rigorous reasoning, all the phenomena to which they give rise. The most insignific? nt and the most gigantic effects, sometimes dissimilar and contradictory in ap- pearance, are often produced by the operation of one and the same law. For example, the law of gravitation, the demonstration of which has conferred immortal fame upon Newton, its discoverer, is literally universal in its influence. It pervades every atom, rules alike the motions of animate and inanimate beings, and is as sensible in the gentle descent of the rain-drop as in the tor- rent of Niagara, or the crash of the avalanche. To the subtle and invisible air it gives the pressure of fifteen pounds upon every square inch of surface, and to the ocean its far greater and almost incredible weight ; and, at the same time, it causes the ship to ride the surface of the one, and the feather, or bal- loon to rise, and the clouds to float buoyantly through the other. By it the lofty structures of man's erection, and the mountains, the mightier architecture of nature, are retained immovably on their foundations. Its influence transcends the narrow limits of our earth, and ascending the heavens, it not only binds satellites to their What common characteristic has this class of phenomena ? What is said of the laws of Physics ? What may we deduce from these ? 4 INTRODUCTION*. planets, and planets to the sun in unchangeable orbits, but it connects sun with sun throughout the whole extent of crea- tion, and is hurrying our solar system with inconceivable swiftness, through an orbit whose period and centre are meas- ureless and unknown. It causes the disturbances as well as the order of nature ; since every tremor, which the planets excite in each other by their mutual attraction, changing as their distance changes, is immediately transmitted to the furthest limits of the system, in oscillations, whose periods correspond to their mighty cause. Like other natural laws, the law of gravitation interprets itself; its operations furnish the means of testing and veri- fying its own truth. Le Verrier's masterly analysis of the per- turbations of Uranus, a planet eighteen hundred millions of miles from the sun, enabled him to calculate and predict not merely the existence, but the mass, period, and position of a new planet, which no mortal eye had ever recognized, and which revolved about the sun at almost twice the distance of Uranus. The con- firmation of a prediction so magnificent, while it gave to the law of gravitation the stamp of undeniable truth, seemed to confer upon the intellect of man an almost divine grasp. 5. The general laws and properties of matter are not only in themselves attractive and objects of profound interest, but a knowledge of them is a preliminary and essential step to the study of every other department of science ; an acquaintance with them is of practical value for everyday business and house- hold uses. No art or trade can be conducted without constant reference to the principles of Physics. Its facts are drawn from the experience of ordinary life, connected into a more orderly and scientific arrangement. Its methods of research are identi- cal with those employed by thinking men in every calling ; and its principles are the principles of common sense. What is said of gravitation? Give the illustrations named in the text. 5. What value have the general laws of matter ? PHYSICS OF PONDERABLE BODIES. THE PHYSICS OF PONDERABLE BODIES. General Properties of Matter. 6. Matter. Our senses bear testimony to the existence of matter in a manner too emphatic and self-evident to admit of dis- cussion. Matter is either simple or compound. 7. Elements. Elements, or simple substances, are those which have resisted all attempts by chemical or other means to reduce them to more simple forms ; for example, gold and other metals, carbon, sulphur and phosphorous are such substances. According to our present knowledge there are 62 elements, but it is not at all improbable that the number may increase or diminish as our means of analysis and decomposition are enlarged. 8. Compounds. Compounds are combinations of two or more elements with each other. Although the number of elements is comparatively small, yet the compounds which may result from their combination with each other are innumerable. 9. Indestructibility of matter. Human agency can cause the atoms of matter to pass from one state, or combination, into another ; but to destroy them, requires the same infinite power which called them into existence. The various forms of matter may be ground to powder or dissipated in vapor ; animals and vegetables may die and be decomposed, their particles may return to the common earth or float invisible in the air, but they are not lost, they enter into an infinite series of new combinations and reappear in other forms of beauty and life. In the ceaseless round of change, the ultimate atoms alone remain unchanged and undestroyed. 10. Atoms. The ultimate constitution of matter has divided the opinions of philosophers from the earliest period of science. Two hypotheses have prevailed ; the one, that matter is composed of irregular particles without fixed size or weight, and divisible without limit ; the other, that " matter is formed of solid, massy, impenetrable, movable particles, so hard as never to wear or 6. What is said of matter? 7. What are elements ? Give examples. 8. What is said of compounds 1 9. Can the atom of matter be de- stroyed, or only enter into new combinations? 10. What two hy- potheses have prevailed in regard to the ultimate constitution of matter ? 6 PHYSICS OF PONDERABLE BODIES. break in pieces," (Newton,) and which, being wholly indivisible, have a certain definite size, figure and weight, which they retain unchangeably through all their various combinations. These ultimate and unchangeable particles are called atoms, (meaning that which cannot be subdivided,) or molecules, (little masses.) It is evident that experiment cannot decide between these rival suppositions, for the ultimate particles are far too small to be visible by any means which human ingenuity has yet been able to devise, and they will probably never come within the limits of our direct perceptions. When we have reduced a mass of matter to the finest impalpable powder, we have made no real approach towards finding its con- stituent atoms ; its minutest particles have the same physical characters as the mass from which they were derived, and of which each is a miniature likeness. Ehrenberg, after exhausting the resources of mechanical contrivance in pulverizing marble, found that its smallest particles were still transparent rhomboids, with angles as perfect as in the finest crystals of calcareous spar. 11. Form of atoms. Two views are now entertained by phi- losophers as to the form of atoms. The first theory supposes that the crystalline form of a body, (or the form from which it was derived,) is that of its ultimate atoms ; for example, a body crystallizing in cubes must, by this assumption, be formed of atoms which are themselves cubes ; a body crystallizing in rhom- bohedrons is formed of atoms which are themselves rhombo- hedrons, and so on for the atoms of other crystalline forms; this view certainly gives an easy explanation of the crystalline form of simple substances, but there are certain objections to it which prevent its adoption. It does not explain amorphism, (bodies destitute of all traces of crystalline form are called amor- phous,) nor dimorphism, (bodies crystallizing in two distinct forms are dimorphous.) The second theory, brought forward by D. Wollaston in 1824, but more fully developed by M. Ampere, supposes each ulti- mate atom to be a sphere possessed of certain forces of polarity which tend to produce the various forms which crys- tallized bodies assume. "We can easily see how 8 spheres placed together might form a cube, 4 to form the base and 4 im- mediately above. By a similar mode of arrangement of particles, all the crystalline forms, complicated as they may be, can be pro- 11. What are the two views of the forms of atoms? Examples. PROPERTIES OF MATTER. 7 duced. Great probability attaches to this view ; we know the sphere to be the simplest form of matter ; it is that form which bodies assume when left more completely to themselves. The rain drop falling from the cloud, the melted lead from the tower, each assume the form of spheres before reaching the ground ; the celestial bodies, it will be remembered, also approach this form. Although this theory fails to explain why the atoms of dif- ferent elements when aggregated should arrange themselves in peculiar crystalline forms, yet by it amorphism may be explained, in that the substance being in a viscous condition, the atoms were not free to obey the forces of polarity ; or that the substance in a melted state, or in solution, solidifying quickly, the particles did not have time to arrange themselves in regular order, but clustered together without symmetry. Dimorphism might occur when, because of different temperature or from some other cause, the forces that attract the atoms to each other change their posi- tion, thus causing the atoms to come together to form crystals different from those usually produced. 12. Magnitude of atoms. A moment's reflection makes it evident that the size of the ultimate atoms of matter must be immeasurably small. The sunbeam discloses countless minute particles of dust floating in the air of the most silent chamber. The perfume of a violet soon fills a large apartment with its deli- cious odor. A portion of its material substance thus gives evi- dence to the senses of smell of its diffusion through a great space in particles immeasurably small, and still the flower has lost neither form nor appreciable weight. Nevertheless these are not the ultimate particles (atoms) of matter, but are definite chemical compounds consisting of several elements. 13. MINUTE DIVISION BY MECHANICAL AND CHEMICAL MEANS. Let us, in order to obtain a more precise idea of the wonderful divisibility of matter, refer to some cases of division by mechanical and chemical means. A bar of silver may be gilded and then drawn into wire so fine that the gold, covering afoot of such thread, weighs less than -gVo IT of a grain. An inch, containing __-^_- of a grain, may be divided How is aniorphism. and dimorphism explained by the second the- ory ? 12. What is said of the magnitude of atoms? 13. Give ex- amples of the divisibility of matter in the silver wire, in Dr. Wol- laston's plated wire, &c. 8 PHYSICS OF PONDERABLE BODIES. into 100 equal parts distinctly visible, and each containing of a grain of gold. Under a microscope magnifying 500 times, each of these minute pieces may be again subdivided 500 times, each subdivis- ion having to the eye the same apparent magnitude as before, and the gold on each, with its original lustre, color, and chemical proper- ties unchanged, represents _ ---!----- parts of the original quantity. Dr. Wollaston, by a very ingenious device, obtained platinum wire for the micrometers of telescopes, measuring only __U__ of an inch in diameter. Though platinum is the heaviest of known bodies, a mile of such wire would weigh only a grain, and 150 strands of it would together form a thread only as thick as a filament of raw silk. A grain of copper dissolved in nitric acid, to which is afterwards added water of ammonia, will give a decided blue color to 392 cubic inches of water. Now each cubic inch of the water may be divided into a million particles, each distinctly visible under the microscope, and therefore the grain of copper must have been divided into 392 million parts. One hundred cubic inches of a solution of common salt will be ren- dered milky by a cube of silver, O'OOl of an inch on each side, dissolv- ed in nitric acid, and the magnitude of each particle of silver thus represents the one hundred billionth part of an inch in size. To aid the student in forming an adequate conception of so vast a number as a billion, it may be added that to count abillion from a clock beat- ing seconds, would require 31*678 years continuous counting, day and night. 14. MINUTE DIVISION. IN THE ANIMAL AND VEGETABLE KINGDOMS. The blood of animals is not a uniform red liquid,'- as it appears to the naked eye, but consists of a transparent colorless fluid, in which float an innumerable multitude of red corpuscles, which in animals that suckle their yoving, are flat circular discs, doubly concave, like the spectacle glasses of near-sighted persons. In man, the diameter of these corpuscles is the 3,600th of an inch, and in the musk-deer, only the 12,000th of an inch, and therefore a drop of human blood, such as would remain suspended from the point of a cambric needle, will contain about 3,000,000 of corpuscles, and about 120,000,000 might float in a similar drop drawn from the musk-deer. But these instances of the divisibility of matter are far surpassed by the minuteness of animalcules, for whose natural history we are indebted chiefly to the researches of the renowned Prussian naturalist, Ehrenberg. He has shown that there are many species of these creatures, so small that millions together would not equal the Give examples from copper and silver. 14. "What are the blood corpuscles and their size in different animals ? PKOPERTIES OF MATTEK. bulk of a grain of sand, and thousands might swim at once through Die eye of a needle. These infinitesimal animals are as well adapted to life as the largest beasts, and their motions display all the phe- nomena of life, sense and instinct. Their actions are not fluid and fortuitous, but are evidently governed by choice, and directed to gratify their appetites and avoid the dangers of their mimic world. The waters of the globe (and sometimes the atmosphere) everywhere are populous with them, to an extent beyond the power of figures to express, or the imagination to conceive their numbers. Their sili- cions skeletons are found in a fossil state, forming the entire mass of rocky strata, many feet in thickness and hundreds of square miles in extent. The smooth slate near Bilin, in Bohemia, contains in every cubic inch about 41,000 millions of these animals. Since a cubic inch of this slate weighs 220 grains, there must be in a single grain 187 mill- ions of skeletons, and one of them would therefore weigh about the one 187 millionth of a grain. The city of Richmond, Va., has been shown by Prof. Bailey to rest on a similar deposit of silicious animal- cules, of exquisite form. Like larger animals, these animalcules are furnished with organs of digestion and reproduction, and a complex circulating system, whose blood corpuscles are proportioned to the vessels through which they flow. It is impossible to form a concep- tion of the minute dimensions of these organic structures, and yet each separate organ of every animalcule is a compound of several organic substances, each in its turn comprising numberless atoms of carbon, oxygen and hydrogen. It is plain from these examples, that the ac- tual magnitude of the ultimate molecules of any body is something completely beyond the reach equally of our senses to perceive, or of our intellects to comprehend. 15. Weight of atoms. As we can form no precise idea of the absolute size of atoms, neither can we of their absolute weight. But modern chemistry has revealed to us with certainty the rela- tive weight of the atoms of the different elements. All chemical compounds have a certain definite constitution ; that is, the same compound is always formed of the same elements, and in the same proportion. Water, for example, is always formed by weight of 1 part hydro- gen and 8 parts oxygen. When a compound is formed, it is supposed that one atom of one element unites with one atom of another, or the union takes 15. What do we know of the weight of atoms? What of the dif- ferent constitution of compounds ? 2* 10 PHYSICS OF PONDERABLE BODIES. place in some other simple proportion as 1 to 2, 2 to 3, &c. ; this method of combination being the simplest we can conceive of. Water, then, is composed of 1 atom of hydrogen and 1 atom of oxygen ; but in water the weight of the oxygen is 8 times as great as the weight of the hydrogen ; therefore the weight of the oxygen atom must be 8 times as great as the weight of the hydrogen atom. Chemists have ascertained the proportions by weight in which the various elements combine among themselves, and these pro- portions are the atomic weights of the elements. 16. Laws of combination. The combination of different ele- ments with each other is regulated by fixed laws. These laws are four in number and every chemical combination is made in accordance with them. a. Law of definite proportion. In every chemical combination the nature and proportion of its constituent elements are fixed, definite and invariable. For example : 100 parts of pure water, however produced, contain 11*11 parts hydrogen, and 88'89 parts oxygen. Again, common salt is always composed in 100 parts, of 23*17 parts of the metal sodium, and 60*48 parts chlorine ; if now we should mingle these elements in any other proportion than those just stated, the excess of one or the other would remain free and uncombined. b. Law of multiple proportions. This law requires that when two bodies unite in more proportions than one, these pro- portions bear some simple relation to each other, as 1 to 1, 1 to 2, &c. ~For example: 1 part by weight of hydrogen combines with 8 parts of oxygen and forms water ; 1 part of hydrogen also com- bines with 16 parts of oxygen and forms binoxyd of hydrogen; these proportions of oxygen with hydrogen, it will be observed, bear the simple relation to each other of 1 to 1 and 1 to 2. In the same manner we may have a series of compounds, as for instance those of nitrogen with oxygen, in which the relation of the atoms of the former is to the latter as 1 to 1, 1 to 2, 1 to How do the atoms of different elements unite among themselves ? What are the atomic weights of the elements? 16. What are the laws of chemical combination ? Their number ? What is the law of definite proportion ? Example. What is the law of multiple pro- portions ? Example. PROPERTIES OF MATTER. 11 8, 1 to 4, and 1 to 5. Again we may have other series of com- pounds in which the relation, though similar, is not quite so simple ; as 2 to 3, 2 to 5, and 2 to 7. c. Law of equivalent proportions. According to this law, when a body A, unites with other bodies B, O, D, the propor- tions in which B, O and D, unite with A, represent in numbers the proportions in which they will unite among themselves, in case such union takes place. For example : take oxygen, (this element uniting with all others, "with the exception of fluorine,) 8 parts of oxygen unite with 1 of hydrogen, 6 of carbon, 16 of sulphur, 28 of iron, 100 of mercury, &c. The numbers attached to the elements, representing the propor- tions in which they will unite with each other, are called their equivalents, because they represent quantities which are exactly capable of replacing each other in combination. For example: if we have a compound of 100 of mercury and 8 of oxygen, the 100 of mercury can be replaced by 28 of iron, 16 of sulphur, &c., and also the 16 of sulphur will unite with 28 of iron, and so for other elements. d. Law of combining number of compounds. According to this law the combining proportion of a compound body is the sum of the combining weights of its several elements. It has just been shown that the equivalents of the several elements are their combining proportions, and it follows as a necessary result, that the proportion in which a compound will unite with another body, or its combining number, is the sum of the equivalents of its constituents. For example : we wish to know the combining proportion of sulphu- ric acid ; sulphuric acid is composed of 1 atom of sulphur, whose equivalent is 16, and 3 atoms of oxygen, whose equivalent is (3 times 8) 24. 24 and 16 equals 40. 40 is the combining number, or, 1 equivalent of sulphur and 3 equivalents of oxygen, that is of sulphuric acid, and the number 40 is the proportion in which sul- phuric acid will unite with other bodies. What is the relation of the atoms to one another? What is the law of equivalent properties'? Example. What is meant by equivalents ? Example. What is the law of the combining number of compounds? What is the combining number of sulphuric acid ? 12 PHYSICS OF PONDERABLE BODIES. The General Properties of Matter. 17. The physical properties of bodies are those external signs by which we recognize their existence. They divide themselves into two classes. The essential or principal, and the non-essen- tial or accessory. The former are common to all bodies, and inseparable from them. They are the proper and only tests of materiality. Where their presence is not evident to the senses, or cannot be proved to exist, there matter does not exist. Thus, it is essential to the existence of every form of matter that it occupy a certain space, that no other body occupy the same space at the same time, and that it offer a certain resistance to motion, which we call weight. In physics these three properties are named magnitude, impenetrability, and gravity. 1. Essential Properties. 18. Magnitude is observed to belong to all bodies which are not so minute as to elude the senses, and to such it may be traced by the reason. We cannot conceive of the existence of any par- ticle of matter so minute as not to occupy space. Magnitude has three dimensions ; length, breadth, and tliick- ness. Its external limits are lines and surfaces. Lines are meas- ured by linear inches, feet, miles, &c. Length and breadth combined, form a surface, whose area is measured by square inches, feet, miles, &c. The quantity of space occupied by a body, called in common language its size, is correctly termed its volume ; and its measurement is expressed in citbic inches, feet, miles, &c. 19. Impenetrability causes matter to occupy a certain space to the exclusion of all other matter. It is evident that two masses of lead, wood, or any other solid substance, cannot fill the same space at the same time. There are many instances of apparent penetration ; but in all these cases, the parts of the body which seem to be penetrated, are only displaced. When a nail is driven into wood, the particles of wood are not divided, but thrust aside. A bullet dropped into a cup of water displaces an amount of the fluid equal to its bulk. Air, which offers 17. How may the physical properties of bodies be classified ? 18. What are the dimensions of magnitude? How are they measured ? 19. What is said of impenetrability? PROPERTIES OF MATTER. 13 no perceptible resistance to our bodies when walking through it, is really as impenetrable as solids. If an inverted tumbler is sunk into water, the liquid will not fill the apparently void space, be- cause it is already full of air. An important application of this property of air is seen in the diving-bell. 20. Gravity is the tendency of bodies to approach the earth and its centre. All bodies, when not supported, fall to the earth's surface ; and, if prevented from falling, they exert a pressure that is the measure of their gravity, and which is called weight. This is one of the most important properties of matter, and the cause of many phenomena which will be fully explained in succeeding chapters. 2. Non-Essential Properties, 21. Non-essential properties. Besides the properties already explained which belong to every individual atom, there are other properties, common to all aggregate forms of matter, which are called non-essential, because we can conceive of the existence of matter without them. They are divisibility, compressibility, ex- pansibility, porosity, elasticity, and inertia. There is another group of properties of endless variety, which are found in some bodies and not in others, or in extremely different degrees in different bodies, and which therefore distinguish the species of matter and may be called specific ; such are ductility, tenacity, color, the attractive power of the lode-stone, &c. They will be explained in their appropriate place. 22. Divisibility. All bodies may be divided into smaller parts, similar to each other and to the entire mass, and these may be again disintegrated, until the particles become so minute as to elude our senses and our instruments. In the arts, the division of matter is carried to an extent which would be incredible, if it were not of daily occurrence, and capable of proof by direct experiment. 23. Expansibility, and compressibility. The same bodies do not always have the same volume, but they may be made to fill a greater or less space without in either instance altering the quantity of matter they contain. Both these changes may bt produced in many bodies by mechanical means, and in all bodies they invariably result from the action of heat. Examples of apparent penetration. 20. What is gravity? 21. What causes the non-essential properties of matter ? 22. What is said of divisibility ? 23. What is the volume of bodies ? 14 PHYSICS OP PONDERABLE BODIES. Wires by which heavy weights are suspended are sensibly in- creased in length. The volume of blank coins and medals is dimin- ished by the stroke of the die. Stone walls are sensibly affected in their dimensions by the daily changes of external temperature. 24. Porosity. Since the atoms of matter are always the same, we can explain the compression and expansion of bodies only by supposing that their atoms are not in immediate contact, but are separated by interstices, which enlarge or diminish as the vol- ume of the body changes. These interstices are called (physical) pores, and in this sense porosity is a general property of matter. In common language, however, we understand by the term pore, an interstice large enough to admit the passage of liquids and gases. This second and restricted species of porosity, sensible porosity, is not a general property of matter, but accidental, and belongs particularly to certain solids. The molecular or physical pores of bodies are permeable only to heat, light and electricity. Almost all animal and vegetable substances present pores which are easily penetrated by fluids. Petrifactions are produced by the infiltration of mineral sub- stances through the pores of the body. Many minerals and strata of rocks are porous, and the object of plowing and other similar mechanical operations of agriculture is to increase the natural porosity of the soil. The metals are not equally porous ; but still they are permeable to liquids and gases under great pressure. In 1661, the Academi- cians of Florence filled a gold sphere with water, and after closing it hermetically, diminished its capacity by pressure ; the water traversed the pores of the gold and appeared in the form of dew on the exterior surface. Faraday found it impossible to make a vessel tight to hydrogen gas even under moderate pressure. 25. Relation of porosity to weight and density. The atoms of different elements are probably of unequal weights, and are placed at variable distances in different bodies ; it results from these circumstances that bodies of the same volume have not the same weight. The weight of a body is always proportional to its mass ; in other words, to the number of material particles Give examples of the change of volume of bodies ? 24. What is said of porosity ? Of physical and sensible porosity 1 Examples illustrating porosity. 25. What is the relation of the weight of a body to its mass ? PROPERTIES OF MATTER. 15 it contains ; and the mass of a substance is greater as the po- rosity is less. The weight of a body is also proportional to its density, which expresses the relation of the masses when the volumes are equal. Of several bodies of equal volumes, that which has the greatest mass is said to "be most dense, and therefore has the greatest weight or gravity. As density increases, the pores become fewer and smaller ; when they are equally distributed, a body is said to be uniformly dense. A comparison of densities affords a constant, specific char- acter to distinguish different substances. The standard of comparison is water; and the number expressing the den- sity, or specific gravity of a body indicates, therefore, how much more or less heavy that body is than an equal volume of water. This important subject will be fully explained here- after. 26. Elasticity is that property of bodies which causes them to resume their form and dimensions on the removal of any force by which they have been bent or compressed. This property is found in a high degree in many bodies, and there are none abso- lutely without it. The limit as well as degree of elasticity is very various. If a force is applied exceeding the limit of elasti- city, the substance is either torn, or it does not again recover its original form and volume. A description of the modifications of this properly belongs to the history of the substances which dis- play them. 27. Inertia or inactivity. No particle of matter possesses within itself the power of changing its existing state of motion or rest. Matter has no spontaneous tendency either for rest or motion, but is equally susceptible to each, according as it may be acted on by an external cause. If a body is at rest, a force is necesary to put it in motion ; and conversely, it cannot change from motion to rest without the agency of some force. A body once put in motion, will continue that motion in an unchanging direction with unchanging velocity, until its course is arrested by external causes. This passive property of matter is called inertia. When we are told that a body at rest will forever remain so, unless it receives an impulse from some external power, the mind To its density 1 What is meant by specific gravity ? 26. What is electricity ? 27. What is inertia? 16 PHYSICS OP PONDERABLE BODIES. at once assents to a statement which embodies the results of our constant experience. But it requires some reflection in one who for the first time considers the subject, to admit that bodies in motion will continue to move forever unless arrested by external forces. Careless observation seems to contradict the assertion. On the earth's surface we know of.no motion which does not require force to maintain as well as produce it We may observe, however, that all such moving bodies meet with constant obstruction from three forces, friction, gravity and the resistance of the air ; and that as one or all of these may be diminished, the motion becomes prolonged and continuous. Be- sides we have familiar instances of a tendency to continue in a state of motion. The wheel of an engine continues to revolve after the impelling force has ceased ; a ball will roll longer and further as the surface on which it rolls is made smoother. When a pail of water is rapidly rotated and suddenly set down, the vessel itself is at that instant brought to a state of rest, but the mobility of the water allows it to continue the motion in its original direction, and it is spilled in con- sequence of its inertia. The planets furnish the only example of constant and unresisted motion. These celestial bodies, removed from all the casual resis- tances and obstructions which disturb our experiments at the earth's surface, roll on in their appointed orbits with faultless regularity, and preserve unchanged the direction and velocity of the motion which they received at their creation. 28. Inertia proportional to quantity of matter. The inertia of a body is proportional to its quantity of matter, and therefore the greater the mass on which a force acts, the greater will be the resistance to either acquiring motion or parting with it. Motion may be continued in a heavy body with a fraction of the force necessary to begin it. A horse draws with comparative ease a load which at first he had hardly strength to move. Time is also required to overcome inertia. What are the obstructions to motion 1 Give examples of a ten- dency to continue in motion. 23. What is said of the quantity of matter affecting inertia ? PROPERTIES OP MATTER. 17 A bullet thrown by the hand will shatter a pane of glass, but shot from a rifle, it will pass through without fracturing it, because there was not sufficient time for the motion of the bullet to be communi- cated to any part of the glass except that which was immediately be- fore it. A tallow candle discharged from a gun will pass through a board. A small bar of wood, suspended at its ends by two threads, may be broken by a sudden blow in the middle without rupturing the threads. If a coin be placed on a card on the top of a small bottle, or similar support, a sudden impulse, as a snap from the thumb and finger will remove the card, leaving the coin undis- turbed. Inertia is the basis of the whole theory of force and motion, and is the most important general property of matter. Physical Forces. 29. Definition of force. Since matter is in itself inert, and in- capable of spontaneously changing its condition, we are obliged to assign the constant changes which we observe in its relations to the action of some cause included under the general name of FORCE. The idea of force is abstract, and like number, space, time, &c., must be referred to the experience or consciousness of each individual. It is difficult and perhaps unnecessary, if not impossible, to give a satisfactory definition of any of them. Force is the name of the unknown cause of a known effect. We know of the existence of such causes only by their effects, which always appear in connection with something material, and may therefore be recognized by our senses. We can investigate the laws of the motions and equilibrium of forces, but their ori- gin, though perceived to be various, is beyond our comprehen- sion. They are powers conferred upon matter by the will of the Creator, to maintain the order of the world. 30. Varieties of force. Of the forces which act upon bodies, some are accidental and intermittent, as the agency of human and animal strength, and the contrivances of machinery ; others act continually upon every kind of matter, and are inseparable from it. To the latter class belong the universal forces of attrac- tion and repulsion. The approach and retreat of bodies, and of their component Example. What of time and inertia? Examples. 29. What is said of Force ? 80. What of the varieties of force ? 18 PHYSICS OF PONDERABLE BODIES. parts, is the basis of all the results produced by physical forces. The attraction of matter manifests itself under all circumstances. It is called universal gravitation, gravity, and molecular attrac- tion, according as it is displayed among celestial bodies, among terrestrial bodies, or between the contiguous particles of matter. Because gravitation exerts its influence through a wide extent, and acts at sensible distances, it is also called an external force, in distinction from molecular attraction, which, acting only upon the constituent atoms of bodies, and at insensible distances, may be called an internal force. 81. Molecular attraction. If the ultimate atoms of matter possessed no property in relation to each other except their mu- tual impenetrability, the world would be like a mass of sand, without variety of state or form. Atoms, when placed in con- tact, would neither adhere, as in solids, nor repel each other, as in gases. We find, however, that the particles of solids cannot be separated without the exertion of considerable force, and the effort is so strongly resisted in the metals, for example, that it is much easier to move the whole mass, than to divide it. Con- sequently there must be a force which holds together the parti- cles of solid bodies in fixed relative positions, and imparts to them an internal structure and an external form. It is assumed that this force is the mutual attraction of atoms, and when it is exerted in uniting the component particles of the same body, it is distinguished by the name of cohesion. 82. Cohesion. The cohesive attraction of particles in contact is an effort of the same kind as the mutual approach of particles at a distance. The same influence which causes two distant bodies to approach, will hold them together when they are united, and resist their separation. The attractive force which manifests itself at the immense distances between the celestial bodies, and which, at very much smaller distances, produces the weight and mutual attractions of bodies at the earth's surface, aught equally to display itself at all possible distances, however small they may be. Probably the attraction of masses is only the resultant of the partial attractions of the atoms which compose them ; or in other words both gravitation and cohesion are related effects of the same universal cause. We know that the atoms of different ele- ments are of different dimensions and forms, some being sphe- 31. What is of said molecular attraction ? 32. What of cohesion ? PROPERTIES OF MATTER. 19 rical, while others are spheroidal or ellipsoidal. Again, all bo- dies may be reduced in bulk by cold and pressure, their atoms are never in actual contact, and the intervals between them, though imperceptible to our senses, are probably very large when compared with the bulk of the atoms themselves. If then, as we may reasonably assume, molecular attraction and gravita- tion are effects of the same cause, they must obey the same laws, and the intensity of the cohesion of atoms will vary in the direct ratio of their quantity of matter, and in the inverse ratio of the square of their distance. The variations of molecular attraction, acting according to the above law on atoms of different forms and dimensions, and placed at very variable distances in different elementary and compound bodies, are sufficient to account for all the modifications of cohe- sive energy which are observed to exist. 33. The measure of cohesion in solids is the force required to change their form by flexion or fracture. If this force were not powerful enough to resist the efforts of gravitation, solids would fall to pieces by the weight of their particles. In obedience to cohesive attraction, the movable particles of fluids are drawn around their common centre, and form little spheres, as drops of dew and falling rain. For the same reason, mercury poured upon paper, collects in small globules in opposition to the gravity of its particles ; and liquid lead, poured through the meshes of a sieve, falls through the air in a metallic shower, whose drops solidify in shot during their descent. 34. Adhesion is the name given to molecular attraction, when it manifests itself in the adherence of surfaces placed in very close contact. It occurs between the surfaces of the same and different bodies, and between solids, liquids, and gases. Its phe- nomena, especially those of capillarity, will be discussed in sub- sequent chapters. Strictly speaking, there is no phenomenon of adhesion as distinct from cohesion ; for in the case of two plates of polished glass, united by a film of oil, it is in reality the force of cohesion between the particles of the oil which holds the plates together. Certain sub- stances are wet by water, while certain others are wet by oil, owing What is said of gravitation and cohesion ? What of the contact of atoms ? 33. What is said of the cohesion of solids ? Examples of cohesion in liquids. 34. What is adhesion ? 20 PHYSICS OP PONDERABLE BODIES. to a species of attraction between the surfaces of the solids and fluids respectively. When, as in the example cited, this wetting occurs, the so called force of adhesion is manifested. Thus glue serves to unite unlike substances, but the union is due to the cohe- sion in the particles of glue, and not to any attraction between the heterogeneous substances. 35. Chemical affinity. When molecular attraction is exerted between the atoms of different elements, it displays remarkable energy, and forms compound bodies, which possess no property in common with their constituents, except their combined gravity. When nitric acid is poured upon copper, intense action follows with the evolution of fuming vapors ; after the action has ceased, the acid and metal have disappeared, and in their place will be found a beautiful deep blue salt, whose weight and that of the vapors will be equal to the combined weights of the acid and copper. The blue salt is entirely different from either of its ingredients, but if a slip of clean iron is dipped into a solution of it, the copper will be precipitated upon the iron with all its characteristic properties. 36. Molecular repulsion. If a definite volume of air is ad- mitted into a vacuum of twice that capacity, it does not, like a solid or liquid body, retain its original volume, but expands and fills the whole empty space. The same will happen whatever may be the relative volume of the air and the vacuum ; in every case the particles of the air will be uniformly distributed through- out the whole void. Since an external force is necessary to hold together the particles of gaseous bodies like air, there must be a force which acts repulsively among their particles ; and the same force offers a resistance when their particles are brought together by mechanical pressure. A similar resistance to compression is displayed in liquid and solid bodies. Liquids can scarcely be compressed at all, and they regain their volume when the pres- sure is removed ; the same property is exhibited by all solids in variable degrees of intensity. 37. Elastic force of heat. The mutual repulsion found to pre- vail among the constituent atoms of bodies is assumed to be due to the elastic force of heat. It is certain that the energy of this repulsion is increased or diminished as heat is imparted to bodies or withdrawn from them. Heat produces the same phenomena What of its identity with cohesion? 35. What is chemical affinity. Example. 36. What is said of molecular repulsion ? PROPERTIES OP MATTER. 21 as mechanical compression and expansion, but in a higher degree. Since the accumulation of heat causes the atoms of bodies to sep- arate, and its removal causes them to approach each other, it must be admitted that whatever may be the nature of heat, it acts as a repulsive force. Its repulsive energy is manifested only at very small distances, and between particles of the same body. If we suppose that the atoms of bodies are each surrounded by a highly elastic atmosphere of heat, which modifies the attraction of the molecules, we shall be able to understand how the attractive and repulsive forces proceed from a common centre, and to account for all the observed phenomena, with which this hypothesis perfectly agrees. 38. Physical states of matter. Matter is presented to us in three physical states or conditions, namely : the solid, liquid and gaseous, (aeriform or vaporous.) We are familiar with many substances which assume the solid and liquid conditions ; most of the metals, for example, in their ordinary state solid, become liquid (melted) when heated. Certain bodies assume either of the three states. Water, for example, liquid at the ordinary temperature, becomes solid (ice) by cold, and vaporous (steam) by heat. And it is the same with many elements. Sulphur, for instance, a solid, by the application of heat, becomes first liquid and upon a continuance of the heat passes off as vapor. Some metals which require the highest temperature of our blast furnaces to melt, and others which even that heat is not sufficient to dispose them to relinquish the solid state, when sub- mitted to the action of the oxyhydrogen blow-pipe or to the heat obtained from the electric pile, immediately liquify, and in a little time vaporize. Of the first class may be mentioned iron ; of the second, platinum. As solids can be made to assume the liquid and gaseous form, so inversely can most gases be converted into liquids and solids by means of intense cold and great pressure. Submitted to their action, carbonic acid, a colorless gas, becomes a clear liquid re- sembling water, and this liquid allowed partially to evaporate, abstracts so much heat from the remaining portion that the latter becomes solidified ; this solid carbonic acid bears an exact resemblance to snow.- 37. What is said of the elastic force of heat ? How is heat known to be a repulsive force ? 38. What are the three physical states of matter ? Mention examples of bodies which may be made to assume the three states ? What is said of carbonic acid ? 22 PHYSICS OF PONDERABLE BODIES. 39. Relations between attraction and repulsion. These dif- ferent states of aggregation result from the definite relations under which molecular attraction and repulsion establish their equilibrium. The excess of the attractive or of the repulsive force will determine whether a body is solid or gaseous, while an equality of both forces produces a liquid. Let A represent the attractive and R the repulsive force, then the three aggre- gate conditions of matter may be expressed by the following formulae : A>R, solid A measure,) includes the cube, fig. 11, the regular octahedron, fig. 9, and rhombic dodecahedron, fig. 12. Each of these forms is perfectly symmetrical, being equal in height, length and breadth. Their axes are three in number, of equal length, and at right angles to each other. In the cube, the axes connect the centres of opposite faces, (fig. 1,) in the octahedron the apices of opposite solid angles, (fig. 9,) and in the dodecahedron the apices of opposite acute solid angles, (fig. 12.) The relation of the axes in these solids to each other may be understood by deri- ving one form from the other. If in the cube (its faces are indi- cated by o) we truncate each of its eight solid angles, fig. 13 is first produced, and as the truncation proceeds, fig. 14, and finally a perfect octahedron. It will be noticed that the centres of 0, the ends of the axes in the cube, correspond to the apices of the solid angles in the octahedron, which are also the ends of axes 13 14 15 Again, if we replace each of the edges of the cube by planes, (i) equally inclined to the faces, as we continue the replacement, we obtain successively the forms represented by figs. 15 and 16 ; finally, as the planes 0, disappear, we obtain the rhombic dodeca- hedron, fig. 13, the apices of its opposite acute solid angles, corres- ponding to the centres of the faces of the cube. If we truncate the 16 17 54. What does the monometric system include? What of the sym- metry of the forms in this system ? What is said of their axes ? What do they connect in the different forms ? How may an octa- hedron be derived from a cube 1 How a rhombic dodecahedron ? SYSTEMS OF CRYSTALLOGRAPHY. 35 edges of the octahedron, fig. 17, the planes (i) are reduced in size, and continuing the removal till these are obliterated, the rhombic dodecahedron results, and, as in the other cases, there is a perfect correspondence in position between its axes and the axes of the other forms. By a reversal of these processes we obtain from the octahedron and dodecahedron the cube, and the octahedron from the dodecahedron. Dimetric System. 55. The dimetric system, (from dis, two-fold, and metron measure,) includes the square prism, fig. 2, and square octa- hedron, fig. 10, bearing the same relation to each other as the cube does to the regular octahedron. In this system there are three axes, all at right angles to each other, but only the two lateral are equal, the third or vertical axis being of varying length. In the prism, the axes connect the centres of oppo- site faces, (fig. 2,) in the octahedron the apices of opposite solid angles, (fig. 10.) If a square prism has each of its solid angles truncated, we shall have first, fig. 18, and finally the square octahe- dron is produced. Tr imetric System. 56. The trimetric system, (from tris, three-fold, and metron, measure,) includes the rectangular prism, fig. 3, the rhombic prism, fig. 4, and the rhombic octahedron, fig. 11. Each of these forms has its three axes at right angles to each other, and all are unequal in length. In a rectangular prism, (the base a rectangle,) the axes connect the centres of opposite faces, fig. 3. In the rhombic prism, (base a rhomb,) the vertical axis con- nects the centres of the bases, the two lateral axes connect the centres of opposite edges, fig. 4. In the rhombic octahedron (base a rhomb) the axes connect the apices of opposite solid angles, fig. 11. If the solid angles of the rectangular prism are removed, we have first, fig. 19, and finally the rhombic How may an octahedron be derived from a rhombic dodecahe- dron? 55. What does the dimetric system include ? What is said of the axes in this system? What do they connect? 36 CRYSTALLOGRAPHY. octahedron. The same result is obtained by removing the basal 19 20 21 edges from a rhombic prism, as seen commenced in fig. 20. Again, replace the lateral edges of a right rectangular prism by planes equally inclined to both faces, and a right rhombic prism is the result ; fig. 21 shows the relation of the two prisms to each other ; the position of the axes in these forms may be seen to correspond. Monoclinic System. 57. The monoclinic system, (from monos, one, and Tdino, to incline,) includes the right rhomboidal prism, (fig. 4.) and the oblique rhombic prism, (fig. 5.) In this system the three axes are unequal, the two lateral axes are at right angles with one another, the vertical is inclined to one of the lateral axes and at right angles with the other. In the right rhom- boidal prism the axes connect the centres of opposite faces, (fig. 9.) In the oblique rhom- bic prism the vertical axis connects the centres of the bases, and the two lateral axes, the centres of opposite lateral edges, (fig. 5.) The trunca- tion of the lateral edges of one prism finally produces the other. The relation of these prisms to each other is seen in fig. 22. Triclinic System. 58. The triclinic system, (from tris, three, and Iclino, to in- How is a square octahedron derived from a square prism? 56. What 'does the trimetric system include ? What do the axes connect in the different forms of this system ? How is the rhombic octahedron derived from a rectangular prism? How from a rhom- bic prism ? How is the right rhombic prism derived from a right rectangular prism ? 57. What does the monoclinic system include ? SYSTEMS OF CRYSTALLOGRAPHY. dine,) includes the oblique rhomboidal prism, (fig. 7.) All the axes are unequal and oblique, the vertical axis connects the cen- tres of the bases ; the lateral axes connect the centres of the lateral edges, (fig. 7.) Hexagonal System. 59. The hexagonal system, includes the hex- agonal prism, (fig. 8,) and rhombohedron, fig. 23. In the hexagonal prism, fig. 8, the vertical axis connects the centres of the bases, the three lateral axes connect the centres of opposite lateral faces or edges and cross each other at an angle of 60, at right angles to the vertical axis. In the rhombohedron, two diagonally opposite solid angles con- sist of three 'equal obtuse or three equal acute plane angles ; the diagonal connecting these solid angles is called the vertical axis ; placed with this axis in a vertical position, the rhombohedron is said to be in position, and looking from above, it will be noticed that the lateral edges are at an equal distance from the vertical axis ; the three lateral axes connect the centres of the lateral edges intersecting each other, as do the lateral axes of the hex- agonal prism, at an angle of 60. Placing the rhombohedron in position, if we remove the six lateral edges, replacing them by planes parallel to the vertical axis, there is produced a regular hexagonal prism, terminated by three-sided pryamids. If their vertical solid angles are also removed, the regular hexagonal prism results. If we remove from an hexag- onal prism three alternate basal edges, and at the other extremity also, three edges, alterna- ting with the first, as shown in fig. 24, and con- tinuing the removal till the original form is ob- literated, a rhombohedron is produced ; it also results by removing, in a corresponding manner, the alternate solid angles from the hexagonal prism. When the plane angles forming the ver- 24 -&- What is said of the length of the axes in the forms of this system ? What do they connect ? How is one prism derived from another ? 58. What does the triclinic system include ? What is said of the length of the axes in this system 1 What do they connect? 59. What does the hexagonal system include? What is said of the axes in the hexagonal prism? What of the axes in the rhombohedron ? What is the appearance when the rhombohedron is placed in position ? 38 CllYSTALLOGKAPHY. tical solid angles are obtuse, the rhombohedron is called obtuse, and if acute, the solid is called an acute rhombohedron. Modified Forms. 60. Modified forms. If bodies in crystallizing assumed only the fundamental forms, there would be but comparatively little variety and beauty in crystalline solids ; it is to the modification of the fundamental forms that we owe that endless variety of crystalline figures which we observe in nature and that are pro- duced in the laboratory. These modified forms are called secon- dary or derivative forms, and are produced by the replacing of the edges and angles of the fundamental forms by planes, which are called secondary planes. The modifications of crystals take place according to two simple laws. 1st. All the similar parts of a crystal may be simultaneously and similarly modified. The forms thus resulting are called holohedral forms, (from Tiolos, whole, and edra, face.) 2d. Half the similar parts of a crystal may be simultaneously and similarly modified ; the forms thus resulting are called Jiemi- hedral forms, (from Jiemisa, half, and edra, face.) A few of the secondary forms of the different systems of crystallization will be noticed. Monometric System. 61. Holohedral forms. By the bevelment of the edges of a cube we have first fig. 25, and finally fig. 26, called a tetrahexa- Jiedron, the faces i 2, being extended until o is removed. 25 By replacing each of the solid angles of a cube by three faces How do we derive the hexagonal prism from the rhombohedron? 60. "What is said of modified forms 1 What are holohedral forms ? What are hemihedral forms ? 61. How is a tetrahexahedron derived from a cube ? MODIFIED FORMS. 39 equally inclined, we have fig. 27, and finally fig. 28, called a tra- pezohedron. 27 62. Hemihedral forms. By truncating the alternate angles of a cube we have figs. 29 and 30, and finally the faces of the cube 29 30 31 disappear, and there results for fig. 29, the tetrahedron, fig. 31, a three-sided pyramid ; this form in seen in iron pyrites, and a sim- ilar form results, for fig. 30. If the edges of a cube are replaced but by one of the two 32 33 34 beveling planes, represented in fig. 25, we have figs. 32, 33, and finally, fig. 34, the pentagonal dodecahedron. . Dimetric System. 63. Holohedral forms. The square prism has its lateral diffe- rent from its basal edges ; modifications of these two kinds of How is a trapezohedron derived from a cube ? 62. What form re- sults from truncating the alternate angles of a cube? How is a pentagonal dodecahedron derived from a cube ? 40 CRYSTALLOGRAPHY. edges take place independently of each other. The planes, inclu- ding the lateral edges, are equal ; these edges may therefore be beveled and truncated, which cannot be with the basal edgess, as they are contained within unequal planes. If the lateral edges of a square prism are truncated, another square prism results, fig. 35 ; if beveled, eight-sided prisms, fig. 36, 35 36 are produced, of different angles, according to the angles of bevel- ment. If the solid angles of a square prism be replaced by two 37 planes, as in fig. 37, a double eight-sided pyramid results, fig. 38. 64. Hemihedral forms.^ If half the solid angles of a square prism be replaced by single planes, as shown in fig. 18, the sca- 39 40 lene pyramid, fig. 39 results, while if two planes replace half the angles, fig. 40 is produced. 68. What is said of the square prism ? What forms result from the truncation and bevelment of the lateral edj How is a 64. How double eight-sided pyramid produced from a square prism 1 is a scalene pryamid produced from a square prism ? MODIFIED FORMS. 41 If on half of the angles only one of the two planes represented in fig. 37 is extended, and the plane on the opposite angle is on 41 42 the same side of the edge, fig. 41, results ; while if the plane is on the opposite side of the edge, fig. 42, is produced. Trimetric System. 65. Holohedral forms. It has been shown that a replacement of the lateral edges of a rectangular prism, produces a right rhom- bic prism ; by varying the inclination of the replacing planes, different rhombic prisms are produced ; a replacement of the basal edges produces other rhombic prisms, which are called (by Dana) domes, (from domus, house,) being placed like the roof of a house. 66. Hemihedral forms. Two different kinds of hemihedrism occur in this system ; the monoclinic, when the lower extremity of a crystal in front and its diagonally opposite differ in their modification from the upper extremity in front, as in tourmaline, 43 44 How the form, fig. 40 ? What of the other hemihedral forms 1 65. How are different rhombic prisms produced from a rectangular prism ? What are domes 1 G6. What different kinds of hemihe- drism occur in the trimetric system 1 42 CRYSTALLOGRAPHY. figs. 43, 44 ; the hemimorpTiic, when all similar parts of one base are modified alike, but unlike the corresponding parts of the 45 46 other as in topaz, figs. 45, 46. * Monoclinic System. 67. Monoclinic system. In the oblique rhombic prism, the lateral edges are two acute and two obtuse, therefore their secon- dary planes are unlike, fig. 47, the four lateral angles are similar, 47 48 49 fig. 48, the basal edges are two obtuse and two acute, therefore, independently modified, fig. 49, shows the obtuse basal edges modified. The oblique octahedron results from the replacement of the solid angles of the oblique rhombic prism ; in this figure there are two sets of planes, in which 1, 1, are on the obtuse angles 50 51 Give Examples. 67. What is said of the oblique rhombic prism ? What of the oblique octahedron ? MODIFIED FORMS. 4.3 of the outer prism, while 1 1 are on the acute angles ; fig. 50 shows the commencement of the replacement, and fig. 51 shows the completed figure. Triclinic System. 68. Modifications. As only diagonally opposite edges or angles are similar, we can have in the crystals of this system but 52 53 54 two planes alike, figs. 52, 53. By the replacement of the basal edges of the prism by homologous planes, an octahedron, having four sets of planes, may be produced, fig. 54. Hexagonal System. 69. Holohedral forms. In the hexagonal prism, the basal edges are alike, as also are the lateral edges and the solid angles. If each basal edge or basal angle is replaced by a single plane, as 55 56 57 figs. 55, 56, there results a double six-sided pyramid, called a dihexagonal pyramid, fig. 57". When each solid angle is re- placed by two similar planes, we have first fig. 58, and finally 68. "What is said of the modifications in the triclinic system ? 69. How is the dihexagonal pyramid produced from the hexagonal prism ? How the berrylloid ? How is a scalenohedron produced from a rhombohedron ? CRYSTALLOGRAPHY. a double twelve-sided pyramid, the berrylloid, results, fig. 59. 5 59 By replacing the lateral angles of a rhombohedron, there results a regular hexagonal prism terminated by a three-sided pyr- amid ; while if the planes m, fig. 60, are enlarged till R is ob- literated, an acute rhombohedron is produced. If, as in fig. 61, the lateral edges of a rhombohedron are beveled, a scalenohedron, 60 61 represented by the dotted lines, fig. 61, results. This solid is included by twelve scalene faces. By the replacement of the lat- eral angles of a rhombohedron by two planes, other scalenohe- drons result, as fig. 62, 70. How does a rhombohedron result from an hexagonal prism ? How a scalenohedron ? How a six-sided pyramid ? How is a tra pezohedral double pryamid produced ? COMPOUND CRYSTALS. 45 70. Hemihedrism. There are a number of kinds of hemihe- drism in this system. By the replacement of the alternate basal angles or edges of an hexagonal prism, a rhombohedron results, as has been shown. Fig. 58 is an hexagonal prism, with two planes on the angles, at either base ; in hemihedral forms, half of these planes are suppressed. If the suppressed planes are first r, then Z, fig. 63, alternate above and below, the form is a sca- lenohedron ; if the occurring plane is the r on each angle of one 63 64 base and the I on each angle of the opposite, as in fig. 64, a six- sided pyramid results. Again, the recurring planes may be the r of both bases, or the I of both bases, and there then results a trapezohedral double pyramid. 71. Compound crystals. Sometimes we find two or more crystals united regularly and symmetrically together. The form, if composed of two individuals, is called a twin crystal. Fig. 65 is a simple crystal of gypsum ; if it be bisected along a &, 65 66 67 68 and the right half be inverted and applied to the other half, it will form fig. 66. If an octahedron, as fig. 67, be bisected 71. What is a compound crystal ? What is said of the crystal of gypsum ? How is the form, fig. 68, produced from an octahedron ? 46 CRYSTALLOGRAPHY. through the dotted line, and the upper half revolved half way 69 70 around be then united to the lower, it produces fig. 68. Both figs. 66 and 68 are twin crystals. The imaginary axis, on which the revolution of half the crys- tal is made, is termed the axis of revolution, and the imaginary section, the plane of revolution. Compound crystals, composed of more than two individuals, are frequently observed, as in the case of the snow-flake, a not unusual form of which is rep- resented by fig. 69, composed of six crystals meeting at a point, or of three crossing each other at right angles. Fig. 70 represents a compound crystal of chrysoberyl. 72. Cleavage. By the application of mechanical force to crystals, we observe that they split in certain directions, leaving even and polished surfaces. The production of such surfaces, in causing the separation of the particles of the crystals, is called their cleavage; the planes along which the separation takes place are called cleavage joints. Cleavage is often obtained with great ease, as, for example, with mica, which may be separated by means of the fingers into thin leaves. Galena, again, cleaves easily, and as the three cleavage planes are at right angles to each other, a cube results. Calc spar also readily splits in three directions, and by this means a rhombohedron is obtained ; while with fluor spar a cleavage of its solid angles produces an octa- hedron. The cleavage of many crystals is obtained with great difficulty, as, for example, with quartz and tourmaline ; in others no cleavage can be produced, owing to the strong cohesion among the laminae. In some crystals but one cleavage is visible, as with What is the axis of revolution in a compound crystal? What is said of snow flakes ? 72. What is cleavage? What are cleavage joints? Give examples of easy cleavage. Examples of difficult cleavage. 47 GONIOMETERS.\l ' mica ; several have two ; others three, as galena and calc spar ; fluor spar has four, blende has six, while others have even more. We obtain by the cleavage of a crystal some one of the thirteen fundamental forms. Varieties of the same mineral have the same cleavage. Cleavage occurs parallel to the faces of the fundamen- tal form, or along the diagonals ; the facility of cleavage and lustre of the surfaces is always the same, parallel to similar faces. 73. Goniometers. Instruments for determining the angles of crystals are called goniometers, (from gonu, angle, and metron, measure.) The principle of the common goniometer is, that when two straight lines cross each other, their opposite angles are equal, as when, fig. 71, the line A ^crosses D, the angle AOD is equal to the angle C E, and A G to D E. Hauy's goniometer, fig. 72, consists of a light semi-circle of brass, accurately graduated into degrees, having a pair of arms which open and shut, moving on a central pivot, 0, by means of the grooves g h and n p ; these arms may be lengthened and shortened at pleasure, and the points a care thus made capable of embracing the faces of any crystal whose angles we wish to determine. 72 71 To measure an angle, we press the external arms of the com- What do we obtain by the cleavage of a crystal ? How does cleavage occur? 73. What are goniometers ? What is the principle of their construction ? What is Hauy's goniometer ? How is a crystal measured by means of it ? 48 CRYSTALLOGRAPHY. pass against the faces of the crystal which enclose the angle, until they accurately touch those planes in directions perpendic- ular to the edge at which they meet ; this done, we tighten the screw 0, by which the arms are confined. As the opposite angles are equal, therefore the angle indicated on the arc, (45 in the present case,) is the angle of the crystal. 74. Wollaston's reflecting goniometer. u The reflecting goni- ometer affords a more accurate method of measuring crystals that have lustre and may be used with those of minute size. The principle on which this instrument is constructed will be under- stood from the annexed figure, representing a crystal whose angle, a I c, is required. The eye looking at the face of the crys- tal 5 c, observes a reflected image of m, in the direction Pn. On revolving the crys- tal till a 5 has the position of 5 c, the same image will be seen again in the same direction, Pn. As the crystal is turned in this revolution till a 5 dhas the present po - sition of 5 c, the angle d 5 c, measures th e number of degrees through which it is revolved. But dbc subtracted from 180 equals the required angle of the crystal. The crystal is therefore passed in its revolution through a number of degrees, which subtracted from 180, gives the required angle. This angle evidently might be obtained by attaching the crystal to a graduated circle which should turn with the crystal." "This object is conveniently accomplished by the ingenious and simple contrivance of Wol- laston, fig. 74. A B is the cir- cle graduated to half degrees. By means of the vernier, F, minutes are measured. The wheel m, is attached to the main axis and moves the grad- uated circle, together with the adjusted crystal. The wheel is connected with an axis that passes through the main axis, which is hollow for the pur- 74. What are the advantages of Wollaston's reflecting goniometer ? GONIOMETERS. 49 pose, and moves merely the parts to which the crystal is attached, in order to aid in its adjustment. The contrivances for the adjust- ment are at p, q, r. To use this instrument, it must be placed on a small stand or table, and so elevated as to allow the observer to rest his elbows on the table. The whole, thus firmly arranged, is to be placed in front of a window, distant from the same from six to twelve feet, with the axis of the instrument parallel to it. Before operation, a dark line should be drawn below the window, near the floor, parallel to the bars of the window ; or, what is still better, on a slate or board placed before the observer, on the table." " The crystal is attached to the movable plate ^, by a piece of wax, and so arranged that the edge of intersection of the two planes, including the required angle, shall be in a line with the axis of the instrument. This is done by varying its situation on the plate g, or the situation of the plate itself, or by means of the adjacent joints and wheel r, s, p." " When apparently adjusted, the eye should be brought close to the crystal, nearly in contact with it ; and on looking into a face, part of the window will be seen reflected, one bar of which must be selected, or a cord stretched across the window for the experiment. If the crystal is correctly adjusted, the bar or cord will appear horizontal, and on turning the wheel n, till this bar, reflected, is observed to approach the dark line below, seen in a direct view, it will be found to be parallel to this dark line and ultimately to coincide with it. If there is not a perfect coinci- dence, the adjustment must be altered until this coincidence is obtained. Continue then the revolution of the wheel n, until the bar or cord is seen by reflection in the next face, and if here there is also a coincidence of the reflected bar or cord with the dark line seen direct, the adjustment is complete ; if not, alter- ations must be made and the first face again tried. A few suc- cessive trials of the two faces will enable the observer to obtain a perfect adjustment." "After adjustment, 180 on the arc should be brought opposite 0, on the vernier. The coincidence of the bar and dark line is then to be obtained by turning the wheel n. As soon as ob- tained, the wheel m should be turned until the same coincidence is observed, by means of the next face of the crystal." What is the principle of its construction ? What is the contri- vance of Wollaston? How is the crystal attached and adjusted? How is the determination made ? 3 50 CRYSTALLOGRAPHY. t{ If a line on the graduated circle now corresponds with o on the vernier, the angle is immediately determined by the number of degrees marked by this line. If no line corresponds with 0, we must observe which line on the vernier coincides with a line on the circle. If it is the 18th on the vernier, and the line on the circle next below o on the vernier, marks 125, the required angle is 125 18', if this line marks 125 30', the required angle is 145 48'." " Some goniometers are furnished with a small polished reflector attached to the foot of the instrument, below the part a, q, and placed at an oblique angle so as to reflect a bar of the window. This is an important improvement, as the reflected bar answers the purpose of a line drawn below the window, and is more conve- niently used. This reflector may be easily added to the common instruments, placing it at an angle of about 45, or such as will reflect the bar to the eye, when looking toward the crystal, while observing." V5. Constancy of crystalline form. Each crystalline solid has a definite form of its own, and as we distinguish the individ- uals of the animal and vegetable worlds by their external ap- pearance, so by the difference in form may the substances which constitute crystalline masses likewise be identified and distin- guished. Fen* example : common salt crystallizes in cubes, alurn in octaliedra, epsom salts in four-sided prisms, saltpetre in six-sided prims, B / acts at P, a point so situated T^v.. '"-<-... / that P A : P A : : A B : A' ff. *'" -*c ^'& The same will be true what- ever be the common direction of the forces ; if the positions of A B and A' B' are changed to A C and A' C', then P R must move to P J?', and equilibrium equally obtains. 112. Resultant of two parallel forces acting in opposite direc- 83 tions. The resultant of two parallel forces, which act in opposite directions, is found by the same construction as before, but it is equal to the difference of the components, and takes the direction of the greater. Its point of ap- plication, fig. 83, is in the prolongation of the line A J>, at the point C", situated so that C B and C A are in the inverse ratio of the forces Q and P. The point C will be further removed as the difference between the forces P and Q are diminished, so that if the forces were equal, the resultant would be nothing, and situated at an infinite distance. How may the truth of this conclusion be proved ? What is the result- ant of two parallel but unequal forces ^ How may it be demonstrated ? VARIATIONS OF MOTION. 75 Thus whenever a body is solicited by two forces which are equal, parallel, and acting in opposite directions, it is impossible to replace them or produce equilibrium by a single force. Such a system of forces is called a couple, and its tendency is to produce revolution around an axis. The general resultant of any number of parallel forces may be found by compounding them, successively, two by two, in the methods already prescribed. 113. Two forces not parallel and applied to different points may have a resultant, if they lie in the same plane. It is found by extending the lines of direction until they intersect. But if the forces are not parallel and lie in different planes, then the directions, though infinitely prolonged, will never intersect, and they cannot have any single resultant, or be in equilibrium by any single force. Dynamical Forces, or Motions. 114. Motion. When statical forces or pressures cease to be balanced, the body on which they act is set in motion. Abso- lute motion is a real change of place in space ; relative motion is a change of the position of a body in reference to others which are considered as fixed, but which may be themselves in motion. Absolute motion is unknown to us. All the motions which we can determine are only relative. Such are the motions on the earth, described with reference to points on its surface considered as fixed ; but these points are con- stantly in motion around the sun, and our planetary system appears to be itself moving through space. 115. Variations of motion. There may be the following vari- ations in the motions of a body : a The whole body may change its place and not return to it ; this is direct motion. It is exhibited in projectiles, &c. & A body, as a pendulum, may change its position and return to it in an opposite direction ; this is vibrating or oscillating motion. 112. What is the resultant of two parallel forces acting in oppo- site directions? Give the demonstration. What is a couple ? How may the general resultant of several parallel forces be found ? 113. What is the resultant of two forces not parallel applied at different points? When not in the same plane ? 114. What is absolute motion 1 IB it known ? Give examples of relative motion. 76 DYNAMICAL FORCES. c The different parts of a body may at the same time move in different directions ; this is called rotation. Instances are the daily rotation of the earth, the revolution of wheels, &c. The direction of motion is represented by a straight line drawn from the point where motion commences, to the point towards which the body is propelled. The direction is rectilinear, when it is constantly the same, and curvilinear, when it varies every moment. 116. Velocity is the space traversed in a unit of time, or the constant relation existing between the space traversed and the time when the body has a uniform motion, that is, when it traver- ses equal spaces in equal times. Velocities, like any other magni- tudes, are compared with each other, and their ratios may be rep- resented by the ratios of lines and numbers. There is no estab- lished unit of velocity, distinguished by a particular name, like feet, and pounds, and the units of length and pressure. To ex- press velocity in numbers we must use the units of time and length. If a number only were employed, without naming the units taken, the velocity would be wholly indefinite. The sim- plest mode is to give the space traversed in a unit of time, which in Physics is generally the second. For example : a man usually walks with a velocity of 2| feet in a second. An ordinary wind has a velocity of 3^ feet, and a hur- ricane 118 feet in a second. Velocities admit of comparison only when they are expressed in the same units. 117. Variable motion. When a body does not pass over equal spaces in equal times, however small they may be, the motion is variable. In this case, the velocity in any given instant, is the relation between the space traversed and the time, when the time is infinitely small ; or the space traversed in a unit of time, sup- posing that the motions were uniform, at that instant. 118. Uniformly accelerated or retarded motion. A motion is uniformly accelerated or uniformly retarded, when the velo- city increases or diminishes equally in equal times. In both cases the distinction must be observed between the body's initial and 115. What is said of the different varieties of motion ? How is the direction of motion represented? What is rectilinear and cur- vilinear motion ? 116. What is velocity ? How is velocity expressed ? What is the unit of terms employed ? Give examples of comparison velocities. 117. What is variable motion? COMPOSITION AND RESOLUTION OP MOTION. Y7 final velocity that with which the body begins, and that with which it ceases to move. Let V represent the velocity, 1), the distance, and T, the time ; then, in uniform motion, V = _? T D = V X T T _ D ~~ 119. Composition and resolution of motion. Since forces which produce pressure would produce motion in the direction of the pressure, if the bodies on which they act were free to move, all the principles of the composition and resolution of pressure, are equally applicable to motions. This important application could not be made, however, were it not for the physical law, that the dynamical effects offerees are proportional to their statical effects. A force which produces twice as much pressure as another, will also produce twice as much motion ; that is, it will either impart ; (a) to twice as much matter the same velocity in the same time ; (&) or to the same matter twice the velocity in the same time ; (c) or to the same matter the same velocity in half the time. This is not an abstract truth, but a law of nature, which could be learned only by experiment. The rules for the composition of pressures may be deduced without any appeal to nature ; but such an appeal is necessary before we can apply them to motions, for they could not be applied if pressures did not produce proportional motions. The dynamical effects of forces might have been as the squares of their statical effects, or the reverse ; a double pressure might have produced a quadruple motion, or a quadruple pressure a double motion ; and in neither case could they be compounded in the simple manner explained. When several forces act on a body, they may be arranged in three ways, according to their direction . The forces may act, (a) all in one direction ; (5) or in exactly opposite directions ; (c) or at some angle. 118. What is said of uniformly accelerated or retarded motion? Give the formulae for velocity, distance and time in uniform motion. 119. What is said of the composition and resolution of pressure and motion 1 What is the physical law mentioned? Mention the illus- trations a, b, c. What is said of the necessity of experiment to deter- mine this law ? V8 DYNAMICAL FORCES. In the first case, the resultant is the sum of all the forces, and the direction is unaltered. In the second, the resultant is the difference of the forces, and takes the direction of the greater. If opposite forces are equal, the resultant is nothing, and no mo- tion is produced. In the third case, a resultant is found to two forces, whether equal or unequal, by the parallelogram of forces, according to the following law. By any number of forces acting together for a given time, a body is brought to the same place as if each of the forces, or one equal and parallel to it, had acted on the body separately and successively for an equal time. Suppose two forces act simultaneously on the point a, fig. 84, one in the direction a x, and the other in the direction a y. Let one force be such that, in a given time, as a second, it will move the point from a to b, while the other will, in the same time, 84 move it from a to c, then by the joint ac- tion of both forces it will be impelled to r in the same time. The first force, by its separate action, would impel the body to b in one second, and if it were then to cease, the second force, or one equal and parallel to it, would impel to r in ff ~" > the same time ; or the body might be carried from a to c, and from c to r ; in either case the result is the same. In the same manner a resultant may be found for three or any number of motive forces, by compounding them, two by two, successively. In order that the body may move in the straight line a r, the two forces must act in the same manner. They may be instan- taneous impulses, which will cause uniform motion ; or both may act continuously and uniformly, so as to produce a uniformly accelerated motion ; or, both forces may act with a constantly varying intensity, increasing or diminishing at the same rate, and the body will still move in a straight line. But if one force is instantaneous and the other constant, or one constant and the other variable, or both varying by different laws, then the body will move in a curve ; but in every case it will reach the point r in the same time that it would have passed from a to b, or from a to c, by the separate action of either force. When several forces act on a body, how may they be arranged ? What is the resultant in each case? Give the illustration. What is said of the manner in which these forces must act? If they act va- riably in time what is the result ] RESOLUTION OF MOTION. 79 120. Examples of the composition of motion are of constant and familiar occurrence. A man in swimming, impels himself in a direction perpendicular to his feet and hands, and if the forces are equal on each side he will move in a resultant line, passing through the centre of his body. Another instance is the flight of birds. While flying, their wings perform symmetrical movements, and strike against the air witli equal force. In the case of flying birds the resistance of the air is perpen- dicular to the surface of the wings, and may be represented, fig. 85, by C A and D A, at right 85 angles to their surface. Nei- ther of these pressures tends to impel the bird straight forward, but it moves in their resultant ; for if the wings are equally extended, and act with equal force, the lines C A, and D A, make equal angles with A B, pass- ing through the centre of the bird, and hence their diago- nal, or A G, the diagonal of equal parts of them, will coincide with A B, and the bird will fly directly forward. 121. Resolution of motion. The motion of a boat impellc 1 by oars is similar to the examples just cited ; but when sails are used, and the force of the wind is transmitted from them to the keel, and modified by the rudder, we have an example of the resolution of motion. Let a 5, fig. 86, represent the length of a vessel, m n the sail supported against the mast at 0, and op the magnitude aril direction of the wind. Construct the parallelogram o p c d, of which p is the diagonal. The force p may be resolved into two forces, of which the first, o c, is parallel to the sail, ami produces no pressure upon it ; and the second, d, is perpendic- ular to the sail, and represents the whole pressure of the wind. But o d may be resolved into two other forces ; the one, of, at 120. Give the examples of composition of motion. Describe fi^. 85. 121. What is said of a sail-boat? What of the resolution of motion in this case ? 80 DYNAMICAL FORCES. right angles to the keel, urges the vessel sideways ; the other, o E, in the direction of the vessel's length, tends to advance it, and 86 represents the whole effective force of the wind. By a skillful application of the principles of the resolution of motion, a vessel may be sailed on a course, within five or six points of being di- rectly opposed to the wind which impels it. 122. Common motion not interfering with particular motion. In connection with this subject it is important to notice, that a motion common to all bodies of a system, does not at all interfere with the particular motions of any one of them, but such motions continue as if the system was at rest. If a bullet is dropped from the mast-head of a ship sailing ever so rapidly, it will fall to the deck on precisely the same spot as if the ship were motionless. A watch is carried without deranging the del- icate movement of its works. The earth moves on its axis at the rate of a thousand miles an hour at the equator, without interfering with the motions on its surface, except in case of the trade winds, and a few similar instances of composition of motion. Impact of Solid Bodies. 123. Transfer offeree. When a force acts on a body, it produces 122. What is said of a common motion not interfering with a par- ticular motion? Give examples. MOMENTUM. Si its effect as soon as motion is diffused among all the molecules, and the force is then transferred from the moving power, into the substance of the thing moved. In consequence of the inertia of matter, if the moving body meet no resistance, and no other force acted upon it, it would continue to move with the same velocity, and in the same direction, forever. 124. Relation of velocity to quantity of matter. Since a bod y absorbs, as it were, the force acting upon it, we can easily under- stand what our experience confirms, that the same force acting upon different bodies, produces very different motions. A charge of powder sufficient to project a bullet, would scarcely stir a cannon ball. The reason commonly assigned, is, that the ball is heavier than the bullet; but if their gravity , and all the resist- ances to motion were removed, the bullet, under the same impulse, would still move as much faster than the ball as its quantity of mat- ter was less. It is a fundamental principle of mechanics, that the same force acting upon different bodies, imparts velocities in the inverse ratio of their quantities of matter. If the same force successively projected balls, whose masses were as the numbers 1, 2, 3, &c., it would impart to them the velocities 1, -J, i, &c., so that a mass ten times larger, would acquire a velocity of only J ff . The pro- duct of each of these masses into its velocity, is the same, for 1 X 1 = 1, 2 X i = 1, &c. ; and this product of the mass into the velocity of a body, is called its momentum, moving force, or quantity of motion. 125. Momentum, velocity. Momentum must not be con- founded with velocity, which is the intensity of a motion, not its quantity. The same force always produces the same momentum, whatever may be the body on which it acts, so that the measure of an impact, is the momentum it imparts. We may describe an impact by saying, that it is equal to 20 Ibs. moved one foot a second, or 1 Ib. moved 20 feet a second, or 2 lb*. moved 10 feet a second ; the momentum being in each case the same. 126. Laws of momentum. It follows, therefore, that 123. What is said of the transference of force when a force act* on a body ? 124. Give examples showing relation of velocity to quantity of matter. What is stated to be a fundamental principle of mechanics? What is momentum ? 125. What is velocity ? How may we describe an impact? 82 DYNAMICAL FORCES. a When the masses are equal, the moments are proportional to the velocities. Z When the velocities are equal, the moments are proportional to the masses. c When neither the velocities nor masses are equal, the mo- ments are proportional to the product of the masses and velocities. From these laws it will be easily seen why great masses, as loaded ships, icebergs, &c., though they move but slowly, exert such crushing force upon objects with which they come in con- tact ; and also why cannon and musket balls, in consequence of their great velocity, are so destructive. 127. Impact. When a body in motion encounters another, the velocity and momentum of both undergo certain changes, which depend on the elasticity of the bodies, and other physical circum- stances. a When a body in motion strikes another at rest, it can con- tinue to move only by pushing this body before it, and it must impart so much momentum, that after impact, both may move with a common velocity. If the masses of the two bodies are equal, it is evident that after impact, the momentum will be equally divided between them, and their velocity will be one half of the velocity of the moving body before collision. If the mass at rest is double the mass in motion, the common velocity will be one third ; and generally, when a moving body communicates motion to a body at rest, the velocity of the two united, will be to that of the moving body as the mass of the latter is to the sum of the masses of both. If a musket ball, whose weight is _*_ Ib. arid its velocity 1300 feet a second, strikes a suspended cannon "ball weighing 48 Ibs., it will put it in motion, and their common velocity will be to that of the bullet as _i_ is to 48 -f-gV r as 1 is to 961 ; the velocity of the two is there- fore , or about 1 feet a second. & Bodies moving in the same direction may impinge, if their velocities are different. If an inelastic body overtakes another, the first will accelerate the second, and the second will retard the first, until they have acquired a common velocity, when they will 126. Mention the laws of momentum. What is said of ice -bergs and musket balls ? 127. What follows when a body in motion strikes another at rest ? When the masses are equal ? When the mass at rest is double the mass in motion ? Give the example in illustra- tion. What is the effect when an inelastic body overtakes matter ? LAWS OP MOTION. 83 move on together. Since the bodies move in the same direction, there can be no increase or diminution of the total momentum by impact, but only a re-distribution. If they are equal in mass, their velocity, after impact, will be half the sum of their previous velocities. If before impact, A had a velocity of 6, and B a velocity of 4, then their common velocity will be 5. The two bodies may have unequal masses as well as velocities. If the mass of A is 8, and its velocity 17, its momentum will be 136. If B has a mass of 6, and velocity of 10, its momentum will be 60. The sum 196, which is the total momentum of the united masses after impact; and the sum divided by the sum f the masses, gives 14, the common velocity. c If two equal bodies, moving with equal velocities in oppo- site directions, impinge on each other, their moments being equal, will be mutually destroyed, and the bodies will remain at rest. The force of the shock, in this case, is equal to that which either would sustain, if, while at rest, it were struck by the other with a double velocity. If the moments of the bodies are unequal, then, after impact, they will move together in the direction of the greater, and their joint momentum will be equal to the dif- ference of their previous moments, and their velocity will be found by dividing that difference by the sum of the masses. d These laws may be shown experimentally, by suspending two balls at the centre of a graduated arc, and producing im- pact according to the conditions described. If two bodies moving in different lines impinge on each other, then, after contact, they will move together in the diagonal of that parallelogram whose sides represent their previous mo- ments and directions. 128, Vis viva. If the body impinged on is immovable, or very large, compared with the moving body, no motion will ensue, and the collision will affect only the point of impact. The effects, (and in case the body at rest is penetrated by the Illustrate what happens when the two bodies have unequal masses as well as velocities ? What is the effect when equal bodies mo- ving in opposite directions with equal velocity impinge ? What is the force of the shock? What is the effect if they are moving with unequal momentum i! How may these laws be illustrated ? 84 DYNAMICAL FORCES. other,) the depths penetrated, are as the squares of the velocities multiplied into the mass of the projectile. If two unequal balls, as a six and twelve pounder, have velocities inversely as their masses, their moments will be equal ; both will move and overturn the same obstacle, but they will not penetrate a body to the same depth, for both will overcome resistance for the same time, and during that time the swifter ball will penetrate twice as far as the other. The penetrating effects of projectiles are equal, when their masses are inversely as the squares of their velocities, so that their moments multiplied into their velocities may be equal. 129. Formula for projectile force. Beaufoy determined that a body of 1 Ib. weight, with a velocity of 1 foot in a second, strikes with a force equal to 0'5003 Ib. To find the force of im- pact of any projectile, we have the general formula, F= 0.5003 MV2. The motion communicated to very large or immovable bodies by an impact of small ones, is not lost, but becomes insensible from its enormous diffusion. Motion can be destroyed only by motion ; friction and resistance disperse, but do not destroy it. 130. Diffusion of motion requires time. An impact can act directly upon only a few of the molecules of the bod}'- to which it imparts motion. The power which projects a bullet, acts on only one-half its surface. The motion must, therefore, be diffused from the parts struck, to all the other parts of the body, before it can begin to move ; and this diffusion requires time, which may be short indeed, but is not infinitely so. It happens, therefore, that a movable body, if struck by another moving with great velocity, may be pene- trated or broken at the point of impact, without being itself put in motion. Such effects appear incredible to persons unacquaint- ed with the inertia of matter, and its consequences. A rifle ball may be fired through a pane of glass suspended by a thread, without shattering the glass, or even causing it to vibrate. 128. What is the result when the body impinged on is immova- ble? What the effect when the body is penetrated? Mention the illustration. When are the penetrating effects of projectiles equal ? 129. What is the general formula for projectile force ? 130. What ia said of the diffusion of motion requiring time ? LAWS OF MOTION. 85 A half open door may be perforated by a common ball without be- ing shut by it. A soft missile, like tallow, or a light one, like a feather, will act with the force of lead, if sufficient velocity is given to it. Firing a tallow candle through a board is a well-known trick of showmen. In ricochet firing, a cannon ball, shot at an elevation of from 3 to 6, rebounds from the surface of water, just as every boy has made flat stones skip from point to point on its surface. The recoil of a gun does not begin to be felt until the ball has left the mouth of the piece. The experiment in proof of this, was first per- formed at Roehelle, in 1667, by order of the Cardinal Richelieu. A cannon was suspended like a pendulum, from the end of along shaft, and a ball shot from it struck precisely as it did when the cannon was fixed ; but if it had begun to move before the ball was dis- charged, the point struck would have been lower, depending on the amount of recoil. 131. The ballistic pendulum, 87 a large mass of wood or metal, suspended freely by a long shaft, is employed to measure the ve- locity of projectiles, on the prin- ciples of impact. (Fig. 87.) The ball is fired into the solid block of the pendulum, and the height to which it oscillates by the blow, is shown by an index " on a graduated arc, and deter- mines the velocity with which the pendulum began to move, when its momentum was equal to that of the ball. 132. Impact of elastic bodies. When collision takes place be- tween perfectty elastic bodies, the loss of momentum sustained by each, is twice as great as in inelastic bodies. For when two clastic bodies strike together, the parts of each are compressed, and when this force ceases, the particles return to their original positions, and impart reciprocally an impact opposite to the for- mer motion of each. If the masses of two elastic bodies are equal, after impact, they will exchange both their directions and velocities. Give examples in illustration. What was Cardinal Richelieu's ex- periment ? 181. Describe the ballistic pendulum. 132. "What is said of the impact of elastic bodies ? 86 DYNAMICAL POKCES. a If both move directly towards each other, after collision, they will both recoil with inverse velocities. ~b If both move, with different velocities, in the same direction, after impact, they will continue in the same direction, but with inverted velocities. c If one body is at rest, after impact, the striking body be- comes stationary, and the other moves on with the velocity of the impinging body. These laws may be experimentally shown with ivory balls, in the following manner. 88 If several equal ivory balls are suspended, as in fig. 88, and the first is let fall on the others, the last only, No. 7, will move, and this starts with the momentum which No. 1 had at the instant of striking No. 2 ; again, No. 7 falling, will cause No. 1 to rise, and this alternate movement of the extreme balls of the series will continue, until de- stroyed by friction, and the resistance of the air. 133. If an elastic body strikes an elastic plane, it will recoil with a velocity equal to that of impact. If the impact is perpen- dicular, it returns in the same direction ; if it is oblique, the body rebounds, under the same angle, in an opposite direction ; or, as it is usually stated, the angle of incidence is equal to the angle of reflection. 134. Newton's laws of motion. Before the principles of me- chanical philosophy were well established, the property of inertia and its consequences were stated by Newton in three formulas, called by him the laws of motion, which are so famous in the history of physical science, and formerly so important, that they ought to be remembered by every student. 1. Every body continues in its state of rest, or of uniform mo- tion, unless compelled to change that state by an external force. 2. Every change of motion is in the direction of the force im- pressed, and is proportional to it. "When the two bodies are equal what is the result ? What when one body is at rest 1 Mention the experiment with the ivory balls. 133. What is the result when an elastic body strikes an elastic plane ? 134. What is said of Newton's laws of motion ? APPLICATION AND THEOKY OF GRAVITATION. 87 3. Action and reaction are equal and contrary ; or the actions of two bodies on each other are equal, and opposite in direction. The first law, is a definition of inertia. The second, is strictly true only of a body at rest ; for if a body already in motion is acted on by another force, or if two forces act together on a body at rest, then it will move in the direction of neither, but between them, according to the law of compo- sition of forces. The third, means nothing more than the equal interchange of momentum, in opposite directions, between bodies which come into collision. Gravitation. 135, Gravitation is that universal force which all matter obeys, and which maintains the order and stability of the universe. The discoveiy of its laws was begun by Newton, in 1666, but not completed until June, 1682 ; when he received Picard's new measurement of the arc of a meridian, a quantity indispensable to his calculations. The laws of gravitation may be stated as follows : Every par- ticle of matter, attracts every other particle in the DIRECT ratio of its mass, and in the INVERSE ratio of the square of its dis- tance. That is, if the mass of one particle is 2, 3, or 4 times greater than the mass of another, its gravity is also 2, 3, or 4 times greater; and if the distance is 2, 3, or 4 times increased, the force of gravity is 4, 9, or 16 times diminished. Let M and m represent the masses, D and d the distances, and Q and g the forces of gravity of two particles, then G: g:: M: m and G : g : : d* : 1)2 136. Application of the theory of gravitation to astronomy. The announcement of these laws was one of those prime discov- eries which mark and make an era in the history of science. For the future, it rendered impossible any retrograde movement, Mention the three laws. What is said of these three laws? 135. What is gravitation ? When and by whom was it discovered ? Wliat are the laws of gravitation ? Give the formulae. 88 GRAVITATION. like that in which men lost sight of the true system of the world, once taught by Pythagoras. When the planetary forces and motions were shown to be identical with those existing at the earth's surface, astronomy rose from a science of mere observa- tion, to the rank of an experimental science of number and quan- tity. Henceforth calculation predicted and verified the results of observation, and thus furnished, astronomy speedily became what it now is, the most perfect branch of Physical Philosophy. Previous to Newton's discovery, the various branches of mathe- matical and mechanical science had reached a point where they could advance no further, without some such principle to reduce them all into a connected system. The discoveries of the ancient geometers, the dynamical experiments of Galileo, the singular proportions observed by Kepler, in the motions of the planets, and the speculations of Hooke upon attraction, smoothed some of the first obstacles in Newton's path of discovery, and pre- pared a state of knowledge in which his master mind could effectually exert its powers. The axioms of dynamics were ap- plied by him to the complete explanation of all the great and many of the minutest phenomena of astronomy. In doing this, he found the mathematics of his age insufficient, and he there- fore invented the method of fluxions, or differential calculus, which, as a means of discovery, " bears the same proportion to the methods previously in use, that the steam-engine does to the mechanical powers employed before its invention."* The consideration of the laws of gravitation, as applied to the elliptic motions of the planets, and their complex irregularities, to the cometary orbits, and the vastly remote systems of binary stars, belongs to celestial mechanics, or astronomy ; we are here concerned only with less grand, but equally interesting phenom- ena, produced by the attraction of the earth upon small bodies, momentarily detached from its general mass. 137. Terrestrial gravity. The laws of gravitation, in the ab- stract and general form in which they have just been stated, do not immediately apply to the attraction of the earth, or of the * HerschePs prelim, discourse. 136. What is said of the announcement of these laws ? What of mathematical science previous to Newton ? What discoveries re- moved some of the obstacles in Newton's path of discovery 1 What application of the laws of gravitation were made by Newton. TERRESTRIAL GRAVITY. 89 other planets. They are not mere particles, but great spherical masses of matter. Newton, however, has demonstrated that a particle of matter, placed without a hollow sphere, is attracted in precisely the same manner as if the whole mass of the sphere were collected into its centre, and constituted a single particle there. The same must be true of solid spheres, since they may be considered as composed of an infinite number of hollow spheres, having the same centre. 138. Form, of the earth. Although the earth is described, in general terms, as spherical, it is not exactly so, but spheroidal, or compressed in the direction of its axis, so as to have some resemblance to the figure of an orange. This deviation is too small to affect the mutual attractions of the earth and planets, at the immense distances which lie between them ; but it is con- siderable enough to cause irregularities in the motions of the moon, and in the weight and fall of bodies, at the earth's sur- face. According to Bessel,* the earth's equatorial, exceeds its polar diameter by nearly 26- miles. (26 '471.) This difference is trifling when compared with the whole dimen- sions of the earth ; in an exact model of 15 inches diameter, it would be only _J_ of an inch ; a quantity too small to be detected by the most practised eye or hand. 139. Local variations of the intensity of gravity. Weight is a particular instance of gravity, the effect of which the earth's attraction is the cause. If the earth were a perfect sphere, the same body would be equally attracted, and therefore have the same weight at every point on its surface : because a sphere is everywhere symmetrical; and the body would be everywhere equally distant from the centre. But a spheroid is not symmet- rical in the same manner, and a body placed at its equator, and a similar one at its pole, stand in different relations to the whole mass, and the weight of either of them will be the greatest at the poles, and gradually diminish from thence to the equator, where it will be least. There is a latitude, intermediate between * Herschel's astronomy, page 135. 137. What is said of terrestrial gravity ? What has Newton de- monstrated of 'the attraction of a hollow sphere ? 138. What is the form of the earth ? How may this trifling difference be illustrated ? 139. What is said of the weight of a bodylf the earth was n sphere ? 90 GRAVITATION. the poles, and the equator, where the earth attracts bodies on its surface, as if it were a sphere ; and in that latitude, bodies fall fall through 16 T '_ (16-0697) feet in a second. Newton and others have determined that the difference of weight due to the el- liptical form of the earth alone, is the ji^th part of the whole difference, which has been found, by repeated experiments, to be T T th part of the total weight of the body. The large remain- der, | F th part, is due to the centrifugal force, produced by the earth's rapid rotation on its axis. This force, which is nothing at the poles, regularly increases from thence to the equator, where it is greatest, and in the same ratio diminishes the sensible gravity of bodies. The same body is therefore specifically lighter at the equator, than at the poles of the earth, in the ratio of 194 to 195. This difference cannot be detected by the balance, because the thing weighed is counterpoised by an equal standard weight, under the same circumstances ; and if both are removed to another station, their weight, if changed, will be changed equally, and a body and its counterpoise once adjusted, will continue to balance each other wherever they are carried. It is not in this sense, that 194 Ibs. at the equator will weigh 195 Ibs. at the poles ; but if we conceive a body, y, suspended by a cord, imagined without weight, passing over a pully at the equator, as in the annexed figure, 89, and connected by other pulleys with #, another equal weight at the poles ; then, although the weights would counterpoise each other in a balance, they would not in this situation, but the polar weight would preponderate, and y would re- quire to be increased by y ljth part, to restore the equilibrium. In consequence of the second law of gravity, the same body is less heavy on the top, than at the base of a lofty mountain, because it will be then further removed from the earth's centre. What as the earth is a spheroid ? What is the difference in weight of a body owing to the spheroidal form of the earth 1 Why cannot this difference be detected by the balance ? How may this differ- ence be illustrated ? What is said of the weight of a body at diffe- rent elevations above the earth's surface ? FORCE OF GRAVITY. 91 A body weighing 1000 Ibs. at the earth's surface, loses 2 Ibs. at an elevation of four miles, and at the distance of the moon, its sen- sible weight would be only five ounces. When a body penetrates below the earth's surface, its sensible gravity is also diminished. Whatever part of the earth is above the body, attracts it towards the surface, while the mass below attracts it in the opposite direction, and the body tends towards the earth's centre, with the difference of these two forces. Could a body be placed in an empty space, at the centre of the earth, it would be sustained there in equilibrium, without any mate- rial support, by the action of equal and opposite attractions. 140. The direction of the force of gravity is a vertical line, which, if produced, would pass through the centre of the earth. This position is always assumed by & plumb-line, (a weight freely suspended by a cord,) and a line or plane at right angles to it, is said to be horizontal. The direction of the vertical, is evidently different for each place, and since this direction determines the terms up and down, these expressions have only a relative mean- ing, and change, as the direction of gravity changes, in passing from one place to another. Two plumb-lines, therefore, can never hang absolutely parallel, but, on account of the magnitude of the earth, their convergence is imperceptible within moderate distances. At greater distances, when miles intervene, the convergence of the perpendiculars must be estimated. Its amount is one minute in a geographical mile. 141. Plumb-line in the vicinity of a mountain. Estimation of the density of the earth. In the vicinity of a mountain, a plumb-line is not truly perpendicular, but drawn to one side by the lateral attraction of the mass. This deviation is measured by observations on the zenith distances of a star, at stations on opposite sides of the mountain, and on the same meridian. It was first noticed in 1738, by the French acad- emicians engaged in measuring a meridian arc in Peru. In 1774, Maskelyne found a deviation of 5' 8", caused by the lateral at- What when a body penetrates below the earth's surface ? What is said of a body at the centre of the earth ? 140. What is the direc- tion of the force of gravity ? What is a horizontal line or plane ? What is said of the terras up and down ? What of the convergence of perpendicular lines? 141. What is the direction of a plumb-line in the vicinity of a mountain 1 92 GRAVITATION. traction of Schehallien, a mountain in Scotland. The accurate investigation of this problem, was one of the highest importance in astronomy, since it furnished the means of determining the mean density of the earth, by comparing its attraction with the attraction of a part of its mass, whose density could be ascer- tained by direct experiment. The same result is attained, with much greater precision, by the famous Cavendish experiment, in which the earth's attrac- tion is compared with that of a mass of lead. Cavendish's determinations of the density of the earth, were made by means of an apparatus suggested by the Rev. John Michell. " Michell's apparatus was a delicate torsion balance, consisting of a light wooden arm, suspended in a horizontal position, by a slender wire, 40 inches long, and having a leaden ball about 2 inches in diameter, hung at either extremity. Two heavy spherical masses of metal were then brought near to the balls, so that their attractions conspired in drawing the arm aside. The deviation of the arm was observed ; and the force necessary to produce a given deviation of the arm, being calculated from its time of vibration, it was found what portion of the weight of either ball, was equal to the at- traction of the mass of metal placed near it. From the known weight of the mass of metal, the distance of the centres of the mass, and of the ball, and the ascertained attraction, it is easy to determine the attraction of an equal spherical mass of water, upon a particle as heavy as the ball placed on its surface. Now the at- traction of this sphere, will have to that of the earth, the same ratio as their densities ; and as the attraction of the earth is equal to the weight of the ball, it follows, that as the calculated attraction is to the weight of the ball, so is the density of water to the earth's density, which is thus determined." (Wilson's life of Cavendish.) A comparison of about two thousand experiments with this delicate apparatus, conducted by Mr. Francis Bailey, determined the mean density of the earth to be 5*6604 times that of water. It is worthy of remark, that Newton, whose guesses were often worth more than the researches of less sagacious men, had con- jectured the earth's density to be between 5 and 6 times the den- sity of water. How is the deviation from a perpendicular measured ? By whom was the deviation first noticed ? Of what importance is its accurate determination? Describe Cavendish's experiment. What is the mean density of the earth ? CENTRE OF GRAVITY. 93 Centre of Gravity. 142. Centre of gravity. The forces with which the earth at- tracts the molecules of all bodies at its surface, may, therefore, be considered parallel to each other, since they converge towards a point, the earth's centre, at an infinite distance, compared with the dimensions of the bodies. The number of these equal and parallel attractions is the same as the number of the molecules ; but since there is in every body a point about which its mole- cules are equally distributed in all directions, all these attractions may be replaced by a single force, applied at this point, which is called the centre of gravity of the body, or the centre of equal and parallel forces. In solids, this is a fixed point, and does not change, whatever may be the position of the body itself ; for, we have already seen, ( 111,) that the point of application of the resultant of parallel forces, is independent of their direction. 143. Experimental determination of the centre of gravity. When a body is freely suspended, it will remain at rest only when the vertical of the centre of gravity coincides with the direction of the cord of suspension ; for two equal forces are in equilibrium only when they act in opposite directions. This consideration affords the means of finding the centre of gravity by experiment. If, therefore, any irregular solid is suspended, as in fig. 90, its center of gravity will lie in the line c d, prolonged through its interior. It will also lie in the line a &, by which the body is a second time suspended, and being found in both lines, it must necessarily be at their intersection. 144. Centre of gravity of regular figures. In case of solids which have a regular figure, and uniform density, it is not ne- cessary to resort to experiment. In such' bodies, the centre of gravity coincides with the centre of magnitudes, and to find it, is a question purely geometrical The truth of this assertion may be shown, if we suppose a plane or line to be divided into two equal and similar parts, so that its molecules are ar- ranged two by two, with respect to the dividing line. Take any two molecules similarly situated, on opposite sides of the di- 142. What is the centre of gravity ? 143. "When will a body freely suspended remain at rest? How is the centre of gravity of an irregular figure determined? 144. What is said of the centre of gravity of a regular solid \ GRAVITATION. vision, their moments will be equal and opposite ; and so also of every other pair ; therefore, the resultant of the system must be at the point of division, and the centre of gravity is there also. The centre of gravity of a circle, or sphere, is at the centre of each ; of a parallelogram or prism, at the intersection of the di- agonals ; and of a cylinder, at the middle point of its axis. To find the centre of gravity of a triangle, fig. 91, draw a line A D, from the vertex to the middle point of the base ; it will divide equally all the lines, as m n, drawn parallel to the _ ^c base. If the triangle is placed so that : the line A D may be exactly over the edge of the prism P Q, each one of the rows of molecules composing the figure, as m n, will be in equilibrium on the edge of the prism, since it is supported at its centre. The same will be true when they are united, and the triangle will not tend more to one side than another ; hence its centre of gravity must be in the line A D, and for a like reason, also in the line B E, and therefore at their intersection G. It may be shown that the point, thus found, divides the line join- ing the summit, and the middle of the base, into two parts, of which the one nearest the vertex is double that nearest the base. 145. Support of a triangular mass at its angles. If it were required to support a triangular block of marble at its angles, we may find what part of the weight will be sustained by each support, by applying the foregoing principles. The weight of the block, fig. 92, which we will suppose to be 45 Ibs., is a force applied to its centre of gravity, g. We have seen that the distance & g, is twice the distance g d, and hence we may resolve the vertical force of 45 Ibs., acting at ^, into two others ; one of 15 Ibs. at 5, and the other of 30 Ibs. at d ; but the last force, since it acts at the middle point of a c, may also be resolved into two others of How may the truth of this be drawn ? What is the centre of grav- ity of a circle or a sphere ? How is the centre of gravity of a tri- angle found ? 145. What is said of a triangular block of marble supported at its angles? EQUILIBRIUM OF SOLIDS. 95 15 Ibs. each, acting the one at a, and the other at c. Hence the weight of the triangle is equivalent to three equal forces acting vertically at its angles ; and the three points of support sustain equal pressures, whatever may be form of the triangle. 146. Centre of gravity lying without the body. The centre of gravity is not, necessarily, in the body 93 itself, but may be in some adjoining space. This is evidently true of the solid ring, fig. 93, and generally of any hol- low vessel, of whatever form. Of a compound body, the centre of gravity is easily found by composition of forces, when the weights and centres of gravity of the parts are known. 147. Equilibrium of solids supported by an axis. A solid is in equilibrium when its centre of gravity is supported. But this condition may be fulfilled in different ways, 94 according to the method of support. If a disk of uniform density, fig. 94, is sup- ported by an axis, passing through the cen- tre , which is also its centre of gravity, it will be in that sort of equilibrium which is called indifferent, because it has no ten- dency to revolve, either to the right or left, but remains at rest in all positions. If the axis passes through &, the disk will be in stable equilibrium ; for if it is turned about its axis, the centre of gravity will move in the arc m n, and being no longer vertically below the axis, it will not be directly supported by it, but tends always to return to its former position. If the axis is at c, the equilibrium is unstable; for, if the centre of gravity is in the least removed from a position vertically above the axis, it cannot return, but it will describe a semi-circle in its descent, until it comes to rest exactly below the point of support. In general terms, therefore, a body attached to an axis may be in stable, unstable, or indifferent equilibrium, according as its centre of gravity is below, above, or within the axis. 148. Equilibrium of solids placed upon a horizontal surface. In bodies placed upon a horizontal surface, the centre of gravity Give the illustration. 146. What is said of the centre of gravity of a ring? 147. When is a solid in equilibrium? When is it in in- different equilibrium 1 When in stable and unstable equilibrium ? 96 GRAVITATION. as in those which are suspended, tends to descend, and if the bodies are free to move, they will rest in one of the positions of equilibrium just named. If rays are drawn from the centre of gravity to every part of the surface, some of these rays will be oblique, and some perpendicular, or normal to the surface, what- ever may be the external form of the body ; and among the nor- mal rays, there is generally a longest and a shortest ray. If the body rests upon the plane, at the extremity of one of the nor- mal rays, its centre of gravity is evidently in the vertical line, drawn through the point of contact, and the body is in equili- brium. But if it rests at the extremity of an oblique ray, the centre of gravity is not supported, since it is not in the vertical of the point of contact, and the body falls. If the normal ray at the point of contact is neither longest nor shortest, but simply equal to the adjacent rays, the equili- brium is indifferent Such is the case with a sphere, placed on a level plane ; it rests in every position, for its centre of gravity 95 cannot fall lower than it is. But this position cannot be assumed by a body not strictly spherical. For example, if an egg rests at the extremity of a longest ray, #<, as in fig. 95, it will be in unstable equilibriun, since motion to either side tends to lower the centre of gravity, and enable it to fall ; but if it rests at the extremity of a shortest ray, a', it will be in stable equilibrium, since any motion side- ways must raise the centre of gravity, and it will, therefore, fall back to its original position. 149. Centre of gravity in bodies of unequal density in diffe- rent parts. If the density of a body is unequal in different parts, 96 its centre of gravity will be external to its centre of mag- nitude, and the body can come to rest in only two po- sitions, when the centre of ^^^^^, gravity is at the highest, and I at the lowest place in the ver- | tical of the point of contact. z^roM^ If a cylinder of this descrip- 148. "What is said of bodies placed upon a horizontal surface? Where is the centre of gravity when the body is placed at the ex- tremity of one of the normal rays ? What is the result when it rests at the extremity of au oblique ray ? FALLING BODIES. 97 tion were placed upon an inclined plane, as in fig. 96, it would be in equilibrium when its centre of gravity was at either e or a ; if at e, and the cylinder were moved a little to the right, the cen- tre of gravity would fall through the arc e a, but at the same time the cylinder itself would perform the apparent contradiction of ascending the plane. 150. Equilibrium of bodies supported in more than one point. When a body is supported by two points, the vertical, from its centre of gravity, ought to fall on the middle of the line which connects them. If a body has four points of support, the vertical should fall upon the intersection of their diagonals. In carriages, if the vertical falls in a different manner, the load is improperly distributed, and the carriage will be liable to upset, in passing over an uneven road. A body resting on a base more or less extended, will be in equilibrium only when the vertical from the centre of gravity falls within the area of the base ; and the body will stand firmer in proportion as the centre of gravity lies lower, and the base is broader. A pyramid is, therefore, the most stable of all struc- tures. The singular feats exhibited by children's toys, and by rope-dancers , depend on the facility with which the centre of gravity is shifted, while it is always supported vertically above the base. Laws of Falling Bodies. 151. Gravity a source of motion If a body at a distance from the earth's surface is not supported, it falls, and the force of gravity, which we have already seen to be the cause of weight or pressure, now manifests itself in producing motion. The body is said to fall ; in reality, the motion is common to both the masses concerned, the earth and the descending body. They move towards each other in the inverse ratio of their masses ; but since the mass of the earth is infinitely greater than the mass 149. Where is the centre of gravity in a body whose density in different parts is unequal ? Give the illustration. 150. Where should the centre of gravity fall in a body supported in two points 1 Where in a body supported by four points? What is said of carriages? What of a pyramid ? What of rope-dancers ? 161. How is gravity a source of motion ? 5 98 LAWS OF FALLING BODIES. of the falling body, the distance through which the earth moves is less in the same ratio, and it cannot be made evident to our senses. Every one has observed the different velocities with which dif- ferent bodies fall. For example : a gold coin falls swiftly, and in a straight line, but a piece of paper descends in a winding course, and with a slow, hes- itating motion. The popular explanation is, that the coin is heavy, and the paper light; but this is not the true reason, for when the gold is beaten out into thin leaves, its weight is the same, but the time of its fall is very much prolonged. The variation is independent of gravity. Since the attraction of the earth acts equally, and independently on all the particles of matter of which a body is composed, it can be of no conse- quence, as far as this attraction is concerned, whether a body contains many particles or few ; each particle is as strongly at- tracted alone, as when united into a mass with others. The dif- ferences in the time and manner of falling, are caused solely by the resistance of the air ; which resistance varies, according to the shape and volume of the body, and not according to its mass, or the number of particles contained in it. This conclusion is established by the guinea and feather experiment. We take a glass tube, fig. 97, five or six feet long, closed at one end and mounted with a stop-cock at the other, and having placed a light and heavy body inside ; a guinea and a feather, or a bullet and a piece of paper ; we withdraw all the air from the tube, by means of an air-pump. Now let the tube be suddenly inverted, and the guinea and the feather will be seen to fall with equal rapidity, and strike the bottom together ; but turn the stop-cock, and ad- mit the air, and the one will descend swiftly, and the other will be retarded, just as it happens when they fall under ordinary circumstances. Thus when no resistance modifies the effects of gravity, it attracts all bodies with the same energy, and gives them the same velocity, whatever may be their weight, and what- ever the kind of matter of which they are composed. The first law of falling bodies is, 1st. In a vacuum, all bodies fall with equal velocity. "What is said of the mutual action of a falling body and the earth ? Why do different bodies fall with different degrees of velocity ? What is the guinea and feather experiment ? What is the first law of falling bodies ? FALLING BODIES. 99 152. Velocity of falling bodies. The fall of a body is a uni formly accelerated motion, because the earth's attrac- 97 tion acts at every moment in the same manner. The body gains a new impulse at each instant, and these impulses being equal, in equal times, the final velo- city is equal to their sum, and proportional to the time of the fall. That is, the velocity of a falling body, at the end of the 2d second, is twice, and at the end of the 3d second, three times as great as at the end of the 1st second, &c. We have, therefore, 2d. The final velocities of a body, falling freely, increase as the times of falling, or they follow the order of the natural numbers, 1, 2, 3, &c. 153. Spaces described by falling bodies. The ve- locity of a body when it begins to fall, is nothing ; but from that moment it regularly increases. Let us represent the velocity acquired at the end of the 1st second by v ; then the average velocity during the same time will be, o -f- v 2 1 the arithmetical mean between o, the starting velocity, and v, the final velocity. A body moving at this rate, will traverse the same space in one second, which it would have fallen in one second ; let this space = g ; then the space being equal to the product of the ve- locity, and the time, $ v, X 1 sec. = g, or v = 2 g ; that is, the final velocity acquired by a body fall- ing one second, is double the space through which it has fallen. It has been ascertained that in our lati- tude, this space is about 16-J- feet (16-0693 feet, see 139) ; and v = 32 feet. In the 2d second, the body star's with a velocity of v = 32 feet, and acquires, at the close, the velocity of 2 ID = 64 feet. The space fallen during the same time is 48 feet ; viz : 32 feet by the velocity ac- quired during the 1st second, and 16 r '_ feet by the gradual action 152. Whv is the velocity of a falling body a uniformly accele- rated motio i ? What is the second law of'falling bodies? 153. What is said of the final velocities of a body falling freely ? 100 GRAVITATION. of gravity, in this second only. Or as before, the space described by the body during the 2d second, is equal to the space it would have fallen with the mean velocity between its initial and final velocities ; i. e. with the velocity the space, therefore, = 3 X 16 T i_ = 48} feet. In the same way we find that the velocity acquired at the end of the 3d second, will be 3 v = 96| feet; and in the same time the body will have fallen, with the mean velocity, 2 v + 3 v 5> through a space of 5 g = 5 X 16JL. = 80 J- feet. A falling body, therefore, descends, in the 2d second of its fall, through three times, and in the 3d second, through five times the space fallen in the 1st second. We have, then, 3d. The spaces fallen through in equal successive times, in- crease as the odd numbers, 1, 3, 5, 7, &c. 154. Whole space described by a falling body. We have seen that the time of falling, and the final velocity, increase ki the same ratio ; and that the average velocity of any fall, is e*actly half the final velocity ; hence, any increase in the time of falling is attended by a corresponding increase of the average velocity during the whole fall. But the whole space described in any fall is jointly proportional to the time, and the average velocity ; if, therefore, the time is doubled, the body falls not only twice as long, but also twice as fast, and it must descend through four times the distance. Again, if a body falls three times as long as another, it also falls with three times the average velocity, and descends, altogther, through nine times the distance. The times being represented by the order of the natural numbers, 1, 2, 3, &c., the spaces are represented by their squares, 1, 4, 9, 16, &c. A body in two seconds falls through four times, and in eight seconds, through nine times the space it descends in one second. Therefore, 4th. 2 he whole spaces described by a falling body, increase as the squares of the times in falling. How may the velocities with which a body falls be estimated ? What is the velocity in the 1st, 2d, and 3d seconds? What is the third law of falling bodies? 154. What is said of the whole space described by a falling body ? FALLING BODIES. 101 155. Result of the average velocity being double of the final velocity. We have seen that a body falling for any time, ac- quires a final velocity which is double the average velocity of the fall ; if, therefore, the action of gravity were suspended at the end of any given time, and the body continued to move with its acquired velocity, it would, in the same time, traverse twice the distance it had already fallen. For instance, the space fallen through in three seconds, is 144f feet, and the final velocity is 96 feet ; now a body falling uniformly, for three seconds, with this ve- locity, would pass through a space of 3 X 96 = 289* = 2X 144f feet. ' 5th. A fiody falling during any time, acquires a velocity which, in the same time, would carry it over twice the space of the first fall 156. Table expressing the laws of falling bodies. The fol- lowing table expresses the 2d, 3d, and 4th laws : Times, ..... 1, 2, 3, 4, 5, t The final velocities, . . . 2, 4, 6, 8, 10, 2t The space for each time, . 1, 3, 5, 7, 9, The whole spaces, . . . 1, 4, 9, 16, 25, t a Let s = the space, t = the time, v = the final velocity, and g = the space fallen in the first second, then from the fore- going laws we may deduce the following equations, by which practical questions are readily solved. (1) v = 2 g t, whence (2) t = ~~ (3) * = g t*, whence (4) t 1 By substituting in (3) the value of t (2) And substituting (4) in (1,) What is the fourth law of falling bodies ? 155. What is the fifth law of falling bodies? Give an illustration. 156. What are the times of falling bodies ? What the final velocities ? What the space for each time ? What the whole spaces ? Explain the formulae given. 102 GRAVITATION. 98 M 157. Verification of the laws of falling bodies. It is evident that the laws of falling bodies cannot be verified by direct experiment, because the results of such an in- quiry would be disturbed by the resistance of the air, and the ve- locity of the fall is too great to be followed with the eye. But there are several indirect methods by which the intensity of the force of gravity may be diminished, without changing its nature. We can cause a falling body to descend so slowly, that the resistance of the air becomes imperceptible, and all the circumstances of the fall may be observed with entire precis- ion. Galileo, who discovered and published these laws, about the year 1600, used an inclined plane in his experiments. The apparatus now generally employed, is called, from the name of its inventor, At- wood's machine. Fig. 98. This apparatus is composed of a vertical column, about seven feet in height, surmounted by a friction pulley R, upon which is suspended a fine silk cord, carrying equal weights, Jf and M', at its extremities. A scale of feet and inches is placed parallel to the path of one of the weights, to measure the spaces through which it falls, and the cor- responding times are shown by the seconds pendulum P. To insure the simultaneousness of the fall with 157. What is the verification of the laws of falling bodies? What did (jalileo use in his experiments ? FALLING BODIES. 108 the beat of the pendulum, the weight is set in motion by the lever D, which is itself moved by an eccentric, (represented at JS,) at- tached to the axis of the seconds hand. The weights M and M' being equal, the force of gravity has no effect upon them, and they remain at rest in any position. But let one of them, as M', be increased by a small additional weight n, and the equilibrium will be immediately disturbed. The- gravity of n being the only disturbing force, the motion produced is of the same kind as the motion of a body falling freely, but the rate of accele- ration, and the space fallen through, are each as much less as the mass of n is less than the combined masses of n -f- 2M. For example: let n be a quarter of an ounce, and the weights M and M, be each 24 ounces, or 96 quarter ounces. The whole mass to be moved, by the action of gravity upon n only, is 193 times the weight of n, and therefore the velocity imparted, and the space fallen through, must be 193 times less than the velocity and space of n falling freely. Now let M' and n attached to it, be allowed to fall from /, the top of the scale, at the moment the click of the pendulum is heard. At the instant of the next beat, the weight will be seen to have fallen exactly 1 inch ; during the second beat, through 3 inches more; during the third beat, through 5 inches ; during the fourth beat, through 7 inches, , fig. 115, which are made to approach by a contrivance similar to that shown in fig. 113. It is evident, that in this last arrangement, the force is applied in the most favorable position for producing the maximum effect in collapsing the spring ; while in Reynier's dynamometer, the force is applied where only the minimum effect is produced, and the instrument is therefore generally employed for determining only very considerable forces. 185. Animal strength. The mechanical effect produced by men and animals, is subject to extreme variation, according to the va- rious circumstances under which it is applied. The effect pro- duced is determined by multiplying the load (or weight) by the speed. There is always a certain relation between the elements, which will give the maximum effect ; for the load may be so great, that it will require all the strength of the animal to support it, and then he cannot move ; or again, the animal may have a speed of motion so great, that he cannot carry any load, however small. 186. Strength of men. It has been found, that the strength of a man may be exerted for a short time, most advantageously, in raising a weight, when it is placed between his legs. The greatest weight that can be raised in this manner, varies from 450 to 600 Ibs ; its average amount does not, however, exceed 250 Ibs. The greatest mechanical effect from muscular force is obtained, when the animal acts simply by raising his weight to a given height, and then is lowered by simple gravity, as upon a moving platform, the animal actually resting during the descent. In other words, the animal affords a convenient mode of raising a given weight, (his own,) to a certain height. Thus, if two baskets are arranged at each end of a rope hung over a pulley, and a weight to be raised i placed in one of the baskets, one or more men, whose weight is greater than that of the load to be raised, What is said of another dynamometer similar in form to Rey- nier's ? 185. What is said of the muscular strength of a man and a horse ? 186. How may the strength of a man be exerted most advan- tageously in raising a weight ? What is the greatest weight that can be raised in this manner 1 What is the average weight ? How is the greatest mechanical effect produced by an animal? HORSE POWER MACHINES. , T 123 can, by getting into the empty basket, raise the weight as often as may be required. It has been found by experiment, that in this way, a man working eight hours, can produce an effect equivalent to 2,000,000 Ibs. raised one foot ; while at a windlass, an effect of only 1,250,000 Ibs. is produced, and at a pile engine, only 750,000 Ibs. In the tread-mill, the daily effect of men of the average strength, is 1,875,000 Ibs. raised one foot. Spade labor is one of the most disadvantageous forms in which human labor can be applied; the force exerted being always much greater than the weight of the earth raised. The muscular effect of the two hands of a man, is about (50 fc) 1,112 Ibs., and for a female, about two-thirds of this quantity. 187. Horse power machines. One of the most advantageous methods of applying the strength of animals, is by machines constructed upon the principle of the tread-mill. In practice, however, it has been found more convenient to apply horse-power to machinery by means of a large beveled or toothed wheel, fixed horizontally on a strong vertical axis. The horses are attached to projecting arms of this wheel, and as they move in their circular path, they push against their collars, and make the wheel revolve. This beveled wheel acts on a beveled pinion attached to a horizontal shaft, in connection with the machinery to be set in motion. The maximum effect which a horse can exert in drawing, is 900 Ibs., but when he works continuously, it is much less. In the machine just mentioned, a horse of average strength produces as much effect as seven men of average strength working at a windlass. According to experiments made in Scot- land, it appears that the average load which a single horse can draw, at the rate of 22 miles per day, in a cart weighing 7 cwt, is one ton, of 2240 Ibs. 188. Table of the comparative strength of men and other an- imals. The following estimates of the relative strength of man and other animals, have been given by the authorities whose Give the example mentioned. What is the effect a man can exert in this way equivalent to ? "What is said of the tread-mill, and spade labor ? What of the effect of the two hands of a man ? 187. What is said of horse power 1 How is it most advantageously em- ployed ? What is the maximum effect a horse can exert in drawing 1 What is the comparative strength of horses and men ? What is said of the load a horse can draw ? 124 THEORY OF MACHINERY. names are indicated, Coulomb's estimate of the labor of a man being in each case taken as the unit. Carrying loads on the back, on a level road. Horse, according to Brunacci, 4*8 " " " "Wessemann, 61 Mule, " " Brunacci, 7*6 In drawing loads on a level road, with a wheeled vehicle. Man with wheelbarrow, according to Coulomb, lO'O Horses in four-wheeled wagon, " " 175 '0 " in two- wheeled cart, according to Brunacci, 243*0 Mule " " " " " " " 233-0 Ox " " " " " " " 122-0 Hassenfratz gives the following comparative estimate. In carrying loads on a lerel road. Man, 1-0 Horse, 8'0 Mule, 8-0 Ass, 4-0 Camel, 31'0 Dromedary, 25 '0 Elephant, 147'0 Dog, TO Reindeer, 3'0 In drawing loads on a level ro&f Man, 1-0 Horse, -7"0 Mule, 7-0 Ass, 2-0 Ox, 4 to 7-0 Dog, 0-6 Reindeer, 0'2 189. Steam power. Water is converted into steam by the ap- plication of heat. Steam is an elastic condensible vapor, capable of exerting great force. During the conversion of a cubic inch of water into steam, a mechanical force is exerted, which may be stated, in round numbers, as equivalent to a ton weight raised one foot high. The water is merely the medium by which the mechanical effects of heat are evolved. The real moving power is the combustible, the coal or wood consumed in the evaporation of the water. The maximum effects from a given weight of coal, in evapo- rating water, and consequent mechanical effect, have been ob- 188. Give the relative weights which different animals can carry on their backs. The relative weights they can draw in wheled ve- hicles. Mention some of Hassenfratz's estimates of the comparative weights different animals can carry and draw. 189. What is said of the conversion of water into steam ? What is the real moving power? What are the maximum effects obtained by coal in evapo- ratincr water ? PRINCIPLE OP VIRTUAL VELOCITIES. 125 tained in Cornwall, England, where a bushel of coal, weighing 841bs., has produced a mechanical effect equivalent to 120,000,000 Ibs. raised one foot. Probably 100,000,000 is the maximum mechanical effect attainable, in regular work, by the consump- tion of a bushel of coal. As the maximum effect produced by man is 2,000,000, and that of a horse, 10,000,000, it follows, that one bushel of coal consumed daily, may perform the work of 50 men, or ten horses. In the chapter on heat and the steam-engine, this subject will be more fully considered. It is introduced here only for the sake of the convenient standards of force it gives us. Theory of Machinery. 190. Principle of virtual velocities. It was shown in 111, that when a body, having a fixed point of support, is acted on by two parallel forces in the same direction, the forces will be in equilibrium, if they are to each other inversely as their distances 116 from the supporting point. ,..., Thus in fig. 116, if an in- .&.... \ flexible rod, supported at n ri' '" --.^ - lp C, is acted on by two forces, L c I W and P, such that, ""*" Jh W:P :: CP : C W then they will be in equilibrium. But in every proportion, the product of the first and last terms is equal to the product of the second and third ; and instead of saying that the forces are in- versely as their distances, the same thing is expressed by W X C W = P X C P The principle may be illustrated in another manner. Let the bar be made to oscillate gently about the point of support, or axis. It is plain that the spaces described by the ends of the bar will be proportional to their distances from the axis ; for the angles at the axis being equal, the arcs af and & h are directly What is said of the mechanical effect produced by the combustion of a bushel of coal, as compared with men and horses if 190. What is said of the principle of virtual velocities ? How may it be illus- trated ? Give another illustration. 126 THEORY OF MACHINERY. proportional to their radii, or distances from the axis, C TFand C P. Hence, W : P : b h : a f, That is, two forces are in equilibrium when they are to each other inversely as the spaces which they describe. The arcs being de- scribed in the same time, represent the velocities, and the prin- ciple is usually thus stated : forces in equilibrium must ~be to each other inversely as their velocities. The products, therefore, of the forces multiplied by their respective velocities, are equal. W x a f = P x b h These products are called the moments of the forces, (126,) and forces are always in equilibrium when their moments are the same. If the movement is doubled or halved, or varied in any proportion, the efficacy of the force is doubled or halved, or varied in the same proportion. Any two forces will balance each other if they conform to the conditions just explained. A force of 1 Ib. will balance one of 1000 Ibs., if they are applied so that the motion of the first, through 1000 inches; is attended by a motion of the other through 1 inch, and vice versa. Any means by which two forces are brought into this relation with each other, constitutes a machine. 191. Machine, power, weight. A machine, then, is an instru- ment or apparatus by which force may be transmitted from one point to another, usually with some modification of its intensity or direction. In the language of mechanical philosophy, the force applied to a machine is called the power ; the place where it is applied, the point of 'application ; and the line in which this point tends to move, is the direction of the power. The resistance to be overcome, is called the weight ; and the part of the machine immediately applied to the resistance, is the working point. The moving powers, and the resistances, are both extremely various ; but of whatever kind they may be, they When are two forces in equilibrium ? What is the result when the moment is doubled ? Give an illustration of the equilibrium of forces? 191. What is a machine ? What is the power? What the weight? What the working point ? UTILITY OF MACHINES. 127 can always be expressed by equivalent weights, i. e., such as being applied to the machine, would produce the same effects. 192. Equilibrium of machines. When the power and weight are equal, the machine is in equilibrium, and it may be at rest, or, as is usually the case, in a state of uniform motion. If a ma- chine in this case is put into uniform motion, it must continue to move indefinitely; for the power and weight being equal, neither of these forces can stop or modify the motion, without some additional force, which is contrary to the supposition. Thus, if an engine draws a railway train with uniform velocity, the power of the engine is in equilibrium with the resistance of the train. At starting, the power is greater than the resistance, and the motion of the train is, consequently, accelerated, until the resistance becomes equal to the power, when equilibrium is again established. If any part of the power is now withdrawn, the power becomes less than the resistance, and the motion is consequently retarded until the train is brought to rest. The mechanical energy, moving force or moment of the power, is found by multiplying its equivalent weight by the space through which it moves, or its velocity ; and the moment of the resistance is estimated in the same manner. As we have just seen, the relation between these movements determines the state of the machine. 193. Utility of machines. It is sometimes said, in illustration of the usefulness of machines, that a great weight may be supported or raised by an insignificant power ; but such statements, if lit- erally understood, are obviously untrue. No machine, however ingenious its construction, can create any force, and therefore the working point can exert no more force than is transmitted to it from the source of power. Every machine has certain fixed points, which are arranged to support any required part of the weight, while the remainder of the weight, and that part only, is directly sustained by the power. This remainder cannot be greater than the power. 194. Relation of power to weight. But if the weight is not merely supported, but raised through a given space, then the power must move through a space as much greater than the 192. When is a machine in equilibrium ? Give an example. How is the mechanical energy found ? 193. What is said of the utility of machines ? 128 THEORY OF MACHINERY. weight moves through, as the weight itself is greater than the power ; in other words, the power and weight must be inversely as their velocities. This inverse proportion is expressed when it is said, that power is always gained at the expense of time. To raise 1000 Ibs. to a height of one foot by a single effort, would require a force equivalent to 1000 Ibs. ; but the same thing may be accomplished by a power of 1 Ib. acting for 1000 times successively, through a space of one foot. If a man by exerting his entire strength could lift 200 Ibs. to a certain height, in one minute, no machine whatever can enable him to lift 2000 Ibs. to the same height in the same time. He may divide the weight into ten parts, and lift each part separately ; or by the intervention of a machine he may raise the whole mass together, requiring, however, ten minutes for the task. On the other hand, it is often the object of a machine to move a small resistance by a great power. In a watch, the moving force of the mainspring is very much greater than the resistance of the hands, revolving about the dial. In a locomotive engine, each motion of the piston backwards and forwards, moves the train through a space equal to the circumference of the driving wheel ; if the length of stroke is one foot, and the circumference of the wheel 12 feet, then the velocity of the piston will be to the velocity of the train, as 2 to 12 ; consequently the power acting on the piston, is greater than the resistance of the train, in the proportion of 12 to 2. 195. Adaptation of the power to the weight in machinery. The use of machines is to adapt the power to the weight. If the intensity, direction, and velocity of the power, were the same as the intensity and direction of the resistance, and the velocity re- quired to be given to it, then the power might be directly ap- plied to the resistance, without the intervention of a machine. But if a small power is required to move a great resistance ; or, if a power acting in one direction, is required to impart motion in another ; or, to impart a velocity greater or less than its own, then it is necessary to employ a machine which will modify the effect of the power in the required manner. 196. Motion of the power employed changed by machines. 194. "What is said of the relation of power to weight ? Give illus- trations. What is said of a watch ? A locomotive? 195. What is said of the adaptation of the power to the weight in machines ? SIMPLE MACHINES. 129 Besides these, the motion of the power may differ from the motion required in the resistance, in a great variety of ways. The power may have a reciprocating motion, as in the locomotive engine, and be required to produce a continuous motion in a straight line, as in moving a train upon a railway. Or, the power may have a rectilinear motion, as a stream, and be employed to produce the circular motion of the stones in a grist-mill, or the reciprocating motion of a saw, in a saw-mill. In every class of machines, the relations existing between the power and the resistance, depend solely on the construction of the machine ; but even a general account of the ingenious con- trivances by which the moving force is regulated, modified, and adapted to the varying conditions and requirements of the resist- ance, would lead us far beyond the limits and design of this work. The Simple Machines. 197. Classification of machines. Machines which consist of only one part, are called simple machines ; compound machines are made up of various combinations of the simple machines. These elementary machines, or mechanical powers, are com- prised under three classes : I. The lever. II. The pulley. III. The inclined plane. The wheel and axle is a modification of the lever ; and the wedge and the screw are essentially the same as the inclined plane. Notwithstanding the endless variety and complexity of ma- chines, their individual parts may always be reduced to one of these classes. Every machine, however complex, is constructed according to the fundamental law, already explained, that the power and weight must be to each other inversely as their velo- cities. 196. What is said of the motion of the power employed changed by machines? Give illustrations. 197. What are simple machines ? What are compound machines? What are the three classes of me- chanical powers ? What is the wheel and axle a modification of? What the wedge and screw ? What fundamental law is every ma- chine constructed according to ? 130 THEOKY OF MACHINERY. 198. The lever. The lever is an inflexible rod, turning about 117" a fixed point of support, or axis, which is called the fulcrum. The parts of the lever extending on each side of the fulcrum, are called the arms of the lever. Levers may be straight or bent, simple or compound. It is usual to divide levers into three classes, according to the position of the fulcrum, in relation to the power and weight. iThey are represented in fig. 117. *-^ In the first class, the fulcrum is between the power and weight. In the second, the weight is be- tween the fulcrum and power. In the third, the power is between the fulcrum and weight. Whatever may be the class of the lever, the power and weight will be in equilibrium when they are inversely as their distances from the fulcrum. In each of the levers in the figure, we shall have, Or P : W: : FW: FP P x FP = W x FW Consequently, the moment of the power, or its tendency to turn the lever, would be augmented either by increasing the power itself, or its distance from the fulcrum. The same is true of the weight. The distance of a force from the fulcrum, is called its leverage. 199. Equilibrium when the forces act obliquely to the lever. In the preceding examples, the direction of the forces is perpen- dicular to the lever ; but they may act obliquely, the only con- dition necessary to equilibrium being, that their moments about the fulcrum must be equal, and their directions opposite. But the effective distance of a force from the fulcrum, is always the 198. What is a lever ? Mention the position of the power, weight and fulcrum in the three classes. When are the power and weight in equilibrium? COMPOUND LEVERS. 131 perpendicular distance from that point to the line of direction of the force. Thus, in fig. 118, if 118 the power acts in the direction B B P, the moment of the power ^s'' \^ is not expressed by P x A F, ,,*''' but by P x BF. Hence, if ~g^''''' \ A the arms of the lever are bent I \ or curved, their effective length V is found by drawing perpen- faj\ JT diculars from the fulcrum, upon the directions of the power and weight. 200. Compound levers. When a given power is required to sustain a considerable weight, and it is not convenient to use a very long lever, a composition of levers, or compound lever is employed. When such a system is in equilibrium, the power, multiplied by the continued product of the alternate arms of the levers, commencing from the power, is equal to the weight mul- tiplied by the continued product of the alternate arms, com- mencing from the weight. For example, the system represented in fig. 119, consisting of three levers of the first class, will be 119 in equilibrium when, P x AF B F> CF"=W DP C F' BF. If the long arms are 6, 4, and 5 feet, and each of the short arms 1 foot, then 1 Ib. at A will sustain 120 Ibs. at D ; but if a simple lever had been used, the long arm being increased simply by adding these quantities, we should have gained a power of only 6 -f 4 -f- 5 = 15 to 1. The pressure on the fulcrum, when the power and weight are in equilibrium, is found by applying the principle of the compo- sition of forces, ( 109.) In a lever of the first class, the resultant 199. What is said of equilibrium when the force acts obliquely to the lever ? Mention example of a bent lever. 200. What is said of compound levers ? When is a compound lever in equilibrium ? Give the formulae ? How is the pressure found when the power and weight are in equilibrium ? What is the resultant in the levers of the three classes 1 132 THEORY OP MACHINES. of the power and weight is a single force, equal to their sum, and passing through the fulcrum ; consequently, the pressure will be equal to the sum of the power and weight. In a lever of the second or third class, the resultant is equal to the difference of the power and the weight. 201. Applications of the lever. Levers of the first class are illustrated by familiar examples. A crowbar used in raising stones,- and a poker used to raise the coals in a grate, are levers of this class. Scissors, snuffers, and pin- cers, are pairs of levers of this class, the joint which connects them being their common fulcrum. The common hammer is a bent lever 120 M of the first class, the claw being the arm applied to the resistance, and the handle, the arm acted on by the power. An example of the bent lever is seen in the ordinary truck, fig. 120, used for moving heavy goods a short distance. In this ma- chine, the axis of the wheels F is the fulcrum, against which the foot is placed, while the weight at R is raised off the ground by the hand, applied at P. One of the most useful applications of the lever is seen in the balance. It consists, essentially, of a lever of the first class, sus- pended at its centre, and therefore having equal arms. The scales are sustained by cords hung from the extremities of the beam, A B, fig. 121, called points of suspension, and these points 121 must be in a line, at right angles to the line joining the centre of motion, and the centre of gravity. The centre of gravity, g, is be- low the fulcrum, for if it should coincide with the fulcrum, the balance would rest in any posi- tion, indifferently ; but if it were above the fulcrum, the beam would be upset by the least dis- turbance. In a perfect balance, all the parts on each side of the centre of gravity must be absolutely equal. In practice, such accuracy is impossible, but the exact weight of a body may be found by the process of double weighing, devised by Borda. 201. Give examples of levers of the first class. Give an example of a bent lever ? What is said of the balance ? What is said of a perfect balance 1 How may th xaet weight of a body b found ? LEVERS. , 133 Let the body to be weighed be accurately counterpoised by means of shot or sand. This being done, remove the body and substitute for it known weights, until equilibrium is again restored. The amount of this weight will exactly express the weight of the body, since being placed under exactly the same circumstances as the body, it produced the same effects. If a balance has been falsified for dishonest purposes, the cheat can be detected by shifting the weights, which produce equilibrium. To find the true weight by means of such a balance, weigh the substance, first in one scale, and then in the other ; multiply the two weights together, and take the square root of the product. The steelyard is a lever of the first class, with unequal arms. The body P to be weighed, is attached to the short arm, A, fig. 122, 122 and counterpoised by a constant weight, Q, shifted upon the longer arm marked with notches to indicate pounds and ounces, until equi- librium is obtained. It is evident that a pound weight at D, will balance as many pounds weight at P, as the distance D C is greater than A C. Levers of the second class occur less frequently. An oar is an example ; the water is the fulcrum, the boat is the weight, and the hand the power. A pair of nut-crackers is a double What is said of the steelyard ? Describe the figure. Give examples of levers of the second class. Describe fig. 123. 134 THEORY OP MACHINES. 123 lever of this class ; and a door moving on its hinges, and a wheel- barrow, are also examples. In levers of the third class, the power being nearer the fulcrum, is always greater than the weight. On account of this mechan- ical disadvantage, it is used only when considerable velocity is required, or the resistance is small. Fig. 123 represents such a lever, WF, moving on a hinge as a fulcrum ; it is plain that the power P, moves through a small arc, and the weight through a large one, and since they are described in the same time, the velocity of the power is less than that of the weight. The common fire-tongs, sugar-tongs, and sheep-shears, are double levers of this class. The most striking illustrations of this class of levers are seen in the animal kingdom. The compact form and beau- tiful symmetry of animals, depend on the fact that their limbs are such levers. The socket of the bone a, fig. 124, is the fulcrum; a 124 strong muscle attached near the socket c is the power, and the weight of the limb, and what- ever resistance Wmay oppose its motion, is the weight. The fore- arm and hand are rai- sed through a space of one foot, by the contraction of a mus- cle applied near the elbow, moving through less than -Jj-th that space. The muscle, therefore, exerts 12 times the force with which the hand moves. The muscular system is the exact inversion of the system of rigging a ehip. The yards are moved through small spaces with great force, by hauling in a great length of rope with small force ; but the limbs are moved through great spaces with comparatively little force, by the contraction of muscles through small spaces with very great force. Examples of compound levers are seen in the ordinary platform scales. They are constructed of very various forms, but all depend upon the principles already "What is said of levers of the third class ? Mention examples of the third class of levers? Describe fig._124. What is said of the rigging of a ship ? THE WHEEL AND AXLE. 135 explained. Fig. 125 represents a weighing machine in common 125 use, and fig. 126 shows its interior construction. The arrangement 126 and combination of the levers are sufficiently obvious on inspection. 202. The wheel and axle. The common lever is chiefly em- ployed to raise weights through small spaces, by a succession of short intermitting efforts. After the weight has been raised, it must be supported in its new position, until the lever can be again ad- justed, to repeat the action. The wheel and axle is a modification of the lever, which corrects this defect ; and, since it converts the intermitting action of the lever into a continuous motion, it is sometimes called the perpetual lever. This machine, consists of a cylinder called the axle, turning on a centre, and connected with a wheel of much greater diameter. The power is applied to the circumference of the wheel, and the weight is attached to a rope, wound around the axle in a contrary Describe the weighing machine, fig. 125. 202. What is said of the wheel and axle? What does this machine consist of? What is the capstan ? 136 THEORY OP MACHINERY. direction. Instead of the whole wheel, the power may be applied to 127 a handle named a winch, or to one or more spokes inserted in the axle. When the axle is hori- zontal, the machine is called a windlass, fig. 127 ; when it is vertical, it forms the capstan, fig. 128, used on shipboard, chiefly to raise the an- chor. The head of the capstan is generally cir- cular, and is pierced with holes, in each of which a lever can be 128 placed, so that many men can work at the same time, exerting a great force, as is of- ten necessary is raising an anchor. The law of equilibrium is the same as in lever. Draw from the centre, or ful- crum c, fig. 129, the straight lines c b and c a, or c a', to the points on which the weight and power act ; a c 5, or a 1 c 5, is evidently a lever of the first class, in which the short arm c b is the radius of the axle, and c a, or c a\ the 129 long arm, is the radius of the wheel. Hence, PX ac= WX cb P: W: : cb: ac The wheel and axle is in equi- librium, when the power is to the weight as the radius of the axle is to the radius of the wheel. In one revolution of the machine, the power descends through a space equal to the circumference of the wheel, and the weight is raised through a space equal to the circumference of the axle ; When are the wheel and axle in equilibrium ? What is said of the relation of the power to the weight ? ANALYSIS OP WHEEL-WORK. 137 hence the power and weight are inversely as their velocities, or the spaces they describe. 203. Trains of wheel-work. The efficiency of this machine is augmented by diminishing the thickness of the axle, or by in- creasing the diameter of the wheel. But if a very great power is required, either the axle would become too small to sustain the weight, or the wheel must be made inconveniently large. In this case a combination of wheels and axles may be employed. Such a system corresponds to the compound lever, and has the same law of equilibrium. The power being applied to the first wheel, transmits its effect to the first axle ; this acts on the second wheel, which transfers the effect to the second axle, &c., until the force, transmitted through the series in this order, arrives at the last axle, where it encounters the resistance. In equilibrium, the power multiplied into the continued product of the radii of all the wheels, is equal to the weight multiplied into the continued product of all the axles. Trains of wheel-work are connected by an endless band, or by cogs raised on the surfaces of the wheels and axles. Cogs on the wheel are called teeth, and those on the axle are called leaves ; the axle itself is named a pinion. The number of teeth on the wheels and leaves on the pinions, is proportional to their circum- ferences, and also to their radii. Hence, the number of teeth and leaves is substituted for the radii of the wheels and axles, and the law of equilibrium is stated as follows. The power multiplied into the product of the number of teeth of all the wheels, is equal to the weight multiplied into the product of the number of leaves in all the pinions. 204. Analysis of a train of wheel work. A system of wheels is represented in fig. 130. If the number of leaves in 5, the pinion of the first wheel, is one-sixth of the number of teeth on the second wheel, 0, the wheel will be turned once by every six turns of the pinion. Let the second pinion, c, have the same re- lation to the third wheel, f ; then the first wheel w r ill revolve 36 times while the third revolves once; and the radius of &, the wheel to which the power is applied, being 3 times the radius of 203. How is the efficiency of the wheel and axle augmented 1 What is said of trains of wheel-work ? How are trains of wheel- work connected ? What are teeth, leaves, pinions ? How is the law of equilibrium stated ? 204. Give the analysis of the train of wheel- work represented .in the figure. 138 THEORY OF MACHINERY. d, the axle which sustains the weight, the velocity of the power is 3 X 36 = 108 times the velocity of the weight. Or, P: W: : 1 : 108 Combinations of wheel-work are employed either to concen- 130 trate, or to diffuse force ; either to set heavy loads in motion by means of a small power, or to produce a high velocity by ex- erting a considerable power. In the first case, the power is applied to the first wheel of the series, and is transmitted in the order already described. In the second instance, this ar- rangement must be reversed ; the power must exert itself on the first pinion, in order to pro- duce rapid revolution of the last wheel. The crane for hoisting goods, is an example of the first kind ; the watch is an instance of the second. 205. The pulley. Fixed pulley. The usual form of this machine is a small wheel, turning on its axis, and having a 131 groove on its edge, to admit a flexible rope ;> or chain. In the simple fixed pulley, fig. 131, there is no mechanical advantage, ex- cept that which may arise from changing the direction of the power. Whatever force is exerted at P, is transmitted, with- out increase or diminution, to the resist- ance at the other end of the cord. From the axis C7, draw C a and (7&, radii of the wheel, at right angles to the direction of the forces ; a C b represents a lever of the first class, with equal arms ; hence, in equi- librium, the power and weight must be equal, and they describe equal spaces. For what are combinations of wheel-work employed? Give ex- amples of such use. 205. What is a pulley ? COMPOUND PULLEYS. 139 206. Movable pulley. When the block or frame is not fixed, the pulley is said to be movable. The 132 weight is suspended from the axis of the -5^ ^ movable pulley, and the cord is fastened at one end, and passing over a fixed pul- ley, is acted on by the power at the other. In this arrangement, fig. 132, it is plain that the weight is supported equally by the power and the beam at D. For the pulley acts as a lever of the second class, whose arms are to each other as 1 : 2 ; the fulcrum is at 5, 1) c is the leverage of the weight, and & a the leverage of the power. The diameter & a is twice the radius & c, therefore equilibrium will obtain when the power is equal to one-half of the weight: i. e. therefore, P: W: : be: be : : 1:2 2 . To raise the weight one foot, each side of the cord must be short- ened one foot, and the power, consequently, passes over two feet. The space traversed by the power, is twice the space described by the weight. 207. Compound pulleys. Sometimes compound pulleys are used, each consisting of a block which contains two or more single pulleys, generally placed side by side, in separate mortices of the block. Such an arrangement is shown in fig. 133. The weight is attached to the movable block, and the fixed one serves only to give the power the required direction. The weight is divided equally among the pulleys of the movable block ; and as we have seen that the power required to sustain a given weight "What is said of the single fixed pulley ? When is the pulley in equilibrium? 206. What is a movable pulley ? What is the general ai'rangement? When will there be equilibrium ? What is the rela- tion between the spaces traversed by the power and the weight 1 207. What is a compound pulley ? 140 THEORY OF MACHINERY. is diminished one-half by a single movable pulley, it follows, that 133 in such a system equilibrium will obtain, when the power is equal to the weight divided by twice the number of movable pulleys. Or P: W: : 1 : 2 P= 134 In this system, as in the single movable pulley, the space through which the weight is raised, is as much less than the space through which the power de- scends, as the weight is greater than the power. P: W: : velocity of weight : velocity of power. If the power is pulled through 4 feet, fig. 133, each division of the cord in which the movable block hangs, will be shortened one foot, and the weight raised one foot. Another system of pulleys is represented in fig. 134. In this arrangement, each pulley hangs by a separate cord, one end of which is attached to a fixed support, and the other to the adjacent pulley. The effect of the power is rapidly augmented, being doubled by each movable pulley added to the system. The numbers placed near the cords, show what part of the weight is sustained by each, and by each pulley. Such a system, however, is of little prac- tical use, on account of its limited range. In the common block system, fig. 133, the motion may continue until the movable block touches the fixed one ; but in this, only till D and E come together, at which time A will have been raised only th of that distance. 208. The inclined plane. Thismechan- Describe the figure. When will equilibrium obtain ? What is the relation between the spaces traversed by the power and the weight? Describe fig. 134. What of the practical value of such a system ? THE INCLINED PLANE. 141 ical power is commonly used, whenever heavy loads, especially such as may be rolled, are to be raised a moderate height. In this way casks are moved in and out of cellars, and loaded upon carts. The common dray is itself an inclined plane. Suppose a cask weighing 500 Ibs. is to be raised 4 feet by means of a plank 12 feet long; it is plain, that while the cask ascends only four feet, the power must exert itself through 12 feet, and hence, 12 : 4 : : 500 : 166f, the force necessary to roll the cask. In mechanics, the inclined plane is a hard, smooth surface, in- clined obliquely to the resistance. The length of the plane is A <7, fig. 135, A B its height, and B {7 its base. The power may be applied, a In a direction parallel to the length ; 5 Or parallel to the base ; c Or in any other direction. In each case, the condition of equilibrium may be derived from the equilibrium of the lever. 209. Application of the power parallel to the length of the inclined plane. When a body is 135 placed upon an inclined plane, fig. 135, its weight, which is the re- sistance to be overcome, acts in A the direction of the force of grav- ity, in the perpendicular line a W. Let the power act in the direction a P, parallel to |4 C; then from c, the point wherethe body touch- ^ -W es the planes, draw c & and c a, perpendicular to the directions of the weight and power ; a c 5 is a bent lever, having its ful- P: W::bc:ab and since the triangles a 5 c and A B C, are similar, P: W:: AS: AC, Or If the direction of the power is parallel to the inclined plane, equilibrium will obtain, when the power is to the weight, as the What is said of the common block system ? 208. What is said of the inclined plane ? Mention the example of the cask. What is the inclined plane in mechanics ? 142 THEORY OP MACHINERY. height of the plane is to its length. While the weight is raised through a space equal to the vertical height of the plane, the power must move through a space equal to its length. If the length of a plane is 10 feet, and its height 2 feet, P must move 10 feet, while W is raised 2 feet ; hence the power and weight are inversely as their velocities. 210. Application of the power parallel to the base of the in- clined plane. In the second case, let the power act in the di- 136 rection a P, fig. 136, parallel to B (7, the base of the plane ; and draw, as before, the lines b a and 5 c : then a 5 c is a bent lever, having its fulcrum at 5, and equi- librium will take place when P : W:: be: ab and the triangles a 5 c and A B O t P: W::AB:0 P = W X^ If the direction of the power is parallel to the base of the plane, equilibrium will obtain, when the power is to the weight, as the height of the plance is to its base. In this case, the space described by the power, is to the space described by the weight, as the base of the plane is to its height. 211. Application of the power in some direction not parallel to any side of the plane. Lastly, let the power act in some di- rection not parallel to any side of the plane ; for example : in the direction a P, fig. 137, draw the lines b cand b a, perpendicular to the directions of the two forces ; then, as before, P: W::bc:ab What is said of the directions in which the power may be ap- plied? 209. What is the relation when the power is applied par- allel to the length of the inclined plane 1 When will equilibrium obtain? What is said of the power and the weight in relation to their velocities'? 210. What is the relation when the power is ap- plied parallel to the base of the inclined plane ? When will equili- brium obtain ? What is the relation betwen the spaces described by the weight and the power ? THE WEDGE. 143 137 But as the triangles a & c and A B C, are not similar, the pro- portion between the arms of the lever cannot be expressed by the sides of the plane. 212. Effect of the power ap- plied. It follows from what has been said, that the eifect of a given power is greater, as the height of the plane is diminished or its length increased ; and that the effect is greatest when its direction is parallel to the length of the plane, for, if the power acts in any other direction, a part of its force is expended, either in increasing the pressure of the body on the plane, or in lifting the weight directly. 213. The wedge. Instead of lifting a load by moving it along an inclined plane, the same result may be obtained by moving the plane under the load. When used in this manner, the inclined plane is called a wedge. It is customary, however, to join two planes base to base. In fig. 138, A B is called the back of the wedge, A C and B G its sides, and d C its length. The power is applied to the back of the wedge, so as to drive it between two bodies, and over- come their resistance. 214. Resistance to be overcome. The resist- ance may act at right angles to the length or to the sides of the wedge. In the first case, it resembles an in- clined plane, when the power is parallel to the base ; and hence the forces will be in equilibrium when the power is to the resist- ance as the back of the wedge is to its length. In the second case, it is similar to a plane when the power is parallel to the length ; and therefore in equilibrium, the power is to the resist- ance as the back of the wedge to its side. The power is supposed to move through a space equal to the length of the wedge, while the resistance yields to the extent of its breadth. 215. Application of the wedge. As a mechanical power, the 211. What is the relation when the power is applied in some di- rection not parallel to any side of the plane 1 212. What is said of the effect of the power applied ? 213. What is said of the wedge ? What is its common form? Describe fig. 138. 214. What is said of the resistance to be overcome 1 What of the movement of the power and the resistance ? 144 THEORY OF MACHINERY. wedge is used only where great force is to be exerted in a limited space. In oil-mills, the seeds from which vegetable oils are ob- tained are crushed and compressed with enormous force by means of a wedge. It is everywhere employed to split masses of stone and timber. The edges of all cutting tools, as saws, knives, chisels, razors, shears, &c., and the points of piercing instruments, as awls, nails, pins, needles, &c., are modified wedges. Chisels intended to cut wood, have their edge at an angle of about 30 ; for cutting iron, from 50 to 60 ; and for brass, about 80 to 90. The softer or more yielding the substance to be divided is, the more acute the wedge may be constructed. In general, tools which are urged by pressure, admit of being sharper than those which are driven by a blow. The theory of the wedge gives but very little aid in estimating its effects, as it takes no account of friction, which so largely modifies the results, and the proportion between a pressure and a blow cannot be defined. 216. The screw. This machine has the same relation to the ordinary inclined plane, as a spiral staircase to a straight one. This relation is shown in fig. 139. By means of the corresponding let- ters and dotted lines, in fig. 140, the position of the different parts of an inclined plane upon a screw, may be distinctly seen. Let an inclined plane be wound around a cylinder, fig. 139, the length of the plane will form the spiral line, called the thread or the screw. The distance between the threads is the height of corresponding parts of the plane. The thread projects from the surface of the cylinder, and is designed to fit in to a hollow 140 spiral, cut in the interior of a block called the nut ; a lever is also 215. Mention applications of the wedge. What is said of cutting tools and piercing instruments ? Give the angle of inclination of the edges of chisels for cutting wood, iron, and brass. What is said of the effects of the wedge and theory ? 216. What is said of the screw ? MECHANICAL EFFICIENCY OF THE SCREW. 145 fixed in the head of the cylinder to which the power is applied, fig. 141. The combining of these parts 141 forms the mechanical power which has received the name of the screw. In working the screw, the resistance acts on the inclined face of the thread, and the power parallel to the base of the screw. This corresponds to the case in which the direction of the power is parallel to the base of the inclined plane. Equilibrium will, therefore, take place when the power is to the resist- ance as the distance between the threads of the screw is to the circumference described by the power. W X h being the distance between the threads, and r the radius of the screw. During each revolution, the power describes a circle, whose circumference depends on the length of the lever, but the end of the screw advances only the distance between two threads; thus in this, as in all cases of the use of machines, what is gained in power, is lost in velocity. 217. Mechanical efficiency of the screw. The mechanical efficiency of the screw is augmented, either by increasing the length of the lever, or by lessening the distance between the threads. If the threads of a screw are of an inch apart, and the power describes a circle of 5 feet, (120 half-inches,) circum- ference, a power of 1 Ib. will balance a resistance of 120 Ibs ; if the threads are J inch apart, 1 Ib. will balance 240 Ibs., the effi- ciency being doubled. 218. Applications of the screw. As the screw exerts great How is the screw moved ? Where does the resistance act ? To what does this correspond in the inclined plane? When will equili- brium take place ? What is said of the power and the screw during each revolution ? 217. How is the mechanical efficiency of the screw augmented 1 Give an example. 1 146 IMPEDIMENTS TO MOTION. pressures through small spaces, it receives numerous applications in presses of all kinds, as in extracting liquids and juices from solid bodies and in compressing soft and light substances, as cotton and hay, into a convenient bulk for transportation. Impediments to Motion. 219. Passive resistances. Besides those resistances which a machine is designed to overcome, there are certain others which arise during the movement of the machine, and oppose its useful action by destroying more or less of the moving power. These forces are designated by the general name of passive resistances, or impediments to motion. Several kinds are distinguished : 1st. When we attempt to cause one body to slide over another, a resistance is experienced, so that it is necessary to use a certain degree of force to commence the sliding, and also to continue the motion after it has been begun. This is the resistance called sliding friction, or simply friction. 2d. When a cylindrical body is rolled on a plane surface, the movement is opposed by a force called the rolling friction. It is seen, for example, in the rolling of carriage wheels on the ground. 3d. The ropes and chains which enter into the composition of some machines, are supposed, in theory, to be perfectly flexible, but as they are not so, a considerable loss of power is caused by their stiffness, or imperfect flexibility '. 4th. The movements of all machines take place either in air or water, and the particles of these fluids which come in contact with the machine, are continually set in motion, which can only happen at the expense of the moving power. This is called the resist- ance of fluids. 220. Sliding friction. If the surfaces of bodies were perfectly hard and smooth, they would slide upon each other without any resistance. But the most highly polished surfaces are, really, (as they appear under the microscope,) full of minute projections and cavities, which fit in each other when two surfaces are brought into contact. The force required to overcome the rough- 218. Mention applications of the screw. 219. What is said of passive resistances 1 What other name is given to them ? Mention the different kinds of passive resistances. APPARATUS FOR DETERMINING FRICTION. 147 ness and consequent adhesion of surfaces, is the measure of fric- tion. This weight, divided by the weight of the body, forms a fraction which is called the co-efficient of the friction. 221. Starting friction ; friction during motion. The amount of force necessary to commence the motion of two bodies, sliding on each other, is, in most cases, greater than the force required to continue the movement uniformly, after it has been begun ; hence this resistance is distinguished into two kinds, starting friction, and friction during motion. They are also called statical and dy- namical friction ; and Whewell proposes to name the former stric- tion, reserving the word friction for the latter. However named, the laws of each can be determined only by experiment. 222. Coulomb's apparatus for determining starting friction. Different observers are by no means agreed in respect to all the laws of friction ; we shall here follow the results obtained in 1781, by the celebrated French philosopher and mathematicfan, Coulomb. In 1831, Morin, by command of the French government, repeated and enlarged the experiments of Coulomb, usually verifying his general conclusions. The principal apparatus used by Coulomb, is represented in fig. 142. It consists of a horizontal table ; a 142 box, A) to receive the weights used to produce the different pres- sures ; a pan, Z>, on which were placed the weights to drag the box along the table by means of a cord passing over a pulley. The box was mounted in slides, of the same substance on which the experiment was to be made, and corresponding slips of the same, or a different substance, were placed under the sliders on the table. 220. What is said of sliding friction? 221. What is said of starting friction arfd friction during motion ? What other names have been proposed for them ? 222. What is said of Coulomb and Morin ? Describe the apparatus Coulomb employed. 148 IMPEDIMENTS TO MOTION. The amount of the weight required to be placed in X>, to move the box from a state of rest, is the measure of starting friction ; and the weight necessary to continue the movements uniformly, is the measure of friction during motion. 223. Results of Coulomb's experiments. Without detailing the experiments: it will be sufficient to state their general results, embraced in the following laws. Friction during movement is, 1st Proportional to the pressure exerted upon the sliding surfaces. 2d. Independent of the extent of the surfaces in contact. 3d. Independent of the velocity of the movement. 4th. Greater between surfaces of the same than surfaces of different materials. 5th. Greatest between rough surfaces, and is diminished by polishing, anfl usually by the use of suitable unguents. Friction at starting is, 1st. Proportional to pressure. 2d. Independent of extent of surface. 3d. Generally increased by polishing the surfaces. The friction at starting, and during the movement, are the same, when the sliding surfaces are hard, like the metals ; but if the bodies are compressible, like wood, the starting friction is much the greatest. When at least one of the surfaces is compressible, the resistance is not always the same, but varies according to the time the surfaces have been in contact If wood slides on wood, the starting friction attains its greatest intensity in two or three minutes ; but if the sliding surfaces are wood and metals, the greatest intensity is not reached for a much longer time, several hours, and sometimes several days. But after a certain time has elapsed, the starting friction is no longer aug- mented by lengthening the time of contact. It appears strange at first, and contrary to our previous ideas, that the friction at starting, and during movement, should not be increased by enlarging the surfaces in contact, and vice versa. The explanation is this. Friction is proportional to pressure ; if, therefore, two bodies have the same weight, and one has twice 223. Give the results of Coulomb's experiments of friction during movement. Of friction at starting. What is said of the frictions when the sliding surfaces are alike ? What when one surface is com- pressible? What when wood slides upon wood ? When wood and metals form the sliding surfaces ? ROLLING FRICTION. 149 the surface of the other, the weight, being equally distributed on each surface, will be twice as great on each point of the surface of the first body, as on each point of the second, and conse- quently, the friction at each point of the first, is twice the friction at each point of the second, and the whole friction must be the same for each body. This law, however, does not hold good in extreme cases. With the same pressure, the friction varies exceedingly, ac- cording to the nature of the surfaces in contact. The following table shows the ratio of friction in several cases, the pressure being 100. Surfaces in contact. Ratio of friction to pressure. At starting. In motion. Wood upon wood, " " " with coating of soap, " " " " oftallow, " '* metals . . O'oO 0-36 019 0-60 0'12 0-68 0-87 0-18 0-12 0-36 014 0-07 0-42 0-08 0-45 0-33 018 0-07 " " " with coating of tallow, Leather bands on wood, .... " " wet ... Metals on metals, " " " with coat, of olive oil, 224. Rolling friction. The resistance experienced in rolling a cylinder along a plane surface, is distinct in character ^rom the friction produced in sliding the cylinder, and very much less in amount. In wood rolling on wood, the proportion of resistance to pressure is from 16, or 6, to 1000, while the sliding friction in the same case, would be as 5 to 10, or 36 to 100, according to the kind of sliding friction. The resistance of rolling friction arises from a slight change of form produced in the body, and the sur- face on which it moves, and corresponding to the amount of pressure. The cylinder is flattened, and the plane depressed, so that the moving force is exerted, in continually moving the body up a very minute inclined plane. 225. Coulomb's apparatus for determining rolling friction. This apparatus employed by Coulomb, consisted of two bars, What IB said of the amount of friction when the surfaces in con- tact are enlarged? Mention the ratio of friction to pressure at starting and during motion of wood upon wood, with coating of soap and tallow. Of wood upon metals, &c. 224. What is said of rolling friclion ? What is the relation of resistance to pressure in wood rolling on wood ? From what does rolling friction arise ? 150 IMPEDIMENTS TO MOTION. horizontal and parallel, with a space between them, fig. 143. A cylinder of the same, or a different 143 substance, was placed transversely across the bars, and loaded with any required pressure by hanging strings upon it, carrying equal] weights at their extremities. An- other string wound several times around the middle of the cylinder, carried a pan c, to receive the weight necessary to produce mo- tion. It is evident that this weight acted always at the extremity of the radius of the cylinder as a lever. 226. Results of Coulomb's ex- periments. From the experiments were derived the following laws : The friction of rolling bodies is, 1st. Proportional to pressure. 2d. Independent of velocity, of the diameter of the cylinder and of the extent of the surfaces in contact. 3d. Greater when the substances are the same than when they are different. 4th. Not diminished by coatings of grease, but is aifected by the polish of the surfaces. If the force which produces the movement, instead of being applied always at the same arm of the lever, fig. 148, were ap- plied horizontally at the centre of the cylinder, or at the upper extremity of its vertical diameter, it would be inversely propor- tional to the diameter. The friction of the axle of a wheel, whether the axle itself turns, or the wheel on the axle, is different from rolling friction. It is somewhat less than sliding friction, but obeys the same laws. The friction of axles may be reduced one-half or one- quarter its original amount by the use of proper unguents. 227. Mr. Babbage's experiment. Mr. Babbage cites an in- 225. Describe Coulomb's apparatus for determining rolling fric- tion. 226. Give the results of Coulomb's experiments. What would be the result if the power were applied horizontally at the centre of the cylinder ? What is said of friction at the axle of a wheel ? RIGIDITY OF ROPES. 151 structive experiment to illustrate the decrease of friction. A block of stone weighing 1080 Ibs. was drawn on the surface of a rock by a force of 758 Ibs. ; placed on a wooden sledge, it was drawn on a wooden floor by a force of 606 Ibs. ; when both wooden surfaces were greased, 182 Ibs, was sufficient ; and when the block was mounted on wooden rollers of three inches diam- eter, a force of only 28 Ibs. was required to move it. 228. Advantages derived from friction. The advantages arising from friction are infinitely greater than the loss of power which it occasions. Without this property of matter, it would be equally impossible to make or use machines, for nothing could be nailed, or screwed, or tied together,, or grasped securely in the hand. From the difficulty of walking on very smooth ice, we may infer how useless would be the effort to move, if our feet met no resistance whatever. 229. Rigidity of ropes. When ropes are used to transmit force, their stiffness occasions a considerable loss of power, amounting, in some combinations of pulleys, to two-thirds of the whole power. The amount of the loss from this cause is modified by many ex- ternal circumstances, such as the dampness of the cordage, its quality, and the manner in which it is made. In general, the re- sistance of ropes is, 1st. Proportional to the tension to which they are subjected . 2d. It increases with the thickness, and is greatest in those that have been strongly twisted. 3d. It is inversely proportional to the diameter of the wheel or cylinder around which the ropes are bent. When a rope is wound more than once round a cylinder, the resistance increases in a geometrical ratio. A wet hemp rope, wound around a cylinder of oak by a power of 1 cwt., will sustain with 1, 2, and 3 coils respectively, a force of 8 cwt., 34 tons, and 25i tons. 230. Resistances of fluids. The resistance which a moving body meets in air and water, is an effect of the transfer of motion from the solid to the particles of the fluid. For the moving body must constantly displace a part of the fluid equal to its own bulk, and the motion thus communicated, is so much loss of the motive 227. Mention Mr. Babbage's experiment. 228. Mention ^ some of the advantages arising from friction. 229. What is said of the rigidity of ropes? What are the laws for the resistance of ropes? What is the resistance when a rope is wound more than once around a cylinder ? 152 IMPEDIMENTS TO MOTION. power. When other circumstances are the same, the denser the medium, the greater will be the resistance which it offers. New- ton demonstrated, that if a spherical body moves in a medium at rest, and whose density is the same as its own, it will lose half of its motion before it has described a space equal to twice its diameter. The resistance encountered by a body moving in water, is 800 times greater than if it were moving with the same velocity in air; for water, being 800 times more dense than air, the body must displace, and communicate its own motion, to 800 times as much matter in the same time. The resistance also depends upon the extent and form of the surface which is directly opposed to the resistance, i. e., at right angles to the direction of the motion. A body with a pointed, wedge-shaped, or curved surface, is less opposed than one whose surface is flat and broad. The resistance increases as the square of the velocity ; for if the velocity is doubled, the loss of motion must be quadrupled, because there is twice as much fluid to be moved in the same time, and it has also to be moved twice as fast. Again, let the velocity be trebled, then the body will meet three times as many particles of the fluid in the same time, and communicate three times the velocity ; therefore the resistance is 3 X 3 = 9 = 3 a . Bodies having the same figure and density, overcome the re- sistance of fluids more easily, in proportion to their size. In cannon-balls, for example, the extent of surface to which the resistance is proportional, increases as the square of the diameter, while the weight or power to overcome resistance, increases as the cube of the diameter. If two balls have diameters in the ratio of 2 : 3, the resistances which they will encounter at the same velocity of projection, will be in the ratio of 4 : 9, and their moving force in the ratio of 8 : 27. 231. Actual and theoretical velocities. In consequence of these impediments to motion, the actual movements of bodies are materially different from the theoretical motions explained in pre- vious chapters. The motion of falling bodies is very far from being 230. What is the resistance which a moving body meets in air and water an effect of ? What did Newton demonstrate? How much greater resistance is offered to a body moving in water than in air with the same velocity ? How does the form of a body effect the resistance ? What is the relation between the density and the velo- city ? Give an example. When bodies have the same figure and density but are of different sizes, what is said of the resistance of fluids ? Give the example of the cannon-balls. THE BALLISTIC CURVE. 153 uniformly accelerated, ( 152,) nor do all bodies fall with equal ra- pidity, as theory requires, and as was seen to be true in the guinea and feather experiment, ( 157.) The resistance of the air, which is very small at first, rapidly increases, and after a certain time be- comes equal to the force of gravity, when the body will no longer be accelerated, but move uniformly through the remainder of its descent. The descent of bodies on inclined planes and curves, deviates still more from uniformly accelerated motion, since the effect of friction is added to the resistance of the air. 232. Ballistic curve. A still greater difference is observed between the actual and theoretical motions of projectiles. Instead of describing a parabola, fig. 144, A E B, the projectile actually describes the curve A CD, called the bal- 144 listic curve, which never attains so great a vertical height, or so long a range as the corresponding parabola, and which, towards the end of its course, continually approaches the perpendicular, E F. A four pound shot, which flies 6437 feet in the air, would traverse in a vacuum, a space of 23,226 feet But, as in the case of friction, the benefits resulting from this state of things overpay the disadvantages. Fish could not swim, nor birds fly, were it not for the resistances of the media they in- habit. The paddle-wheels of a steamer would not move it, nor its rudder guide its course, if they met no resistance to their movements. And we can very well dispense with a perfect theory of projectiles, if thereby the rain is prevented from de- scending with the destructive velocity of hail-stones. 231. What is said of actual and theoretical velocities ? What is said of the motion of falling bodies 1 What is said of the descent of bodies on inclined planes and curves ? 232. What is said of the motion of projectiles? What is the form of the ballistic curve? What are among the advantages resulting from resistance to motion ? 154 HYDROSTATICS. HYDROSTATICS. 233. Hydrodynamics treats of the peculiarities of state and motion among fluid bodies ; it may be divided into hydrostatics, hydraulics, pneumatics, and acoustics. 234. Hydrostatics treats of the general properties of fluids at rest, their nature, gravity, pressure, &c. Fluids are bodies in which the reciprocal attraction of the molecules is in equilibrium with the elastic force of heat. Their particles have perfect mo- bility, freely moving among one another, and their masses assume always the form of the vessels containing them. 235. Elastic and non-elastic fluids. Fluids are divided into elastic and non-elastic, but this is not a well-defined distinction, for we cannot draw a perfect line of demarkation between those fluids which are but slightly compressible and elastic, as water, and those which, like air and the gases, are compressible in a high degree. Fluids of one class have properties common to the other, with but slight modifications. We shall therefore first treat of the physical properties of fluids generally, reserving for after consideration the properties of the more eminently elastic fluids or gases. 236. Compressibility. Liquids were, for a long time, consid- ered as absolutely incompressible. But the researches of Canton, in 1761, Oersted, in 1823, and others, have proved that all liquids are slightly compressible. The piezometer (piezo, to press, and metron, a measure,) is an instrument designed to measure the compressibility of liquids. Oersted's apparatus, fig. 145, con- sistsof a strongglass cylinder ; twenty-four or twenty-five inches in height, mounted on a stand, the upper part is accurately closed by a brass cap, through which passes the funnel tube R, to supply the vessel with water, and a cylinder, furnished with a piston, moving by the screw P. In the interior is a vessel A, containing the liquid to be compressed, having a capillary tube at its upper part, which bends and descends to the mercury, 0, contained in the lower part of the vessel. This capillary tube is 233. What of hydrodynamics 1 Into what may it be divided 1 234. What does hydrostatics treat of ? What are fluids ? 235. Into what classes may fluids be divided ? What is said of these classes ? 236. What is said of the compressibility of liquids ? COMPRESSIBILITY. 155 subdivided into equal parts, and the number of these parts the vessel A, can contain, is accurately 145 determined. There is also in the interior of the cylinder, a tube of glass, furnished with a graduated scale ; this tube is closed at its up- per end, and has its lower end im- mersed in the mercury, 0. This instrument is called a manometer, and is, when at rest, filled with air. In order to experiment with this apparatus, we fill the vessel A, with the liquid to be compressed, and by means of the funnel >ff, fill the cyl- inder with water, having previously placed mercury in its lower part. Turning the screw JP, we make the piston descend ; in consequence, the air in the tube, B is compressed, and the mercury is elevated ; thede- gree of elevation shows the amount of pressure, (the number of pounds or atmospheres) ; at the same time, the mercury rises in the capillary tube, and gives the measure of the compression of the liquid in A. Supposing each division of the capillary tube held but a millionth part as much as the vessel A, then if the liquid to be compressed was water, (at the pressure of one atmosphere,) we should ob- serve the mercury to rise between 49 and 50 divisions. There is one correction to be made of the observations obtained by this instrument ; it might be supposed that the capacity of A, would be invariable, the exterior and interior walls being compressed equally by the liquid, but it is not so ; the interior capacity of the vase undergoes the same diminution as would a body of glass of the same form and volume, submitted to the same pressure. This diminution amounts to about 33 ten millionths, ( T __3_3___) of the primitive volume, for one atmosphere. The corrected re- sults of the researches of M. M. Culloden, and Sturm, are as Describe the piezometer. Mention the compressibility of different liquids. What is said of M. Aime's experiments? 156 HYDROSTATICS. follows : at the temperature of 32 F., and with a pressure of one atmosphere. Mercury was compressed .... 5*03 parts in a million. "Water, deprived of air, was compressed 51 '3 " not " " " " " 49'5 Sulphuric ether " " 13'3 Acetic acid " " 42 -2 Sulphuric acid " " 32' Oil of turpentine 73' The contraction of liquids is, within certain limits, in direct proportion to the pressure. With the piezometer mentioned above, experiments with a pressure as great as 30 atmospheres have been made. M. Aime has, with a different form of appa- ratus, compressed liquids under the enormous pressure of 220 atmospheres. 237. Elasticity. As liquids are slightly compressible, it fol- lows that they must have a certain elasticity. This is shown upon removing the pressure from a compressed liquid ; it imme- diately returns to its former volume. Liquids have also elasticity from the stability of form they may take. Drops of liquid, placed upon a surface they do not wet, become spheres ; if these be struck, they flatten, but immediately resume the spherical form, as with small particles of mercury or drops of water covered with dust. Again, this is shown when we attempt to remove a drop of water, or other liquid, from a surface for which it has strong attraction ; the drop will elongate as we apply the sepa- rating force, but immediately resumes its former position and shape, when it is left to itself, because of its elasticity. 238. Equality of pressure. Liquids transmit pressure equally in all directions. Liquids transmit, in all directions and with the same intensity, the pressure exerted on any point of their mass. In order to comprehend this statement, let fig. 146 be a vessel filled with a liquid, and furnished with a number of equal cylinders, in each of which there is a piston. The vessel, as also the liquid, are supposed to be without weight, consequently, none of the pistons have a tendency to move. If we apply a pressure to the piston A, it will be forced inwards, and the other pistons, J5, (7, D, and E, of equal area, will each be forced outwards 237. What is said of the elasticity of liquids? Mention examples. 238. What is said of the equality^of pressure of liquids ? (I UNIVEKS: COMPRESSIBILITY. with the same pressure. So that if the pist inwards with a force of one pound, it would be found necessary to apply a force of one pound to each of the other pistons, in order to keep them in their place. If the area ofZ> and C was two or three times that of A, then the pressure upon them would be two or three times as great. We cannot perfectly demonstrate, that liquids transmit pressure equally in all di- rections, (because we cannot obtain for experiment, as would be necessary, liquids without weight, and pistons working^without friction,) but we can show that this pressure is exerted in all directions, by the simple apparatus, fig. 147, consisting of a cylinder, furnished 147 with a piston and terminated by a sphere ; on this sphere are placed small tubes, jutting out in all directions ; upon filling the sphere and cylinder with water, and pressing upon the piston, tho water is forced out from each of the tubes. 239. Downward pressure of a liquid, proportioned to its depth. That liquids press down- wards, and that this pressure increases with the depth, may be shown by the apparatus, fig. 148, consisting ot a metal cylinder containing a piston, (7, moving water tight, and resting upon a spring; if this instrument be placed vertically in a liquid, the piston is forced in with a pressure equal to the weight of a column of the liquid, lohose base is equal to the magnitude of thepiston, and whose height is equal to the depth of the liquid below the surface. 240. Pressure on the bottom of a vessel. The pressure of a How may this be illustrated ? Why can it not be perfectly demon- strated ? How may we show that liquids exert pressure in all di- rections? 239. What is said of the downward pressure of liquids ? 148 158 HYDROSTATICS. liquid on the bottom of a vessel, is independent of the shape of the vessel, and is equal to the weight of a column of liquid, whose base is that of the containing vessel, and whose, height is equal to that of the contained fluid. In order to demonstrate that the pressure is independent of the form, M. Haldat contrived the apparatus, fig. 149. It consists of a tube, A B c, bent twice 149 at right angles. On A, may be placed the vessels J/and P, of equal height, but of different forms. The tube A B c is filled with mercury, which rises to an equal height in A and c ; M is then placed on A, and filled with water ; the mercury immediately rises in c, to a certain point, as a. We then replace M by P, and fill with water as before. The mercury will again rise to the point a, as it did when the vessel M was on A ; it is evident that the pres- sure transmitted to the mercury in the direction A B, was the same, in both cases, proving, most conclusively, that the pressure does not depend upon the quantity of liquid, for the vessels M and P, differ greatly in capacity. However, the area of the base formed by the surface of the mercury, and the vertical height formed by the column of water, were the same in both cases, and upon these How may this be illustrated ? 240. What is said of the pressure on a bottom of a vessel? Describe Haldat's apparatus. What is the pressure of a liquid in a vessel having vertical walls ? LATERAL PRESSURE. 159 as stated above, does the pressure depend. In the case of a vessel having vertical walls, the pressure would be equal to the weight of the liquid the vessel contained. 241. Upward pressure. We have shown that pressure was exerted from above, downwards ; it follows, from the law of equality of pressure, (238,) that a corresponding force is exerted from below, upwards. This pressure is made very manifest by the buoyancy experienced when we plunge the hand into a liquid of great density, as mercury. In order clearly to demonstrate this upward pressure, a tube of glass is taken, open at both ends, fig. 150, having at the lower end a disc of glass, B, which is supported by means of a thread from its centre. The whole is then placed in a vessel 150 of water and abandoned to itself; the disc will remain attached to the end of the cylinder, because of the upward pressure of the water. If now the inte- rior tube is carefully filled, the disc will not fall until the level of the water within the tube is the same as that in the outer vessel, which proves that the upward pressure is equal to the weight of the interior column, and therefore the upward pressure, in any vessel, is in proportion to the height of the liquid column. 242. Pressure on the walls. The pressure of a liquid on any portion of a lateral wall, is equal to the weight of a column of liquid, which has for its base this portion of the wall, and for its height the vertical distance from its centre of gravity to the surface of the liquid. As in fig. 151, the pressure on the point C, of the wall is equal to the weight of the column A B, for the pressure of this is communicated laterally, to all the particles lying on the same horizontal plane. 243. Lateral pressure increases with the depth. As the pressure of a liquid on any point of a wall, is equal to the weight of its corresponding verticalc 151 A 241. What is said of the upward pressure of a liquid ? How may it be made manifest ? Describe the apparatus by which it may be clearly demonstrated. 242. What is said of the pressure of a liquid on the lateral walls ? Describe the figure 151. 160 HYDROSTATICS. 152 column, therefore the lateral pressure of a liquid in any vessel, increases with the depth, as in fig. 152, the liquid column A C, pressing with a certain force on D, the column E F will press on G, with a force as much greater, as E Fis greater than A C. This may be further illustrated by placing the appa- z ratus, fig. 148, in a horizontal position, the piston will be forced in with a pressure corresponding to the depth ; also, if it is placed in any position in- termediate between the horizontal and vertical, the piston will be pressed in, thus proving con- ~~ J clusively, that pressure is exerted in all directions. 244. Total pressure on the walls. Let us, in the vessel A B A 153 D CD, fig. 153, have the side A B, divided into 10 equal parts, supposing the pres- sure at 1 to be one pound, then the pressure at 2 would be two pounds, at 3 three pounds, &c., as the intensity of the pressure increases directly with the depth. The average intensity of pressure would be found at the 5th division, (a point midway between the 1st and 10th,) and the total pressure on the walls would be the same as if it sus- tained the average intensity over the whole lateral surface, and therefore the total pressure upon a wall of such a vessel, is equal to the weight of a column of the liquid ichose base is equal to the area of the side, and whose height is equal to one-half of the depth of the liquid in the vessel. This is true, whether the vessel be vertical or inclined outwards or inwards. In the case of a cu- bical vessel, this pressure on one side would be equal to one-half the weight of the liquid contained in the vessel. 245. Total pressure on the bottom and sides of a vessel. The total pressure exercised on the bottom and sides of a vessel, is much greater than the weight of the liquid contained in the vessel. In the case of a cubical vessel, the pressure exerted on the bottom is equal to the whole weight of the liquid, ( 240,) the pressure exerted on each side is equal to half the weight of the liquid, ( 244,) on the four sides, it is equal to twice its weight, conse- quently, in a cubical vessel, the pressure exerted on the bottom 243. What is said of the lateral pressure increasing with the depth ? Illustrate by the figure 152. 244. What is said of. the total pressure on the walls of a vessel] 245. What is the total pressure on the bottom and sides of a vessel ? THE CENTRE OF PRESSURE. 161 and sides, is equal to three times the weight of the contained fluid. 246. Table, showing the pressure in pounds, per square inch, and square foot, produced ~by water at various depths. Depth in feet. Pressure per square inch. Pressure per square foot. 1 0-4328 62-3232 2 0-8656 124-6464 3 1-2984 186-9696 4 1-7312 249-2928 5 2-1640 311-6160 6 2-5968 373-9392 7 3-0296 436-2624 8 3-4624 498-5856 9 3-8952 560-9088 10 4-3280 623-2320 By aid of the above table, the pressure of water on any sur- face of a vessel containing it, can be determined. As, for ex- ample, the pressure of water on a square foot, at the bottom of a vessel twenty-three feet in depth ; at two feet, the pressure is 124-6464; at twenty feet, ten times as much ; = 1246-464; at three feet, 186-9696. 1246-464 + 186-9696 = 1433-4336, the pressure of water on a square foot of surface, at a depth of twenty-three feet. That the pressure produced at great depths is really immense, can be shown by confining a piece of wood at great depths in the sea. The pressure forces the water into the pores, so that it will not be capable of floating afterwards. A bottle, the body of which is square, if tightly corked and lowered into the sea, will be broken by the pressure. If the body of the bottle is strong and cylindrical, the cork will be forced in. Below a certain depth, divers cannot penetrate, and the same may, perhaps, be true of fishes. 247. The centre of pressure. The centre of pressure in a mass of fluid, is a point where all the elementary pressures are equally balanced, or are in equilibrium. It is always placed lower than the centre of gravity, since it would coincide with it, were it not that the lower masses of fluid were compressed by What if the vessel has a cubical form ? 246. Give the pressure upon a square inch and square foot at the depth of 1, 2, 4, 5 and 10 feet ? Determine the pressure of water on a square foot 23 feet below the surface. What facts illustrate pressure at great depths I 247. What is the centre of pressure ? 162 HYDROSTATICS. . \. c those above. The position of this point is determined by cal- culation. 1*& In a vessel whose sides are parallelograms, the centre of pressure is on a line which divides into two eqaal parts the hor- izontal layers, at a point one-third of the distance from the lower part. As in the vessel, fig. 154, the centre of pressure is 154 on a line A B, at the point C, one-third of the distance from the lower part B. 2d.In a triangular vessel, standing on gits base, the centre of pressure is on the vertical line, reaching from the centre of the base to the apex, at a point one-fourth of the distance from the lower part. As in fig. 155, the centre of pressure is at the point c, one-fourth of the vertical line A B: if the same vessel rests on its apex, the centre of pressure is at the point midway between the centre of the base and the apex, as in fig. 156, at the point c, one-half of the vertical line A B. 248. Level surface of a liquid. That the B ~~* surface of a liquid must be level, is evident from the mobility of the particles. This results from the attrac- 156 tion of gravitation, and also because of the j^ fact, that when a body is free to move, its centre ""'of gravity will descend as low as possible. Mountains do not sink and press up the inter- mediate valleys, because the cohesion of the particles is opposed to gravitation, but if th e mountains were liquefied, the ridges would sink down, and the valleys would rise, until the whole mass would have a uniform level surface. A perfectly level surface on the earth, means one in which every particle is equi-distant from the centre, and is therefore a truly spherical surface. A terrestrial surface of large extent would show a differ- ence of elevation of about four inches in a mile. In making a canal, therefore, in order to have it level, there must be this deduction from the terrestrial line. In small vessels, the surface of the liquid What is the position of this point in a vessel whose sides are par- allelograms? What in a triangular vessel placed on its base ? What when placed on its apex ? 248. What is said of the level surface of a liquid? What does a perfectly level surface on the earth mean ? EQUILIBRIUM OF LIQUIDS IN COMMUNICATING VESSELS. 163 when at rest, is a perfectly horizontal plane, being in perfect equilibrium. The sphericity of the earth is illustrated by the fact, that the masts of a vessel at sea are seen long before its hull is visible, whereas, were the surface of the water a perfect plane, the larger object would first become visible. 249. Many liquids in the same vessel. If, instead of a single liquid in a vessel, we have a number, having different specific gravities, we shall find that the relative position in which they will come to rest, will be in the inverse ratio of their specific gravity. Thus, if mercury, water and oil, are placed in a vessel, and after shaking them well together, they are allowed to rest, in a little time it will be found, that there are three layers ; the mercury, being the heaviest, lies at the bottom ; the water, lighter than the mercury, forms a layer immediately above ; the third layer consists of oil, it being less dense than either of the other liquids. 250. Equilibrium of a liquid in communicating vessels. If two or more vessels communicate with each other, the liquids in both or all the vessels stand at the same level. This law rests upon the fact, that the pressure of liquids at equal depths, is equal in all directions. If the fluid stands at a higher level in one vessel than the other, the particles of the former exert a greater lateral pressure on the channel of communication than the other can; these particles are, 157" therefore, continually pushed upwards, until they exert an equal and opposite pressure, which obtains when the col- umns are at an equal height. The effect is the same, whatever may be the size and number of the vessels. Fig. 157 represents a number of vessels of M different shapes and capacities, con- nected with a common reservoir; if we pour water into one of them, it will rise to the same height in the other vessels. The only circumstance af- What is said of the sphericity of the earth? 249. lifferent den What is the re- sult when liquids of different densities are placed in the same vessel ? Mention the illustration. 250. What is said of the equilibrium of liquids in communicating vessels ? Describe the figure. 164 HYDROSTATICS. fecting this law would be capillarity, which, if certain of the tubes were very small, would cause the liquid to rise jn them to a higher point than in the others. Practical advantage is made of a knowledge of this law in the construction of aqueducts, or closed pipes, to supply towns and cities with water. The aqueduct often passes over very uneven surfaces for great distances, and the water is distributed to the houses by smaller pipes, branching from the greater ones. So long as the dis- tributing pipes do not rise above the level of the fountain head, the water will continue to flow. 251. Artesian wells. Water spouts from artesian wells for the same reason that liquids, in communicating vessels, tend to assume the same level, and streams flow toward the ocean. The crust of the earth consists often of various beds or strata, some per- meable to water, like the sandstones, while others are impervious. Fig. 158 represents a portion of the earth containing two imper- 158 meable strata, C C, B B, and one pervious stratum, A A, between them. Supposing the latter to be in communication with more elevated lands, from which water filters in, then we should have a natural basin, from which the water could not escape, because of the impermeable strata above and below. If the upper strata are pierced by an artesian well, F #, the water, tending always to place itself in equilibrium, would rush up to a height towards the level line H D, and owing to friction, would, perhaps, reach the intermediate level K. Several very deep wells of this sort have been sunk in the salt regions of Virginia and Ohio. The famous well of Grenelle, in Paris, is 1806 feet deep, and the 251. Describe artesian wells. What is said of that at Grenelle ? HYDROSTATIC PARADOX. 165 water rises 112 feet above the surface, having a temperature of 83 d -75 F., (the annual mean temperature of Paris being 53 F.) Over six hundred gallons are discharged each minute from this wonderful fountain, and without variation in quantity. 252. Equilibrium of liquids of different densities in commu- nicating vessels. -When two liquids of different densities are placed in communicating vessels, their surfaces will not rest at the same point or level ; for in communicating vessels, the heights of the liquid columns are in the inverse ratio of the densities of the liquids. If mercury is first poured into the lower part of the apparatus, fig. 159, and the tube A B is then 159 filled with water, this last will exert a pressure on the mercury, causing it to be depressed in A B, and rise in the other tube. Measuring the height of the columns of mercury CD, and water, AB, which are in equilibrium* they will be found to be as 1 to 13-59. These numbers represent the den- sities of water and mercury. 253. Hydrostatic paradox. This term is applied to a practical illus- tration of the law of equality of pres- sures, and in proof of the seemingly paradoxical proposition, that a quan- tity of fluid, however small, may be made to counterbalance another, however large. We have seen ( 237) that the pressure ex- erted on one of the pistons, fig. 146, would be felt equally on the rest, however great their number. If the pressure, instead of being communicated by a weight, was induced by a column of fluid acting upon a bellows, we should have the ordinary form of illustrating the hydrostatic paradox. The hydrostatic bellows, fig. 160, consists of two boards, B C, and CD, connected with leather or India-rubber cloth, in such a manner that the upper board can rise and fall, like the common air bellows. The tube P E communicates with the interior of the apparatus. Sup- posing the tube to have a cross section of one square inch, and 252. What is said of the equilibrium of liquids of different densities in communicating vessels? 253. What is the hydrostatic paradox! Describe the hydrostatic bellows. 166 HYDKOSTATICS. D the top of the bellows to have a surface of 100 square inches, a 160 pound of water in the tube would lift 100 pounds on the bellows, the weight of the water acting with a pressure equal to itself, (1 lb.,) on each square inch of the surface. The pressure is caused by the height of the column of water ; for if we use a smaller tube, for the same bulk of fluid, the height of the column of water will be greater, and will raise a greater weight ; if the tube be larger, the column will not be so high, and will not raise so large a weight. Another example, showing that a small quantity of water, through the medium of extended fluid surface, may produce a pressure of hundreds or thousands of pounds, is a cask filled with water, and which has a small tube screwed tightly in its top. A small quantity of water placed in the tube, will burst the cask ; for, let us suppose the tube to have an area of a thirtieth of an inch, and to contain, when filled, half a pound of water, then the pressure exerted on each square foot would be more than 2000 Ibs., a pressure greater than an ordinary cask can sustain. 254. Hydrostatic press. The hydrostatic press acts upon the principle just explained ; and if compared to the hydrostatic bellows, employs a strong forcing-pump, instead of the lofty tube, and a barrel and piston, instead of the leather and boards. The main parts of this machine, fig. 161, consist of a small forcing-pump A, in which is a piston worked by a lever. This pump communicates with a large and strong cylindrical reservoir, B, by a tube indicated by the dotted lines in the figure. In this cylinder a water-tight piston moves, bearing at its upper end a flat metallic plate, between which and the top of the frame, D, the substance, if, to be compressed, is placed. The cylinders are filled by means of the curved tube H, one end of which rests in a vessel containing water, or oil, the other terminates in the barrel A, and has a valve at its end What is the experiment of the cask and tube 1 254. Describe the hydrostatic press. How are the cylinders filled with water ? THE HYDROSTATIC PRESS. 167 opening upwards. This valve opens when the piston is raised, thus drawing in water, and closes when the piston descends. 161 By working the piston, the barrels A and B are completely filled with water. The orifice 0, is in connection with a stop-cock, by which the water can be drawn off, when we wish to reduce the pressure. The pressure exerted on the water in A, by depressing the piston, is transmitted with equal force throughout the entire mass of the fluid. The surface of the water in A, therefore, presses up the piston above it, with a force proportioned to its area. If the cylinder B has an area of 200 square inches, and the small cylinder an area of half a square inch, the pressure of the water on the piston above B, will be 400 times that applied at the lever. But let the arms of the lever be to each other as one to fifty, then when a force of fifty pounds is applied at the long arm, the piston will descend with a force of 2500 pounds, (50 X 50 = 2500,) and there will be exerted, theoretically, a force of 1,000,000 pounds upon the piston in B, (50 X 50 X 400 = 1,000,000,) or, How is the pump set in operation? What is the result of a great difference in the area of the pistons ? How does the length of the arms of the lever affect the result ? 168 HYDROSTATICS. deducting one-fourth for the loss occasioned by the different im- pediments to motion, a man would still be able to exert a force of 750,000 pounds. The hydraulic press is of extensive use in the industrial arts. It is employed for compressing cloth, paper, hay, and gun-powder, candles, vermicelli, and numerous other articles, to which the proper form or condition is imparted by severe pressure. The tubes of the famous Britannia tubular bridge over the straits of Menai, were raised by means of a powerful hydraulic press. 255. The water level. The water level, fig. 162, is an appli- cation of the law of the equilibrium of liquids in communicating vessels ; it may consist of a metallic tube, bent upon its extremities, 162 to each of which is adapted a vertical glass tube; this is mounted on a tripod. Water is poured into E, until the liquid is elevated in the tubes of glass. The equilibrium being established, the level of the water in the two tubes is the same ; that is, the sur- faces of the liquid in D and E, are on the same horizontal plane. By this instrument we can determine whether one point is more elevated than another, as A and B. By placing a sight-board at A, the observer, directing his eye along D E, immediately above the liquid, has the sight-board placed higher or lower by an as- sistant, until its centre is on the same horizontal line with D and E ; measuring then the height A M, and subtracting it from the height of D E, above B, we find how much higher the point A is than R 256. The spirit level, is a more accurate instrument than the above. It consists, fig. 163, of a tube, A J?, sheathed in brass, How much force can a man thus easily exert? 255. Describe the water level. How are determinations made with it ? ARCHIMEDES' PRINCIPLE. 169 CD, slightly curved, and filled with alcohol, except a small space, JLf, occupied by a bubble of air. This always rises, to occupy 163 the more elevated part. "When the instrument is placed hori' zontally, the bubble remains in the centre, at a fixed mark, but when it is inclined, the bubble ascends. 257. Archimedes' principle. When solids are immersed in fluids, they displace a quantity of the latter, equal to their own bulk; a legitimate consequence of their own impenetrability. When a body is plunged in a fluid, its surfaces support the pres- sure of those particles it touches. Let a cube, fig. 164, be im- mersed, with two of its faces horizontal. The vertical faces being- opposite, and the pressures against them being in contrary di- rections, they neutralize each other. The upper horizontal face is pressed downwards by a col- 164 umn of water, whose base is this face, and whose height is A J9, and the lower horizontal face is pressed up- wards by a column with an equal base, and having a height D B. The cube must, therefore, be floated up- wards, by a force which is the dif- ference between these two pressures, that is, equal to the weight of a mass of water corresponding in size to the immersed body. Consequently this pressure, opposing itself to gravity, the weight of the body is propor- tionally diminished, and it follows, that a body plunged in a liquid loses a part of its weight, equal to the weight of the liquid displaced. 256. Describe the spirit level. 257. What is the effect when solids are placed in water ? What pressure is exerted on a cube sustained in water, as in the figure 1 What is the result of the ac- tion of these pressures ? 8 170 HYDROSTATICS. This principle was discovered by Archimedes, about 230 years B. C., and is called after him, the Theorem of Archimedes. That it is correct, may be proved by means of the hydrostatic balance, fig. 165, from one of the arms of which is hung a hollow cylinder, 165 or bucket, A, having a cylindrical mass of copper, .Z?, exactly fitting into it, and hanging from it by means of a fine wire. Having ex- actly counterpoised the beam by weights on the other arm, fill up the glass vessel with water, until the cylinder B is wholly im- mersed. The cylinder will then appear to have lost weight, the other arm going down. If the bucket A, is now exactly filled with water, the equilibrium will be restored ; proving that the immersed body has lost in weight equal to its own bulk of water. "Who was this principle discovered by ? Describe the action of the hydrostatic balance. CARTESIAN DEVIL, 171 258. Equilibrium of floating bodies. Accepting the Theorem of Archimedes, agreeably to the last section, it follows, that if the immersed solid be of the same weight as the displaced fluid, the former will remain at rest in the fluid, in any position in which it may be placed, the upward pressure exerted upon the solid being equal to its own weight. If the solid is more dense than the fluid, its weight being greater than the upward pressure, the body will sink ; while if the immersed body is less dense than the fluid, it will rise until it has displaced a volume of water equal to its own weight ; that is, the body floats. For this reason, cork, wood, wax and other light bodies, placed in water, support themselves on its surface. In order that floating bodies may take a state of stable equilibrium, it is necessary, 1st. That they displace a weight of liquid equal to their own bulk. 2d. That their centre of gravity be below the centre of pressure, and in the same vertical. We may, however, still have stable equilibrium, when the centre of pressure is below the centre of gravity, but then it must be below a certain point called the me- tacenter, which can be determined by calculation. (In a slightly rolling, floating body, the point of intersection of the vertical, through the centre of gravity when at rest, is called the meta- center.} The knowledge of these points is of great value in the loading of a vessel ; if the metacenter coincides with the centre of gravity, the equilibrium is stable in any position of the ship. Fishes are in a state of equilibrium when immersed in their own element, and in order to preserve this state at different depths, they have an air bladder, by contracting or expanding which, their bodies acquire the same density as that of the water in which they are. 259. Cartesian devil. The hydrostatic toy, known as the car- tesian devil or ludeon, exhibits the principle just stated. It con- sists of a small glass or enamel figure, fig. 166, at whose head is fixed a bulb of glass, 0, having a small hole in its lower part, and filled with water to such an extent, that when placed in the cylinder of water as represented, it will remain in any position. Over the vessel's mouth is tightly fixed a piece of caoutchouc. If 258. What is said of a solid immersed in a liquid, when it is of the same density as the displaced fluid I When the body is of greater density? What two conditions are necessary that floating bodies take a state of equilibrium ? What is the metacenter 1 What is said of the advantages of a knowledge of these points ? What is said of fishes ? 259. Describe the cartesian devil. 172 HYDROSTATICS. the caoutchouc be pressed upon, while the figure is near the surface of the water, the air below is compressed, and this pres- sure will be conveyed through the water to the air contained in 166 ; this will be compressed into a smaller bulk, and sufficient water will enter to render the apparatus heavier than water, when it will fall. On removing the pressure, the air expands in 0, and expels the water which was previously forced into it, and the apparatus rises. By a contrivance similar to this, the beautiful nautilus shell rises, to float upon the surface of the sea, or sinks again at pleasure, by a voluntary contraction or expansion of an internal cavity. 260. Density. Different bodies, with the same volume, have different weights, owing to their containing unequal quantities of matter. This quality of bodies is called their density, or specific weight, and signifies the relation of the weight to the volume. The determination of density of a solid or liquid body, consists in ascertaining its weight, and also that of an equal volume of water, and in dividing the first weight by the second. Three methods are resorted to for determining the specific gravity of solids and liquids : a, by the balance, ft, by the hydrometer, and c, by the flask. 261. Specific gravity of solids heavier than water. The solid (heavier than water) whose weight is to be ascertained, being attached by means of a silk thread to the arm of a bal- lance, and accurately weighed, will, upon immersion in water as in fig. 167, lose weight. This loss is equal (according to the principle of Archimedes) to the weight of a volume of water equal to that of the immersed body. Subtracting the weight of the substance in water from its weight in air, and dividing the latter by the difference, the product will be the specific gravity required. Example. A piece of iron weighed in air, 460 grains, in water, 401-16 grs. Then 460 401 '16 = 58'84 grs., which equals the weight Why does pressure oil the India-rubber cause the figure to sink ? Why does it rise ? 260. What is the density a body i What does it signify ? How are densities determined ? 261. Describe the method for the determination of the density of a substance by means of the balance. State the example given. SPECIFIC GRAVITY OF SOLIDS IN WATER. 173 of a volume of water equal to the iron, and 460 -f- 58'84 = 7*8 = specific gravity of the iron. 262. Specific gravity of solids lighter than water. If the body be lighter than water, it must be attached to some solid (whose weight in air and water is known) 167 sufficiently dense to sink it in water. The ( j compound mass is weighed first in air, and then in water, and the loss determined, the weight lost by weighing the heavy body alone in water being known, the weight of the light body in air, divided by the difference be- tween these losses, gives the specific gravity. Example. A substance weighed in air, 600 grs., attached to a piece of copper, it weighed 2647 grs., in water 2020 grs., suffering a loss of 627 grs. The copper itself loses, when weighed in water 230 grs., 627 230=397, then 397 -5- 604 = '660 the specific gravity of the substance. 263. Specific gravity of solids soluble in water. To determine the specific gravity of a solid soluble in water, we must weigh it while immersed in a fluid, in which it is not soluble, as oil of turpentine, alcohol, &c., its specific gravity, compared with that of the liquid being ascertained. To determine its density, compared with that of water, we have now only to multiply the specific gravity, thus found, by that of the fluid employed. Example. A substance soluble in -water was weighed in oil, and its specific gravity, compared with the oil, was 2 '6, the specific gravity of the oil was '87 ; then 2'6 X '87 = 2 '262 the specific grav- ity of the substance. 264. Nicholson's areometer. This instrument, used for de- termining the density of solids, consists of a hollow cylinder of metal or of glass, B, fig. 168, having attached to its lower end 262. How is the specific gravity of a solid lighter than water deter- mined ? State the example given. 263. How is the specific gravity of a solid soluble in water determined 1 State the example given. 174 HYDROSTATICS. a cone, #, loaded with lead, which causes the apparatus always to 168 assume an upright position when placed in wa- ter. The upper part of the cylinder is termi- nated by a rod, on the end of which is a small cup, -4, for holding weights. The whole appa- ratus must have a less specific gravity than water, so that a certain weight, as X, must be put in the cup, to sink the areometer to the water mark 0. If we wish to determine the specific gravity of a body, (whose weight must be less than X,} we place the body in the cup A, and add weights till is brought to the level of the water. The weight of X (the coun- terpoise) minus the weights last added, will ibe the weight of the body in air. It is now taken from A, and placed in C ; it will there weigh as much less as the weight lost in water. We have now the data for determining the specific gravity of the solid. For example : if the counterpoise weighed 250 grs., and the mass of lead whose weight we wish to ascertain, requires 50 grs. to be added in order to bring it to the point 0, then (250 50) 200 is the weight of the lead in air ; placing now the mass on (7, we should find that it would require the addition of IT '47 grs. on A y in order to counterbalance it ; consequently the specific gravity is 11-45. (for 200 *- 17-47 11 -45.) If the substance is lighter than water, we confine it under a little cage of iron wire placed on (7, which prevents its rising. 265. Specific gravity bottles are made of various forms and sizes, according to the particular object to which they are to be applied. The more common variety consists of a small light flask, (holding from 100 to 1000 grains,) with an accurately fitting stopper. There is often a small hole through the stopper, to allow the escape of any excess of liquid which may have been placed in the flask during filling. A better form is seen in fig. 169, in which the stopper is hollow, and fits the flask so perfectly, that any liquid may be easily re- moved from the joint. Fig. 170 represents a form of specific gravity flask, which has advantages over most others. The flask is filled to a point A on the stem, the interior upper part wiped perfectly clean, and the stopper then inserted. If the liquid cx- 264. What is Nicholson's areometer? How is the specific gravity of a solid determined by this instrument? Give the example. 265. Describe the ordinary specific gravity flask. Mention other forms. SPECIFIC GRAVITY. 175 pands, it will rise in the tube, but cannot overflow and soil the 1VO 169 exterior, as would be the case were other bottles used. In this form there is no danger of loss from evaporation. In many specific gravity bottles, a small thermometer is placed in the stopper, that the temperature of the liquid during the operation may be noted. 266. Method with a flask. We use this method only for de- termining the specific gravity of solids in powder. A small bottle or flask with an accurately ground stopper is used. Having carefully filled the flask with water and dried it, we place it on the balance, together with the powder, whose specific gravity we wish to determine, and whose weight in air we know, after having counterbalanced it, we take the flask from the pan and throw in the powder, and then replace the stopper ; a portion of the water is displaced by the powder ; after drying the flask, we place it upon the pan and counter-balance. The number of grains added, represents the weight of a volume of water equal to that of the powder. The calculations are made in the same manner as in the other cases. 266. How is the specific gravity of a substance in powder deter- mined ? 267. How is the specific gravity of a liquid determined by the balance ? 176 HYDROSTATICS. IS 267. Specific gravity of liquids by the balance. To one arm of the balance, we attach, by means of a wire, a solid (as pla- tinum,) on which the liquid whose specific gravity we wish, has no action ; then, after weighing the platinum in air, we weigh it in water, and then in the given liquid, as oil, we observe the loss of weight the mass undergoes in these two liquids ; these two numbers (the losses) represent the weight of equal volumes of water and the unknown liquid. Example. The platinum weighs 275 grs. in air, in water, 262'5, losing 12' -5 grs. ; in oil, 253'75 grs., losing 11 '25 grs. ; then 11 '25 -f- 12'5 = "9, specific gravity of the oil. 268. Areometers. These instruments generally consist of a 171 glass tube, terminated by a globe or long bulb, loaded with mercury or shot, fig. 171, so that they may as- sume a perpendicular position when placed in liquids. Upon or within the tube is a properly graduated scale, which allows of the determination of the density of the body by the greater or less depth it sinks in the liquid. Hydrometers for liquids lighter than wa- ter, sink to such a depth, if immersed in pure water, that the glass tube with the scale stands above the surface, those for liquids heavier than water, sink in that fluid to the very top of the scale. In both species, the water line is marked with or 1, and the figures Ion the scale give the specific gravity corresponding to the depth of the immersion. Very often the figures on the scale, (and these are much the more convenient,) indicate at once the specific gravity. More often, however, the hydrometers are graduated in an arbi- trary manner. Besides the areometers by which the specific gravity of any fluid may be determined, others are made for particular liquids. In which case, the scale is so graduated as to express the component parts per cent., by weight or volume. Such are called per cent, areometers or hydrometers, and are named after the liquid they are used for testing, as acid hydrometers, beer hydro- meters, wine hydrometers, &c. Baumes' hydrometers are very 268. What are areometers ? "What is said of hydrometers for li- quids lighter than water? What of those for liquids heavier than water ? PRESSURE OF FLUIDS. 177 much used, being constructed for fluids both heavier and lighter than water. The one for the more dense fluids, sinks in pure water to the zero point of its scale ; this is its highest point. The lowest point on the scale is 15, to which it descends when im- mersed in a solution of fifteen parts of common salt, in eighty -five of water. Fifteen degrees are marked between these two ex- treme points. The one for fluids lighter than water, has its zero at the point to which it sinks in a mixture of ten parts of common salt, and ninety of water, and ten degrees where it stands in pure water. The space between these two points is divided into ten degrees. In both these hydrometers, the scale of equal divisions is extended throughout the length of the tube. 209. By the specific gravity bottle. In order to determine the specific gravity of a liquid, use is made of a small flask or bottle. The weight of the bottle being known, it is first filled with water and weighed, afterwards with the liquid, whose spe- cific gravity is desired, and again weighed ; we have now the weights of equal volumes of water and of the second liquid, from which we deduce the specific gravity. Example. Supposing the bottle held 852 grains water, and 784 grains of oil, the specific gravity of the oil is '921, for 784 -r- 352 = '921. Very often the bottle is made to hold just 1000 grains of water, then upon determining the number of grains of the fluid of un- known density it holds, we have at once its specific gravity. What is said of the zero, and the scales? What is said of per cent, areometers ? Describe Baume's hydrometer for liquids lighter than water. Those for liquids heavier than water. 269. How is the specific gravity flask used to determine the density of a liquid ? 8* 178 HYDRAULICS. HYDRAULICS. 270. Hydraulics, (from hudor, water, and aulos, a pipe,) is that part of hydro-dynamics which treats of the art of conducting and elevating fluids, especially water, and the construction of all kinds of instruments and machines for moving them, or to be moved by them. 271. Pressure of fluids upon the containing vessel. When a vessel is filled with water or any other liquid, its sides are sub- mitted to two pressures acting in contrary directions. The at- mospheric pressure, acting from without inwards, and the pres- sure of the column of fluid acting outwards against the sides. If a vessel so circumstanced has one of its sides pierced, and the pressure from within outwards is stronger than the external pressure, the liquid will flow out ; while if the external pressure is the stronger, the fluid will not escape. This may be shown by filling a glass vessel, as a wine glass, with water, placing a piece of paper over its top, and then carefully inverting it. Holding it in this position, the fluid will not escape, the external (atmos- pheric) pressure against the paper, being greater than the weight of the column of water pressing downwards. The mass of liquid escaping from an orifice in a vessel, is called a vein. 272. Appearance of the surface during a discharge. A vessel containing liquid, discharging itself by means of an orifice, does not always preserve a horizontal surface. When the vein issues 172 173 270. What is hydraulics? 271. "What is said of the pressures upon a vessel filled with liquid ? How may this be shown ? What is a vein? 272. What is the appearance of the surface of a vessel dis- charging liquid from an orifice in its lower part or in its side ? What do the movements depend upon ? TORRICELLIAN THEOREM. 179 from an orifice in the bottom of a vessel, and the level of the liquid is near the orifice, the liquid forms a funnel-pipe, fig. 172 ; if the liquid had a rotary movement, the funnel is formed sooner. If the orifice is at the side of the vessel, there is a depression of the surface upon that side, above the orifice, fig. 173. These movements depend upon the form of the vessel, the height of the liquid in it, and the dimensions and form of the orifice. 273. Theorem of Torricelli. When a liquid escapes from an orifice in a vessel, owing to the excess of the internal pressure, the volume which escapes depends on the section of the orifice, and the velocity with which the liquid molecules move at the moment of their escape from it. This velocity depends upon the density of the liquid, the excess of pressure at the opening, and the friction of the liquid, both at the opening and against the walls. When the aperture is made in a very thin wall of a large vessel, so as to remove, as much as possible, the causes tending to modify the motion of the escaping fluid, the laws of the escape are comprised in the fol- lowing theorem, discovered by Torricelli, in 1643, as a conse- quence of the law of the fall of bodies discovered by Galileo. Liquid molecules, flowing from an orifice, have the same velocity as if they fell freely in vacua, from a height equal to the ver- tical distance from the surface to the centre of the orifice. 274. Deductions from the Torricellian Theorem. 1. The velo- city depends on the depth of the orifice from the surface, and is in- dependent of the density of the liquid. Water and mercury in vacuo would fall from the same height in the same time ; and so escaping from an orifice at the same depth, below the surface, would pass out with equal velocity ; but mercury, being 13 '5 times as heavy as water, the pressure exerted at the aperture of a vessel filled with mercury, will be 13 -5 times as great as the pressure exerted at the aperture of a vessel filled with water. 2. The velocity of liquids is as the square roots of the depths of the orifices below the surfaces of the liquids. Thus stating the velocity of a liquid escaping from an orifice one foot below the surface, to be one ; from a similar orifice four feet 273. What does the volume of the liquid escaping from an orifice depend upon? Upon what does its velocity depend? State the The- orem of Torricelli. 274. What is the first deduction drawn from Torricelli's theorem ? Give the illustration of water and mercury. What is the 2d deduction? Give illustrations of this deduction. 180 HYDRAULICS. below the surface, it will be two, and at nine feet three, at sixteen fast four, and soon. 275. Theoretical and actual flow. The actual flow from an orifice, is the volume of liquid which escapes from it in a given time. The theoretical flow, is a volume equal to that of a cylinder which has for its base the orifice, and for its height the velocity, furnished by the theorem of Torricelli. That is, the theoretical flow is the product of the area of the orifice multi- plied by the theoretical velocity. It is observed that the vein escaping from an orifice, contracts quite rapidly, so that its di- ameter is soon only about two-thirds of the diameter of the ori- fice. If there was no contraction of the vein after leaving the orifice, and its velocity was the theoretical velocity, the actual flow would be the same as that indicated by theory. But its section is much less than at the orifice, and its velocity is not so great as the theoretical velocity, so that the actual flow is much less than the theoretical flow ; and in order to reduce this to the first, it is necessary to multiply it by a fraction which is named " the co-efficient of contraction." From comparative experiments made by a great number of observers, it is learned that the actual flow is only about two- thirds of the theoretical flow. 276. Means for obtaining a constant discharge. In order to verify many of the laws of hydraulics in an accurate manner, it is necessary to maintain a constant pressure on the escaping liquid, thereby obtaining a constant velocity at the orifice. This may be done in various ways, as by allowing the water to flow into the reservoir in a little larger quantity than can escape from the orifice ; the excess being discharged through a tube or orifice at the upper edge of the reservoir. Also by means of the syphon, an instrument which will be hereafter described. 277. Constitution of veins. The form and constitution of liquid veins have been studied by Savart. He observed, 1st, that the fluid issuing vertically from an ori- fice made in a plane, and thin horizontal wall, is always com- posed of two distinct parts, fig. 174, the portion nearest the ori- 275. "What is meant by the actual flow from an orifice? What is the theoretical flow? What is meant by the co-efficient of contrac- tion ? What proportion does the actual flow bear to the theoretical flow? 276. What means are used for obtaining a constant discharge of liquid from a vessel ? CONSTITUTION OP VEINS. 181 fice is calm and transparent, like a rod of glass, gradually de- creasing in diameter. The second, on the con- trary, is always agitated, and takes an irregular form, in which are regularly distributed elon- gated swellings, called venires, whose maxi-| mum diameter is greater than that of the ori- fice. 2. In the second part of the vein, the liquid is not continuous ; for if we employ an opaque liquid, as mercury, we can see through the vein, fig. 175. The apparent continuity in a vein of water, is owing to the fact, that the globules which constitute it succeed each other at a dis- tance inappreciable to the eye. Savart found that the venires are formed of disseminated globules, elongated in the tranverse direction of the vein, and that the contractions or knots are formed of globules, elongated in the longi- tudinal way, fig. 175. He also found that the limpid part of the vein is formed of annular swellings which originate very near the orifice, propagating themselves at unequal intervals to the troubled part, where they separate, of the same form at the instant of their separation, but changing periodically. 3. The annular swellings arise from a peri- odical succession of pulsations near the orifice, which must be produced by very small oscilla- tions of the entire mass of the liquid, so that the velocity of the flow is periodically variable. The number of these pulsations is in direct ratio with the swiftness of the flow, and in inverse ratio with the diameter of the orifice ; they are sufficiently rapid and regular to give rise to a well characterized sound. The air has no influence on the dimensions of the veins, or on the sound they produce. 27T. What two distinct parts have been observed by Savart in a liquid vein ? What is said of the second part of a liquid vein ? What is said of the constitution of these ventres ? What is the limpid part of the vein formed of? What is the course of these annular swellings? What is said of the number of pulsations ? What is the effect of the sounding of a musical instrument near the veins ? 182 HYDROSTATICS. 4. If we produce, with a musical instrument at some distance, the same or a similar sound, the vein undergoes a remarkable modification ; the swellings and knots assume more regularity, and usurp the transparent part, which almost entirely disap- pears, the flow of the liquid from the orifice remaining the same as at first. 5. The constitution of veins thrown out in any direction is essentially the same ; but the number of pulsations is diminished in proportion as the vein is thrown out more vertically upwards. 278. Contraction of the vein. The vein, escaping from a cir- cular orifice, preserves a circular section, but a varying diameter. Its diameter at first being equal to the orifice, is diminished ra- pidly, until, at a distance a little greater than its first diameter, the section of the vein is but about two-thirds that of the orifice. If the vein flows directly downwards, the decrease in size con- tinues to the troubled part. If the jet issues horizontally, the decrease is scarcely noticeable ; if it is directed upwards, at an angle of 25 to 45, the vein preserves its own diameter ; but if its angle surpasses 45, its section increases to the troubled part. By suspending solid particles in the water, we render the cur- rents that are formed, visible. These solid particles direct them- selves, in curved lines, towards and into the orifice, as a centre of attraction, fig. 176. The particles in immediate contact with the orifice, not moving so easily as those within, must cause contraction ; so> also, we can see that gravity in accelerating the velocity, must cause continual decrease in the section of the jet. 279. Escape of liquids through short tubes. We often place in an orifice, to increase the flow, a short tube, (called an adjutage) either cylin- drical or conical. If the vein pass through the tube without adhering to it, the flow is not modified ; if the vein adhere, (the liquid wetting the interior walls,) the contracted part is dilated, and the flow increased. In the last case, and with a cylindrical ad- What influence has the direction of the vein upon its constitution ? 278. "What is said of the contraction of the vein 1 What is said of the contraction if the direction of the vein is directly downwards? What when issuing horizontally ? How may these currents be seen ? 279. What is said of the escape of liquids through short tubes? ESCAPE OP LIQUIDS FROM CAPILLARY TUBES. 183 jutage, its length not being more than four times its diameter, the flow is augmented about one-third. Conical cones, converging towards the exterior of the reservoir, increase the flow still more than the preceding, the flow and velocity of the vein varying with the angle of convergence. Conical adjutages, diverging towards the exterior, give the greatest flow ; they may give a flow 2 4 times as great as that which an orifice of the same di- ameter in a thin wall furnishes, and 1 '46 times greater than the theoretical flow. 280. Escape of liquids through long tubes. When a liquid passes through a long straight tube, the flow soon diminishes greatly in velocity, because of the friction which takes place be- tween the liquid particles and the walls. It is again further di- minished by the same cause, if there be any bends or curves in the tube. The discharge is very much less than it would be from an orifice in a thin wall, and therefore the tube is generally inclined ; the liquid then passes down an inclined plane, or it is forced through by pressure, applied at the opposite end. 281. Escape of liquids from capillary tubes. Fluids escaping from capillary tubes, (tubes having a fine or hair-like bore,) are subject to the following laws, (the tubes being of glass.) 1. For the same tube the flow is proportioned to the pressure. 2. With tubes having an equal pressure and length, the flow is proportional to the 4th power of their diameters. 3. For the same pressure and the same diameter, the flow is in inverse ratio to their length. 4. The flow increases with the temperature. The inequalities in the flow of different liquids under the same circumstances does not seem to depend on their viscosity or their density ; for alcohol flows slower, and oil of turpentine, or sugar solution, faster than water. So also nitrate of potash solution, flows faster than pure water, and serum flows less swiftly ; alcohol added to serum retards its movement, while if nitrate of potash so- lution be added to the mixture, the serum recovers its usual ve- locity. These experiments made with glass tubes, were repeated on the bodies of animals recently killed, by injecting the various What is the amount of flow with a cylindrical adjutage ? What is said of the effect of conical tubes ? What form gives the greatest flow ? How does the actual flow then compare with the theoretical flow ? 280. What is said of the escape of liquids through long tubes 1 281. What are the laws of the escape of liquids through capillary tubes ? 184 HYDROSTATICS. fluids into the principal arteries. The results were found to ac- cord, tending to prove that the circulation of blood and other fluids in the arteries and veins of living bodies, is subject to the same laws as the flow of liquids in capillary tubes of glass. 282. Jets of water. As the velocity of a liquid escaping from an orifice is the same as that which a body acquires falling from a height equal to the distance from the level of the liquid to the orifice, a jet of water escaping from a horizontal opening, up- wards, should rise to the level of the liquid in the reservoir. But this never quite takes place, (fig. 177,) because of 1st, 177 the friction in the conducting tubes destroying the velocity 2d, the resistance of the air 3d, the re- turning water falling upon that which is rising. The height of the jet is increased by having the orifi- ces very small, in comparison with the conducting tube; piercing them in a very thin wall, and inclining the jet a little, thus avoiding the effect of the returning water. 283. Velocities of streams. The velocity of streams varies very much. The slower class of rivers have a velocity of less than three feet per second, and the more rapid, as much as six feet per second, which gives re- spectively about two and four miles per hour. The velocities vary in different parts of the same transverse section of a stream, for the air upon the surface of the water, as well also as the solid bottom of the stream, has a certain effect in retarding the current. The velocity is found to be greatest in the middle, where the water is deepest, fig. 178, somewhere in m, below the surface ; then it decreases with the depth, towards the sides, being least at a and b. 284. Stream measurers. To measure the velocities of streams, various means are employed. The most simple is a glass bottle "What is said of viscous liquids? What is said of serum ? What is said of the circulation of blood. 282. What is said of jets of water ? Why does not the jet rise to the theoretical height ? How ma} 7 the height be increased ? 283. What is said of the velocities of streams 1 Where is the velocity greatest ? WATER-WHEELS. 185 filled with water, sunk just below the level of the current, and provided at the cork with a small flag, that stands above the surface. Or a wheel may be used, furnished with float-boards, placed in the stream and immersed, so that the whole surface of the boards are covered with water. The friction in this case is very small, so that the wheel revolves with very nearly the velocity of the stream. By observing the number of revolutions of the wheel in a given time, we can ascertain the rapidity of the current. To ascertain the velocity at different depths, the simplest instrument is Pictot's tube : it consists of a tube bent nearly at right angles, terminated by a funnel-shaped mouth, the upper part of the tube, above water, is of glass. In order to observe with this instrument, it is placed in the direction of the stream, at the depth we wish to ascertain its velocity. If the water was still, the height within and without the tube would be equal, but if it is in motion, the water will rise in the tube to counterbalance the force with which the water is impelled, (the impulse of the stream,) the column of water in the tube rising higher as the velocity of the stream is greater. 285. Water-wheels. The motive power of water is of exten- sive practical importance, from the number of machines driven by water-wheels. The over-shot wheel. Fig. 179 is used when the supply of water is moderate and variable. 179 The water is delivered at the top of the wheel, which may move with the hands of a watch, as in the figure, or the reverse. It is furnished with buckets of such a shape as to retain as much of the water as possible, until they reach the lowest practica- ble point on the wheel, and none after' that point. In this wheel the effect is produced both by impact, and by the weight of the water. The under-shot wheel. Fig. 180 receives its impulse at the bottom; it is furnished with float-boards instead of buckets. If they are placed at right angles to the rim of the wheel, they may turn either way. When the wheel is required to 284. "What are stream measurers? What is the most simple ? De- scribe other forms of stream measurers ? What is Pictot's tube? Describe its mode of action. 285. Describe the over-shot wheel. How is the effect produced in this wheel ? 186 HYDROSTATICS. turn only in one direction, the float-boards are placed as in the * 180 figure, so as to represent an acute angle towards the cur- rent, the water acts then partly by its weight. The breast wheel. Fig. 181 is moved both by the weight and momentum of the .water. It is furnished with buckets, formed to retain the : water as long as possible. The : breast-wheel is the form most generally adopted, as it allows of a larger diameter for a given fall than the overshot-wheel, with more economy of power than the undershot-wheel. According as the water is received above or below half-past nine, or half-past three on the watch, the wheel is called a high or low breast wheel. 181 A more distinct idea of these different water wheels may, per- haps, be gained by illustration from the face of a watch. In the breast .wheel, the water may be received, [(according to the desired motion of [the wheel,) between eight and "eleven o'clock, or between one and four o'clock. In the over-shot wheel, the motion usually is the same in direction as the hands of the watch. The water is received as near the summit as possible, and the buckets are so shaped as to retain the water to the lowest practicable point in its descent, corresponding to about five on the face of the watch. The turbine is a horizontal water-wheel, revolving entirely submerged, and is, of all forms of water-wheel, the most ener- getic and economical of power. The water descends in the ver- tical axis of the wheel, and is delivered through a great number of curved buckets, so arranged, that the escaping water is nearly a tangent to the diameter of the wheel. It runs in a stationary What is said of the under shot wheel ? What is said of the float- boards in this wheel ? What is said of the breast-wheel ? Illustrate the operation of these wheels from the face of a watch. What is the turbine wheel ? LIQUIDS IN CAPILLARY TUBES. 187 case, also provided with cells, curved in the opposite direction, through and against which the escaping water acts. Over 80 parts in a hundred of the whole power are saved by this wheel. Capillarity. 286. Capillary phenomena. The laws of the equilibrium of liquids of which we have treated, do not obtain unless the vessels are of considerable diameter ; when the vessels are very small, the laws of equilibrium are entirely different. For example : when we plunge a tube of very small diameter, open at both ends, in a liquid, if the tube becomes wet, the liquid is elevated within and upon the outside, and maintained at a height more considerable as the diameter of the tube is smaller, fig. 182. If the tube does not become wet, there will be a depression, greater as the tube is of smaller diameter, fig. 183. 182 183 287. Laws of the rise and fall of liquids in capillary tubes. It has been demonstrated by M. Gay Lussac, that the elevation and depression of liquids in capillary tubes is in accordance with the three following laws : 1st. There is an elevation when the liquid wets the tube, and a depression when it does not. 2d. The elevation and depression are in an inverse ratio to the diameters of the tubes when the diameters do not exceed 2 or 3 m. m. (-07874, to -11811 inches.) 3d. The elevation and depression vary with the nature of the liquid and the temperature, and is independent of the substance of the tubes and thickness of their walls. 288. Cause of capillarity. Since capillary phenomena take place as well in the atmosphere as in a vacuum, it is plain that the air does not influence their production, but that they are due to the 286. What is said of the equilibrium of fluids in very small ves- sels? 287. What are the laws of the ascension and depression of liquids in capillary tubes ? 288. What is the cause of capillarity ? 188 CAPILLAKITY. molecular attraction of the liquid on itself, and on the substance of the solid body ; actions which are manifested only at very small distances. 289. Cause of the curve of liquid surfaces by the contact of solids. The form of the surface of a liquid in contact with a solid, depends upon the relation which exists between the at- traction of the solid for the liquid, and the liquid particles for each other. Any liquid particle, as m, fig. 185, is submitted to three forces, viz : 1st, of gravity, which acts in the direction mp, 2d, the attraction of the liquid particles, acting in the direction m F, and 3d, the attraction of the solid acting in the direction n m ; according to their intensities the resultants of these forces may take three directions. If the attraction of the liquid particles is double that of the solid for the liquid, the surface of the liquid will be perpendicular to the resultant m R, fig. 184, and it will remain level. If the attraction of the liquid particles is less than double that of the solid for the liquid, the resultant will have the direction m It, fig. 185, and the 184 185 186 surface will be concave ; while if the attraction of the liquid par- ticles is greater than double of the solid for the liquid, the resultant will be in the line m R, fig. 186, and the surface will be convex. 290. Influence of the curve on capillary phenomena. The curved surfaces in capillary spaces are called, respectively, con- cave and convex meniscuses ; the ascent or depression of liquids in such spaces, are owing to these forms. Let a ~b c d, fig. 187, represent a concave meniscus, the particles of which are sus- tained in equilibrium by the forces before mentioned ; these par- 289. Upon what does the form of the surface of a liquid in con- tact with a solid depend 1 What is the resultant when the attrac- tion of the liquid particles is double that of the solid for the liquid ? When the attraction of the liquid particles is less than double? When the attraction of the liquid particles is greater than double ? 290. What are the curved surfaces in capillary spaces called 1 LIQUIDS IN CAPILLARY TUBES. 189 tides do not exercise any pressure on those below them, conse- quently no layer in the interior of the tube exerts a pressure equal to one without. But because of the condition of equili- brium in fluids, the liquid will be raised by molecular attraction, 187 188 until the pressure exerted in the interior d a n m, is equal to the pressure exerted exteriorly, by any column o p, which has its base on the same layer. Where as in fig. 188, the meniscus is convex, the equilibrium still exists, for the liquid molecules, being repelled from the ca- pillary walls, do not attract those below them, and therefore the pressure on any layer n m, in the interior of the tube, is less than if the space g h i k was filled, for the molecular forces are much more intense than gravity ; therefore the liquid falls in the tube, until the pressure on the base n m, is the same as that on any point ^, of the layer. 291. Law of the elevation and depression of liquids in capil- lary tubes. It has been demonstrated by Laplace, that the at- traction of the meniscus is equal to a constant co-efficient, de- pending on the nature of the liquid and that of the tube. In a cylindrical tube with a circular base, experience has demon- strated, that the concave surface is sensibly a hemisphere, with a radius equal to half the diameter of the tube. The attraction of the meniscus is, therefore, in inverse ratio with the radius, or the diameter of the tube, and in consequence, the liquid column will be raised by this force to a height which varies according to its intensity. The length of the liquid column contained in the tube is a little less than calculation (according to the above rule) would indicate, because of the weight of the meniscus, but this error is very small, less as the capillarity of the tube is less, the What is said of the action of the concave meniscus ? What is said of the action of the convex meniscus? 291. To what is the attraction of tfife meniscus equal ? What is the form of the con- cave surface in a cylindrical tube ? 190 CAPILLARITY. influence of the weight of the meniscus decreasing rapidly as the diameter of the bore diminishes. The height of the liquid in the tube is, therefore, never absolutely in inverse ratio to the diam- eter, but the law is nearly exact when we add to the height one- sixth of the diameter of the tube, which is the correction re- quired for the weight of the meniscus. Corrections for this error, being thus made, the law would be correct, had the meniscus an accurately spherical surface, but this does not obtain, but when the diameter is very small (2 or 3 m. m., 07874, or '11811 inches) the surface in general ceases to be truly spherical, and the ascent or depression depends on the curve of the surface, which varies much more rapidly than the diameter of the tube. 292. Depression of mercury in capillary tubes. The rapidity in which capillarity diminishes, in tubes of great diameter, is seen in the following table. TABLE OF DEPRESSIONS OF MERCURY IN CAPILLARY TUBES. Diameter of tube. Depressions in m. m. according to Laplace. According to Young. According to Jaoby. According to Cavendish. 20' m. m. 0-038 0-031 0-031 15- 0-137 0-111 0-118 0-131 ID- 0-445 0-402 0-406 0-406 S' 0-712 0-669 0-673 0-820 6' 1-171 1-139 1-134 1-377 5' 1-534 1-510 1-513 1-735 4- 2-068 2-063 2-066 2-187 3- 2-918 2-986 2-988 3-054 2-5 3-566 2- " 4-454 4-887 4-888 4-472 The numbers contained in the first column have been calcu- lated by M. Bouvard, according to the formula of Laplace ; those of the two last columns have been obtained directly by experi- ment. 293. Ascent of liquids in capillary tubes. For all liquids, the ascent or depression in capillary tubes, decreases according to "What is the relation between the attraction of the meniscus and the diameter of the tube ? Why is the length of the column in a tube less than that indicated by theory? What is the correction re- quired for the weight of the meniscus? Has the meniscus always an accurately spherical surface ? 292. Mention some figures from the table showing the rapidity in which capillarity diminishes in tubes of great diameter. 293. What is said of the ascent f liquids in ca- pillary tubes ? LAWS OF THE EQUILIBRIA! OP FLUIDS. 191 analogous laws. If the tubes are very small, the heights aug- mented with one-sixth of their diameter, are inversely as the di- ameters. If the tubes are very large, we may ascertain very accurately the heights to which liquids would rise by very com- plicated calculations, or we may obtain, approximately, their ca- pillary effects, in supposing them proportional to the depression mercury undergoes in tubes of the same diameter. For the same tube, and for the same liquid, the capillarity depends much on the temperature, decreasing more rapidly than the density. According to M. Gay Lussac, the elevation of water in a capil- lary tube of 1 m. m., (-03937 in.) is 30m. m., (-11811 in.) and dif- ferent liquids elevate themselves, in the same tubes, to heights, which are in the following relation. Water, 100- Saturated solution of chlorid of ammonium, 102*7 " " sulphate of potash, 95-7 " " " " copper, 84- Nitric acid, 75' Hydrochloric acid, 70 -1 Alcohol, 40-8 Oil of lavender, 37*5 294. Laws of the equilibrium of liquids between parallel or inclined laminae. Phenomena analogous to those presented in capillary tubes, may be observed when two laminae, plunged in a liquid, are brought near to each other. If the laminae are made wet, the liquid elevated between them, is terminated by a cylindrical surface ; if not moistened, the liquid is depressed, and is terminated by a convex surface ; and it is observed that 1st. A liquid is regularly elevated or depressed between two laminae, inversely as the interval which separates them. 2id. That the height of the ascension or depression for a given interval, is half that wJiich would take place in a tube having a diameter equal to that of the interval. When we plunge two inclined laminae (with their line of con- tact in a vertical position) in a liquid which wets them, a concave surface may be observed between them, fig. 189, the liquid rising toward the upper point of their line of contact. The Mention the elevation of different liquids in tubes of 1 mille- metre diameter. 294. What is said of the equilibrium of liquids between two laminae? What are the laws which have been ob- served of this phenomena ? What is the form of the curve a liquid takes between two laminae ? 192 CAPILLARITY. surface of the liquid takes the form of the curve known in geom- 189 etry, under the name of the equilateral hyperbole ; this curve is produced by capillarity. 295. Movements of drops of liquid between laminae. When a drop of liquid is contained in a conical tube, or between two laminae having their lines of contact horizontal, the liquid, if it wets the tube or laminae, is terminated by two concave surfaces, fig. 190, and the liquid is precipitated towards the summit of the angle ; because the radius of the curve 190 being smaller at the point m', than at m, the pressure **' at the point m' will be greater than at the point m. If the liquid does not wet the surrounding body, the drop terminating in a convex meniscus, fig. 191, elongates itself toward the summit of the angle, be- cause the radius of the curve, being smaller at the point m', than at the point m, the pressure at m will be greater than at m'. 296. Attraction and repulsion of light floating bodies. The attraction and repulsion which we observe between 191 light bodies floating on the surface of liquids, is due to capillarity. The floating bodies are drawn near to each other either when they are or are not moistened, and repelled if the liquid wets only one of them. For, supposing we have two parallel vertical laminae at a capillary distance, plunged in a liquid which \vets them, the exterior and interior surfaces of the same laminae, sit- uated at the same height, and plunged in the same liquid, are 295. What is said of a drop of liquid placed between two laminae, as in fig. 190, that it wets 1 What is the result when the drop of liquid does not wet the laminae ? 296. What is said of the attrac- tion and repulsion of light bodies floating on the surface of liquids ? ENDOSMO&E. 193 pressed; and as all the points of the interior surfaces of the laminae which are not wetted by the liquid, are pressed from without inter- nally, with a force as much greater as the points are more elevated, it is plain, that if the laminae are movable, they would be drawn towards one another. If the two laminae were not wetted by the liquid, then any two corresponding points on the two faces of the laminae, situated below the interior level of the liquid, are pressed equally, while a point that is wetted by the liquid only externally, experiences a pressure which, not being destroyed, would make the laminae, if movable, draw near each other. Lastly, in that case, where one of the laminae was wetted and the other not, the interior liquid is depressed against one and elevated against the other, and by a reasoning similar to that already em- ployed, we may see that the parts of the laminae which are covered on both sides by the liquid, are equally pressed from without and from within, but that in the upper part of the first, and the lower part of the second, the pressures are exerted from within outwards, and in consequence, the laminae must be repelled. 297. Effects produced by capillarity. A needle covered with grease, placed lightly upon the water, floats, because, not being moistened by the liquid, there is produced a depression in which it is supported. So, many insects walk and skim on the surface of water without plunging in. Oil and other burning-fluids in lamps, and the melted tallow and wax of candles, are supplied to their flames by means of the capillarity of their wicks, so there is an absorption of liquids in wood, in sponge, in cloth, and in all bodies that possess sensible pores. Endosmose. 298. Endosmose. Closely allied to capillarity are the phenomena of endosmose, which have been very accurately studied, particu- larly by M. Dutrochet, who brought forward his researches, in the year 1827 ; and by Prof. Graham, more lately. When two liquids capable of mixing with each other, are separated by a membra- nous partition or wall, two currents become established, proceed- ing, one from within outwards, called exosmose, (from ex, outward, Describe the action when two laminae are wetted by the liquid in which they are placed. What is the action when the laminae are not wetted by the liquid 1 What is the action when one of the laminae is wetted and the other is not? 297. Mention some of the effects produced by capillarity ? 298. What is said of endosmose, and who have been its chief investigators ? 194 ENDOSMOSE. and osmos, impulsion,) and another in the contrary direction, called endosmose, (from endon, inward, and osmos.} 299. Endosometer. The existence and rapidity of these cur- rents is ascertained by the endosometer, an instrument which may be thus constructed. To a membranous pouch or bladder is fit- ted, hermetically, a glass tube as in fig. 192. 192 The jar or bladder, and part of the tube, is filled with a dense liquid, as a strong solution of gum or sugar, and placed in a tall cylindrical jar, which is then filled with distilled water, until it stands exactly at the level of the fluid in the tube. For very exact experiments^ this level is constantly maintained by the addi- tion to, or the removal of the water in tne outer jar. After a time, gum will be found in the outer vessel, a current from without, inwards, also taking place. If we wish to determine more ac- curately the actual as well as the com- parative flow of different liquids, we may use an apparatus constructed as follows. Over the open mouth of a ^bell jar, of a few ounces' capacity, is ; placed a plate of perforated zinc, to "support firmly a piece of fresh ox- bladder, which is securely tied over it. To the upper aperture is at- tached a graduated tube, open at both ends, the capacity of whose interior bears a certain definite relation, as _l o th, to that of the lower opening of the bell jar ; so that a rise or fall in the tube as of 100 m. m. (3*937 in.) indicates the entrance or removal of a stratum of liquid, 1 m. m. (0'03937 in.) thickness over the whole surface. 300. Necessary conditions. According to M. Dutrochet, in "What is the result when two liquids capable of mixing with each other are separated by a membranous partition 1 299. What is the endosometer ? How may it be constructed ? Mention another form. How are endosometers set in operation ? 300. What are the necessary conditions for producing endosmotic phenomena? 301. What is said of materials for septum ? What is said of inorganic ma- terials ] What of chemical action ? ORGANIC SOLUTIONS. 195 order successfully to produce the phenomena of endosmose, it is necessary, 1st. That the liquids ~be susceptible of mixing. 2d. That they are of different densities. 3d. That the membrane or wall (septum} which separates them is permeable to one or both liquids. 301. Materials for septum. All thin animal and vegetable membranes, thin plates of burnt clay, slate, marble, pipe-clay, &c., produce endosmotic effects in a more or less notable degree. Of inorganic materials, those which contain most silicic acid areless permeable. A chemical action on the materials of the septum, invariably takes place, (excepting with alcohol and cane sugar solutions,) whether it is formed of bladder or of earthenware. Where the partition is not susceptible of being acted upon, the endosmotic action is very slight. 302. Direction of the current. The endosmose current is in general directed towards the more dense liquid, but alcohol and ether are exceptions ; they acting as denser liquids, although lighter than water ; so also as acids are more or less diluted, there is endosmose towards the acid or towards the water. The excess in the quantity of the liquid which passes into the endosometer, is proportional to the surface of the membrane, and to the dif- ferent heights to which the liquids mount in capillary spaces, the elevation taking place from that side of the liquid which has least capillary action. 303. Organic solutions. Neutral organic substances, such as gum-arabic, urea and gelatine, produce but little endosmotic action. Of all vegetable substances, sugar solution ; and albumen among animal bodies ; are those which, with equal density, possess the greatest power of endosmose. The figures attached to the follow- ing substances, indicate the proportional height to which the liquids rose when the endosometer, being filled successively with solutions of them, of the same density, was placed in pure water : gelatine 3, gum 5, sugar 11, albumen 12. 304. Inorganic solutions. Neutral salts do not possess any peculiar power of endosmose, but diffuse themselves with nearly 302. What is generally the direction of the endosmose current ? What is the excess of the quantity of liquid which passes into the en- dosometer proportional to ? 303. What is said of neutral organic solutions? What vegetable and animal substances have the greatest power of endosmose 1 Mention the proportional height to which the liquids rose in the tube when the endosometer was filled with gelatine, gum, sugar and albumen. 196 ENDOSMOS& the same rapidity as if no porous partition was used. Alkaline solutions greatly accelerate endosmose. This may be observed, even in solutions which contain but 1 part of the alkaline salt in 1000 of water. In moderately dilute solutions (containing not more than 2 per cent, of the salt) the action is most rapid. 305. Theories of endosmose. Many theories have been pro- posed to account for these phenomena : such as that endosmose was due to an unequal viscosity of the two liquids ; to currents of electricity passing in the direction of the endosmose ; to the un- equal permeability of the membrane for the two liquids, or, that the phenomenon was due to capillary action, joined to the af- finity of the two liquids. Very probably endosmose depends on the same forces that produce capillarity, but obviously they are not the only forces which exert influence, for we find that heat, which always diminishes capillarity, augments the strength of the en- dosmose. 306. Endosmose of gases. There is endosmose between gases, as between liquids ; if we connect two vessels containing dif- ferent gases, having a dry membrane between them, the gases will gradually mix, equal currents being established in both ; but if the membrane is moist, unequal currents, (that, is endos- mose,) are formed. So, a soap bubble placed in a jar of carbonic acid, will, in a little time, burst, owing to the increase of volume caused by endosmose. 307. Absorption of gases. All bodies possessed of sensible pores have, in a more or less considerable degree, the property of absorbing gases. Box-wood charcoal possesses this property in the most remarkable degree, 1 volume of it absorbing 90 volumes ammonia, 81 volumes hydro-sulphuric acid, 32 volumes of car- bonic acid, 9 volumes oxygen, &c. If the charcoal is moist- ened, its absorbing power is diminished one-half, which proves that this power is due to porosity, and in consequence to capillary action ; other kinds of charcoal have less and very varying absorp- tive powers ; those which are very porous and extremely com- 304. What is said of neutral salts? What of alkaline solutions? What of moderately dilute solutions ? 305. Mention some of the the- ories that have been proposed to account for endosmose phenomena. Upon what probably does endosmose depend ? 306. What is said of the endosmose of gases? How may it be illustrated ? 307. What is said of the absorptive powers of box-wood charcoal # What is the effect of moistening the charcoal ? What is said of other charcoals and their porosity ? PHENOMENA OF ABSORPTION. 197 pact, possessing this property in a less degree than others. Po- rosity, however, although an essential condition of the absorp- tion of gases, must be confined within certain limits. 308. Phenomena of absorption in plants and animals. In Physiology we distinguish absorption from imbibition, applying the first term to those phenomena where there is a penetration of a substance (liquid or gaseous) in the tissues of a living being, while imbibition is the penetration of a gaseous substance into a porous body deprived of life, either organic or inorganic. In all vegetable life, absorption is taking place from all parts of the plant, but chiefly from the spongioles which terminate the roots, and from the leaves. These organs absorb water, carbonic acid, and ammonia, whose constituents are the necessary food of the plant. Capillarity only elevates the liquid in the lower part for the plant, it does not produce the upward current ; the liquid, with the salts it contains, rises by the combined agencies of capillarity and endos- mose, assisted by the exhalations from the leaves, which produce a diminished pressure in the upper part of the pores of the plant. The inferior animals are formed of cells, and they are supplied with food by imbibition and endosmose. In the superior animals, there is absorption, as is shown by the fact, that madder, taken by certain animals, penetrates their bones, coloring them red. A substance is more easily absorbed, provided that it wets the membrane. Fats which do not wet are not absorbed, but it has been shown by M. Bernard, that if they are formed into an emulsion with pancreatic sugar, that absorption takes place quickly. So Dr. Leze has observed that cod-liver oil (used as a medicine) acquires more energy, when made into an emulsion, because it is more com- pletely absorbed. As with endosmose, it is observed that heat favors absorption, so also after an abundant transpiration or a bleeding, absorption is augmented. 808. "What is the distinction made between absorption and imbi- bition ? What is said of the absorption in vegetable forms ? Men- tion the causes which produce the ascent of liquids in the pores of plants. "What is said of the inferior animals? What is said of the absorbability of gases, and emulsions, of cod-liver oil 1 198 GASES. Gases. 309. Gases are aeriform fluids, elastic, transparent, usually colerless and invisible. The force of cohesion has no activity in gases, whose molecules are self-repellent in consequence of the action of heat. Tension and elastic force, are expressions for the repulsive power of gases, specific in each case, and modified by varying conditions of temperature and atmospheric pressure. 310. Gases and vapors. triform, or elastic bodies, are di- vided into two groups or classes, called respectively, (1.) Gases, and (2.) Vapors. In permanent gases, the elasticity or tension is such that they sustain all differences of temperature and pressure with only corresponding changes in bulk or volume. The gases now considered permanent, are the elements, oxygen, nitrogen, and hydrogen, and the compounds, oxyd of carbon and binoxyd of nitrogen. Non-permanent gases. In another large class of gases, chiefly compounds, cold and pressure, alone or united, are capable of overcoming the force of repulsion, and reducing them to the liquid state. Such are chlorine, ammonia, cyanogen, and sulphurous acid. Vapors are formed by the action of heat upon liquids, and they retain the elastic or aeriform condition, only so long as the temperature essential for their existence is maintained. It is as- sumed that the aeriform state of bodies is, in all cases, due to the repulsive power given to their molecules by heat, and hence it follows, that by a sufficient degree of cold and pressure, all gases would be reduced to the fluid, or even to the solid condition. But in the present state of our knowledge, this truth has been only partially realized. 311. Gases, simple and compound. The number of gases we are now acquainted with is thirty -four, of which four are simple, viz : oxygen, nitrogen, hydrogen, and chlorine. Seven gases are found free in nature, viz : oxygen, nitrogen, carbonic acid, light carburetted hydrogen, heavy carburetted hydrogen, sulphurous acid, and ammonia. 312. The atmospheric air, its composition The most common of all the elastic fluids is atmospheric air, which envelopes the earth in an aerial ocean, over forty-five miles in depth. Air is a mechanical mixture of the two simple elements, nitrogen and ox- 309. What are gases ? What is said of the force of cohesion ? What of tension? 310. What is said of permanent gases? What of non-permanent gases? What of vapors? 311. What is said of simple and compound gasea ? INEUTIA OF AIR. 199 ygen, in the proportion, by volume, of 20-80 volumes of oxygen to V9-20 volumes of nitrogen. By weight it is composed of 23'01 parts of oxygen, and *T6'99 parts of nitrogen; besides these, it contains small proportions of carbonic acid, carburetted hydrogen, &c., so that in 10,000 volumes of air, there are Nitrogen, 7910 Oxygen, 2091 Carbonic acid, .... 4 Carburetted hydrogen, ... 4 Ammonia, trace. 10,000 313. Atmospheric air the type of permanent gases. Nearly all of the mechanical properties of the air apply without modifi- cation to all the permanently elastic fluids. But some of these when applied to vapors, require to be restricted and modified by various circumstances. Air possesses, in common with liquids, the characteristic properties of fluids, such as the free motion of its particles among each other, the power of trans- mitting pressure in all directions, &c., while it is distinguished from solids and liquids by its great compressibility and elasticity. 314. Impenetrability of air. Air is impenetrable. This may be shown by inverting a hollow vessel, as a tumbler, upon the sur- face of water ; when pressed downward the water will not rise and fill the tumbler, because of the impenetrability of the air. The di- ving-bell depends on this quality of air : it consists of a large bell- shaped vessel, sunk by means of weights into the sea, with its mouth downwards. Notwithstanding the open mouth, and enor- mous pressure of the sea, the water is excluded from the bell, because of the air contained within. 315. Inertia of air. Wind is only air in motion. If the air had no inertia, it would require no force to impart motion to it, nor could it acquire momentum. We know that the force en- countered by a body moving through the air, (that is, displacing the air,) is in proportion to the surface exposed, and the velocity with which it is moving, (120.) The sailing of ships, the direction of balloons, the wind-mill, 312. What is the composition of atmospheric air? Mention the proportion of its constituents in 10,000 parts. 313. What is said of the similarity of the air to all permanent gases ? 311. How may the impenetrability of air be shown? 315. What is said of the in- ertia of air 1 200 GASES. and the frightful ravages of the tornado, are all familiar examples of the power of moving air, and consequently proofs of the in- ertia of air. 316. Expansive force of air. The molecular forces hold to- gether the particles of solids in fixed positions, while they allow liquid molecules liberty to move in all directions. In gases, the molecular forces are completely subordinate to the repulsion im- parted by heat. Under normal conditions, the atmosphere is in a state of equilibrium between the earth's attraction, and its own expansive force. If we dis- turb this condition of equili- brium, we see evidence of the exercise of the power of expan- sion. In fig. 193, a moist blad- der, partly filled with air, is sub- jected to a partial vacuum under the air-bell. As the pressure in the bell is diminished by work- ing the air-pump, the portion of confined air expands, and dis- tends the flaccid bladder, which again contracts as soon as the equilibrium of pressure is restored by opening a communication with the external air. 317. Weight of the air. If a vessel whose capacity is 100 cubic inches, be exhausted of air and weighed, and after filling it with dry air at the ordinary temperature and pressure, it is weighed again, it will be found that its weight is 31*011 grains more than at first; that is, 100 cubic inches of air weigh 31 'Oil grains. Air is the standard of comparison in density for all gases and vapors. It is obvious that if we fill the globe, fig. 194, or any vessel of known capacity with any other gas than atmospheric air, we could ascertain the weight of a certain quantity of such gas, and by comparing this weight with an equal bulk of air, ascertain its density. Careful at- tention to a variety of circumstances (the more prominent of which 316. What is said of the expansive force of air ? How may it be shown 1 317. What is said of the weight of the air? How do we determine the density of the other gases? ATMOSPHERIC PRESSURE. 201 are the temperature and atmospheric pressure) are necessary, in order to insure correct results. 194 318. Limits of the atmosphere. The atmosphere extends upward to a great height. Considering it as made up of successive layers or strata, since all of them are subject to gravitation, the lower layers must be compressed by those above them; consequently, the nearer we approach the earth, the more dense we find the air, and the higher we ascend, the more rarefied it is. As the air possesses a very great expansive force, we might suppose it would ex- pand indefinitely toward the planetary spaces. But the expansive force of the air decreases as it is more dilated, and again it is diminished by the lower tempera- ture, in the more elevated regions of space, so that an equilibrium is formed between the expansive force and gravity, which draws the particles toward the centre of the earth. Hence there is a limit to the atmosphere. From the weight of the atmos- phere, its decrease of density as we ascend, and from certain optical phenomena, its height has been estimated to be about forty- five miles. 319. Atmospheric pressure. That the atmosphere exercises a measurable pressure upon the earth, is well de- monstrated by the glass vessel, fig. 195. The upper part of this vessel is her- metically closed by a bladder ; its lower edge rests upon the well ground plate of an air-pump. As the air is gradually exhausted, the surface of the bladder will become more and more depressed, xintil, finally, the membrane bursts, with a sharp report, owing to the pressure! of the atmosphere upon it. The above experiment only demon- strates the downward pressure of the 195 818. What is said of the limits of the atmosphere? Why does not the air expand indefinitely ? What is the height of the atmoa- r^.arP ? 9* 202 GASES. atmosphere. By the Madgeburgh hemispheres, it may be shown that the atmospheric pressure is exerted in all directions. 196 This apparatus is composed of two hol- low hemispheres of brass, fig. 196, whose edges, accurately fitting, are well greased ; one of the hemispheres is furnished with a stop-cock, with which connection is made with an air-pump. Upon placing them to- gether upon the air-pump, and exhausting the air, it will be found that the hem- ispheres can no longer be separated, no matter in what position they may be held ; proving that the atmospheric pres- sure which keeps the hemispheres to- gether is exerted in all directions. Rings adapted to each hemisphere, enable two persons to test their strength against the atmospheric pressure. 320. Measure of the atmospheric pressure. Although we have demonstrated the atmospheric pressure in the two preceding exper- iments, yet we have not estimated its amount ; this was first done by Torricelli, a disciple of Galileo, in 1643. To repeat his experi- ment, a tube of glass closed at one end is selected, A , fig. 197, about 32 inches in length. Holding the tube mouth upward, it is completely filled with mercury, and inverted, after closing the orifice with the thumb, with its lower end placed in a vessel con- taining mercury. The liquid column will, on removing the thumb, immediately fall some distance, and after several oscil- lations will come to rest at n, a height at the level of the sea, of about thirty inches above the level a c, of the mercury in the vessel. The space n B, above the mercury, is the most complete vacuum attainable by mechanical means, and is called the Torricellian vacuum. If, after having closed the mouth of the tube, we lift it out of the dish, we shall find that the weight of the column of mercury pressing against the finger is very con- siderable. When we place the tube in the vessel of mercury, we have this same force exerted, the column of mercury tending to flow out of the tube, and another force, the weight and pres- 319, How may it be shown that the atmosphere exercises a pressure upon the earth ? Describe the Madgeburgh hemispheres ? What may be proved by them ? 320. What was Torricelli's exper- iment ? What is the Torricellian vacuum ? PRESSURE UPON THE HUMAN BODY. 203 sure of the atmosphere, tending to push the mercury up in the tube. The length of the mercurial column, it is evident, is in proportion to the atmospheric pressure, and 197 under ordinary circumstances, as we have seen, the atmospheric pressure is equivalent to a column of mercury thirty inches in height We may now easily estimate the pressure on any given surface, as, for example, a square inch. If we should take a tube whose base is a square inch, and repeat the above experi- ment, the column a n would, as before, be sustained at a height of thirty inches ; but the weight of a column of mercury thirty inches in height and one inch square, is very nearly fifteen Ibs, ; therefore the atmospheric pressure on a square inch is fifteen Ibs. If the tube' were filled with a lighter liquid than mercury, a proportionally longer column would be sustained by the pressure of the at- mosphere: the length of the column being in- versely as the densities of the two fluids. If water, which is about 13'5 times lighter than mer- cury, was used, the column of water sustained would be 13'5 times as long as the mercurial column, or about thirty-four feet. 321. Pressure upon the human body. The air, as we have seen, transmits pressure equally in all directions ; consequently every object exposed to the atmosphere at sea level, is pressed upon all parts of its surface, with a force amounting to fifteen Ibs. to the square inch. The sur- face of a human body of average size, measures about 2000 square inches; such a body sustains, therefore, a pressure of 30,000 Ibs., or fifteen tons. It would seem, at first, that such a pressure would crush the individual subjected to it, but this great force is entirely neutralized, because the atmospheric pressure is equal in all directions. All the cavities and pores of the body are filled with counteracting air, which presses with an equal force in every direction. How may the pressure on any given surface be estimated ? What is the atmospheric pressure in a square inch of surface ? What would be the effect if a lighter liquid than mercury was used 1 821. What is the pressure upon the human body ? Why does not this pressure crush individuals subjected to it . 204 ttASES, 322. Construction of barometers. Barometer is the name given to Torricelli's tube. This instrument has different forms, according to the use for which it is designed. There are, how- ever, certain conditions to be fulfilled hi the construction of ba- rometers, whatever may be their form. 1st. It is necessary that the mercury be perfectly pure and free from oxyd, otherwise it adheres to the glass ; again, by im- purities, its density is changed, and the height of the column in the barometer is greater or less than it should be, 2d. It is necessary that there be a perfect vacuum above the surface of the mercury in the tube ; for if there be a little air, or vapor, as of water, the elasticity of these will continually depress the mercurial column, preventing its rising to the true height. To obtain a perfect vacuum, a small portion of pure mercury is boiled in the barometer tube, and when cooled, another portion of mercury is added, and again boiled, and so on, until the tube is full; by this means the air and moisture which adhered to the walls of the tube are driven out, completely. The boiling must not be too long continued, otherwise a portion of oxyd will be formed, which will dissolve in the mercury and alter its density. The tube being filled, we invert it in a vessel of pure mercury. In order to deter- mine whether there is not some air or moisture in the tube, we in- cline the tube quickly ; if the mercury gives a dry metallic sound when striking the summit of the tube, it is a proof of their absence, while, if they be present, the sound is deadened. 323. Pascal's experiments. The experiment of Torricelli ex- cited the greatest sensation throughout the scientific world, and the explanation he gave of it was generally rejected. Pascal, who flourished at that time, perceived its truth, and pro- posed to subject the experiment to a test which must put an end to all farther dispute. " If," said Pascal, " it be really the weight of the atmosphere under which we live, that supports the column of mercury in Torricelli's tube, we shall find by transporting this tube to a loftier point in the atmosphere, that in proportion as we leave below 322. What is a barometer 1 What are the necessary conditions to be fulfilled in the construction of barometers ? How is a barom- eter filled with mercury ? How may it be determined whether the interior of the tube is free from air and moisture ? 323. What is said of Pascal's experiment? How was it conducted? THE PRINCIPLE OF THE BAROMETER. 205 more and more of the air, there will be a less column of mercury sustained in the tube." Pascal therefore carried a Torricelli tube to the top of a lofty mountain, called the Puy-de-Dome, in Auvergne, (central France.) It was found that the column gradually dimin- ished in height as the elevation to which the instrument was carried increased. He repeated this experiment at Rouen, (France,) in 1646, with a tube of water, and found that the column was sustained at a height of about thirty- four feet, or 13 '5 times greater than the height of the column of mercury. 324. Apparatus illustrating the principle of the barometer. By means of the air-pump and the apparatus, fig. 198, the prin- ciple of the barometer is beautifully shown. The apparatus consists of a large bell glass, R, with two syphon barometer tubes attached. One of them, B, has its cistern within the bell. The other ba. rometer, whose cistern is without the bell, communicates with its interior by the cur- ved tube 1 1'. When this apparatus is placed on the air-pump, and exhausted of air, the mercury in B falls in proportion to the vacuum produced, and rises in the tube Gl, in the same proportion. In B we see the effect of diminished pressure, as on a mountain or in a balloon ; in C the pres- sure of the external air caused the mer- cury in it to mount, forming a gauge of the exhaustion. When the air is allowed to enter, the mercury in the tubes re- sumes its former position. 325. Height of the barometric column at different elevations. The following table gives a comparative view of the height of mercury in the barometer at different elevations above the sea. 198 What is said of his experiment with a tube of water? 324. De- scribe the apparatus illustrating the principle of the barometer. 826. Mention the height of the barometer at the elevation of 5000 feet, of 10,000 feet, of 6 miles, &c. 206 GASES. At the level of the sea, the mercury stands at 31 inches, 5,000 feet above " " " " " 24 '797 " 10,000 " [height of Mi JEtna,] " " 15-000 " 15,000 " [height of Mt Blanc,] " " 16-941 " 3 miles " 15*000 " 6 " [above the top of the loftiest mountain,] 7 -500 " 9 " 3*750 " 15 1-875 326. Oisteni barometer. The cistern barometer is the most 199 simple form of this useful instrument. It consists of , a Torricelli's tube of glass, filled with mercury and plunged into a vessel containing the same metal ; this vessel or cistern is of various forms. That it may be transported easily, the cistern is di- vided into two compartments, m, n, fig. 199, the upper division is cemented to the tube, communicating with the atmosphere by the small hole a. The two com- partments are united by the narrow neck into which the lower part of the barometer tube enters, fit- ting closely, although not touching the walls ; leaving only so small a space, that capillarity will not allow the mercury to escape from the lower compartment when we incline the barometer. So that in whatever posi- tion we place it, no air can enter the lower end of the tube. This barometer is always fixed on a wooden sup- port, at the upper part of which is a graduated scale, whose zero is the level of the mercury in the cistern. The sliding scale i indicates the level of the mercury in the tube. There is attached to barometers also a slider, moving by the hand upon which is a vernier, by means of which we can distinguish very small va- riations. But the level of the mercury in the cistern varies as the column of mercury in the tube ascends or descends, for then a certain quantity of mercury passes from the cistern into the tube, or the reverse, so that the zero (the level) changing the graduation on the scale, does not indicate the true height of the barometer. 327. Fortin's barometer. This error is avoided in 326. What is said of the cistern barometer 1 shown in fig. 199. How is it mounted? Describe the form GAY LUSSAC'S BAROMETER. 207 the barometer of Fortin, which differs from the cistern barom- eters only in the cistern. Fig. 200, represents this cistern. The lower part is of deer-skin, and is elevated or de- 201 pressed by means of the screw, G, pressing the plate DB. At the upper wall of the cistern is fixed a small ivory needle, A, whose point corresponds exactly to the zero of the scale, graduated on the case. At each observation with this instrument, care is taken to make the level of the mercury in the cistern, corres- pond with this point, which is accomplished by turn- ing the screw up or down. This form of Barometer has been adopted by the Smithsonian Institution, and is made by Green, of N. Y. 328. Gay Lussac's barometer. Gay Lussac's syphon barometer, fig. 201, consists of two tubes of the same internal dimensions, united by a very capillary neck, both closed at their upper part, the air entering the cistern through the hole a. The large tubes being of the same interior diameter, the capillary action is mu- tually destroyed. The capillary tube is made small, so that when we turn the instrument over, it remains full, because of its capillarity. For meas- uring the height of the mercury, there are two scales, E and Z>, grad- uated in different directions, having their common zero at 0, on a line intermediate between the two mer- curial surfaces ; so that by adding the indications of these two scales, we have the difference in the level of the mercury in the two tubes. But a quick move- ment, transportation in a carriage or on horseback, may divide the mercurial column in the capillary tube, and thus allow the air to pass into the long arm, whereby the accuracy of the instrument would be destroyed. In order to obviate this inconvenience, M. Bunten has modified the instrument as represented in fig. 202. The long arm A drawn out to a point, enters into and is soldered to a larger tube, K, which is 327. Describe the cistern of Fortin's barometer. 328. "What is said of Gay Lussac's barometer ? How is the instrument graduated 1 208 attached to the capillary tube. With this arrangement, should bub- 202 bles of air even pass through the capillary tube, they can- not enter the long arm, but are retained in the top of K. These bubbles of air have no influence on the observations, A and may be driven out by simply heating the tube. 329. Wheel barometer. The wheel barometer is an instrument of no scientific value, but has a certain pop- ular interest as it purports to declare the state of the weather. The apparatus consists, fig. 203, of a dial plate attached to a syphon barometer having a small cylindrical cistern, upon whose surface rests a float ; this is attached to a silk string, which winds around a pulley, 0, and is terminated by the counterpoise P ; the axis of the pulley carries a needle, which rests upon the face of the dial plate. When the pressure of the atmosphere changes, the column rises or falls in the tube accordingly, and carries along 203 with it the float. The pulley turns and moves the needle to the words rain fair changeable, &c., which are de- signed to correspond to certain heights of the mer- curial column. 330. Causes of error. In order to obtain the true height of the mercury in a barometer, we must, after making the observation, determine by calculation the error caused by capillarity, and by the variations of density, caused by changes of temperature. 331. Correction for capillarity. When the barom- eter tube is of capillary diameter, the surface of the mercury in it becomes convex (290) and the depres- sion is greater by as much as the tube is more capil- lary. For correcting this error, it is necessary to know the diameter of the tube, and then by means of the table, (292,) ascertain the depression, which must al- ways be added to the observed height. 332. Correction for temperature. In all mercurial barometers, we must have regard to the temperature, for as heat expands mercury, it diminishes its density, and in consequence, under the same atmospheric pres sure the mercury would rise as much higher as the temperature was more elevated. Consequently baro- Whatis Bunten's improvement? 329. What is said of the barometer ? How are the movements of the mercurial column indi- cated ? 330. What are causes of error in making thermometric ob- servations? 331. What is said of the correction for capillarity ? ANEROID BAROMETER. 209 metric observations cannot be compared, unless they were taken at the same temperature, or are brought by calculation to the same. As it is entirely arbitrary what temperature shall be chosen, that of melting ice has generally been taken. A table showing the expansion and contraction of mercury at different temperatures may be found in the section upon heat. 333. Aneroid barometer. This instrument, invented by M. Vidi, is a barometer without mercury, and possesses the advan- tage over others of having a small 204 size, of being exceedingly porta- ble, and of giving sufficiently accu- rate indications for most purposes. It consists of a circular copper box, the cover of which is very thin, and which is hermetically sealed, after the air is exhausted from its interior. This is contained in a metal box, fig. 204, about four inches in diame- ter, and which has a dial plate like that of a watch. Variations in the pressure of the atmosphere, will cause the cover of the exhausted box to be more or less depressed. By means of a combination of levers and springs, the move- ments of the centre of this cover are communicated to a pointer which moves over the graduated plate. Fig. 205, shows the interior construction of this instrument. To the cover M, of the exhausted box, 205 are attached two uprights, S t which act upon a lever, P, by means of a pin which unites them. This lever, (P,} is at- tached to a bar, K, which moves freely on two pivots, placed at its extremities. A lever B, unites the bar K, to the plate A, which presses on two springs. By means of a spring, represented in the fig- ure, the rod E, in connection with A, communicates any movement to the bent lever H, which causes a metallic wire to uncoil itself 332. What is said of the correction for temperature ? 333. What is said of the aneroid barometer ? What does it consist of? Describe its interior construction. 210 GASES. from the axis 0, of the pointer, and which thus transmits any move- ment to it. 334. M. Bourdon's metallic barometer. M. Bourdon, of Paris, has invented a barometer which, with great simplicity of construction, has all the advantages of the aneroid. The essential part of the instrument, fig. 206, consist of a very thin and elas- 206 tic brass tube J., bent into the form of an arc of a circle. This tube, exhausted of air and her- metically closed, is attached on- ly at its centre, so that the ends are free to move. With a dimin- ished atmospheric pressure, the ends separate from each other. If the atmospheric pressure in- creases, the ends come nearer together. By means of the metallic wires^ &, Z>, and the spring, c, these movements of the ends of the tube are commu- nicated to a needle moving over a graduated plate. The same principle Bourdon has applied to the construction of manometers for locomotives and other steam boilers, and they are now extensively used. 335. Variations of the barometric height. When we observe a barometer during many days, we notice that not only does its height vary from day to day, but also in the same day. The amount of these variations increases from the equator towards the poles. The greatest variations, (excepting extraordinary cases,) are 6 m. m. (-2362 in.) at the equator ; 30 m. m. (1-181 in.) at the tropic of cancer; 40 m. m. (1-5748 in.) in France, and 60 m. m. (2-3622 in.) 25 from the poles. The greatest variations take place in winter. The mean diurnal height is the average of twenty-four successive observations, taken from hour to hour. M. Ramond has found th e 334. What is said of Bourdon's metallic barometer ? Describe its construction. 335. What is said of barometric observations? What are the greatest variations ? When are they greatest ? What is the mean diurnal height f What the mean annual height ? ACCIDENTAL VARIATIONS. 211 height of the barometer at noon to be the mean of the day. The mean monthly height is the average of the thirty mean daily heights of a month. The mean annual height is the average of the three hundred and sixty-five mean daily heights of a year. At the equator the mean annual height is 758 m. m. (29483 in.) It increases, passing from the equator, and attains its maximum of 763 m. m. (30-04: in.) between the latitudes of 30 and 40 ; it de- creases in more elevated latitudes. The mean monthly height is greater in winter than in summer, because of the cooling, and consequent increased density of the atmosphere. 207 The scale, fig. 207, shows the barometric variations of the dif- ferent months. Equal distances, taken on the lower horizontal line ; d y represent the duration of the different months, and the curved lines at the commencement of each interval, the mean barome- tric heights corresponding to the successive months. We have then curves, whose inflexions make known the variations of the mean from one month to another. The four curves represent the monthly means as observed at Calcutta, O, j. f. m. a. m. j. j. a. s. o. n. d. at Havana, H ; Paris, P, and at St. Petersburg, S P. The differ- ence of the curves represent, with great distinctness, the differences of the mean barometric heights. Calcutta and Havana, on the same latitude, have, it will be seen, very different monthly means. 336. Variations observed in barometers are of two kinds. 1st. Accidental variations, which do not offer any regularity in their movements, and which depend on seasons, the direction and geographical position. 3d, Diurnal variations It was about the year 1722, that the hourly variations of the barometer were proved to take place in a regular manner. From that time, many observers have labored to determine the extent and the periods for the different parts of What is said of the mean annual height at the equator and at other points? What is said of the mean monthly height in winter ? Describe fig. 207. 836. What is said of accidental variations? Men- tion Humboldt'a observations on diurnal variations. 212 GASES. the earth. Alex. Humboldt, with others, has demonstrated by a long series of very accurate observations at the equator, that the maximum of height corresponds to 9 o'clock in the morning ; the barometer then falls to its minimum at four, or half-past four o'clock in the afternoon ; it then rises, attaining a second maxi- mum about ten o'clock at night. These movements are so reg- ular they almost serve to mark the hours like a clock, but they are very small. M. Humboldt found that the distance between the highest point in the morning, and the lowest point in the af- ternoon, was but two m. m. In the temperate zones, these di- urnal variations also take place, but are very difficult to ascertain, because of the accidental variations, so that it requires extended and very accurate observations in order to determine them. The hours of the maximum and minimum of the diurnal variations, appear to be nearly the same in all climates, varying a little with the season. Thus in winter, (in France,) the maximum is at nine o'clock in the morning, the minimum at three o'clock in the af- ternoon, and the second maximum at nine o'clock in the evening. In summer, the maximum takes place before eight o'clock in the morning, the minimum at four o'clock in the afternoon, and the second maximum at eight o'clock at night. In spring and in autumn, the critical hours are intermediate. 337. Relation between barometric changes and the weather. Those variations of the barometer which are not periodic, are generally supposed to be indications of changes in the weather. For it has been noticed that those days in which the column of mercury was 29 '72 inches in height, there was very changeable weather ; that in a majority of those days when the mercury rose above this point, there was fine weather, when it fell below this point, stormy weather, snow or rain, prevailed. It is from these coincidences between the height of the barometer and the state of the weather, that there is marked on the scale or dial plate of barometers, at certain heights, the words stormy, rain or snow, variable, fine weather, Ac., and it is supposed that when the mercury stands at the height indicated respectively by these words, we should have corresponding weather : now although this may be true to a certain extent, yet a little reflection will What is said of the maximum and minimum diurnal variations ? 33*7. "What is said of the relation between barometric changes and the weather? By what ' t are changes of the weather indicated in the barometer? RULES FOR BAROMETRIC CHANGES. 213 show the faHacy of such indications. The height of the mercu- rial column varies with the position of the barometer, and conse- quently two barometers, in different places, not upon the same level, would indicate different coming changes. The changes of weather are indicated in the barometer, not by the actual height of the mercurial column, but by its changes of height. 338. Rules by which coming changes are indicated. The following rules may, to some extent, be relied upon, but for rea- sons already stated, must be taken with a considerable degree of allowance. 1. When the mercury is very low, high winds and storms are likely to prevail. 2. Generally the rising of the mercury indicates the approach of fair weather ; the falling of it shows the approach of foul weather. 3. In sultry weather the falling of the mercury indicates coming thunder. In winter, the rise of mercury indicates frost. In frosty weather, its fall indicates thaw, and its rise indicates snow. 4. Whatever change of weather suddenly follows a change in the barometer, may be expected to last but a short time. 5. When the barometer alters slowly, a long succession of foul weather will succeed if the column falls, or of fair weather if the column rises. 6. A fluctuating and unsettled state in the mercurial column, indicates changeable weather. 339. Measure of heights by the barometer. Since the level of the mercury in the barometer falls, as we ascend above the earth, we see that it is possible to determine by barometric observations, the elevation of a mountain, or of any other place above or be- low the level of the sea. If the atmosphere had a uniform den- sity, we could ascertain, by a very simple calculation, the height to which the barometer was raised, from the amount of the fall of the mercurial column ; for mercury, being 10,466 times heavier than air, a fall of one m. m. (0*3937 in.) of the barometric column, would indicate that the column of air had diminished 10,466 m. m., (41 2 '054 in.) and therefore the height measured would be 10,466 m.m. But as the atmospheric pressure dimishes very rapidly in density as we ascend, such calculations are of no value 338. Mention the rules by which coming changes are indicated ? 339. What is said of the measurement of heights by the barometer ? 214 GASES. except for small elevations, and it is necessary to determine the rate of diminution in density of the air, in proportion as it is further removed from the earth. Formulae have been given by means of which we can, for any given latitude, at once calculate from the barometric observation the real height. Tables have also been constructed by which we can easily calculate the level between any two places, when we know the height of the barom- eter and the temperature of the atmosphere. 340. Balloons. Bodies in air (like solids plunged in liquids) lose a part of their weight, equal to the weight of the air dis- placed. From this it follows, that if a body weighs less than an equal volume of air, it will rise in the atmosphere until it meets with air of its own density : hence heated air, smoke, &c., rise, because they are less dense than cold air. Dr. Black, of Edinburgh, announced in 1767, that a light vessel filled with hydrogen gas would rise in the air ; and Cavallo, in 1782, communicated to the Royal Society in London the fact, that soap bubbles, filled with hydrogen, would ascend in the atmosphere. The brothers Montgolfiers, in 1782, first constructed balloons. These con- sisted of globes of cloth, lined with paper. The one that they first exhibited publicly, was a globe about thirty feet in diameter, open at the lower part, below which was placed a fire. This, expanding the air within the globe, diminished its density, and the balloon rose to a height of nearly a mile. Hot air balloons are, therefore, (in allusion to their inventors,) usually called Montgolfiers. Balloons filled with hydrogen were first introduced by Mr. Charles, pro- fessor of physics in Paris, in 1782, and in November of the same year, Pilatre de Rozin made the first serial voyage, in a balloon filled with hot air. The ascension took place from Boulogne. Soon after, M. M. Charles and Robert, in the garden of the Tuilleries, re- peated the same experiment in a balloon filled with hydrogen gas. At this epoch, serial voyages multiplied. In January, 1784, seven persons rose from Lyons, three from Milan, connected by means of a tube with anoth- er balloon, H, filled with hydrogen, the stop-cocks r, r, being closed, the apparatus was placed in the vaults of the Observa- tory at Paris, where there is a uniform temperature. When the balloons had ex- actly this temperature, their stop-cocks were opened, and after a time there was found in each balloon a uniform mixture of hydrogen and carbonic acid ; notwith- standing the great difference in density between the two gases, carbonic acid be- ing 22 times as heavy as hydrogen. This interpenetration, or movement of gases! toward one another, is called diffusion. 2. In a mixture of gases, the pressure, (or elastic force,) exer- cised ly each of the gases, is the same as it was when alone. This law may be demonstrated by filling a number of tubes over mercury with different dry gases, having their volume, and the pres- sure to which they are subjected equal ; upon decanting these gases into a graduated vessel filled with mercury, the pressure will be as before, and the volume, equal to the combined volume of all the gases, proving the law stated. The rapidity with which the diffusion takes place, varies with the specific gravity of the gases. The more widely two gases differ in density, the more rapid is the process of intermixture. This law is stated by Prof. Graham as follows : 348. What is the first law of the diffusion of gases ? How did Berthollet demonstrate this? What is the second law of the diffu- sion of gases ? How may this law be demonstrated ? Upon what does the rapidity of the diffusion depend ? 5JiJ2 GASES. 3. The velocities with which gases diffuse themselves, are in inverse ratio to the square root of their specific gravities. Prof. Graham used a tube about half an inch in diameter, and from six to fourteen inches in length, fig. 216. The tube was closed 216 with plaster at its upper end, and filled dry, with the gas to be examined, and its lower end placed in water. The air and gas both passed through the plaster, and the water ascended in the tube. Care was taken to maintain the surface of the water within and without the tube on the same level, in order that the results might not be modified by the disturbing force of gravity. The tube being filled with hydro- gen, it was found that while one volume of air was passing into the tube, 3*83 volumes of hydrogen were passing out. This is the amount which the above law requires, for the density of the air being one, its square root is one, and its diffusiveness one. The density of hydrogen is 0'069, its square root is 0'02632 and its diffusiveness is --!--- = 3-7984, instead of 3'83, as deter- mined by experiment. The uniform composition of our atmosphere, (312,) is a wonderful illustration of the prevalence of the law of diffusion, or interpenetra- tion of gases. Under all circumstances, and at all heights, over the sea, and on the loftiest mountains, we find the same proportions in its several constituents, not excepting those minor ones which might at first appear to be due to local causes. 349. A striking method of illustrating the diffusion of gases, is by the apparatus, fig. 217. This consists of a porous earth- enware cell, (from a Bunsen's battery,) to the open mouth of which is cemented a funnel, whose barrel is lengthened by a glass tube. Supporting the end of the tube, by means of a clamp, in the lower vessel containing colored water and holding over the porous cell a bell jar filled with hydrogen ; bubbles of gas will escape rapidly from the tube through the water. If the hydrogen bell is removed, the colored water immediately rises in the tube. The effect is due to the diffusive action taking place be- tween the air in the porous cell and the hydrogen in the jar, How did Prof. Graham perform his experiments ? 349. What other apparatus is described 1 What is the influence of temperature on the diffusion of gases ? DIFFUSION OP GASES. 223 for as the hydrogen passes into the cell more rapidly than the air passes out, consequently the volume in 217 the cell is increased, and the excess es- capes through the water. Upon removing the bell of hydrogen, the conditions are re- versed; the cell now contains hydrogen, which diffusing itself into the air more ra- pidly than the air enters the vesesl, causes a diminution of volume, and the water rises in the tube. After a short time, perfect equilibrium is restored, the water in the tube assuming the level of that contained in the vessel. By an elevation of temperature, the rate of diffusion of equal volumes of different gases, becomes accelerated, for heat dimin- ishes the density of all gases, but the rate of diffusion does not increase as rapidly as the expansion of gases by heat, conse- quently the same absolute weight of any gas will be diffused more rapidly at a low ^ than at a high temperature. 350. Table of diffusion of gases __ following table gives the specific gravity of the several gases, the square root of their density, the reciprocal of that square root, (i. e. the calculated diffusiveness of the gas,) and the actual numbers obtained by experiment. DIFFUSION AND EFFUSION OF GASES. Name of gas. Specific gravity. 1 _1 |/Density.! 4/Densitv Velocity ot diffusion. Rate of effusion. 3-613 Hydrogen, 06926 02632 3-7994 3-83 Light carburetted hydrogen, 559 7476 1-3375 1-344 1-322 Carbonic oxyd, 9678 9837 1-0165 1-0149 1-0123 Nitrogen, 9713 9856 1-0147 1-0143 1-0164 Heavy carburetted hydrogen, 978 9889 1-0112 1-0191 1-0128 Oxygen, 1-1056 1-0515 9510 9487 950 Sulphuretted hy- drogen, 1-1912 1-0914 9162 95 Carbonic acid, 1-52901 1-2365 8087 812 821 Sulphurous acid, 2-247 1-4991 6671 68 850. Mention the diffusive power of the different gases. 224 GASES. 850. Effusion. The rate of effusion indicated in the last col- umn of the table above, are results obtained by Prof. Graham, upon the rapidity with which the different gases escape into a vacuum, through a minute aperture, about _i of an inch in di- ameter, perforated in a thin sheet of metal, or of glass : it will be observed that the rates of diffusion and effusion of the different gases coincide very nearly with each other. 351. Transpiration of gases. Gases pass through capillary tubes into a vacuum, according to laws similar to those ob- served in the case of liquids. The rate of transit for each gas, (or velocity of transpiration) is independent of its rate of diffu- sion. The laws observed are as follows: 1. The rate of transpiration for the same gas increases di- rectly with the pressure, that is, equal volumes of air at differ- ent densities, require times inversely proportioned to their den- sities. For example : a volume of double the density of the atmosphere would pass through a capillary tube in half the time that would be required for air at its usual density. 2. With tubes of the same diameter, the volume transpired in equal times is inversely as the length of the tube. If thirty cubic inches were transpired from a tube ten feet in length, in five minutes, a similar tube, twenty feet in length, would transpire only fifteen cubic inches in the same time. 3. As the temperature rises, the transpiration of equal vol- umes becomes slower. Whether the tubes were of copper or of glass, or whether a porous mass of stucco was used, the same uniformity in the re- sults was obtained. The rate of transpiration of the different gases under the same 350a. What is meant by the effusion of gases ? 351. What issaid of the passage of gases through capillary tubes? What is the first law of the transpiration of gases ? Give an example ? What is the second law ? Give an example. What is the third law \ What effect has the material of the tube ? GASES WITH LIQUIDS. 225 circumstances, varies with the nature of the gas. It is inde- pendent of their densities or any of their known properties. TABLE OF TRANSPIRABILITY OF GASES. Name of gases. Time for transpiration of equal volumes. Velocity ot transpiration. Oxygen, rooo r Air, 9030 1-1074 Nitrogen, 8768 1141 Binoxyd of nitrogen, 8764 1-141 Carbonic oxyd, 8737 1144 Protoxyd of nitrogen, 7493 1-334 Hydrochloric acid, 7363 1-361 Carbonic acid, 7300 1-369 Sulphurous acid, 6500 1-538 Sulphuretted hydrogen, Light carburetted hydrogen, 6195 5510 1-614 1-815 Ammonia, 5115 1-935 Cyanogen, 5060 1-976 Heavy carburetted hydrogen 6051 1-980 Hydrogen, 4370 2-228 Of all gases tried, oxygen has the slowest rate of transpiration, and hence is taken as the standard of comparison for the other gases, in the preceding table. It is observed that a mixture of two gaaes, having different rates of transpirability, does not always exhibit a transpirability which is a mean of the gases when separate. With carbonic oxyd, air, oxygen and nitrogen, the rates of transpiration are in direct proportion to their densities : but these are, probably, merely coincidences, as no regular connection with the densities of the other gases can be traced. 352. Mixture of gases with liquids. When a gas comes in contact with a liquid, even when there is no chemical action, the gas is absorbed in a quantity varying with the pressure to which it is subjected, and with the kind of gas. Thus the constituents of the atmosphere are always found in the water with which it is in contact. This may be proved by the apparatus, fig. 218, consisting of a flask, V, furnished with a bent tube, both filled with the water to be examined. Upon boiling the water in the flask, the dissolved gas What is taken as the unit of transpirability ? Give the trans- pirability of different gases? Is there any observed relation be- tween the density and transpirability of a gas ? 852. What is said of the mixture of gases with liquids ? 10* 226 separates, and is collected in the graduated tube, e, filled with raer- 218 cury. By the analysis of the collected gaseous mix- ture, the proportion is found in which each of the gases existed in the li- quid which has been ope- rated upon. Experiment has de- monstrated that the mix- ture of gases with liquids [is in accordance with the three following laws. 1. For the same gas, the same liquid, and the same tempera- ture, the weight of the gas absorbed is proportional to the pres- sure; that is, that at all pressures the wlume dissolved is the same. 2. The quantity of gas absorbed is greater as the tempera- ture is lower. 3. The quantity of gas ichich a liquid will dissolve, is inde- pendent of the quantity and nature of the other gases it holds in solution. Thus, if instead of two elastic fluids, the atmosphere was composed of many, each would be absorbed as if it were alone, keeping in ac- count the pressure which is proper to it. Thus oxygen, forming one- fifth of the atmosphere, water, under ordinary conditions, absorbs precisely as much oxygen as if the atmosphere were entirely com- posed of this gas, sustaining a pressure equal to one-fifth that of the atmosphere. 353. Absorption of gases by solid bodies. Most porous solid bodies possess the property of absorbing many times their volume of gases without any chemical action taking place. The con- densed gases have always a much greater elasticity than the at- mosphere, always being disengaged when the temperature is raised. The absorption of different gases by charcoal, has al- ready been noticed. (307.) According to M. Dobereiner, platinum, in a state of extreme di- 353. What is said of the absorption of gases by solid bodies ? What is said of the absorption of oxygen by platinum ? What is the force with which the oxygen in this case is condensed ? HYDROGEN LAMP. 227 vision, (platinum sponge,) as also iridium, absorb from 200 to 250 times their volume of oxygen, without combining chemically with it, and as oxygen forms but one-fifth part of the atmosphere, they are condensed with a force equal to 1000 or 1250 atmospheres. M. M. Saussure and Dobereiner, discovered that the gases condensed in porous bodies, acquired new chemical properties, and M. M. Thenard and Dulong, have demonstrated that the property ; possessed by spongy platinum ia due to its porosity ; for thin sheets of metal, packed closely together, pulverized or crushed glass, or porcelain, produced the same phenomena, though not to the same extent. 354. Hydrogen lamp. The absorption of hydrogen by pla- tinum sponge, is accompanied with such an elevation of temper- ature, that the metal becomes incandescent. The hydrogen lamp invented by Dobereiner depends on this fact ; one of the most convenient forms of this apparatus is seen in fig. 219. It consists of a vessel containing water mixed with sulphuric acid, and having suspended from its cover a glass cylinder, con- nected with the stop-cock, R. Within the 219 cylinder is suspended a mass of zinc. Sup- posing R to be closed, and the zinc and water in contact, hydrogen is generated, which, as it accumulates, displaces the water until the zinc is not touched by the liquid ; the evolution of hydrogen then ceases. If we now open R by pressing upon the lever c, a jet of hydrogen escapes by the aperture o, and is directed upon a mass of platinum sponge placed in P, which becoming red, inflames the hydrogen. At the same time that R is opened by press- ing upon c, a small lamp, L, is moved forward, and its wick coming in contact with the ignited jet of hydrogen, is in. flamed. When we cease to press on c, the stop-cock closes, and the lamp returns to its original position by means of a spring and rack movement. If the platinum loses its property of inflaming hydrogen, it may be restored by heating it to redness in a hydrogen flame. To what is this absorptive power of platinum due ? 354. What is said of the effect of the absorption of hydrogen by platinum sponge ? Describe DObereiner's hydrogen lamp ? 228 GASES. 220 221 355. Bellows. The most common instrument for producing a current of air is the ordinary bellows, fig. 220, consisting of two leaves of wood united by leather, and having at their smaller extremity a tube of metal ; a valve is placed in the lower leaf, opening upwards. When the leaves are pressed together, the valve s closes, and the con- tained air escapes through t. But when the leaves are separated, air rushes in through the valve and also through the tube, through which last it is ejected upon pressing the leaves together. 356. Bellows with a continuous blast. In the ordinary bel- lows, the blast of air is intermittent. Where a continuous jet is wanted, as at a smith's forge, a double blast bellows is used fig. 221. This consists of three pieces of wood, of which one, D, is immovable, the others are connected with this by means of leather. The apparatus is divided into two compart- ments, U V, the blast-pipe communicates with the one above ; in the lower one, air is introduced through the lower valve, S. When the lever is drawn down, as shown by the arrow, the valve, S, closes, and the air being com- pressed, passes into Z7 through the valves r r, raising C B, and partially escaping through the tube. With the reverse mo- tion, (accelerated by the weight P,) the valves r r close, and the exterior air enters Fby the valve S. During this time, the upper weight, P', causes C to descend, and thus there is continually an escape of air by the blast-pipe. The weight may be replaced by a spring. 355. Describe the ordinary bellows. 356. What is the construc- tion of the double bellows with a continuous blast ? BELLOWS. 229 222 357. Furnace blowers. In great forges, and in furnaces, blowing machines are employed, by means of which a large vol- ume of air is forced into the fire; these machines are of very various construction. Fig. 222 represents one of them ; it consists of a cast iron cylinder, containing a piston, p, of which the rod, t, passes, air tight, through a packing box, d ; there are four valves, two of which a a' opening in- wards, draw in air ; the air passes out through the valves b b' which open outwards. The piston is set in motion by a steam engine or water wheel ; during its descent the valves a and b' only are opened ; through the first, air is drawn in, through the second, it is expelled ; during the ascent of the piston, the other valves a' and b, act in the same manner. The expired and compressed air is received into the tube g h, through which it is conveyed to the furnace. 358. Escape of compressed gases. When a compressed gas escapes from any opening in a thin wall, the velocity of its es- cape depends on the difference of the interior and exterior pres- sures, and on the density of the gas passing out. It has been proved, 1. That with the same gas at the same temperature, the ve- locity of its flow into a vacuum is the same at any pressure. That is, if we had a vessel filled with air, compressed at 1, 2, 3 or 1000 atmospheres, and allowed it to escape by a small orifice, the ve- locity of its flow would be the same during the whole time of its discharge. But the quantity of the gas that could escape in the same time would vary, being evidently proportional to the density 357. Describe the furnace blower represented in the figure. 358. What is said of the escape of compressed gases ? What is the first law that has been proved ? Give an illustration. 230 GASES, of the gas, that is, to the pressure. If the escape took place in a gas, as air, instead of in a vacuum, the velocity is then proportional to the difference between the elastic force of the interior and exte- 2. The velocity of the escape of gases into a vacuum is in inverse ratio to the square root of their densities. Where the gas escapes through long tubes instead of through orifices in a thin wall, the velocity is very much diminished, be- cause of the friction, and is less in proportion as the tube is longer and its diameter smaller. 359. Pneumatic ink bottle. In the pneumatic ink bottle, fig. 223, the ink in the tube c is kept con- stantly at nearly the same level. By inclining the bottle it may be filled as seen in A. The ink in A tends to force itself in the tube C, but is opposed by the atmospheric pressure, which is much greater than the pressure of the column of ink in A. As the ink in G is consumed, its surface, falling, will allow a small bubble of air to enter A, where it will exert an elastic pressure, and cause the ink in C to rise a little higher. This effect will be continually repeated until the bottle is emp- tied of ink. Bird-cage fountains are constructed on a similar principle. 360. The syphon. The syphon used for decanting liquids, de- pends for its operation on the principle of atmospheric pressure. It consists of a bent tube, Z>', fig. 224, having one of its arms longer than the other. It may be filled by turning it over, and pouring the liquid in, or by immersing the shorter arm in a vessel of water, and applying the mouth at 5' ; upon exhausting the air, the water will be forced up by atmospheric pressure, to sup- ply the place of the air withdrawn, and there will then be a con- tinual discharge until the vessel is emptied. The two branches being filled with liquid, the pressures ex- erted at the points b and n will be equal, for they are on the same level ; but the pressure exerted^at b' will be greater, because of the column n b', and the liquid will escape from this long branch What is the second law ? 359. "What is the pneumatic ink bot- tle ? 360. What is the syphon ? How is it set in operation ? INTERMITTENT SYPHON. 231 because of this excess of pressure, and will draw with it the liquid in the shorter branch ; if the end of this be immersed, 224 there will be a continual discharge as long as b is below the surface of the liquid, for the atmospheric pressure will cause the liquid to ascend, to supply the place of that which is passing out ; otherwise there would be a vacuum produced. It is evident that water could not be raised by means of a syphon more than thirty-four feet : for a column of water of that height is in equilibrium with the pres- sure of the atmosphere. (320.) The velocity of the flow from a syphon will be the same as if the liquid fell freely from a height equal to the distance between the level of the liquid in the vessel and the end of the long arm. To avoid the necessity of filling a syphon by pouring, the form represented in fig. 225 is employed. To 225 use this instrument, the open end, 5', of the longer limb is closed by the finger, while a partial vacuum, created by sucking at the small ascending tube, ta, occasions the liquid to pass over as in the ordinary syphon. 361. Intermittent syphon. Tantalus' vase. Fig. 226, consists of a vessel, A, containing a syphon, of which one of the branches opens below the bottom ^ n of the vessel; the other is curved. When water is poured into the vessel A, it will rise to the same height in the interior of the tube as it attains out- side. The tube will not act as a syphon until the vessel is filled to the height n, but when it reaches that point, 226 227 r the water will flow through a, into the long branch, filling it com- What determines and limits its operation ? What is the velocity of the flow from a syphon ? What is the advantage of a branch syphon ? 232 GASES. pletely, and the syphon being now supplied, will discharge water until the vessel is emptied. The syphon may be concealed in a little image, fig. 227, B, representing Tantalus, so that just before the water touches his lips the syphon is filled, and the vessel is emptied. 362. Intermittent springs. There exist in nature intermittent springs, the water flowing regularly for a time, and then sud- denly ceasing. In these springs the opening, as at a, fig. 228, 228 communicates with a subterranean cavity C, by means of a chan- nel, a n 5, which has the form of a syphon. This cavity is grad- ually filled, until at last the water attains the level n n, when the syphon is filled, and the water escapes. If the syphon discharges the water faster than it flows into (7, after a time its level would be lowered to 5 ; air would then rush in by the syphon, the flow of water would cease, and would not recommence until it had again attained the level n n. 363. Intermittent fountain. The intermittent fountain con- sists of a vessel of glass, (7, fig. 229, whose aperture for the ad- mission of water is hermetically sealed by an accurately ground stopper. A glass tube A, passes through the vessel C, its upper end termi- nating above the surface of the liquid ; its lower end rests in a cop- 361. Describe the intermittent syphon called Tantalus' vase. 362. What is said of intermittent springs? Describe their mode of action. AIR-PUMP. 233 229 cf = per cistern, B, which has a small aperture for the escape of water. The globe being partially filled, the water escapes through the capillary or- ifices of the tube atZ>, in consequence of the atmospheric pressure transmit- t ed through the lower end of the tube A. When the end of this tube becomes covered with water, which after a time happens, (because the orifice in the cistern B, does not allow so great a flow of water as can escape from the tubes atZ),) the exterior air cannot enter the globe, and in consequence the flow ceases. The water continu- ing to escape from D, in a little time the surface is so much lowered, that the end of the tube, A, is out of water ; the air then entering the globe, the escape recommences, and so continues at intervals until C is emptied of water. 364. Air-pump. The air-pump designed to produce a vacuum in any confined space, was invented by Otto Guericke, burgomaster of Madgeburgh, in 1650. It consists essentially of a hollow cyl- inder of metal or glass, ^4, fig. 230, in which the piston, J9, works air-tight. The cylinder is connected by the tube, c c, with the plate E E, on which the receiver D rests. A valve, d, opening upwards is placed in the piston, B, At the end of the tube c c, terminating in the barrel, is a second valve, #, also opening up- wards. This valve is connected with the rod &, which moves air- tight through the piston, B. As the piston rises, this valve opens, and closes when the piston descends. By means of the stop, jP, we may open and close communication between the re- ceiver and the barrel of the pump, or with the external air by removing the plug/. To exhaust the receiver D of air, the piston B, is raised by a lever, (not seen in the figure,) when the air, expanding, passes through the air-way whose valve, a, is raised with the piston, by its friction on the 363. Describe the intermittent fountain, fig. 229. 364. Who was the inventor of the air-pump ? Describe its construction. 234 GASES. rod 6. The air before contained in D, is now diffused through the additional space in the cylinder A, below the piston B. By the de- scent of this piston, the valve a is instantly closed, and the air con- fined in the cylinder escapes through d, the valve in the piston. At each full stroke of the piston, the air in D thus experiences a renewed rarefaction, until at last a good vacuum is obtained. 230 The extent of the exhaustion of air is measured at every in- stant by a gauge. This gauge shows the difference in level which the mercury takes in the two branches of a curved tube, one end of which is closed, and the other open as in a barometer. This tube is covered by a glass cylinder G. When the level of the mercury in both branches of the tube is the same, the va- cuum is perfect, and it is more or less incomplete as the difference in level is greater or less. From a graduated scale upon the tube, the precise amount of the exhaustion is ascertained. An air-pump with two cylinders is often used, the pistons of which are alternately raised and depressed. 365. Tate's double acting air-pump. In this pump a double piston acts in a single cylinder, and the instrument may be re- garded as a single-barreled pump, capable of performimg its work with only one-half the usual motion. Fig. 231 represents Describe its mode of action, determined ? How is the extent of the exhaustion VACUUM LIMITED. 235 this pump ; A and B are solid pistons connected by a rod, and moved by the piston rod A If, which passes through the stuff- ing box S; V and are valves opening outwards. 231 R is a tube in connection with the plate of the pump. On raising the pistons, the air above A is forced through the valve V, into the atmosphere, while a va- cuum is being formed beneath the piston J5. "When a reaches the top of the cylinder, the air from the receiver rushes through the pipe R, into the lower part of the cylinder. In a downward stroke, the air beneath the piston B is propelled through the valve V into the atmosphere, while a vacuum is being form- ed above the piston A, and so on. The double piston performs a double duty at every single stroke as compared with the common pump. To effect the same exhaustion, the driving power moves over only half the space, and as the exhaustion proceeds, the pressure requisite for moving the pistons, becomes less and less ; the contrary is the case in the common air pump. 366. Vacuum limited. It is plain, on a moment's reflection, that by mechanical means alone, it is impossible to produce a perfect vacuum. There must always remain a certain volume of air, inferior in tension to the gravity and friction of the pump valves. By employing an atmosphere of dry hydrogen to rinse out the residue of common air from an exhausted receiver, an approach to a perfect vacuum is made, inversely as the density of the two gases. Also by using carbonic acid for the same end, and absorbing the residue of this gas by dry quick-lime pre- viously placed on the pump plate, a perfect vacuum may be pro- duced ; but by chemical and not by mechanical means. *36T. Pneumatic experiments. Very numerous and instructive experiments may be made by means of a good air-pump and its accessory apparatus, a full account of which would occupy too much of our limited space. The catalogues of the leading in- strument makers will be found to contain all needful details for the successful performance of these experiments. The principles involved have been already sufficiently explained. 365. What is said of Tate's air-pump ? How is the piston con- structed ? What is the position of the valves? Describe the ope- ration of this pump. 366. Why is the vacuum limited ? How is a perfect vacuum possible ? 236 GASES. 368. Compressing machine. This machine is used to com- press the air or any other gas ; it is constructed like the air-pump, the only difference being that its valves open in a contrary di- rection, viz : downwards. Fig. 232 represents a longitudinal section of one form of this ap- paratus. When the piston, P, is lowered, the air is compressed, and passes into the receiver, D B D ; when the piston is raised, the valve a is opened hy the exterior air which rushes into the barrel of the 232 233 pump, while the compressed air in the receiver closes the valve, 0. It is evident, that by every stroke of the piston, as much air as fills the cylinder is driven into the receiver, R, which becomes therefore filled with an atmosphere proportionally more dense than the external air. 369. Archimedes' screw. The Archimedes' screw, is a ma- chine said to have been invented by Archimedes in Egypt to aid the inhabitants in clearing the land from the periodical over- flowings of the Nile. The in- strument varies in its form, ac- cording to the manner and pur- poses of its application. To render the principle upon which it works intelligible, let us sup- pose a tube bent in the form of a cork-screw and inclined in the manner shown in fig. 233. 368. "What is said of the compressing machine ? 369. What is Ar- chimedes' screw ? Describe the principle, upon which it works. ARCHIMEDES' SCREW. 23T If a ball be placed in A, it will fall to B, and there remain at rest ; 234 if the screw be now turned so that the mouth A, is placed in its low- est position, the point B, during such 235 a motion, will ascend, and will as- sume the highest position it can have. The ball will then fall to G; by con- tinuing the revolution of the screw, the ball will ascend in the tube, and finally will be discharged from the upper mouth. The same would hap- pen with a portion of liquid. If the lower extremity of the screw was immersed in a reservoir of liquid, it would gradually be carried along the spiral as the screw was turned, to any height to which the screw might extend. In practice, the screw is more commonly formed of a cylin- der, to the walls of which is attached a spiral thread, as shown in fig. 231. Besides liquids, these machines are used for elevating ores in mines, or grain in breweries, &c. They are commonly used at an inclination of about 45, but may be used at 60 ; revolving 100 to 200 times a minute. What is the usual form given to this machine in practice ? For what are they used ? What is the angle at which they are placed ? 238 GASES. 370. Chain pump. The chain pump consists of a cylinder, fig. 235, whose lower end is immersed in the water of the reser- voir B, and whose upper part enters into the bottom of a cistern, O y into which the water is to be raised. An endless chain is car- ried around the wheels above and below, and is furnished at equal distances, with circular plates, which fit closely into the cylinder. As the w^heel is revolved by means of power usu- ally applied by a winch, the circular plates successively enter the cylinder and carry the water up before them into the cistern, from which it passes out by a spout. 371. Pumps. Pumps are designed to elevate water and other 236 liquids above their former level. They are of various construction, but raise the liquid by the atmos- pheric pressure, by direct pressure, or by the efifect of the two com- bined. They are commonly called I either suction, or forcing pumps, ,or both united. 372. Suction pumps. The suc- tion pump, fig. 236, is composed of ) a tube, -4, whose lower end is im- mersed in the water to be elevated. This is attached to the body of the I pump, C, which contains a piston .furnished with a valve, r, opening j up ward. The upper extremity of the tube ^4, also contains a valve, o, opening in the same direction. When the piston is elevated from | the lower part of the pump by working the handle, L, the valve \r, closes, and a partial 'vacuum is produced, but the elastic force of the air in A, causes the valve o, to open, and part of the air thus passes into C. The air in the tube is thus rarefied, and the water rushes up to such a height, 3*70. Describe the construction and mode of operation of the chain pump. 371. What is said of water pumps? 372. Describe the suction pump and its operation. Why cannot water be raised in such a pump more than thirty-four feet ? SUCTION AND LIFTING PUMP. 239 that the weight of the column of water raised, added to the elasti- city of the interior air, keep it in equilibrium with the atmospheric pressure. When the piston descends, the valve o closes by its weight, and prevents the return of the air from the body of the pump, C, into the tube A. The compressed air opens the valve r, and thus escapes into the atmosphere through B. After a number of strokes of the piston, fewer as the capacity of the tube a is less, the water will be elevated above the lower valve ; now when the piston is low- ered, the valve r will open and the water pass above it. Upon ele- vating the piston, r closes, and the water is raised in B, and escapes through the spout S, As in this and the following pump, the air is elevated to the top of the tube by means of atmospheric pressure, it is evident, that even in the most perfectly constructed pumps, the distance from the level of the water to the top of the pump, must not exceed thirty-four feet, (320,) but those of ordinary construction contain defects, so that generally we do not gain a greater height than twenty-six or twenty-eight feet. But after the water has passed over the piston, the height to which we may elevate it, is limited only by the power applied at the piston ; for it is the ascensional force of this which elevates the water. 373. Suction and lifting pump. Sometimes the water raised above the piston, instead of passing upwards in the tube in which the piston works, rises by a lateral ascensional tube $ furnished with a valve, which prevents the return of the wa- ter, as shown in a r S, fig. 236. That the rising of the water in the tube is due to the atmospheric pressure, may be de- monstrated by the apparatus, fig. 23V. After forming a vacuum in the reservoir which con- tains the vessel of water, the liquid will not rise in the tube when the piston in the pump, P, is raised, but upon admitting the air it is rapidly elevated, as usual. 374. Forcing pump. In the forcing pump, the piston has no valve. The lower part of the 237 373. "What is said of the suction and lifting pump ? How may it be demonstrated that the rise of water is due to atmospheric pres- sure 1 240 GASES. cylinder in which it works is placed in the water to be elevated, so that the valve r, fig. 238, which opens upward, is always im- mersed. The ascending tube a 5, contains a valve, S, also opening upwards, and an air chamber, m n. 238 "When the piston is raised, 5 is closed, and water is introduced by the open valve r; upon the descent of the piston, r closes, and the water is forced into the ascending tube a b. The reservoir, m n, filled with air, is designed to render the jet of vapor contin- uous. When the water is forced by the piston into the tube, the air is compressed in m n ; re-acting afterwards by its elasticity, it con- tinues to drive the water into the upper part of the tube, after S is closed, and while the piston is rising. It is found necessary to have the air-cham- ber twenty -three times the capacity of the body of the pump, in order to render the jet continuous. 375. Rotary pump. The rotary pump is a mechanical contrivance for raising water by a continuous rotary movement. Fig. 239 represents one of 239 874. What is the construction of the forcing pump ? What is the use of the air reservoir? What must be the capacity of the air- chamber in order to work effectively ? 375. Describe the rotary pump, fig. 239. What is the mode of its operation ? HIEKO'S FOUNTAIN. 241 the most successful of these, (Gary's.) Within a fixed cylinder is included a movable drum, 5, attached to the axis, A, and moving with it. The heart-shaped cam surrounding A, is immo- vable. The revolution of B, causes the plates or pistons c c to move in and out, in obedience to the form of the cam. The water enters and is removed from the chamber through the ports or valves, L and M ; the directions are indicated by the arrows. The cam is so placed that each valve is in succession forced back into its seat when opposite E, while at the same time the other valve is driven fully into the cavity of the chamber ; thus forcing before it the water already there, into the exit pipe H, and drawing after it, through the suction pipe F, the stream of supply. "When the pump is set in action, the suction pipe is gradually exhausted of air, in which, consequently, the water ascends, and being drawn into the cylinder, it is carried around by the plates c c, in the manner just described. This is the form of pump often employed in the steam fire- engines which are now coming into use. 376. Fire-engine. In order to obtain a continuous and pow- erful jet of water from fire engines, they are usually constructed with two forcing pumps, which are alternately discharging water into a common air chamber. The pistons are moved by brakes, having an oscillating motion. The water from both pumps, forced into the air chamber, escapes through a long leathern hose, terminated by a metal tube, which serves to direct the jet. 377. Hiero's fountain. In this apparatus we also obtain a jet of water by means of compressed air, produced in this case by a column of water. A common form of this apparatus is repre- sented by fig. 240. It consists of a metallic cistern and two globes of glass. The cis- tern, D, communicates with the lower part of the globe N, by the tube B ; a second tube, A, joins the globes, ending in the upper part of both ; M is partially filled with water ; and lastly, a third tube passes through the cistern, and terminates at the bottom of M. The upper extremity of this tube has a small orifice, from which the jet of water issues. Upon pouring water into the cistern, D, the liquid descends to jV", by the tube J?, consequently the water in the lower globe, 376. What is said of fire-engines ? 377. "What is said of Hiero's foun- tain ? Describe the fig. 240. What is the mode of its operation ? 11 242 GASES. 240 N, supports, besides the atmospheric pressure, the pressure of the column of water in the tube. This pressure is transmitted to the air in the globe, Mj which, reacting on the water, forces it out through the jet, as seen in the figure. If there was no friction, and no resistance from the air, the water would spout to a height equal to the difference in level of the water in the two globes. 378. Hydraulic rain. In the hy- draulic ram, the momentum of a part of the fluid in motion, is effective in rais- ing another portion. A simple form of this apparatus is seen in fig. 241. The water descends from the spring or brook, A , through the pipe B, near the end of which is an air chamber, D, and rising main, F. The orifice at the ex- treme end of j5, is opened and closed by a valve, E, opening downwards. "When the valve E is open, the water flows through B, until the current be- comes sufficiently rapid to raise the valve E, and thus to close the orifice. The water in B having its motion thus sud- denly checked, exerts a great pressure, and having raised the valve C, will rush into the air vessel D, where it com- presses the air. The compressed air in D, because of its elasticity, 241 causes the water to rise in the pipe JP, until the water in A B, is 878. What is said of the hydraulic ram ? Describe its construction. SAFETY TUBES, 243 242 brought to rest. When this takes place, the pressure is again insuffi- cient to sustain the weight of the valve E, which opens, (descends,) the water in B is again put in motion, and the same series of effects ensue as have already been described. The hydraulic ram, when well constructed, is capable of utiliz- ing about 60 per cent, of the moving power. 379. Safety tubes. Chemical apparatus is often supplied with " safety tubes," in order to avoid explosions, and to prevent the mixing of the liquids contained in the different vessels of the ap- paratus. Supposing that from the flask m, fig. 242, a gas was disengaged, whichpassed, by means of the tube a 5, into a vessel, -4, containing water, to absorb the gas. Upon withdrawing the heat, the gas in the flask would have a less elastic force, and the liquid in A would thus rise in the tube and pass over into rn, destroying the process and often breaking the ves- sel. To avoid this inconvenience, safety* tubes are used. The simplest consists of a straight tube, G 0, fig. 243, passing through the cork, and dip- ping into the liquid in the flask, a short distance below the surface. When the tension of the gas in M, diminishes, the atmospheric pressure exerted on the surface 243 of the liquid in E, will cause a portion to rise in D A, and de- press that contained in C, so that air enters, and the equili- brium is restored. Again, if more gas is generated than can escape through the exit tube A D, the tube C prevents the bursting of the flask, for the li- quid escapes by the tube until the aperture o, is open, when the excess of gas escapes. The hydrostatic pressure exerted upon the flask M, is measured by the height of the vertical column HO. What is the mode of operation? 379. What are safety tubes? What is said of fig. 242 ? Describe the straight safety tube, fig. 242. IT, 244 THEORY OF UNDULATIONS. Another form of safety tube, (called an S tube,) consists of a tube bent in the shape seen in fig. 244, having often upon it a bulb, a. This tube is adapted to the neck of the generating vessel, M ; the curve is filled with water or some other liquid. 244 It is plain that if the elastic force or pressure is the same within as without, the liquid will beat the same height, d c, in both branches of the curve; if, however, the elastic force of the gas within the retort diminishes, the column will fall, and soon, the air passing the curve and rising through the li- quid, will enter the vessel and restore the equilibrium ; thus pre- venting the liquid in h, from pass- ing into the retort. Explosions are prevented, as has already been explained, in regard to fig. 243. THEORY OF UNDULATIONS. 380. Origin of undulations. By the operation of certain forces, the different parts of all bodies are, ordinarily, held in a state of equilibrium or rest. If the molecules of a body are disturbed by any extraneous force, they will, after a certain interval, re- turn to the state of repose. This return is effected by the par- ticles approaching the position of equilibrium, and receding from it, alternately, until at length the body, by the resistance of the medium in which it is placed, and by other causes, is gradually brought to rest. The alternate movements thus produced, are va- riously expressed by the terms vibrations, oscillations, waves or undulations, according to the state or form of the body in which such movements occur, and the character of the motions which are produced. 381. Progressive undulations. Undulatory movements are of two kinds, progressive and stationary. In progressive undula- "What is said of the S safety tube, fig. 244 ? Describe the mode of its operation. 380. What is the effect when the molecules of a body are disturbed by any extraneous force ? How is the return of the bodies to the position of equilibrium effected ? What are the alternate movements called ? VIBRATIONS. 245 tions, the particles which have been immediately excited by the disturbing cause, communicate their motion to the particles next them, and as this movement of the particles is successive, the position they assume at any particular moment during their mo- tion, appears to advance from one place to another. This kind of undulation is observed in a cord made fast at one end, while the other is smartly 245 shaken up and down ; the portion of the cord nearest the hand will assume the position in fig. 245, I, m d E 0. Such a wave does not continue stationary ; the moment it is formed, it advances toward the other extremity of the cord, II, rVwr on reaching which, III, an inverted curve is produced, V m ' IV, and the wave returns, V, to the position from which it started, the relative position of the elevation and depression being reversed. This alternate movement may be repeated a number of times before the cord comes to rest. These are sometimes called waves of trans- lation. 382. Stationary undulations. Undulations are termed station- ary when all parts of the body assume and complete their motion at the same time. Thus, when a cord stretched between A B, fig. 246, is drawn at the middle from its rectilinear 246 position, it ultimately re- covers its original position, _^ after performing a series A\tf^:::f:~~ ~~~ ~~~~~~~~~ ~ "." I ~ - - - : ^pfe of vibrations, in which all ~~"~ : --IIIV_"ir_V----"" parts of the cord participate. , 383. Isochronous vibrations. Those vibrations that perform their journey on either side of their normal position in equal times, are termed isochronous, (from isos, equal, and chronos, time.) 381. What is said of progressive undulations ? How may these motions be produced ? Describe the fig. 245. What else are such, waves called? 382. What are stationary undulations ? 246 THEORY OF UNDULATIONS. The movements of a pendulum furnish a perfect illustration of such vibrations. (161.) 384. Phases of undulations. In every complete oscillation, or 247 perfect wave, the following parts may be recognized. The curve a el d c, fig. 247, is called a wave. The part ^ -a e 5, which rises above the position of equilibrium, is called the phase of elevation of the wave, e being the point of greatest elevation ; the curve 5 dc, is called the phase of depression of the wave, the point d, being that of greatest depression. The distance of the highest point ,) is termed an oscillation or vibration, and the time occupied in performing it is called the time of oscillation. The vibrations of tense strings are isochronous. 389. Laws of the vibration of cords. Calculation and exper- iment have demonstrated, that the vibration of cords is in accord- ance with the four following laws. 1. The tension being the same, the number of vibrations of a cord is in inverse ratio to its length. That is, if an extended cord, as of a violin, makes in a certain time a number of vibrations, represented by 1, then, in order to make a number of vibrations, represented respectively by 2, 3,4, the cord must be , , \ as long. 2. The tension being the same, the number of vibrations in cords of the same material, is in the inverse ratio of their thick- ness or diameter. That is, if we take two cords or wires of the same length, of cop- per or steel, as those of a piano, one of which is twice the diameter of the other, and which vibrate equal lengths, the small one will make, in the same time, twice as many vibrations as the larger. 3. The number of vibrations of a cord is proportional to the square root of the weight it carries. That is, if we represent by 1 the number of vibrations made by a cord, extended by a weight of 1, then the number of vibrations made by a similar cord of the same length, in the same time, becomes respectively 2, 3, 4, &c. when the weight is increased, to 4, 9, 16, , the mo- vable bridge, B, must be advanced toward the fixed bridge D, until the length of the cord is but eight-ninths of that which produces the note C. Proceeding in the same manner for the other notes, it will be found, that the length of cord corresponding to each note, is represented by the following fractions. Notes - C. D. E. F. G-. A. B. Kelative length of cord, 1 4. 3 | _8- In continuing to move the bridge on the sonometer, it will be How are these sounds designated in English? How in French? 450. What is the object of the sonometer"? What has been ascer- tained from it? Describe its construction. How is the numerical relation between the different sounds determined ? What is the rel- aitve length of the different cords ? What relation does the eighth sound bear to the fundamental sound 1 What is said of other oc- taves ? 282 ACOUSTICS. found, that the eighth sound, the octave, is produced by a length of cord half that of the fundamental sound. Upon this note, an octave higher than the fundamental note, we may construct a scale, each note of which is produced by the vibration of a cord half as long as the same note in the preceding gamut. In the same manner we may have also a third and a fourth scale. 451. Relative number of vibrations corresponding to each note. In order to ascertain the relative number of vibrations corresponding to each note in the same time, it is sufficient to reverse the fractions of the preceding table. For by the princi- ples already established, (389,) the number of vibrations is in in- verse ratio of the length of the string. Representing, therefore, the number of vibrations corresponding to the fundamental note C, by 1, proceeding as above, we form the following table : Notes, C. D. E. F. G. A. B. Relative number of vibrations, 1 . i 2. $- l -$ Which indicates, that in producing the note D, nine vibrations are made in the same time that eight are made by the fundamental note C. So, when the note E is sounded, five vibrations are made for four of C ; for B, fifteen to eight of C, &c. 452. Absolute number of vibrations corresponding to each note. By setting the siren, or Savart's wheel, in unison with a given sound, we obtain the absolute number of vibrations corresponding to it. If we set the siren in unison with the fundamental C, in order to obtain the number of vibrations corresponding to the other notes, as D, we have but to mul- tiply it by the fraction &, &c. But the fundamental C varies with the nature, length, and tension of the cord of the sonometer, and therefore the number of vibrations may be represented by an infinite variety of numbers, corresponding to the different scales. The notes of the scale whose gamut corresponds to the gravest sound of the bass, are indicated by 1. To notes of gamuts more elevated, are affixed the indices 2, 8, &c. ; to graver notes are affixed the indices, 1, 2, &c. The number of simple vibrations corresponding to the note C, is 128, and in order to obtain the number of vibrations corresponding to the other notes, we have 451. How are the relative numbers of vibrations corresponding to each other determined ? What are these numbers ? What do these numbers indicate? 452. How is the absolute number of vibrations corresponding to each note found? How are the different gamuts indicated? LENGTH OF SONOROUS WAVES. 283 but to multiply this number by the fractions indicated in (451,) which gives the following table. Notes, - - C. D. E. F. G. A B. Absolute number of simple vibrations, 128 144 160 170 192 211 240 The absolute number of vibrations for the superior gamut, is obtained by multiplying the numbers in the table successively, by 2, by 3, by 4, &c. ; for the lower gamut, we divide the same numbers by 2, by 4, &c. Thus, the number of vibrations of A3 is 214 x 4 = 856 simple vibrations, or 428 complete vibrations. It must, however, be stated, that there is a slight difference of opinion as to the actual number of vibrations producing a particular note. Thus A3 of the pitch adopted at different orchestras, which in the above table is stated to be produced by 428 vibrations, varies as follows : Orchestra of Berlin Opera, .... 437 '32 Opera Comique, Paris, 427 '61 Academic de la Musique, Paris, ... 431*34 Italian Opera, " 424 '14 In piano-fortes, which, for private purposes, are generally tuned below concert pitch, A3, is produced by about 420 vibrations in a second. There has been a curious progressive elevation of the diapason (pitch) of orchestras, since the time of Louis XIV, when the la in the orchestra was (according to Sauveur) 810 simple vibrations, ( = 405 complete vibrations,) per second ; the number at the grand opera is now 898, or nearly a tone higher. This rise has taken place mainly in the present century being a semi-tone since 1823. The comparative rarity of tenor voices has been thus accounted for. The causes of this change, (which is still in progress, 1 ) would demand some space to explain. But the prevalence of military music with wind and stringed instruments, is a principal cause. 453. Length of sonorous waves. It is easy to ascertain the length of a sonorous vibration, if we know the number of vibra- tions made in a second. For, as sound travels at the rate of 1118 feet per second, if but one vibration is made in that time, the length of the wave must be 1118 feet; if two vibrations, the length of each must be half of 1118, = 569 feet, &c. * What is the number of vibrations corresponding to the different notes ? How are the number of vibrations for the notes of other gamuts obtained? What is stated as the actual number of vibra- tions producing a particular note ? 453. How is the length of so- norous vibrations ascertained ? 284 ACOUSTICS. C, corresponds, as we have seen, to 128 vibrations per second ; the length of its waves is, therefore, (1118 -f- 128,) = 8 '7 3 feet. The following table indicates the length of the waves correspond- ing to the C of successive scales. Length of wares in feet. Number of vibrations in a second. C 3 .... 70' 16 C 2 .... 35' 32 C 1 .... 17-5 64 C 1 .... 8-73 128 C 2 .... 4-375 256 C 3 .... 2187 512 C 4 .... 1-093 1024 454. Interval. Interval is the numerical relation existing be- tween the number of vibrations made in the same time by two sounds, or it is that which indicates how much one sound is higher than another. The interval of C to D, is called a second ; of C to E, a third ; of C to F, a fourth ; of C to G, a fifth ; of C to A, a sixth ; of C toB, a seventh; of C to C, an octave. The following table gives the inter- vals of successive notes, obtained by dividing the vibrations of one note, by the vibrations of the note immediately preceding it. Notes, - - C. D. E. F. G. A. B. C. Relative number of vibrations, 1 -| f |- - 1J5 2 Interval, | u> ia 3. i_o 3. i| It may be observed, that there are but three different intervals, 2. i_o LJ.. The first is called major tone. The second minor-tone. The third major-semi-tone. A comma is the interval between the minor tone y, and the major tone |. is I.Q., differing from a unit but by JL. Unless the ear is well trained, it cannot appreciate this difference, just as the eye is not disturbed by small alterations in the proportion of objects, the symmetry and form of which are pleasant. 455. Flats and sharps. If we wish to write a tune with scales more or less grave, it would seem necessary to take the notes in different octaves. But from one octave to another, there is too great a difference in most cases, and the scope of our instruments would not permit us to find all the sounds needed. Musicians have therefore inserted, betwen the sounds of the nat- ural gamut, intermediate sounds, which are designated under the Give the length of the waves corresponding to the C of successive scales. Give the number of vibrations per second. 454. What is an interval in music ? What are the different intervals ? How many intervals are there ? What is said of the comma ? 455. What are flats and sharps 1 CONCORD AND DISCOKD. 285 name of flats and sharps. These intermediate sounds bear the name of the lower note, followed by the word sharp, r of the upper note followed by the word^af. A note sharped or flatted, is elevated or lowered in the musical scale in such a manner, that the rapidity of its vibrations is increased or diminished in a certain ratio which varies for the different parts of the scale. Therefore, between all notes of the natural gamut, there are two intermediate sounds, a flat and a sharp. In music, the sharp is indicated by the sign (:fftr) and the flat by the letter (6.) 456. Concord and discord. Concord is the simultaneous pro- duction of many sounds, producing on the ear an agreeable sen- sation. Concord only takes place when the difference in the number of vibrations of simultaneous sounds is in a simple ratio, so that the ear readily discovers the relation. If the ratio is com- plicated, the ear is disagreeably affected, and discord results. The most simple concord is, evidently, unison (447,) in which the two sounds correspond to the same number of vibrations. After uni- son, comes the octave ; of which one of the two sounds has double the number of vibrations of the other. Representing the fundamental sound by 1, the acute octave will be represented by 2, and the grave octave by |. Consequently, every alternate vibration of the upper note, coincides with the commencement of the lower. After the octave, the most simple concords, are the fifth, 2, the sharp note being produced by three vibrations, while the grave note is pro- duced by two in the same time, correspoding to the interval C to G. This concord is termed a fifth, because the note G- is the fifth from C. A similar explanation applies to the numerical names of the other concords. The fourth, or A, corresponds to the interval C to F. The major third, or 1, corresponds to the interval C to R The minor third, or |, is the interval E to G. In fig. 280, the dots represent musical notes ; those vibrations which occur simultaneously, and therefore increase each other's power, are connected by vertical lines. How is a note sharped? How is a note flatted? 456. What is concord 1 When does concord take place f When does discord result ? What is the most simple concord ? Which is most simple after unison? What is the fifth? Mention the other concords. Show their relation to each other. 286 ACOUSTICS. Octave Fourth Major ) Third f Minor Third Thus the most simple concords are those in which the vibrations of the sounds are between themselves, as the numbers 4 : 3, 5 : 4, 6 : 5. 280 457. Perfect concord. Perfect concord, which produces on the ear the most agreeable musical sensation, is formed with ' . , . , Fifth three sounds, of which the number of vibrations is in the most simple relation between them- selves and the funda- mental sound. In the most agreeable accord, the relation between these sounds is 4, 5, 6. Thus, C E G. G B D, form two perfect accords. 458. Chromatic scale. In the diatonic scale, as we have seen, the in- tervals, though nearly equal, do not correspond. In order to do away with this inequality semi-tones have been introduced between the entire tones. The octave is thus made to consist of seven natural and five semi- tones. But even in this, the chromatic scale, the intervals are not perfectly equalized, though in practical music it is assumed that they are so. 459. Beating. When two sounds are produced at the same time which are not in unison, alternations of strength and feeble- ness are heard, which succeed each other at regular intervals. This phenomenon, called beating, discovered by Savart, is easily explained. Supposing that the number of vibrations of the two sounds was 30 and 31 ; after 30 vibrations of the first, and 31 of the second, there would be coincidence, and in consequence, beating, while at any other moment, the sonorous waves not being superin- posed, the effect would be less. If the beatings are near to each other, 457. What is perfect concord 1 Mention the perfect concords. 458. What is said of the chromatic scale ? 459. What is beating ? How is it explained t SENSIBILITY OF THE EAK. 287 there is produced a continuous sound, which is graver than the two sounds which compose it, since it comes from a single vibration, while the other sounds are made of 30 and 31 vibrations. 460. Diapason, tuning-fork. The diapason is a familiar in- strument, with which we may produce, at will, an invariable note ; its use regulates the tone of musical instruments. It is formed from a bar of steel, curved, as seen in fig. 281. It is sounded by drawing through it a 281 smooth rod of steel, large enough to spring open the limbs, and its vibra- tions are greatly strengthened to the ear by mounting it, as in the figure, upon a box of thin wood, open at one end. A diapason, giving C3, or 256 vibrations in a second, produces a sound comparable with that from an organ tube. The diapason is ordinarily formed to produce A3, corresponding to 428 vibra- tions in a second. The whole diatonic scale is thus con- veniently constructed, by a series of dia- pasons, arranged as in fig. 282, upon a sounding-box, A A. 461. Sensibility of the ear. Ac- cording to Savart, the most grave note the ear is capable of appreciating, is produced by from seven to eight complete vibrations per second. When a less number is made, the vibrations are heard as distinct and successive sounds. The most acute musical sound recognized, was produced by 24,000 complete vibra- 282 tions per second. Savart maintains, however, that this is not the extreme limit of the sensibility of the ear, which is capable ,.,.,.. A ***. re. tm. Jh, sol. la. ,n. v. * of wonderful training. *T * J A The same physicist has also demonstrated, that two complete vibrations are sufficient to What is the result if the beatings are near to each other ? 460. What is the tuning-fork 1 How may the sound be strength- ened ? 461. Which is the most grave note the ear can appreciate ? Which is the most acute musical sound recognized ? 288 ACOUSTICS. enable the ear to determine the rapidity of these vibrations ; that is, the height of the sound produced. If his wheel made 24,000 vibrations in a second, the two require but __L__th of a second. The ear may, therefore, compare sounds which act only during this wonderfully brief interval. Many insects produce sounds so acute as to baffle the human ear to distinguish them ; and naturalists assert, that there are many sounds in nature too acute for human ears, which are yet perfectly appreciated by the animals to which they are notes of warning, or calls of attraction. 3. Vibration of air contained in tubes. 462. Sonorous tubes. Mode of vibrating. In wind instru- ments, with walls of suitable thickness, the column of air con- tained in the tubes alone, enters into vibration. The material of the tube has no influence upon the sound, but ef- fects the timbre, (446,) in a striking and important manner. The pitch of the sound produced, depends partly 011 the size and situa- 283 284 tion of the embouchure ; still more on the manner of imparting the first movement to the air, and partly also on varying the length of the tube containing the column of air. Sonorous vibrations are produced in tubes in a number of ways. 1. By blowing obliquely into the open end of a tube, as in the Pandean pipe. 2. By directing a current of air into an embou- chure, or near the closed end of the tube. These tubes are called mouth pipes. 3. By thin vibrating laminae of metal, or of wood, called reeds, or by the vibra- tion of the lips, acting as reeds. 4. By a small flame of hydrogen gas. 463. Mouth-pipes. Fig. 283 represents the embouchure of an organ tube, fig. 284, that of a whistle or flageolet. In these two How many vibrations are necessary before the height of the mu- sical sound may be determined ? What of sounds too acute for hu- man ears ? 462. What is said of the vibration of wind instruments ? Upon what does the pitch of the sound depend ? How are sonorous vibrations produced in tubes ? REED PIPES. 289 figures, the air is introduced by the opening, i, (called the lu- miere) ; Z> o, is the mouth, of which the upper lip is beveled. The foot, P, fig. 284, connects the pipe with a wind-chest. When a rapid current of air passes through the inlet, it encounters the edge of the upper lip, which partially obstructs it, causing a shock, so that the air passes through 5 o in an intermittent manner. These pulsations are transmitted to the air in the tube, making it vibrate, and producing a sound. In order to have a pure sound, there must exist a certain relation be- tween the dimensions of the lips, the opening of the mouth, and the size of the lumiere. Again, the length of the tube must bear a certain ratio to its diameter. In those wind instruments, like the flute, flageolet, &c., in which various notes are produced by the opening and closing of holes in their sides by means of fingers or keys, there is a virtual variation in the length of the tube, which determines the pitch of the various notes produced. The number of vibrations depends upon the dimensions of the tube and the velocity of the current of air. 464. Reed pipes. A reed is an elastic plate of metal, or of wood, attached to an opening in such a manner, that a current of air, passing into the opening, causes the plate to vibrate. This vibration is propagated to the surrounding air. Reeds are found in hautboys, bassoons, clarionets, trumpets, and in the Jewish harp, which is the most simple instrument of this species. Fig. 285 represents a reed-pipe, mounted on the box of a bellows, Q. A glass, jE, in one of the walls of the tube, allows the vibrations of the reed to be seen. The case, H, serves to strengthen the sound. Fig. 286 represents the reed separated from the tube. It is composed of a rectan- gular case of wood, closed at its lower end, and open at the top, at a point o. A plate of copper, c c, contains a longitudinal opening, de- signed to allow the passage of the air from the tube, M N, through the orifice o. An elastic plate, i, almost closing the aperture, is confined at its upper end. The sliding rod, r, curved at its lower end, permits the regulation of the pitch, by alterations in the length of the vibrating part of the plate. When a current of air passes in through the foot, P, the reed vibrates, alternately opening and closing the aperture. The vibrations being very 463. How is the air thrown into vibration in mouth pipes ? Upon what does a pure sound depend 1 "What is the use of the keys 1 464. What is a reed ? What is the construction of the reed 1 What is the action of a current of air passing into the pipe ? 13 290 ACOUSTICS. rapid, the sound produced \ariesin pitch with the velocity of the current. This sound is transmitted to the exterior air through the opening 0. In this kind of reed, the vibrating plate passes through the aperture, 285 286 without its walls, and the tone is remarkably pure and free from any harshness. In the French horn, the trumpet, and other similar instruments, the sound is produced by the vibration of the lips of the performer, acting like reeds. 465. Gas jet. A jet of hy- drogen gas, or of common illu- minating gas, burned within a tall tube of glass, or other ma- terial, occasions, if accurately adjusted, a musical note. A simple form of this arrange- ment is seen in fig. 287, where hydrogen, generated by the action of dilute sulphuric acid on zinc in the bottle, is burned from the narrow glass tube, within one of larger dimensions. It is better to take the gas from a reservoir, or gas jet, with a key interposed, to regulate the volume of the flame. The cause of the vibrations and sound in this case is to be found in the pe- riodical explosions of small portions of free gas, mingled with common air. The heat occasions a powerful ascending current of air, momentarily extinguishing the flame, and at the same in- stant permitting the mixture of the atmospheric oxygen with a portion of inflammable gas. The expiring flame kindles this ex- plosive mixture, and relights the jet. As these successive phe- nomena occur with great rapidity, and at regular intervals, the necessary consequence is a musical note. 466. Musical instruments. The principles already explained in this chapter, will illustrate the peculiar power of the several In what instruments do the lips act as reeds? 465. Explain the vibra- tions from a gas jet. What causes the sound ? 466. What is eaid of wind instruments ? How are these instruments sounded ? VIBRATION Of AIR IN TUBES. 291 sorts of musical instruments in common use. It is inconsistent with our limited space to describe, in detail, these several instru- ments. Such details belong to a special treatise on 28 7 music. Musical instruments are divided, chiefly, under the head of wind and stringed instruments, and those like the drum, in which a membrane is the source of vibration. Wind instruments are sounded, either with an embouchure, like a flute, or with reeds. The first division includes the flute, pipe, flageolet, &c., ' and in the second are found the clarionet, bas- soon, horns, trombones, &c. The organ also be- longs to this division, and is, incomparably, the grandest of all musical instruments, as its power and majesty is without parallel in instrumental combinations. Stringed instruments are all compound instru- ments. The sounds produced by the vibration of the cords, are strengthened by elastic plates of wood, and inclosed portions of air, to which the cords communicate their own vibrations. They are vibrated either by a bow, as in the violin, by twanging, as in the harp, or by percussion, as in the piano. Drums are of three sorts ; the common regimental or snare drum, which is a cylinder of brass, covered with membrane, and beaten on one end only ; the bass, or double drum, of much larger di- mensions, and beaten on both heads ; and thirdly, the kettle drum, a hemispherical vessel of copper, covered with vellum, and sup- ported on a tripod. This drum has an opening in the metallic case, to equalize the vibrations. They all depend, of course, upon the vibration of tense membranes. (398.) 467. Laws of Bernoulli on the vibration of air in tubes. The following laws of the vibration of air contained in tubes, were discovered by Daniel Bernoulli, a celebrated geometrician who died in 1782. We may divide the tubes into two classes. a. Tubes of which the extremity opposite the mouth is closed. 5. Tubes open at both extremities. a. Tubes of which the extremity opposite the mouth is closed. 1st. The same tube may produce different sounds, the number of vibrations in which will be to each other as the odd numbers 1, 3, 5, 7, &c. Name some in each class of stringed instruments. How are they sounded ] What of drums ? What peculiarity is in the kettle-drum f 292 VOCAL AND AUDITORY APPARATUS. 2d. In tubes of unequal length, sounds of the same order correspond to the number of vibrations, which are in inverse ratio of the length of the tubes. 3d. The column of air vibrating in a tube, is divided into equal parts, which vibrate separately and in unison. The open orifice being always in the middle of a vibrating part, the length of a vibrating part is equal to the length of a wave corresponding to the sound produced. 5. Tubes open at T)oth extremities. The laws for tubes open at both extremities, are the same as the preceding, excepting that the sounds produced are repre- sented by the series of natural numbers, 1, 2, 3, 4, &c. ; and that the extremities of the tubes are in the middle of a vibrating part. Again, the fundamental sound of a tube open at both ex- tremities, is always the acute octave of the same sound in a tube closed at one extremity. 468. Results of experiment. The laws of Bernoulli are not exactly confirmed by experiment. With tubes having a bouche, or reed, graver sounds are obtained than those indicated by theory. That these laws may accord with theory, tubes must be used, of which the section is very small in relation to the length, and the air must be set in vibration in all the circumference of the tube, and not on a single side, as is generally done. VOCAL AND AUDITORY APPARATUS. THE VOICE. 469. Vocal apparatus of man. The vocal apparatus of man consists essentially of three parts, the trachea, the larynx, and the mouth. The lungs and trachea perform the part of a bellows or wind chest of an organ. The larynx corresponds to the mouth-piece, or that part of the organ tube which gives the pe- culiar character to the sound. The mouth and nasal passages correspond to that part of the tube above the mouth-piece from which the vibrations of the column of air are thrown into the atmosphere. The air comes from the lungs through the trachea, 467. What are the laws of Bernoulli on the vibration of air in tubes of which one extremity is closed 1 What the laws when both extremi- ties are open? 4G8. What results are obtained by experiment ? 469. Of what does the vocal apparatus of man consist? What office does each of these parts perform 1 THE LARYNX. 298 which is a tube formed of cartilaginous rings, and is delivered into the larynx, an organ nearly closed by two membranes. MQller has shown that the larynx is essentially a reed instrument, furnished with a double membranous tongue. In this the voice is pro- duced; for if an opening is pierced in the trachea, below the larynx, the air escapes by this opening, and it is not possible to produce a sound. If an opening is made above the larynx, it does not prevent the formation of sound. Magendie mentions the case of a man who had a fistulous opening in his trachea, and who could not speak unless he closed it, or wore a tight cravat. 470. The Larynx. This organ is composed essentially of four pieces of cartilage, called respectively the thyroid, cricoid, and the two arytenoid cartilages. In 288 fig. 288, showing a vertical section through the larynx and glottis, the position of the thyroid and cricoid cartilages is seen in 55, dd. The thyroid cartilage is made of two flat plates whose upper edges are curved somewhat like the letter 3, and forms a prominent projection on the throat of man, visible ex- teriorly, and vulgarly called Adam's Apple. The cricoid cartilage, aa, lies below the thyroid cartilage, and is in fact only an enlargement of one of the cartilaginous rings forming the wind-pipe. The position of the arytenoid cartilages is over the cri- coid cartilages. These several cartilages, with the hyoid bone, serve as points of attachment for the muscles forming the pro- per vocal apparatus. The two chief tongues of the glottis, or proper vocal cords, cc, extend from the thyroid cartilage to the arytenoid cartilages, and leave between them a fissure, the rima vocalis, or glottis, shown better in fig. 289. This fissure leads on one side into the trachea, which lies below the larynx, and on the other into the cavity of the larynx itself, which com- municates with the cavities of the mouth and nose. Besides the proper vocal cords, there are the ventricular cords, dd, situ- ated a small distance above them in the epiglottis ; they are less devel- What does MOller say of the larynx? 470. Describe the larynx. Where is the glottis situated 1 Describe fig. 288. 294 VOCAL AND AUDITORY APPARATUS. oped than the first. The ventricular cords have no part in the produc- tion of vocal sounds, which, however, they doubtless serve to modify and strengthen in the same way as the conical case surmounting an organ tube. (See H, fig. 235.) Between these two sets of cords are seen the deep depressions, called the ventricles of the glottis. 290 471. The Glottis. A clear idea may be obtained of the form and action of the glottis, by supposing two pieces of India rubber stretched over the orifice of a tube, so that a small fissure is left between them, fig. 29-0. By forcing air through such a tube, sounds will be pro- duced, varying with the tension of the membranes and the dimensions of the aperture. The glottis is a fissure-like opening, bounded by similar membranes. By means of a series of small muscles, the vocal cords may be extended or relaxed, at pleasure, while other muscles afford the power of altering the width of the vocal fissure. 472. Mechanism of the voice. The formation of sound in the larynx, as has been already suggested, is produced by the vibration of the vocal cords, acting as a species of membranous reed, under the influence of air from the lungs. The sound being produced as in ordinary reeds (464) by the intermittent current of air. 289 The glottis is the original seat of the sound, and although other parts of the respiratory apparatus have a certain in- fluence in modifying the tone, they have no share whatever in the production of the sounds, or in determining their pitch. When at rest, the lips of the glottis are wrinkled and plicated, so that the air in respiration passing through the fissure fails to put the membranes in vibration. But as the musician tunes his instrument by increasing or dimin- ishing the tension of its vibrating strings, so something like this occurs with the human larynx. These What is said of the ventricular cords? 471. How may a clear idea of the glottis be obtained 1 How are the vocal cords moved ? 472. How is sound produced in the larynx ? What is the original seat of sound t How are sounds produced by the glottis ? Describe fig. 289. RANGE OF THE HUMAN VOICE. 295 two conditions of the glottis are beautifully shown by the two parts of fig. 289, from Mailer. The upper shows the organ at rest, the vocal cords, cc, being relaxed, while in the lower, these cords are shown as in the act of vibrating ; the small air pas- sage, 0, opening into the trachea is never closed. When sounds are to be produced, the fissure is contracted and the membranes receive the degree of tension necessary for vibration. The sound varies according to the tension of the membranes, the magnitude of the fissure and the form and magnitude of the passages, through which the air, thus put in vibration, passes before it issues into the atmosphere. 473. Range of the human voice. In speaking, the range of the human voice is subject to but very little variation, being generally limited to half an octave. The entire range of voice in an individual is rarely three octaves, but the male and female voice taken together may be considered as reaching to four. Voices are variously denominated according to the extreme limits of their register proceeding from the highest to the lowest in the scale, as follows : soprano, contralto, tenor and basso. The soprano and contralto are voices found only, (with rare exceptions,) in females and children ; the tenor and basso are men's voices. There are intermediate compli- cations among them, the mezzo-soprano intervening between the con- tralto and soprano, and the barytone between the tenor and the basso. Since every individual organ differs from another, no exact limits can be assigned to these several classes of organs. The mean limits, how- ever, for each of these three classes, as determined from the experiments of Caignard de la Tour, Savart, and others, is as follows, the numbers annexed being the number of double vibrations of the glottis produced in a second of time. Soprano, KA Mezzo-Soprano, < Q O , Contralto, 1 ( 52S ( 3^2 ( 220 Tenor, j 13 2 Barytone, | no Basso, -J g<-> 5 474. Ventriloquism, stuttering, &c, Ventriloquism is sup- posed by many investigators to consist chiefly in the use of in- 473. What is the range of the voice in speaking? What is the entire range of the male and female voices 1 How are voices classified ? Give the number of vibrations of the glottis for the soprano, tenor, con- tralto, basso, &c. 296 VOCAL AND AUDITORY APPARATUS. spiratory sounds ; this is true only to a certain extent. The art of the ventriloquist depends greatly on the correctness of ear and flexibility of organ, through which common tones are modulated to the position and character in which the imaginary person is supposed to speak : other means often being used to heighten the deception, as concealing the face that the play of organs may not be observed ; often in speaking with expiratory notes, the air expelled by one expiration is distributed over a large space of time, and a considerable number of notes. In stuttering the several organs of speech do not play in their normal succession, and thus are continually interfered with in convulsive impulses and inefficient adjustments. The cause of this result lies almost wholly in the nervous apparatus which rules over the organs of speech. One important remedial means is to study carefully the articulation of the difficult letters, and to practice their pronunciation repeatedly and slowly. In deaf and dumb persons the organs of speech have originally no essential defects. The true cause of their dumbness lies in their inability to perceive sound. The impossibility of appreci- ating the several sounds, and thus gradually acquiring the power of properly adjusting the organs of speech, is the chief reason why the second infirmity is associated with the first. 475. Production of sounds by inferior animals. Mammifers. Voice is common to all mammifers, but speech, (the articulation of vocal sounds,) is the peculiar privilege of man. The sounds which the different animals produce are peculiar to the class to which they belong, thus the horse neighs, the dog barks, the cat mews, &c. These various modifications depend on the peculiar structure of the larynx, but more upon the form and dimensions of the nasal and other cavities, through which the vibrating air passes. The cat is distinguished from other mammifers by the almost equal development of the inferior and superior vccal cords. Many of its notes are almost human. The horse and ass are supplied with only two vocal cords. Animals which howl, and are heard at great distances, have generally large laryngeal ventricles. 474. What is said of ventriloquism ? "What menns are used to heighten the deception? What is said of stuttering ? What is the cause of this result? What of the organs of speech in deaf and dumb persons? 475. What is said of the sounds produced by .inferior animals? Upon what does the modification of these sounds depend? What is said of the cat and horse 1 What of howling animals ? THE EAR. 297 476. Birds are furnished with two larynx, a superior and in- ferior, which serve at the same time for the entrance andexit of air, and for the purposes of vocalization. The upper larynx, which corresponds to the larynx in mammifers, can only be re- garded as an accessory of the voice. The lower larynx is the true larynx ; it is placed at the lower part of the trachea, where it branches. Those birds in which it is absent are voiceless. The voice of birds is produced like that of mammifers, by the vibra- tion of the cords of the glottis. 477. Insects in general, produce sounds- remarkable for their acuteness. Their sounds are produced in a great number of ways, some effecting it by percussion, and some by the friction of exterior horny organs upon each other, as, for example, in the grass-hopper. In others, the swiftly recurring beatings of the wings produce sounds, as with the musquito. Many insects pro- duce sound by the action of some of their organs on the bodies around them, as, for example, the various insects which gnaw wood. THE EAR. . 478. Auditory apparatus of man. In the ear, impressions are not at once made upon the sensory nerve, by the body which ori- ginates the sensation, but they are propagated to it, through a medium capable of transmitting them. This medium is the at- mospheric air. The organ of hearing in man is composed of three parts ; the external ear, the middle ear, or tympanum, and the internal ear, or labyrinth. 479. The external ear consists of (1) the pinna, or pavilion, #, fig. 291, which collects the soniferous rays, and directs them into (2) the auditory canal, or meatus auditorius, &. The peculiar form of the pinna, with its numerous elevations and depressions, has not as yet been satisfactorily shown to be re- lated to the principles of acoustics. 476. What is said of voice in birds? What of the lower larynx ? What of voiceless birds? 477. What is said ef the sounds produced by insects? How are they produced ? 478. What is said of the ear ? Of what parts is the ear composed 1 479. Of what does the external ear consist ? What is said of the pinna ? What of the tympanum 1 13* 298 VOCAL AND AUDITORY APPARATUS. The auditory canal proceeds inwards from the pinna, to the tympanum, c ; it is an elliptical tube, about an inch long. Its interior is protected by hairs, and by a waxy secretion. 480. The middle ear, tympanum, or tympanic cavity. The 291 middle ear is a cavity in the petrous bone, and is, therefore, sur- rounded by walls of bone, (which have been removed in fig. 292, to show the interior construction.) This cavity, which is filled with air, is somewhat hemispherical in form ; it measures about half an inch in every direction. The auditory canal is directed into this cavity, but is separated from it by a thin oval membrane, the tympanic membrane, which is placed obliquely across the end of the canal, and at an angle of about 45 ; its outward plane looking downwards. Into the tympanic cavity there are ten openings. 1. That of the auditory canal ; 2, 3, the fenestra ovalis, and fenestra rotunda, so called from their form, situated opposite the auditory canal, and like it, over both are stretched thin elastic membranes. 4. The Eustachian tube, a membranous canal, which extends from the anterior of the tympanum to the pharynx, and forms part of the respiratory passage behind the mouth ; its office is, like the hole 480. What is the middle ear? What is said of the tympanic membrane ? What is said of the openings into the tympanic cavity ? What is said of the chain of bones ? THE INTERNAL EAR. 299 o, and the 293 in a kettle drum, to preserve a permanent equilibrium between the air in the cavity, 292 and the external air. When this is ob- structed, deafness re- sults, because the air in the tympanum is prevented from vi- brating freely. 5. The mastoid cells. The other openings are for the passage of various nerves and muscles. The tympanum is crossed by a chain of bones, three in number, fig. 293. The malleus, or hammer bone, m, the incus, or anvil, stapes, or stirrup, t. They are connected with each other in such a manner as to allow of slight movements. This chain of bones is attached at one end, as is shown in fig. 291, by the handle of the malleus, to the tympanic* membrane, and at the other by the foot of the stirrup, to the membrane of the fenestra ovalis. o " The muscles which act upon these small bones are *^=* supposed to have the power of giving more or less ^ tension to the membranes which they connect, and thus rendering them more or less sensitive to sonorous undulations. 481. The internal ear, called, from its complicated structure, the labyrinth, has its channels curved and excavated in the petrous bone, the hardest of any in the body. The labyrinth consists of three parts ; the vestibule, the semicircular canals, and the cochlea. The vestibule, <7, fig. 291, is a central chamber, excavated in the petrous bone ; in it are a number of openings, for branches of the auditory nerve, small arteries, &c. In its external wall, the fenestra ovalis is found. The semicircular canals are three in number, opening into the vestibule at its posterior and upper part, and placed in planes at f What is said of the muscles that act upo n these bones ? 481. Of what does the labyrinth consist ? What is the vestibule ? 800 VOCAL AND AUDITORY APPARATUS. right angles to each other. Within these canals are placed flex- ible tubes, of the same form, called membranous canals. The cochlea, i, is a conical tube, wound spirally, making two and a half turns. It resembles a snail's shell in appearance ; whence its name. Its interior is divided by a spiral lamina, called the lamina spiralis, into two passages which communicate by a little hole in the upper part of the helix. Between the membra- nous and the bony labyrinths, a peculiar liquid (the perilymph) intervenes, which also fills the cavities and cochlea ; the mem- branous labyrinth is distended by another liquid, (the endo- lyrnph.) Within the labyrinth thus filled with liquid, the ter- minal filaments of the auditory nerve are placed. Fig. 292 is a magnified view of the labyrinth, showing the form and relation of the vestibule, semicircular canals and cochlea, partly laid open, so as to display their interior construction. 482. Common theory of the function of the auditory parts. The explanation usually given of the functions of the various parts of the ear, is as follows. The waves of sound passing into the external ear, are collected and directed into the auditory canal, and strike upon the tympanic membrane, which is thrown into vibration. The chain of bones connecting the tympanic membrane with the oval one, participate in the movement, and convey it across the tympanic cavity. Under the impulses thus communicated to it, the oval membrane vibrates, and likewise the liquid in the labyrinth, and so the filaments of the auditory nerve become affected, and the sensation of sound is transmitted to the brain. This explanation is exceedingly imperfect, as it assigns no use for many of the most complicated and delicate arrangements of the ear, and gives no explanation of the manner in which this organ presents to the mind the various relations of sound. 483. Function of the drum, cochlea, and canals. As has been stated, (443-46,) the physical peculiarities existing in the waves of sound, which we are able to perceive, are three ; 1st. The in- tensity, namely, the loudness or feebleness of the sound. 2d. Its note or pitch, and 3d. Its timbre or quality. The ear, it is apparent, is affected by each of these peculiarities, What are the semicircular canals ? What is the cochlea? 482. What is the common theory of the function of the auditor} 7 parts \ What is said of this explanation ? 483. What are the physical pe- culiarities of sound? ORGANS OF HEARING IN ANIMALS. 801 and conveys them to our mind. Dr. Draper, in his Human Physiol- ogy, has suggested the following points, which may or may not be confirmed. 1st. That the drum is for the measurement of intensity. 2d. The cochlea for the recognition of wave-length, or pitch ; and 3d. The semicircular canals for the appreciation of quality. It has been proved by the experiments of Savart and Milller, that when the tension of the tympanic membrane is increased, the sono- rous undulations pass with less readiness through it. Under natural circumstances, this is accomplished by a muscle, (the tensor tympani,) which contracts it to such an extent as to bring the membrane to a standard tension. The mind judges of the degree of force neces- sary to produce this result, and so estimates the intensity of sound. The first third of the spiral lamina contained in the cochlea, is bone, the intermediate portion is membranous, and the residual, muscular. This lamina is broadest at the bony part, the base, and tapers off toward the apex, reminding one of the structure of the harp, or the gradually shortening strings of the piano. It is sup- posed that each external musical note does not throw the lamina of the cochlea into vibration throughout its whole length, but causes only a special part to vibrate ; thereby, the particular nerve fibril supplying that portion, is affected, and thus a distinct sensation is communicated to the br#in, corresponding to the pitch of the note. As the intensity of sounds is assumed to be judged of by the tympa- num, and their pitch by the cochlea, there is a strong presumption that the semicircular canals have the function of distinguishing their qual- ity. So little is known, however, of the mechanical peculiarities on which distinctions of quality in sounds depend, that we cannot trace out the form of the organ calculated to distinguish them. The pre- sumption that the function of the semicircular canals is for the appre- ciation of quality, is strengthened by facts drawn from comparative physiology. Let us therefore examine the 484. Organs of hearing in the lower animals. The zoophytes appear to be wanting in the sense of hearing, and no special au- ditory apparatus has been discovered in insects, although they do not appear to be altogether insensible to sound. In the mol- lusca, the organ is a sack, filled with the liquid, in which the last fibrils of the acoustic nerve are diffused, or a nerve fibril, in connection with a little stony body, (an otolith,) included in a sack What office does Dr. Draper assign to each part of the ear ? How is the tension of the tympanic membrane increased ? What is said of the vibration of the laminae of the cochlea by musical notes ? 484. What is said of the zoophytes ? What of the mollusca ? What of lizards 1 302 HEAT. of water. These animals can only distinguish one noise from another, or their quality, and that imperfectly, and have no percep- tion of musical notes. This organ, corresponding, as is assumed, to the semicircular canals, increases in complexity as we rise in the scale of being. In lizards and scaly serpents, the ear commences with the tympanic membrane ; and there is added a conical coch- lea. As we pass through them, the plan is further developed ; the tympanic cavity, Eustachian tube, the chain of bones, &c., ap- pear. In birds there is a continued improvement, and all the serial tubes of mammals have external ears, while a full develop- ment of all the auditory parts is reached only in man. PHYSICS OF IMPONDERABLE AGENTS. 485. We have been occupied, hitherto, with the consideration of those topics connected with the forces of attraction and re- pulsion, as manifested in the form and other sensible properties of matter, at rest, or in motion. These forces have been already denned, (29 and 30,) and limited. It now remains to consider certain other remarkable forees called HEAT, LIGHT, and ELECTKI- CITY, and commonly styled the IMPONDERABLE AGENTS, because the presence or absence of their manifestations causes no sensible difference in the weight of matter containing them. HEAT. 1. General Remarks. 486. What is heat ? Heat is the agent whose presence or ab- sence awakens in us the sensation of warmth or coldness. The three physical states of matter, namely, the solid, liquid, and gaseous, (38,) are due to this agent. " Like all other physical agents, it is manifested and measured by its effects upon matter. While we call it an imponderable agent, it is, so far as we know, inseparably connected with changes in the physical and chemical condition of matter. Heat is properly a species of motion. 487. Definition of terms. 1st. Expansion, the most con- spicuous effect of heat upon a body, whether solid, fluid, or gas- What is said of birds, , being known, the linear expansion of t may be calculated. Such an instrument is a pyrometer. All those just described (5 18, 520) equally illustrate linear expansion. 524. Cubical expansion may be shown by the apparatus, fig. 315. The ring of metal, m, allows the ball of copper, a, merely to pass through it at the ordinary temperature. If the ball is heated, it expands in all directions, and will then no longer pass through the ring, but rests upon it, as is shown in the figure. As the ball cools, it gradually returns to its original dimensions, and again passes through the ring as before. 525. Relation between cubical and linear expansion If a solid is perfectly homogeneous, it will expand uniformly in every What two kinds of expansion are recognized in solids ? 523. How- is linear expansion illustrated? Describe fig. 814. What is such an instrument called ? 524. How is cubical expansion shown ? 326 HEAT. direction, by the same elevation of temperature ; that is, its 315 length, breadth and depth, will be increased in the same proportion. If a solid was heated to a certain temperature, and increased in length one one-thousandth of its original length, its surface would have increased two one-thousandths of its original area, and its volume, three one-thousandths : of its original bulk. This theoretical view is found to be !r" nearly, but not quite true, in fact. 526. Expansion of crystals. Crystals of the monometric system, (54,) like common salt, fluor spar, &c., expand equally in all directions. In this system all the crystallogenic axes are equal, and at right angles to each other. In crystals of all other systems, the expansion is the same in only two directions, (dimetric system, 55,) or it is dif- ferent in all three, (57, 58,) depending upon the position of the crystallogenic axes to each other. The amount of expansion in some crystalline compound bodies, e. g., fluor spar, aragonite, sulphate of barytes, quartz, &c., is found to be greater than in metals, contrary to the generally re- ceived opinion. [H. Kopp.] 527. Uniformity in the expansion of solids. Between 32, and 212 F., the rate of expansion in solids is very uniform, that is, the increase in volume which a solid undergoes is equal for each degree of temperature between these two points. When solids are exposed to temperatures much above 212, and espe- cially when near the temperature at which they fuse, or melt, their ratio of expansion is found to increase with each increment of temperature, except steel, whose expansion for 1 is less at high temperatures. The expansion of solids is variously measured. Lavoisier and La- place placed a bar of the substance under examination in a water bath. One end was fixed, the other free, and touched the end of a lever, turning by any expansion of the bar, and causing a movement in a telescope attached to the lever. This read off the expansions from 32 to 212, upon a scale placed at a proper distance. 625. When are linear and cubical expansion equal ? What is this ratio? 526. How do crystals of the monometric system expand? How in other systems ? What is said of expansion in some com- pounds compared with metals from which they are derived ? INCREASE OF MEAN EXPANSION BY HEAT. 327 528. Table of the expansion of solids. In the following table, the expansion of the more important substances is given ac- cording to the best authorities. 1,000,000 parts at 32 F. At 212 F- become Expt In length. insion. In bulk. Authority. English flint glass, Glass tube, (French,) Platinum, . . . Palladium, . . . Tempered steel, . Antimony, . . . Iron, 1,000,811 1,000,861 1,000,884 1,001,000 1,001,079 1,001,083 1,001 182 1 in 1248 1 in 1148 1 in 1131 1 in 1000 1 in 926 1 in 923 1 in 846 1 in 316 1 in 382' 1 in 377 ( 1 in 333 1 in 309 1 in 307 1 in 282 Lavoisier ^\^^ I s^ t ne object, as from A to T, and it continues /^O^J ^"" i fl its new direction in a straight line until it leaves the body, vdieu it again resumes a di- rection, T F, parallel to its first course. 593. Lens The burning glass or double conyex lens, has the form shown in fig. 336. The axis of 'the lens is the straight 336 lirfe M F, passing through the cen- tres of the faces. The focus, F, is the point where the refracted rays converge after being transmitted F -through the lens. It is only with a lens of rock salt, that the rays of all our sources of heat can be con- densed, for a lens of glass affects only the solar rays, and becomes itself heated by artificial heat. A lens of ice was made in England in 1763, having a diameter of 3 metres, (118*112 in.,) at whose focus gun-powder, paper,and other com- bustibles were inflamed. Burning glasses have generally more power than mirrors of equal diameter. Both produce their more intense effects on high mountains after a fall of snow, for then the air is free from mois- ture, and the solar rays lose less of their intensity in passing through it. CALORIMETRY. 8. Specific Tieat. 594. Calorimetry, (calor, heat, and metron, measure,) is the measurement of the quantities of heat which different bodies absorb or emit during a known change in temperature, or when they change their state. Water, having the highest specific heat, is selected as the standard of comparison in these experi- ments. The thermal unit, in this country and in England, is the quan- tity of heat which is necessary to raise a pound of pure water 593. How does a lens affect heat -rays? Explain the burning glass from fig. 335. What is said of ice for a lens? When are the best effects of burning glass seen- Why? 594. What is calorimetry ? What is the standard of comparison ? W hat is the thermal unit here ? What in Europe? METHOD OP MIXTURES. 867 from 32 to 33 F. In France, and in Europe generally, the thermal unit is the quantity of heat necessary for raising one kilogramme (2-20486 Ibs.) of water from to 1 C ( = 32 to 33-8 F.) 595. Specific heat. Different bodies have different capacities for heat ; that is, equal weights of different bodies require une- qual quantities of heat to raise their temperature a certain num- ber of degrees. If equal weights of water and mercury at the same temperature be placed over the same source of heat, it will be found, that the mercury becomes heated much more quickly than the water. That when the water is heated 10 the mercury will have become heated 330 ; the capacity of water for heat is, therefore, 33 times as great as that of mercury. Each substance in this regard has its own capacity for heat. This relation is called caloric capacity, or more commonly, specific heat. Three methods have been devised for determining the specific heat of bodies : these are, 1st, the method of mixture ; 2d, the melting of ice ; 3d, by cooling. 596. Method of mixture. This method is exceedingly simple in theory, and approximate results may thus be easily obtained. If a pint of water at 150 be mixed quickly with a pint at 50 F., the two measures of water will have a temperature of 100, or the arithmetical mean of the two temperatures before mixture. If, however, a measure of mercury at 50 be mingled with an equal measure of water at 150, the temperature of the mixture will be 118. The mercury has gained 48 while the water has lost 32. Hence it is inferred, that the same quantity of heat can raise the temperature of mercury through twice as many de- grees as that of water, and that the specific heat of water is to that of mercury as 1 : 0*47 when compared by measure. If, however, equal weights of these bodies be taken, the re- sulting temperature is then still more in contrast. A pound of mercury at 40, mixed with the same quantity of water at 156, produces a mixture whose temperature is 152-3. The water loses 3-7, while the mercury gains 112-3, and therefore, taking 595. What is specific heat? Illustrate this from water and mercury. What is their relative capacity for heat? How in regard to other bodies ? What methods are given for determining specific heat ? 596. Describe the method of mixtures. Is the comparison made by weight or measure ? Illustrate it from the case of mercury and water. How is it applied to solids ? 368 HEAT. the specific heat of water as 1, that of the mercury will be 0-033, since, 3-7 : ! : : 112-3 : x = (0-033.) In determining the specific heat of solids by this method, a weighed mass of each substance is heated to the proper degree, and is then plunged into a measure of water of known temperature and weight. The elevation of temperature produced in each case is carefully noted. 597. Method of fusion of ice. This method is founded on the quantity of ice melted by different bodies in cooling, through the same number of degrees. The most simple form of experiment consists in placing the heated body, TF", whose specific heat is to be determined, in a cavity made in a compact block of ice, fig. 337, and then clo- 337 sing the cavity by a plate, 5, of the same material. During the cooling, a definite weight of the ice is melted, and the specific heat is determined from 1 the weight of the fusion-water produced as com- pared with the temperature and weight of the sub- ' stance under trial. Several sources of error attach to this method of experiment. Lavoisier and Laplace contrived the apparatus, fig. 338, called a calorimeter. It consists of three vessels made of sheet tin or copper. In the interior vessel, c, pierced with holes and closed by a double cover, is placed the substance whose specific heat is to be determined. This is en- 338 tirely surrounded by ice contained in the second vessel, 5, and also on the cover. In order to cut off the heat of the surrounding air, the exterior vessel a, is also filled with ice. The water from the ice melted in this outer vessel, passes off by the stop-cock, r. The body in the interior vessel, cooling, melts the ice surrounding it, and the water from it flows off through the stop-cock, s, and is weighed. The specific heat of different substances is determined in this apparatus by the comparative weights of the water produced during the experiments ; in which a certain weight of each 597. What is the 2d method? Describe fig. 337. Describe the calorimeter of Lavoisier, fig. 388, and its use. How is specific heat measured by this. How in case of a liquid ? What objections exist ? METHOD OF COOLING. 369 body cools from an agreed temperature, e. g., (212 F.,) to 32, the constant temperature of the vessel C. The specific heat of a liquid is determined by placing it in a ves sel, as of glass, whose specific heat is known. The amount of ice melted by the liquid, is the whole quantity of water produced, minus that which would be melted by the glass alone. This method, though excellent in principle, is subject to many in- accuracies, which render the results incorrect. 598. Method of cooling. This method is founded on the dif" ferent rates of cooling of equal masses of different substances ; those having the greatest specific heat cooling most slowly. Equal volumes of the bodies, whose specific heat is to be de- termined, are placed successively in a very thin metallic vessel, in the centre of which is a delicate thermometer. Solids must be reduced to powder in order to render their conductibility as equal as possible. The vessel containing the body under exam- ination, is surrounded by a second vessel, maintained at a con- stant temperature, or better, in a vessel from which the air is ex- hausted. The times required to cool the bodies a certain number of degrees, as from 212 to 60, compared with the time required to cool water through the same thermometric interval, represents approximately the specific heat of the bodies in question. 599. Specific heat of gases. The specific heat of gases is either the quantity of heat which is necessary to raise the gases 1 in temperature, compared either with an equal weight of water, or with an equal volume of air. The specific heat of gases is gen- erally determined when under a constant pressure, but some- times when confined within a given volume. 600. Tables of the specific heats of solids, liquids and gases. In the following tables, the first column gives the specific heat of different elementary solids and liquids as determined by Reg- nault. The second column gives the atomic weights, (on the hydrogen scale,) and the numbers in the third column are the product of the multiplication of those in the first, by those in the second column. The law deduced from this relation is given in 604. 598. What is the third method? On what is it founded? How is it applied? How to solids? What precautions are used? In what terms are the results obtained ? 599. What is the specific heat of gases ? How is it generally determined ? What is the mode in com- parison with air ? 16* 370 HEAT. SOLIDS. Water - 100. Names. Specific heats. C. Atomic weights. P- Product, C x p. Aluminum, . . Sulphur, .... Iron, CoMlt, .... Nickel, . . . . Copper, .... 0-2143 0-2026 01138 0-1070 0-1086 0-0952 0*0956 13-7 16- 28- 29-5 29-6 31*7 32'6 2-94 3-24 319 316 3-21 3-02 312 Selenium, . . . Tin, 0-0762 00562 40- 59' 3-04 3-31 Platinum, . . . Lead, 0-0324 0*0314 98-7 103*7 3-20 3-26 Phosphorus, . . Arsenic, .... Silver, .... Iodine, .... Antimony, . . . Gold 01887 0-0814 0-0570 0-0541 0-0508 0*0324 31- 75- 108- 127- 120-3 197' 5-85 610 616 6-87 611 6"38 Bismuth, .... 0-0308 208- 6-41 Mercury, (liquid,) Mercury, (solid,) Bromine, (liquid,) Bromine, (solid, 28C. LIQUIDS 0-03331 0-03241 OH094 0-08432 100 100 80 80 3-33 3-24 6-74 The following table of the specific heat of gases contains the results as obtained by Delaroche and Berard. Simple gases or mixtures. For the same volume air being 1. For the same weight air beinsj ! For the same weight water being 1 . Air, .... I'OOO 1*00 0*2669 Oxygen, . . . 0-9765 0*8838 0-2361 Hydrogen, . . Nitrogen, . . 0-9033 1-000 12*3401 1-0318 0*2936 0-2753 Compound gases. Carbonic acid, 1-2583 0*8280 0-2210 Protox. nitrogen, 1-3503 0*8878 0-2369 Olefiant gas, 1-5530 1*5763 0-4207 Oxyd of carbon, 1-0340 1*0805 0-2884 600. What is shown in the tables here given ? Give the results for iron, and mercury, and hydrogen. SPECIFIC HEAT AND ATOMIC WEIGHT. 371 601. Mechanical compression, affecting specific heat. Any change affecting the relative distance between the particles of a body, varies its specific heat. 602. Decrease of temperature in the atmosphere from eleva- tion. The specific heat of aeriform bodies, like that of solids and liquids, increases by condensation and diminishes by rare- faction. The continued diminution in temperature as we ascend in the atmosphere, is due chiefly to this cause. The average diminution in temperature in ascending from the sea level is 1 F. for every 300 feet. Supposing the average temperature of the air at the level of the sea, near the equator, to be 80, and toward the poles 0, the figures in the second and third column of the following table will express approximately the temperature at different elevations. Decrease of temperature in the atmosphere from elevation. Altitude in feet. Equatorial temperature. Arctic temperature. o- 5,000' 10,000- 15,000- 20,000- 25,000- 30,000- 80 64 '4 48 -4 31-4 12'8 r-6 30 '7 18'5 37-8 58-8 82-l 1091 140'3 603. Specific heat of the same body in a liquid or solid state. A body in the liquid state has a greater specific heat than when it is in the solid form, as might naturally be concluded from the fact, that the addition of heat is necessary to convert the solid into a liquid. Thus ice has a specific heat of 0-505, water being 1000, sulphur (solid,) 0-2026 fluid, 0*2340 ; phosphorus, between 45 and 6, 0-1887, at 212, 0-2045, &c. The high specific heat of water moderates very greatly the rapid- ity of natural transitions from heat to cold and from cold to heat, owing to the large quantity of heat emitted or absorbed by the ocean in accommodating itself to variations in external temperature. 601. How does mechanical compression affect specific heat ? 602. How do condensation and the reverse affect the specific heat of gases? What is the average diminution of temperature in ascending in the air? Illustrate these differences from the table. 603. How do the specific heats of the same substance as solids and liquids compare ? Illustrate this from the table. How does the specific heat of water affect climate 1 372 HEAT. 604. Relation between the specific heat and atomic weight of elements. Dulong and Petit, from their researches upon the el- ements, were led to conclude, that the ultimate atoms of all ele- ments possessed the same capacity for heat, and they accordingly announced the law, that, The specific heat of elementary substances is in inverse ratio to their atomic weights. This law appears to be true for most of the elements, as will be seen by examining the table of atomic weights and specific heats in 600. It will be noticed, that the one increases in al- most the exact proportion in which the other diminishes, and that by multiplying them together, a very nearly constant pro- duct is obtained. Some elements, as those given in the lower part of the table, gives a product (CXp) double of the others. So that equivalent weights of these would contain twice as much heat as equivalent weights of those first given. 605. The relation between the specific heat and atomic weight of compounds is expressed by Regnault in the following law. In all compound bodies containing the same number of atoms and of similar chemical constitution, the specific heats are in inverse ratio to their atomic ID eights. 9. Liquefaction and solidification. 606. Latent heat. During the conversion of a solid into a liquid, or of a liquid into a gas or vapor, a certain quantity of heat disappears which is not perceptible for the time to the ther- mometer or to the senses. This is called latent heat. 607. Disappearance of heat during liquefaction. That a large quantity of heat disappears during the liquefaction of a solid is apparent from the following experiments. Let a pound of ice and a pound of water, each at the tempera- ture of 32, be exposed to the same source of heat in precisely similar vessels. It will be found, at the moment when all the ice is melted, that the water into which it is converted has still the temperature of 32 ; while the temperature of the other pound 604. "What did Dulong and Petit infer respecting atomic weights and specific heats of elements? What is their law? How is this law illustrated in the table in 600? What numbers produce a con- stant product? 605. What is the relation between the specific heat and atomic weights of compounds ? Give Regnault's law. What exceptions are these laws subject to? 606. What is latent heat ? What changes give evidence of it? 607. What experiment illus- trates the disappearance of heat during liquefaction ? LATENT HEAT. 3T3 of water has risen from 32 to 174. As both have received the same amount of heat, it follows, that the 142 which have dis- appeared r have been used in converting the ice into water, and have become latent. If a pound of water at 212 be mixed with a pound of pow- dered ice at 32, when the ice is melted the two pounds will have the temperature of only 52 ; the ice gains only 19 while the water loses 161. Here again 142 have disappeared or have become latent. 608. Liquefaction and congelation are always gradual, owing to the absorption or evolution of heat during these processes. If this was not so, water at 32 would immediately become s ice, upon losing the smallest additional portion of its heat, and on the other hand, ice would suddenly pass from the solid to the liquid state by the smallest addition of heat. This fact, coupled with the law of irregular expansion of water, will explain why ice never acquires any very great thickness. The high specific heat of water acts to moderate the natural changes of temperatures. 609. Table of latent heat. The most accurate experiments upon this subject have been made by M. Person ; he concludes that, The latent heat of fusion is obtained ~by multiplying the dif- ference between the specific heat of the substance in its liquid and solid form, by the quantity obtained by adding the number 256 (an experimental constant furnished by researches upon the latent heat of water) to the melting point of the substance in question. TABLE OF LATENT HEAT. F. Water = 1 F Water f -I Water, Nitrate silver, " potash, Zinc, Silver, Tin, 142-65 113-34 85-26 50-63 "37-92 25-65 i-ooo 0-704 0-598 0-355 0-265 0-179 j Cadmium, Bismuth, Sulphur, Lead, Phosphorus, Mercury, 25-44 22-75 16-85 9-65 9-05 5-11 0171 0159 0118 0'067 0*063 0-035 Give the particulars. How much heat disappears in this experi- ment? How is the same fact otherwise illustrated ? 608. Why are liquefaction and congelation gradual? What if this was not so? Explain this more particularly. Why is the air chilled when snow and ice melt ? 609. What is Person's law regarding latent heat ? Explain the table. 374 HEAT. The number in the second columns may be considered as the number of pounds of water that could be raised 1 F. by the heat emitted during the congelation of one pound of each of the substances included in the table. 610. Freezing mixtures. Solids cannot pass into the liquid state without absorbing and rendering latent, a certain amount of heat. If the heat necessary for the liquefaction is not sup- plied from some external source, the body liquefying will ab- sorb its own sensible heat. A knowledge of this fact enables us a't pleasure, in the hottest seasons and climates, to produce ex- treme degrees of cold. The so-called freezing-mixtures are compounds of two or more substances, one of which is a solid. These, when mixed together, enter into combination and liquefy. The operation should be so conducted, that no heat can be absorbed from external sources, and hence as the substances liquefy, a depression of temperature results, proportional to the heat rendered latent. The most convenient freezing mixture is salt 1 part, and ice or snow 2 parts, universally used in the freezing of ices and creams. With this freezing mixture, a temperature of 4 or 5 below zero can be maintained for many hours. A solution of equal parts of nitre and sal-ammoniac will reduce the temperature from 50 to 10 F. Very well constructed ice-cream freezers are now commonly sold in the shops, in which an adroit use has been made of the laws of radiant heat, to facilitate the rapidity of this operation. Thilorier, with a mixture of solid carbonic acid and sulphuric acid, or sulphuric ether, obtained a temperature 120 below zero. More lately, Mitchell obtained by the same means a temperature of 130 and 146 F. At the former temperature, alcohol (den. 798) had the consistency of oil, and at the latter temperature resembled melting wax. In the liquefaction of metallic alloys, a similar depression is ob- served. When an alloy composed of 207 parts lead, 118 tin and 284 bismuth,' is dissolved in 1617 parts mercury, the temperature will sink from 63 to 14 F. In producing extreme degrees of cold, the substance to be operated upon is first cooled to a certain degree by a less powerful freezing mixture, before the more energetic one is used ; the full effect of the latter is thus obtained. 610. On what fact do freezing mixtures rest 1 What are freezing mixtures? What is the most convenient mixture 1 What others are noticed in the table and what temperatures do they produce ? What of metallic alloys ? How Iowa temperature has been olftained by solid carbonic acid and sulphuric ether? How are freezing mixtures most economically applied ? Give examples from the table. LAWS OP FUSION. 375 TABLE OF FREEZING MIXTURES. Substances. Parts by Weight. Cooling. Sulphate of soda, Hydrochloric acid, 8 5 from -+- 50 to Snow or ice, 2 " x " 5 Common salt, 1 Sulphate of soda, Dilute nitric acid, 3 2 " +50 "3 Sulphate of soda, 6 Nitrate of ammonia, 5 , " + 50 " 14 Dilute nitric acid, 4 Snow or ice, Chlorid of calcium, 3 4 " + 20 " 14 611. Laws of fusion Expansion (the first effect of heat) has a limit, at which solids become liquids. The powers of cohesion are then subordinate to those of repulsion, and fusion results. Fusion takes place in accordance with the following laws. 1st. All solids enter into fusion at a certain temperature, invariable for the same substance. 2d. Whatever may ~be the intensity of the source of heat when the fusion commences, the .temperature remains constant until the whole mass is fused. The freezing points of some of the more important substances are given in the following table. TABLE OF FUSING POINTS. F. Authority. || C F. | Authority Mercury, Oil of vitriol, 39 30 Regnault. Bismuth, Lead, 518 ) 633-2f PerSOn Bromine, 4 Zinc, 773 Daniell Ice, 32 Antimony, 963-6 Plattner Phosphorus, 111 "5 ScrOtter. Silver, 1873 Daniell Potas'm, (ab't,) 131' Copper, 2004.8 Plattner Yellow wax, 143'6 Person., Gold, 2016 1 Sodium, (ab't,) Iodine, 190' 2 24 "6 Cast iron, 2786 -p. . ( above f Danie11 Sulphur, Tin, 239' 451' ( Person Wro'ght iron, Platinum, \ 3280 J 4591-2 Plattner 612. Peculiarities in the fusion of certain solids. Certain solids soften before becoming liquefied, while others never be- come entirely fluid. 611. What limits has expansion? Explain this table. "What are the laws of fusion ? 376 HEAT. Thus many organic substances, as tallow, wax and butter, soften at temperatures below those at which they fuse. This is undoubtedly owing to the fact, that they are composed of several separate substances which melt at various temperatures. Those metals, like iron and platinum, capable of welding, soften before they fuse. Pieces of such metals heated until they soften, may be joined together by hammering, or severe pressure. Some substances, again, never attain perfect fluidity, as is the case with glass and certain metals, which always remain more or less viscid. The fusion of sulphur also presents striking pecu- liarities. (See Chemistry.) 613. Refractory bodies. Substances difficult of fusion are c alled refractory bodies. Among the most refractory bodies are silica, the earths lime, baryta, alumina, 5, &c. This statement how- ever is found to be somewhat inaccurate, although in practice it may be assumed to be nearly correct. From the experiments of Regnault, it appears that the sum of the latent and sensible heat increases with the temperature by a constant difference of 0'305 for each degree F., as is shown in the following table. Temp. Latent heat i Sum Af lateU heat and een- 'sible heat. Latent heat Sum ot latent heat and sensi- ble heat. 32 68 86 104 140 194 212 1092'6 1067 '4 1054 "8 1042 '2 1017 -0 979 '2 966 '6 1124-6 1135 '4 1140 -8 1146 -2 1157 -0 1173 -2 1178 '6 248 284 320 338 374 410 446 939'6 914 '4 889 '2 874 '8 849 '6 822 '6 995 '6 1187'6 1198 '4 1209 "2 1212 '8 1223 -6 1232 '6 1241 -6 639. Mechanical force developed during evaporation. During the conversion of a liquid into vapor, a certain mechanical force is exerted. The amount of this force depends on the pressure Give the latent heat of steam according to several authorities. 638. What is the whole amount of heat in steam? How has this been generally stated? Give an example. What correction have the results of Kegnault supplied? What is the co- efficient of cor- rection for each degree F. I 639. What is developed during evapo- ration 1 ALEMBICS. 393 of the vapor and the increase in volume which the liquid under- goes. Equal volumes of different liquids produce unequal amounts of vapor at their respective boiling points. 1 cubic inch of water expands into 1696 cubic in. vapor at b. point- 1 " " alcohol " " 528 " " 1 " " ether " '" 298 " " 1 " " turpentine " 193 " " " " " Now although the latent heat of equal weights of other vapors is less than that of steam, yet no advantage would arise in generating vapor from them in place of water in the steam-engine. For equal volumes of alcoholic and aqueous vapor contain nearly the same amount of latent heat at their respective boiling points, and such is the case to a great extent with other liquids. The cost of the fuel in generating vapor would be in proportion to the amount of latent heat in equal volumes of the vapor. 11. Condensation of vapors and gases. 640. Liquefaction of vapors, or the conversion of vapors into liquids, is accomplished in three ways. 1st, by cooling ; 2d, by compression ; and 3d, by chemical affinity. Only the two first of these methods will be spoken of. When vapors or gases are condensed into liquids, the same amount of heat is given out as sensible heat which was absorbed and rendered latent when they assumed the aeriform condition. 641. Distillation is the successive evaporation and condensa- tion of liquids. The process depends on the rapid formation o vapor during ebullition, and the condensation of the vapor by cooling. Distillation is used, first, for the separation of fluids from solids, as the distillation of ordinary water, to separate the impurities con- tained in it; 2d, for the separation of liquids unequally volatile, as in the distillation of fermented liquors, to separate the volatile spirits from the watery matter. 642. Alembics. Distilling apparatus of various kinds are em- Upon what does the amount of force depend ? Give the volumes of vapor produced by a cubic inch of water, alcohol, &c., respec- tively. Why is there no advantage in steam power from liquids of low boiling point? What determines the cost of fuel ? 640. How are vapors condensed into liquids ? How much heat is evolved in this process ? 641. What is distillation ? What is it used for ? 17* 394 HEAT. ployed in the arts, according to the special purpose to which they are applied. The alembic, fig. 349, is the most ancient ; its invention is attributed to the Arabs. It consists of three parts ; first, the boiler or still, C ; second, the head or dome, c ; and third, the condenser or worm v 7?, S, r. The liquid to be distilled is placed within the boiler, which is made 349 of copper or of iron, and is ; heated by the fire beneath. The head is made of such a shape, that any portion of the liquid mechanically carried over with the vapor, is re- stored to the boiler. The worm into which the vapor passes is a spiral tube, con- tained in a vessel of cold wa- ter, whereby the vapor is con- densed and flows into the re- ceiving vessel, r. As the water is rapidly warmed by the latent heat evolved, from the condensed vapor it must be continually renewed. By means of the tube, t', the cold water is introduced at the bottom cf the vessel, where the vapor should be perfectly condensed, and the warm water rising, escapes through the outlet tube, t. With this ap- paratus the ordinary distillations are carried on in the large way. 643. Retort and receiver. Where small quantities of liquids are to be distilled, as in the ordinary operations of the labora- tory, retorts or flasks are used. 350 Retorts are vessels of glass, sometimes of por- celain or earthenware, and of the shape repre sented by fig. 350, R. The heat of a lamp ma} 7 be applied to the na- ked glass if the retort contains only water ; but if a denser fluid is used, then it is always safe to protect the glass by a sheet iron pan containing sand. In this way, even sulphuric acid and mercury may 642. What is the alembic 1 Describe fig. 349. How is it used ? 643. What is a retort ? Describe the apparatus, fig. 350. FRACTIONAL DISTILLATION. 895 351 be safely boiled in glass. In other cases, where it is desired to avoid a heat above 212, the retort is heated through the medium of a water-bath. The receiver may consist of a simple flask attached to the neck of the retort, as represented by S. The cooling is effected by water from a faucet, dropping continually on a cloth or paper wrapped around it. This arrangement is sufficient where the vapor is quite easily condensed, but where volatile liquids are distilled, other means of condensation must be resorted to. The most efficient apparatus for laboratory use is, Liebeg's condenser, fig. 351, is a glass condensing tube, A A\ surrounded by a larger tube, B, of metal or glass, and mounted on a foot. A funnel conveys cold water- from a reservoir to the lower end of the encasing tube, and the escaping warm water flows from the delivery tube into a vessel beneath. The vapors to be conden- sed arrive from the flask or retort, by the tube, d, and meeting the cold walls of the condensing tube, are liquefied and flow into the receiver, /?. A similar arrangement was employed by Lavoisier and Laplace in their experiments upon calorimetry. 644. Fractional distillation. Liquids of different volatility, as water and alcohol, the various ethers and essential oils, when mingled, are separated by what is c,&\\zdi fractional distillation. In the laboratory this is conducted by changing the recipient from time to time, as the boiling points and specific gravities of the liquids may indicate. In the arts, however, alcoholic and other liquids are concentrated by a single distillation, by the use of an apparatus con- sisting of successive chambers, in which the products condense in the inverse order of their volatility, and the latent heat set free by the condensation of the more condensible is made to maintain the more volatile in vapor for the next compartment, LIQUIDS IN THE SPHEROIDAL STATE. 407 phuric acid nearly at its boiling point. With sufficient precautions a number of liquids may be thus piled one upon the other. 663. The rapidity of evaporation of bodies in this state in- creases with the temperature of the plate, as is proved by the following experiments of Boutigny. The same quantity of water, (0-10 gramme, or 1-534 grs.) was evaporated in each case. With the plate at the temp, of 392, the water evap. in 20*7 seconds. " " " " " " " 752, " " " " 91 " " " " dull red heat, " " " " 73 " " " bright " " " " " " 60 " Water in the spheroidal state evaporates much more slowly at its temperature of ordinary ebullition. Thus when the plate was at the temperature of 212, O'lO grms of water evaporated in 4 seconds, and when at the temperature of 392, in 207 seconds, or less than one-fiftieth part as rapidly. 664. The temperature of the vapor from a spheroid is nearly the same as that of the plate upon which it rests, which proves that the vapor is not disengaged from the mass of the liquid. 665. A liquid in the spheroidal state is not in contact with the heated surface beneath This must appear on reflection upon the facts already stated, and may be demonstrated as fol- lows. A horizontal silver plate is surmounted by a tube of the same metal, fig. 363, whose lower edges have two longitudinal slits opposite to each other. The plate is 353 placed upon the eoli- pile, which is nicely adjusted to a perfect level by the screws in the triangular base. Silver is employed to avoid the formation of scales of oxyd of cop- per, which would in- interfeve with the ob- servation by interposing themselves to the light. When the plate heated over the lamp reaches the proper tempera- ture, a portion of water is placed upon its centre, and immediately assumes the spheroidal condition. Placing the eye on a level with 663. What is the rapidity of evaporation of bodies in this state 1 ? Give examples. How does it compare with the evaporation at boil- ing point? 664. What is the temperature of the vapor? 665. How is it proved that a liquid in this state does not touch the plate 1 Ex- plain the experiment, fig. 363. 408 HEAT. the surface of the plate, and looking through the apertures, in the sides of the tube, the flame of a candle opposite may -be distinctly seen. This could not happen if the liquid was in contact with the plate. If a thick and heavy silver capsule is heated to full whiteness over the eolipile, it may by an adroit movement be filled entirely with wa- ter, and set upon a stand, some seconds before the heat declines to the point when contact can occur between the liquid and the metal. When thishap- pens, the water, before quiet, bursts into steam with almost explosive violence, and is projected in all directions, as shown in fig. 364. A repulsive action is exerted between the spheroid and heated surface. This proposition follows indeed as a conse- quence of the last. It has already been demonstrated, that a liquid does not wet a surface, when the cohesion which exists between its particles is double of their adhesion for the solid. (289.) This adhesion is not only diminished by heat, but a re- pulsive action is exerted between the hot body and the liquid, which becomes more intense as the temperature is higher. This repulsive action is strikingly demonstrated by the following ex- periment of Boutigny. A few drops of water were let fall into a basket, formed of a net- work of platinum wires, heated red hot. The water did not pass through the meshes, even when the basket was rapidly rotated. But when the metal was sufficiently cooled, the water immediately ran through in a shower of small drops, or was quickly dissipated in vapor. It would also seem, that vapors, like liquids, are repelled from the heated surface, for Boutigny found, that a hot silver dish was not attacked by nitric acid, or one of copper by sulphuric acid or ammonia. The latter substance had no action upon either iron or zinc at a high temperature. The suspension of chemical affinity un- der certain conditions of high temperature, is a fact of great interest in the physics of the globe. 667. The causes which produce the spheroidal form in liquids are at least four. 1st. The repulsive force of heat exerted between the hot surface and the liquid, and which is more intense as the tempera- ture rises. 666. Why does not a spheroid wet the hot surface ? What is the evidence of repulsion ? How is it shown by experiment ? How is it with vapors 1 667. What is the first cause named as producing this state ? THE SPHEROIDAL STATE. 409 2d. The temperature of the plate is so high, that the water in momentary contact with it, is converted into vapor, upon which the spheroid rests as upon an elastic cushion. i 3d. The vapor is a poor conductor of lieat, and thus prevents the conduction of heat from the metal to the globule. Another cause which prevents the liquid from becoming highly heated is, that the rays of heat from the metal are completely reflected from the surface of the liquid. This is shown by the fact, that if the water be colored by lampblack, heat is absorbed, and the evaporation is much more rapid. 4th. Evaporation from the surface of the metal carries off the heat as it is absorbed, and thus prevents the liquid from en- tering into ebullition. The form of the oblate spheroid, which the liquid assumes, is the combined result of the cohesion of the particles to each other and the action of gravity upon the mass. 668. Freezing water and mercury in red hot crucibles. The remarkable phenomena of freezing water and even mercury in red hot crucibles, are striking examples of the production of the spheroidal state of liquids. Boutigny placed H portion of liquid sulphurous acid in a red hot vessel. It assumed the spheroidal state immediately, at a tem- perature below that of its ebullition, that is, below 14 F. A little water placed in the spheroid becomes therefore cooled below (32) its freezing point, and is converted into ice. Faraday placed in a heated crucible a mixture of solid carbonic acid and ether, which immediately assumed the spheroidal state. Into it was plunged a metal spoon containing mercury ; almost im- mediately the mercury was frozen into a solid mass. The tempera- ture in this case was probably as low as 148F. 669. Connection of certain phenomena with the spheroidal state. On the principle explained, the hand may be bathed in a vase of molten iron, or passed through a stream of melted copper unharm- ed, or one may stir fused glass under water without danger. In all similar cases, if the temperature be sufficiently high, the moisture of the hand assumes the spheroidal state, and does not allow of contact with the heated mass. If however the hand is drawn ra- pidly through the melted metal, contact is mechanically pro- What the 2d ? What is the 3d 1 What is the 4th 1 What deter- mines the form of the spheroid? 668. How are water and mercury frozen in a red hot crucible ? Explain the cause. 669. What sin- gular facts are explained by the spheroidal state? Why is injury not suffered in these exposures 1 18 410 365 duced, and injury follows this rashness. The finger, moistened with "ether, may be, for the same reason, plunged into boiling water without injury. 670. Explosions produced by the spheroidal state. The ex- periment illustrated by fig. 364, may be modified to illustrate ex- plosions, and some other interesting facts consequent on the spheroidal state. A copper bottle, fig. 365, is heated as hot as possible over a double current lamp, and in this state a few gram- mes of pure water are introduced by a pipette. The water at once assumes the spheroidal con- dition, and has a temperature (as may be as- certained by a thermometer) below that of its ebullition. If the neck of the bottle is now tightly closed by a good cork, the evap- oration is so slight, that the pressure of the vapor within is not immediately sufficient to drive out the cork. If however the lamp is withdrawn, the metal will soon cool suffi- ciently to allow contact of the water with it. There will then be so suaden an evolution of a large volume of vapor as to drive the cork from the bottle with a loud explosion. 671. Steam boiler explosions may sometimes be explained by a knowledge of the principles here elucidated. Thus, whenever from any cause a deficiency of water occurs in a boiler, as when the pumps fail of a supply, or when by careening a part of the flues are laid bare while the fire is undiminished, a part of the boiler may become heated even to redness. Water coming in contact with such over-heated surfaces, would first assume the spheroidal state, and almost at the next instant burst into a vol- ume of vapor so suddenly as to rend the boiler with frightful violence. Numerous accidents are on record where the explo- sion has been so sudden as not to expel the mercury from the open gauges. The fact that explosions on our American rivers have occurred most frequently just at or after starting from a landing, is explicable on the view here presented ; the vessel, while landing and receiving freight, being careened so as to ren- der the exposure of some part of the flues possible. 670. How may this condition explain certain explosions 1 Illus- trate it from. fig. 365. 671. What may be said of steam-boiler ex- plosions 1 THE STEAM ENGINE. 411 672. Applications and effects of the spheroidal state of liquids, are not unfrequent in common life and in manufactures. The most common example of the spheroidal state is that of a drop of water on a heated stove, which moves around in a spheroidal mass, slowly evaporating. The laundress determines whether her flat- irons are heated sufficiently for her purpose by touching the surface with a drop of saliva on the finger. If it bounds off, the iron is judged to be heated to a proper temperature. In the manufacture of win- dow-glass, constant application is made of the principles here ex- plained. The masses of glass are first formed into a rude hollow cyl- inder by blowing them in wooden moulds. In order to prevent the charring of mould, its interior is moistened with water, which, as- suming the spheroidal state, protects the wood while it does not in- juriously cool the glass. Saline solutions are more efficacious for tempering steel than pure water. Now as the point of ebullition of saline solutions is higher than that of pure water, contact between the liquid and the metal is produced sooner, and thus the steel is cooled more quickly, and the temper is better. Melted metals, like iron or copper, allowed to fall into water, do not throw the water into violent ebullition, as might |be supposed, but pass in a brilliant stream to the bottom of the vessel, the water in contact with the metal assuming the spheroidal state. THE STEAM ENGINE. 673. Historical. The principles involved in the construction and theory of the steam engine, have already been sufficiently discussed. A few words must suffice respecting their practical applications in the discovery and perfecting of this remarkable machine. fc- For the first rudiments of our knowledge of steam as a motor, we must go back, as upon many other so-called modern inventions, to Egypt, where, 130 years B. C., Hero, or Heiro, describes in his ' Spiritalia Sen Pneumatica,' among many other curious con- trivances, (377,) what he calls the eolopile. 674. The eolopile is a metallic vessel, globular, or boiler- shaped, containing water, and provided at top with two horizontal jet pipes, bent into the form of an 8. 672. Give a familiar example of the spheroidal state. In what processes of the arts is it seen? 673. Where do we find the earliest knowledge of steam as a motor ? 674. Describe Hero's eolopile. What is this in fact ? What other form has it ? 412 HEAT. This apparatus, fig. 366, is suspended over a flame, and being free 366 to move, when the water boils, the steam rushing out, strikes against the atmosphere, and the recoil drives the apparatus around with great rapidity. This is in fact a direct action rotary steam engine, and undoubtedly the earliest mechanical result achieved by steam power. It has often been re-in- vented, in numberless forms, in modern times. In another form the eolopile is made to blow by its jet the flame of a lamp, and in this case the boiler is fixed and filled with alcohol in place of water, the jet descending through the flame of the lamp as in the apparatus seen in fig. 362. Hero de- scribes also other devices where steam was the moving power. 675. First steamboat. Blasco de Garay, a sea-captain of Barcelona, in Spain, in 1543, moved a vessel of 200 tons burthen three miles an hour by paddles propelled probably by steam, as the moving force came, it was said, from a boiler containing water, and liable to burst. This experiment was made on the 17th day of June, 1543, in pres- ence of Commissioners appointed by the King, Chas. V., whose re- port secured the favor of the ci-own to the projector. But what ia unaccountable, nothing more ever came from this singular success. De Garay probably employed Hero's eolopile on a large scale, as Hero's work above named was about that time translated into several languages and generally diffused. 676. Baptista Porta, and Solomon De Caus, the first at Naples in 1601, and the second a Frenchman in 1615, both re-describe the eolopile of Hero, but in a very inferior form to the original, and without adding anything to what was before known. GIOVANNI BRANCA of Rome, in 1629, also describes a contrivance for obtaining a rotary motion from steam blowing against the pad- dles of a wheel, shaped like an ordinary water wheel. This impo- tent form of steam apparatus has been again re- described in much more modern times. 677. Otto V. Guerick, the inventor of the air-pump, about 1650, first conceived and executed the idea of using the pressure of the atmosphere as a moving force, for raising water or lifting weights. His rude apparatus did not involve the use of steam, 675. What did Blasco de Garay accomplish? When and how was this? 676. What is said of B. Porta and S. de Caus ? 677. What did V. Guerick accomplish and when ? SAVARY'S ENGINE. 413 but he produced a vacuum by the air-pump, which then drew up by a rope and pulley a platform with weights. The production of a vacuum by the condensation of steam remained still to be discovered. 678. The Marquis of Worcester, in 1663, in his ' Century of inventions,' describes what he calls 'a water commanding engine, an admirable and most forcible way to drive up water by fire.' Unfortunately no figure of Worcester's engine exists, but his de- scription of it leaves no doubt that he used steam to create a vacuum into which water afterwards rose to be again expelled by fresh steam, as was accomplished later with more success in Savary's engine. 679. Savary's engine. In 1698, Capt. Thos. Savary obtained a patent ' for raising water and occasioning motions to all kinds of mill work by the impellent force of fire.' His apparatus can hardly be called an engine, or machine, since it has no moving parts except the valves turned by hand, Fig. 367 is Savary's engine. Two boil- ers, L and D, are connected together by the pipe, H. Two ' condensers,' P and P' , are connected with the larger boiler, L, by pipes entering at top of both, and capable of being alternately shut off from the boiler by a valve, moved by the lever Z. By two branch pipes beneath the condensers, communication is estab- lished at pleasure, by the aid of the cocks 1, 2, 3, 4, alternately with the well by T, and the open air by the outlet pipe S. The boiler, L, being in action, the condenser, P, for example, was filled with steam, the cocks 1 and 3 being closed. By moving Z, the condenser, P', was next filled with steam also, cocks 2 and 4 being closed, and at the same in- stant cock 3 being opened, the water rushed up through T, to fill the vacuum occasioned by the condensation of the steam in P. The lever, Z, was then moved to close P' and open T again to the boiler. Cock 4 now admitted cold water to P' and cock 1 being opened, the di- rect pressure of the steam from the boiler forced_the water out of P, 678. What was the Marquis of Worcester's invention ? 679. What was Savary's patent for, and when ? Describe his apparatus, fig. 367, and how the discharge was made continuous. 414 HEAT. in a stream through the discharge pipe, S. The water in P' was also discharged in the same manner, and so on, alternately, each con- denser was fille.d with cold water, and again discharged, maintaining a continuous stream of water from S. To supply the waste of water in the boiler, L, the contents of the smaller boiler, D, were from time to time forced by superior steam pressure into L, through the pipe H, (provided with a valve for that purpose,) reaching near the bot- tom of D, whose capacity was such as to fill L to a suitable height. The boiler, D, was then re-filled through the pipe, E, from the sup- ply box, X, attached to the discharge pipe. All the details of Savary's contrivance show a nice adjustment of means to the end to be accomplished, and evince much inge- nuity and sound judgment. 680. Papin's steam cylinder, Newcomen's engine Denys Papin, (Prof, of Mathematics at Marburg,) whose name is con- nected with the high-steam digester, fig. 364, suggested in 1690 the use of steam to produce a vacuum in Otto and Guerick's cylinder (677) in lieu of the air-pump before used. For this purpose he constructed the cylinder of sheet iron, and built a fire beneath its bottom, to boil a portion of water there placed. "When the cylinder was filled with steam, the piston before held up by a latch, descended as the steam was condensed. No practical re- sult followed this clumsy contrivance, on which Papin's countrymen rest his claims to be considered as the inventor of the steam engine. THOS. NEWCOMEN, in 1710, first put in practice the use of a cyl~ inder and piston in the steam engine, in which the steam was al- ternately admitted and again condensed by a stream of cold water. This engine, like all following it, up to Watts' remarkable im- provements, operated against the pressure of the atmosphere, and was effectual in only one direction, i. e., was a single acting engine. 681. The atmospheric engine is well illustrated by the appa- ratus shown in fig. 368, which was contrived by Dr. Wollaston, to show the nature of Papin's cylinder. A glass, or metallic tube, with a bulb to hold water, is fitted with a piston. This piston-rod is hollow, and closed by a screw at a. What is said of this invention? 680. Who suggested the use of steam to form a vacuum, and when ? What followed this suggestion ? Who first employed a cylinder and piston with success? 681. How is the atmospheric engine illustrated by fig. 868 ] What great source of loss existed in all atmospheric engines ? WATT'S IMPROVEMENTS IN THE STEAM ENGINE. 415 This screw is loosened to admit the escape of the air, and the water is boiled over a lamp : as soon as the steam issues freely 368 from the open end of the rod, the screw is tightened, and the pressure of the steam then raises the piston t6 the top of the tube, the experimenter withdraws it from the lamp, the steam is condensed, and the air press- ing on the top of the piston forces it down again; when the operation may be repeated by again bring- ing it over the lamp. In all the early steam engines, the steam was con- densed within the cylinder, either by water applied externally, or by a jet of water thrown directly into the cylinder. It is very obvious, that a great loss of fuel and time was thus involved in bringing up the cylinder again to 212, before a second stroke could be made NEWCOMEN and SMEATON constructed very large engines, however, on this principle, and applied their power directly to the pumping of mines. Although Smeaton introduced an improved class of me- chanical work and many improvements in minor details, and better boilers, he succeeded only in raising the average duty of steam engines from about five and a half millions of pounds, raised one foot by a bushel of coals (80 Ibs.) burned, to about nine and a half millions, in his best engines. A good pumping engine now raises from ninety to one hundred and thirty millions of pounds for every bushel of coals burned 1 682. Watt's improvements in the steam engine. The steam engine as it was left by Smeaton was, as we have seen, only a steam pump, confined to the single function of raising water, and incapable of general use, as well from its imperfections as from the enormous cost of fuel it required. Watt, in 1763, was a maker of philosophical instruments at Glasgow, and had occasion to repair a model of the Newcomen engine. The study of this machine and its defects, led Watt to construct a new model, in which the steam was condensed in a separate vessel, in connec- tion with which he subsequently found it advantageous to use an air-pump to aid in keeping the vacuum good, as it was other- wise vitiated by atmospheric air leaking in, and coming from the water of the boiler. These ideas were matured and realized by What is farther said Newcomen and Smeaton] What was the duty or power of their best machines? 682. How did Watt find the steam engine ? What led him to improve it ? In what did his im- provements chiefly consist ? 416 HEAT. 1765, and in 1769 he took out his patent, in which all the essen- tial features of our modern steam engines are included. In con- nection first with Mr. Roebuck, of Carron Iron-works, and sub- sequently with Mr. Boulton, of Soho, he put his ideas in practice, and by reserving to the patentees one-third part of the saving of fuel effected by his improvements, his genius was rewarded by the accumulation of a princely fortune. Watt's invention of low-pressure condensing engines stands without a parallel in the history of science for the perfect realization of all the conditions of the problems to be solved the perfect mastery of the laws of nature and the use of matter, by which they were ac- complished, and the thorough exhaustion of the subject even in its minutest details, so that to this day we have no improvements in this machine involving a single principle unknown to Watt. In the beauty and perfectness of mechanical work, in size of parts, and the strength of boilers, we r have machines greatly superior to^any Watt ever saw, but it was his genius that rendered those perfections pos- sible, and supplied the very power by which they have been worked out. 683. The low pressure or condensing engine. The low pres" sure engine is employed in all situations where economy of fuel and the best mechanical effect from it are the ruling considerations, and where lightness and simplicity of construction is unimportant. This machine now remains almost exactly as Watt left it. Owing to the nearly perfect vacuum obtained in it by the condenser and air-pump, a much less boiler pressure of steam is required to produce a given mechanical result, e. g. ; if the vacuum is equal to fourteen Ibs. atmospheric pressure, then a steam pressure of six Ibs. would give an efficient moving force of twenty Ibs. to the machine. Hence the propriety of the term ' low pressure' en- gine ; but in practice it is found advantageous to use higher pres- sures in the condensing engines than Watt ever contemplated. Fig. 369 is a section of the cylinder, A, condenser, e, air-pump, hot and cold well, and a view of the most important attached parts of a modern condensing engine. The cylinder, A, is seen receiving steam at top through the throttle-valve, a, driving down the piston, B, with its rod, C. A stream of cold water injected into the con- denser, e, has completely condensed all the residual steam of the for- Give the date of his discoveries and patent. What is further said of his invention ? ^ 683. Why is this called a low pressure engine 1 Why a condensing engine ? When is it chiefly employed ? Describe fig. 369, and the functions of the several parts. THE HIGH PRESSURE ENGINE. 417 mer stroke which lias found its way from A by the eduction pipe, d, so that the piston, B, is descending into a nearly perfect vacuum, (623.) The hot water of this condensation is constantly drawn off 369 S _ V through the valve, k, by the air-pump whose valves, ii, rise to allow its flow into the hot well, /, whence it finds its way, solicited by the plunger pump, S, to the boilers by the pipe, P, and its valves, o o. The cold water pump, q, supplies a steady stream of cold water by the spout, r, to the cold well. By the time the piston, B, has reached its lowest point of descent, the valve rod, F, and eccentric bar, S, have moved so as to open the lower steam ports and reverse the direction of the piston, when the steam above, B, is in its turn taken into the condenser, e, by the appropriate channels, and re- moved as already explained for the downward stroke. The piston rod, C, and valve and pump rods, are counnected above with the great working-beam, whose further extremity conveys the power of the engine by the pitman, G, through the crank pin, H, to the main shaft, K, on which is the fly-wheel, L, to give steadiness of motion to the whole apparatus. The arrows show the motion of these parts as the piston descends. The governor, z, controls the throttle valve, a, by connections not shown in this drawing. 684. The high pressure engine. In this machine, the escape steam is driven out against the pressure of the atmosphere, and no attempt is made to utilize its capacity to form a vacuum, con- 684. How does the high pressure engine act? What beside steam could be used in it, and why ? 18* 418 HEAT. 370 sequently this form of apparatus could be used as well with con- densed air, or any other elastic fluid, as with steam, if there was any other that could compete in economy with it. The lightness, sim- plicity, and low cost of the high pressure engine, makes it avail- able in spite of its uneconomical use of steam, in many situations where a" condensing engine would be unavailable. The steam arrives by the pipe, Z, fig. 370, to the steam chest, E, and is admitted alternately by the ports e d, to the top and bottom of the cyl- inder, A A, as the valve rod, S, actuated by the eccentric, /, on the main shaft, opens and shuts the ports by the slide valve in K. The escape steam makes its exit through g, to the atmosphere. The pitman, P, conveys the motion of the piston, G, to the crank, Q, and the main shaft, on which is the large fly- wheel, x, to accumulate momentum. The flow of steam is regulated by the governor, V, whose balls fly out with the centrifugal force of a more rapid motion, and by the rod, h, b, close more or less the throttle valve, seen in sec- tion in Z; the pump, o o, supplies water to the boiler, and is moved by the rod and eccentric, g, on the main shaft. Cut off. The supply of steam both to the high and low pres- sure engine is further regulated by a contrivance called the ' cut off,' which may be set to cut off the flow of steam entirely, or at any portion of the stroke, as one-half, or one-third. The expan- sion of the steam then completes the work, and great economy of fuel is found to follow its use. 685. Steam boilers. The form of steam boilers varies very much with the purpose to which they are to be applied. On land, large boilers may be safely used, which would be wholly valueless at sea, or on a locomotive engine. Plate-iron strongly riveted and braced, is the material combining the greatest economy and strength. Copper can be used only when the fuel contains no sulphur, and is the best material to resist corrosive Describe the figure 370. What is the ' cut-off,' and how does it act? 685. What is said of steam boilers ? MECHANICAL POWER OF STEAM. 419 agents. Simple cylindrical boilers, laid horizontally, with a fire- flue under the whole lower surface, are commonly used for high pressures. When these are made large enough to receive the furnaces within and distribute the heat in interior flues, they are called Cornish boil- ers. When their construction is still further modified, with reference to the greatest possible increase of fire surface, they are called loco- motive boilers, as in the annexed figure, 371 ; being the common lo- comotive boiler seen in 371 section. D, is the feed- door, for fuel to the fur- nace or fire box, A, which communicates by numer- ous small horizontal'tubes, entirely surrounded by water, with the base of] the chimney, B, into which the blast of exhaust steam from the engine is driven at K. E, is the steam chamber, where a trumpet tube in the dome conveys the dry steam on its way to the cylinder through F. Steam boilers are supplied with hot water by a force pump, and gauge cocks indicate the water level. 686. Mechanical power of steam. Horse power. As steam engines were originally employed to take the place of horses in raising water it was natural to estimate their power by the number of animals they replaced. The value of any force is correctly stated as the number of pounds raised one foot high in a given time, (foot-pounds.) As the use of steam became general, the term horse-power was retained, but its use was restricted by Watt to mean 33,000 Ibs. raised one foot per minute, or nearly 2,000,000 Ibs. raised one foot per hour. As one cubic inch of water converted into steam yields in round numbers 1,700 cubic inches of vapor, its mechanical effect at atmos- pheric pressures, is equivalent to raising 15 Ibs. 1,700 inches, (or 142 feet,) in a tube of one inch area. But 15 Ibs. raised 142 feet, is the same thing as 142 times 15 Ibs. raised one foot, or 2,130 Ibs., or nearly a gross ton. The total mechanical force developed by changing one cubic inch of water into 1,700 cubic inches of steam is therefore nearly one ton. Only 60 or 70 parts of this power are however regarded as ac- Describe figure 371. 686. What is the origin and meaning of the term horse power? How did Watt limit it ? How is the mechan- ical power of steam illustrated from a cubic inch of water ? 420 HEAT. tually available in use, deducting friction and loss from other causes. Therefore the evaporation of a cubic foot of water in an hour, sub- ject to this deduction, will give the full force of about 1,000 cubic inches of water converted into steam, as the expression of one-horse power, (viz. 33,000 x 60 m. = 1,980,000 Ibs.,) or nearly 2,000,000 Ibs. raised one foot. This is a somewhat rough approximation, but it gives constants easily remembered and sufficiently near the truth. A boiler of one-hundred horse power means, then, a boiler capable of evaporating 100 cubic feet of water per hour. In practice it is common to allow in large land engines for every horse power, one square foot of fire bars in the boiler, three cubic feet of furnace room, ten cubic feet of water in the boiler, and ten cubic feet of steam chamber. In locomotives and steamships these propor- tions vary very much. 687. Evaporating power and value of fuel. In England, engi- neers estimate ten pounds of bituminous coal for every cubic foot of water (i. e. every horse power) to be evaporated. In carefully constructed boilers, however, this effect is produced by seven or eight pounds of coal. In the Cornish boilers, where a very large evaporating surface is allowed, five pounds of coal only, and some- times less, are used per horse power. In the U. S., anthracite coal averages ten pounds of water evaporated, for every pound of coal burned. This would give 6 *25 Ibs. of anthracite for each cubic foot of water evaporated. A well regulated current of va- por conducted over the flame of bituminous coal by Dr. Fyfe, raised the evaporative effect produced 37 per cent, above what was obtained from the unassisted coal. This increase is due to the decomposition of the steam by the hot fuel, and the conse- quent effect of the pure oxygen on the carbon. Well seasoned wood, (beech or oak,) still containing about 20 per cent, of water, and well dried peat, have about equal evaporating power, and are only about two-fifths as effective as an equal weight of ordinary bi- tuminous coal. Welter has observed that those quantities of a combustible body which require an equal amount of oxygen for combustion, evolve What proportion of the whole power is regarded as available? What relation has a cubic foot of water to a horse power ? What is meant by a boiler of one hundred horse power ? What proportions of fire bars, furnace room, and water and steam room are allowed in land boilers? 687. What is said of the evaporating power of coals? What is the case with American anthracite ? What is the effect of of vapor of water on a coal of fire? What is the comparative value of wood, peat and coal ? What was Welter's observation I CURRENTS IN AIR AND GASES. 421 also equal quantities of heat : although later researches show this conclusion not to be strictly true, it is supported by many facts. In all cases of combustion, the action is reciprocal, the oxygen is burned in the fuel as truly as the fuel by the oxygen, and therefore the same amount of heat is generated by a given amount of oxygen, whether in converting carbon into carbonic acid, or hydrogen into water. To burn one part of carbon, requires 2*66 parts of oxygen, (C 3 = 16 -f- 6 = 2'66,) and to burn one part of hydrogen, requires 8 parts of oxygen. It has been proved experimentally, (by Rumford,) that 78 parts of water are raised from 32 to 212 by burning one part of carbon, while one part of hydrogen so burned will raise 236'4 parts of water through the same degrees. It therefore follows that one part of oxygen, burning carbon, will heat 78 -5- 2 '66 = 29 '25 parts of water from 32 to 212 ; and also that the same quantity of oxy- gen, in burning hydrogen, will heat 236'4 *- 8 = 29'56 parts of water through the same degrees. The heating effect of oxygen may therefore be assumed to be 30, or in units of heating power 3,000. If the heating effect of pure carbon is taken at unity, the relative heating effects of the other combustibles will range as follows, for equal weights : hydrogen, 3 ; vegetable oil, 115 1'22; ether, 1'02; carbon, 1 ; wood charcoal, 0'96; alcohol, 0'86; good coal, 0'77 ; dry wood, 0'46; wood, (with 20 per cent, water,) 0'35 ; peat, 0'33 0'38. (Knapp.) PROF. W. R. JOHNSON ('experiments on coals') and others, argue as the result of experiment, that the total amount of carbon in a fuel is the measure of its practical evaporative power. His re- sults very nearly sustain this view. He found also that about 86 per cent, of the total heating power were expended in evaporating water, and about 14 per cent, were lost in the products of com- bustion. Of the total heating power, by calculation, about 26 per cent were lost in practice as deduced from the experimental effects stated in his tables. VENTILATION AND WARMING. 688. Currents in air and gases depend upon principles which have already been fully explained but the subjects of ventila- tion and artificial heating are of such great importance in daily life, that they demand a brief space for separate consideration. Illustrate this. What is the heating power of oxygen 1 What is the relative heating power of hydrogen, aporization explained on this theory 1 436 HEAT. ^ molecules, and an external work in overcoming the forces which oppose themselves to the expansion of the vapor. When, on the contrary, a gas or vapor is liquefied by compression, the external work is supplied, and the internal work due to the co- hesive force which draws the atmosphere togther, is transformed into heat. Again, when a liquid solidifies, the internal work which unites the molecules is transformed into heat, and appears as sensible heat. It is evident that this theory would modify the ideas generally received of the amount of heat in bodies. Thus the heat which is rendered latent, when a solid is liquefied, cannot be regarded simply as being insensible ; it must be considered as destroyed, or, more properly, as being converted into motion. 711. Unit of measurement, the foot-pound. In the experi- ments upon the mechanical equivalent of heat, the unit adopted in England and in this country, is the foot-pound, or the me- chanical force expended in raising a pound weight, one foot high. (686.) In Prance and other European countries, the unit adopted is the mechanical force expended in raising one kilogramme, (2-2056,) one metre, (39'37 in.) high. 712. Relations of heat and force. It has already been stated, (491,) that motion or mechanical force produces heat. When heat is produced, mechanical force is destroyed. The connection between heat and mechanical force appears more intimate, when it is shown that a given quantity of the one may be converted into a determinate quantity of the other. Hence it has been concluded that mechanical force is transformed into heat, and conversely, that heat is transformed into motion, when it is de- 713. Determination of the mechanical equivalent of heat. According to the preceding theory, the mechanical equivalent of heat is independent of the nature of the body by whose agency the transformation of mechanical force into heat is effected ; hence the same result should be arrived at, whatever course of experiment is adopted. Mr. J. P. Joule, of Manchester, Eng., has made the most exact determination of the mechanical equiv- alent of heat in a series of very careful and elaborate experi- ments, conducted between the years 1840 and 1843. He deter- mined the mechanical equivalent of heat in a number of ways, "What limits it? 710. How does it explain changes of state or volume ? (1.) When a solid is melted ? (2.) When a gas is liquefied ? How does it affect our views of latent heat ? 711. What is the unit of heat measurement 1 712. What is the relation of heat to force 1 RESULTS OF JOULE S EXPERIMENTS. 437 reversing the question, and determining the amount of heat pro- duced by a certain expense of mechanical force. One method was by the compression of gases ; compressing air with a great force in a copper receiver, in one series of experiments filled with air only, and in another with water. The whole appa- ratus was placed in the w^ater of a calorimeter, whose temperature, before and after the experiment, was carefully determined. The heat developed by the friction of water and of oil, was determined in an apparatus consisting of a brass paddle-wheel, having revolving vanes working between stationary vanes. This wheel was made to revolve by the descent of a known weight, and thus the mechanical force exerted could be determined. A similar apparatus, of smaller size, and made of iron, was used for experiments on mercury. In all cases, the apparatus was placed in a metallic vessel filled with the liquid, and the temperature noted before and after the experiment. In his experiments on the friction of solids, Mr. Joule used an ap- paratus consisting of a vertical axis, which carried a beveled cast-iron wheel, against which a fixed cast-iron wheel was pressed by a lever. The whole was plunged in an iron vessel filled with mercury, the axis passing through a hole in the lid. In all of these experiments, the temperatures were noted by thermometers, which indicated a va- riation of temperature of the one two-hundredth of a degree F. 714. Results of Joule's experiments. In the following table are given the most important results obtained by Mr. Joule. The second column gives the results obtained in air, the third column, the same results corrected for a vacuum. Material employed. Equivalent (in foot-pounds) in air. Equivalent in vacuo. Mean. Water, . . 773-640 772-692 772-692 Mercury, (773-762 I 776-303 : 772-814 775-352 774-083 Cast-iron, . j 776-997 I 774-880 776-045 773930 774-987 715. Conclusions deduced from the above experiments. 1. That the quantity of heat produced ~by the friction of bodies is always proportional to the force employed. 2. That the quantity of heat capable of increasing the tem- 713. What is the relation of the equivalent of heat to the body heated 1 How did Joule determine the mechanical equivalent of heat by gases? How for liquids ? How for solids ? 714. What are the results of Joule's experiments ? 438 HEAT. perature of one Ib. of water (weighed in vacuo, and between 55 and 60) ~by 1 F., requires, for its evolution, the expenditure of a mechanical force represented l)y the fall 0/772 Ibs. through the space of one foot. Consequently a force of one horse power (686) would raise 42*7 Ibs. of water 1 F. each minute, and would bring it to boil from 60 in two and a half hours. Prof. Thomson (Phil. Mag., Feb. 1854) says, it is mathematically demonstrated from the dynamical theory of heat, that any substance maybe heated 30 F. above the atmospheric tem- perature, by means of a properly contrived machine driven by an agent, spending not more than one thirty-fifth of the energy of the heat communicated, and that a corresponding machine, or the same machine worked backwards, may be employed to produce cooling effects. Where water power abounds, the heat of friction has been used to warm buildings, and an apparatus has been constructed in Paris, in which water is converted into steam by friction solely. 716. The sources of heat already alluded to, (491,) might very profitably be here considered at greater length, but want of space compels the omission of anything more under that head, although its discussion would be both interesting and profitable. 715. What conclusions follow! What is the thermal effect of a horse power 1 Electrical machine of Nairne for both electricities. M Fig. 381 a. OPTICS. 489 OPTICS. 717. Optics. Light. Optics, (from the Greek verb, optomai, to see,) is that branch of physical science which treats of the nature and properties of light. Light is the agent which, acting upon the eye, produces the phenomena of vision. 718. Nature of light. In regard to the nature of light, a great diversity of opinion has prevailed among philosophers. (a) Corpuscular theory. Sir Isaac Newton maintained that the phenomena of light are produced by luminous corpuscles thrown off from burning bodies, each particle producing, in its flight, vibrations in the surrounding ether similar to the waves produced by a stone falling into the water. (5) Undulatory theory. Huyghens maintained, in opposition to Newton, that light consisted solely of vibrations in an ethereal medium, without the onward progress of any substance what- ever. This theory has been investigated and defended by many of the ablest philosophers ; by Young, Malus, Fresnel, Brewster and others, and is now generally received. The undulations producing the phenomena of sound take place in the same direction that the sound itself moves ; but the vi- brations of light are supposed to move at right angles to the di- rection in which light is propagated. It is difficult to explain all the phenomena of light even on this theory. (c) An oscillatory theory of light has been recently proposed by Mr. Rankine, of Glasgow.* In this theory, thepar tides of lu- miniferous ether are supposed to rotate on their axes, by the in- fluence of a species of magnetic force, which is wholly destitute of effect in producing resistance to compression, so that it is no longer necessary, as in the undulatory theory, to suppose the luminiferous medium to have the properties of an elastic body. The same mathematical formulae are employed, with this hypoth- esis, as for the undulatory theory. Whether this theory can be * See transactions of the British Association for 1853, p. 9. 717. From what is the term optics derived ? Of what does optics treat? What is light? 718. "What was Newton's theory of the na- ture of light? What was Huyghen's theory? In what respect do these two theories agree ? In what respect do they differ ? How- are the vibrations of light supposed to differ from the vibrations which produce sound ? What is the oscillatory theory of light ? 440 OPTICS. applied to explain all the phenomena of physical optics, remains to be proved. 719. Relation of different bodies to light. All bodies are either luminous, transparent, translucent, or opaque. (a) Luminous bodies are those in which light originates, as the sun, and burning bodies. (Z>) Transparent bodies allow light to pass freely through them, thus permitting the form of the other bodies to be distinctly seen through them. Such are water, air, and polished glass. Such substances are also said to be diaphanous, (from dia, through, and phainOj to shine.) (c) Translucent bodies permit only a portion of light to pass, and in so irregular or imperfect a manner, that the outline of other bodies cannot be clearly seen, as through rough glass and oiled paper. (d) Opaque bodies are those which do not ordinarily allow any light to pass through them, as wood and the metals. But all bodies, even the metals, may be made so very thin as to become partially transparent or translucent. 720. Rays, pencils, and beams of light. A single line of light is called a ray. A pencil of light is a collection of rays diverg- ing from a common source, or converging to a point. A learn of light is a collection of parallel rays. Diverging rays are those which gradually separate from each other. Converging rays are those which tend to meet in a common point ; hence we have the terms diverging pencils, and converging pencils of light. 721. Visible bodies emit light from every point and in every direction, the rays diverging from each point in right lines. Let ABC, fig. 382, be three points in any visible object ; from each of these points, light is emitted in diverging [pencils, as partially represented in the figure. In this figure certain points are seen, where rays Ifrom A B C, cross each other, and between them are vacant spaces. No such vacant spaces exist, but the rays from all points in the object are cross- ling each other at every point in the space where Ithe object is visible. 719. What are luminous bodies? What are transparent bodies? What are translucent bodies? What bodies are called opaque? 720. What is a ray of light 1 What is a pencil of light ? What is a beam of light ? What are diverging rays ? What are converging rays? 721. In what direction do visible bodies emit light? VELOCITY OF LIGHT. 441 722. Propagation of light in a homogeneous medium. A me- dium is something existing in space, capable of producing phe- nomena. A medium is called luminiferous, which is capable of transmitting light ; and is said to be homogeneous when the composition and density of all its parts are the same. All space is supposed to be pervaded by a luminiferous medium, called lumi- niferous ether, and yet the particles of this ether may act upon each other at great distances. In a homogeneous medium, light al- ways moves in straight lines. If any opaque body is placed in a direct line between the eye and a luminous body, the light is intercepted. When light enters a dark chamber by a very small opening, the course of the light becomes visible by illuminating the fine particles of dust always floating in the air. Rays of sun-light are thus easily demonstrated to move in straight lines. 723. Velocity of light. Light travels with such amazing ve- locity, that for any distances on the surface of the earth, the time occupied in its passage from one point to another is totally inap- preciable by ordinary means. In 1676, Roemer, a Danish astronomer, observed that the eclipses of the first satellite of Jupiter, which occur at uniform intervals of time when the earth is moving in that part of her orbit nearest to, or most remote from Jupiter, are constantly retarded when the earth is moving from that planet, and as regularly accelerated when the distance between the earth and Jupiter is diminishing. He found that when the earth was in that part of her orbit most distant from Jupiter, the eclipses of the first satellite take place 16 m. 36 s. later than when in the opposite part of her orbit. FoucaulVs apparatus for measuring the velocity of light. Notwith- standing the prodigious velocity of light, M. Foucault has succeeded in measuring it, by employing a revolving mirror, according to the method devised by Wheatstone for measuring the velocity of elec- tricity. In describing this apparatus, we shall suppose the proper- ties of mirrors and lenses to be already understood. The apparatus of M. Foucault is represented in fig. 383. The shutter of a dark chamber is pierced with a square opening, K, be- hind which a fine platina wire, a, is stretched vertically. By means What is a medium ? What is a luminiferous medium ? What is meant by luminiferous ether ? 722. How does light move in a homogene- ous medium ? How is this demonstrated 1 723. What is said of the velocity of light ? Who first determined the velocity oflight? How did he determine it 1 Describe Foucault's method of determining the velocity of licht. 19* 442 OPTICS. of a mirror, a beam of solar light is made to enter the chamber, and being divided by the platinum wire, it falls upon an achromatic lens, L, of long focus, placed at a distance from the platinum wire less than double the distance of its principal focus. The image of the 883 platinum wire would be formed in the axis of the lens, somewhat enlarged. But the beam of light, after passing the lens, falls upon the plane mirror, m, which revolves with great ve* locity, and being re- flected by it, an image of the platinum wire is formed in space, which image is displaced with an angular velocity, double the velocity of the mirror.* This image is received by a concave mirror, M, so fixed that its centre of curvature coincides with the axis of rotation of the revolving mirror, m. The pencil reflected by the mirror, M, returns backward and is again reflected by the mirror, m, and passes back through the lens, L, and forms an image of the platinum wire, coinciding with the wire itself, if the mirror, m, revolves slowly. In order to view this image without obscuring the pencil of light which enters the chamber by the opening, K, a piece of plate glass, V, with parallel faces, is placed between the lens and the platinum wire, inclined in such a manner that the rays reflected fall upon a powerful eye-glass, P. If the mirror, m, remains stationary, or if it revolves slowly, the returning ray, M m, falls upon the mirror, m, in the same position it occupied at the first reflection, and returning in the direction it came, it meets at a the plate glass, F, and is partially reflected and formed in d, at a distance, a d, equal to a o, an image which is seen by the eye by means of the eye-piece, P. * To demonstrate this, let mn, fig. 383 a, be the revolving mirror, O, an object placed before it, and forming its image at 0' ; when the mirror arrives at the position m' n', the image will be formed at 0". But the angles, 0' 0", and mem' are equal, because their sides are perpendicular to each other. But the inscribed angle 0' O 0" is measured by half the arc 0' 0", and the angle m c m', is measured by the entire arc m m' ; hence the arc 0' 0", is double m m', which thus demonstrates that the angular velocity of the image is double the angular velocity of the mirror. Is the velocity of light the same in all substances ? THEORIES OF LIGHT. 443 The revolving mirror, w, causes this image to be repeated at each revolution, and if the velocity of rotation is uniform, the image does not change its' position. When the velocity does not exceed thirty revolutions per second, the successive appearances of the image are distinct, but when the velocity is greater, the impressions upon the eye are continuous, and the image appears constant. When the mirror, m, revolves with great rapidity, its position is sensibly changed during the interval occupied by the light in passing from m to M, and back again from M to m, and the returning ray, after reflection by the mirror, m, takes the direction m b, and forms an image in i; thus the image has deviated from d to i. Strictly speaking, there is some deviation even when the mirror turns slowly, but it is appreciable only when it has acquired a certain magnitude, by making the rotation of the mirror sufficiently rapid, or by taking the distance, M m, sufficiently great. By means of the deviation in the position of the image and the velocity of rotation, the time re- quired for the light to pass from m to M, and back again, becomes known, making I = M m, I' = L in, r = O L, n = the number of revolutions per second, JE = the absolute deviation d i, and V = the velocity of light per second. M. Foucault obtained the following formula for the velocity of light. _ 8 * I 2 n r 6 (I + I' ) In the experiments of M. Foucault, m M, was only about four yards, but by giving the mirror, m, a velocity of 600 or 800 revolu- tions per second he obtained a deviation of from eight one-hundredths to twelve one-hundredths of an inch. Experiments have been made with the same apparatus to deter- mine the velocity of light in liquids. For this purpose a tube, A B, three yards long, is filled with distilled water, or any other liquid, and placed between the revolving mirror, m, and the concave mirror, M ', similar to M. The rays of light reflected by the revolving mir- ror in the direction, m M', pass twice through the column of fluid in the tube, A B, before returning to the mirror, V. The returning ray is reflected at c, and forms an image at A. The deviations of the rays which traverse the liquid are greater than the deviation of the rays which are propagated in air alone, which shows that the velo- city of light in fluids is less than in air. 724. No theory of light is entirely satisfactory. In the cor- puscular theory of light, advocated by Newton, it was supposed that fluids and solids attracted the light, and refraction was ex- 724. How does the diminished velocity of light in fluids favor the undulatory theory of light if 444 OPTICS. plained by supposing that light moves faster in dense bodies than in air, as is known to be the case in regard to sound. According to the undulatory theory, it is known that waves or undulations must move slower in dense bodies than than in rarer media. The discovery of Foucault, that light actually moves slower in denser media, tends to confirm the undulatory theory. The immense power of resisting compression which a medium ought to possess, in order to transmit transverse vibrations with a velocity so much greater than the motions of the swiftest plan- ets or comets, is an objection against the undulatory theory that has not yet been satisfactorily answered. The discussion of the theories of light belongs to the higher de- partments of mathematics. 725. Properties of light. (a) Absorption. Light falling upon any substance is either absorbed, dispersed, reflected, or refracted. If it disappears entirely, it is said to be absorbed ; as when light falls upon black substances. No substances absorb all the light, for the fact that the blackest substance is still visible, shows that its different parts emit some of the light which they receive. (5) Dispersion. Light falling upon opaque bodies, causes them to become luminous, or to emit light in all directions, and thus become visible. Such bodies are said to disperse light, be- cause they scatter the light in all directions from which they are visible. Bodies owe the property of dispersing light to the innumerable little facets of the particles composing their rough surfaces. Only part of the light is thus irregularly reflected or dispersed, while much of it is probably absorbed or destroyed. (c) Reflection. When light falls upon polished surfaces, or on bodies having naturally smooth and uniform surfaces, it is thrown off in a regular manner, as a ball rebounds from a hard floor. If a ray of light, S A, fig. 384, falls upon a polished surface, B C, it will be reflected in the direction A R. If N A is drawn perpen- dicular to B C, S A N will be the angle of incidence, and N A R will be the angle of reflection, and the two angles will be equal. What important objection to the undulatory theory has been men- tioned? 725. How is light disposed of when it falls upon any ma- terial substance ? When is light said to be absorbed ? What Is the dispersion of light ? What occasions the dispersion of light ? When is light reflected f PROPERTIES OF LIGHT. 445 384 385 The lines S A, NA, and A R, will all lie in the same plane ; we have therefore the following rules : 1st. The incident ray, the perpendicu- lar at the point of incidence, and the re- flected ray, are all situated in the same plane. 2d. The angle of incidence and the angle of reflection aie equal. (d) Refraction. If a straight rod is placed obliquely, partly- immersed in water, it appears broken or bent just where it enters the water. If a coin, a, fig. 385, is placed in a cup, in such a po- sition that it is just hidden from view, and water is then gently poured into the cup, the coin will appear to be lifted up and will become visible. Let c d be the surface of the water, the ray, a b, is so bent or re- fracted, at the surface of the water, that the coin appears as if placed at a'. This bending of the rays at the surface of any transparent medium is called refraction. Let CB, fig. 386, be the surface of water in a vessel, S A a ray of light incident at A, and N A N' the per- pendicular, A R the reflected ray, and A T the direction of the ray which enters the water and is re- fracted ; then The angle S A N is called the angle of incidence of the ray S A. The angle N A R is called the angle of reflection, which is in all_cases equal to the angle of incidence. The line NAN', is called the normal. The angle T A N' is called the angle of refraction- If we take A a, fig. 387, equal to A b, and draw a m and b n, each perpendicular to N A N', then am is the sine of the angle of incidence, and b n is the sine of the an- gle of refraction, and am ~bn~ is invariably the same for any given medi- um, whether the angle of incidence is in- 386 Mention the two principal laws which govern the reflection of light. Explain what is meant by refraction. What is meant by the angle of incidence ? "What is the angle of refraction ? What is the index of refraction ? What is the index of refraction for water? for glass 1 for diamond ? 446 OPTICS. creased or diminished ; hence the quotient obtained by dividing a. m by bn, is called the index of refraction. The index of refraction varies for different media; thus for light passing from air into water, it is about *., for light passing from air into glass, about Ji, and about 4 when light passes from air into diamond. These fractions inverted give the index of refraction for light passing out of water, glass, and diamond, into air. When light passes from a rare to a denser medium, it is reflected towards the perpendicular or normal, and when it passes from a dense to a rarer medium, it is refracted from the perpendicular or normal. The general law of the refraction of light is thus stated. The incident ray, the refracted ray, and the perpendicular to the re- fracting surface at the point of incidence, lie in the same plane ; and the sine of the angle of incidence hears a constant ratio, 41^ am bn in the same medium, to the sine of the angle of refraction. 726. The amount of light reflected increases with the angle of incidence. When light falls upon a transparent medium perpen dicular to its surface, nearly all the light enters the medium, and only a small portion is reflected. As the light falls more and more obliquely upon the medium, the amount of light refracted diminishes, and the amount reflected increases. If we look at the image of the sun in water at midday, and again near sunset, we shall see a remarkable difference. Near sunset the image is so brilliant, the eyes can scarcely bear to look at it, while at midday we observe it without difficulty. The image of objects at a little distance are seen in water more distinctly than the images of near objects, because the light from distant objects falls more ob- liquely upon the water and a greater amount is reflected. 727. Internal reflection. When light passes through a trans- parent medium, a portion of the light is reflected at each surface. In fig. 388, S A is a ray of light incident upon the first surface of State the general law of refraction. 7 26. In what position of the incident ray is the greatest amount of light reflected ? Why does the image of the sun seen in water appear brighter when it is near the horizon than at midday ? UMBRA AND PENUMBRA. 447 388 a transparent medium. A portion is reflected in A R. A T is the refracted ray, and T V the emergent ray, but a portion of the light is reflect- ed at the second surface in the direction T A', of which a part emerges in the direction A' R', and a part suffers a se. cond reflection downward from A', and a part emerges, and another portion suffers successive internal reflections be- fore it is either lost by absorption or finally emerges on one or the other side of the medium. In general only the rays A R, T V, and A' R', have sufficient intensity to be visible to the naked eye. 728. Total reflection. When light passes from a dense to a rarer medium, the angle of refraction is greater than the angle of incidence, and when the angle of refraction is 90, the angle of incidence is much less. For water it is 48 35', for ordinary glass it is 41 49', consequently a ray of light traversing water or glass at greater angles cannot escape into the air, but is totally reflected, obeying the ordinary law of reflection. The propor- tion of light suffering internal reflection from a surface of glass or water, constantly increases from the perpendicular to the point where total reflection takes place. Fig. 389 shows light radiating from a point below the surface of water and escaping into the air, the angle of 389 emergence increasing much faster than the angle of incidence, till the light emerges par- allel to the surface of the water, after which total reflection takes place. To an eye placed below the surface of j the water, all objects above the horizon would be seen within an angle of 97 10', or double the angle of total reflection for water. 729. Umbra and Penumbra. When an opaque object is held in a pencil of light proceeding from a luminous point, as s, fig. 390, a dark and well defined shadow is produced, which increases 727. What is internal reflection ? 728. When is light totally re- flected ? What are the angles of total reflection in water and glass respectively ? How does internal reflection differ at different angles ? What is the apparent extent of the visible horizon, to an eye placed below the surface of water ? 729. Explain the terms umbra and penumbra. 448 OPTICS. in size as it becomes more distant. The dark shadow is called an 390 umbra. If the light proceeds from a luminous body, having a sensible mag- nitude, as A, fig. 391, besides the dark shadow, or umbra, where no part of the luminous body is visible, there will be a much broader partial shadow called the penumbra, 391 392 where a part only of the luminous body is visible. The dark- ness of the penumbra gradually increases from the extreme bor- der, which is too faint to be easily seen, to the umbra or full shadow, as is shown in a section of the shadow, at fig. 392. 730. Images produced by light transmitted through small ap- ertures. If a white screen is placed near a small opening in a 393 dark chamber, the rays of light which pass through the opening will form on the screen inverted images of ex- ternal objects. It will be seen in fig. 393, that the rays of light from the top and the bottom of the object cross each other in the small opening, and thus invert the image. If the aperture is small, the image will be formed in the same manner, whatever be the form of the aperture. But if the opening is large, the image will be indistinct, or entirely disappears. 731. Intensity of light at different distances. The intensity of light at any distance from a luminous body, is in an inverse proportion to the square of the distance. Let 0, fig. 394, be a luminous point; at 1, 1, place a board one foot square ; it will cast a shadow that will cover a space two feet square at double the distance, three feet square at three times the distance, and four feet square at four times the distance. The areas will therefore be, 1, 4. 9, 16, and the intensity of the light at the distances 1, 2, 3, 4, will therefore be in the proportions of 1, 1, 1, JL. Is there any clear line of demarkation between the umbra and pe- numbra ? 730. How are images produced by light passing through a small opening 1 Why is the image inverted? 731. What is the relative intensity of light at different distances from a luminous body? MIRRORS. 449 V32. The absolute intensity of light from any luminous ob- ject, will be equal to the intensity of each lu- minous point, multiplied by the number of lu- minous points, and divided by the square of the distance from the luminous object at which it is seen. A given surface will receive the greatest amount of light when placed exactly facing the luminous object, or when at right angles to the direction of the rays. The amount of light received will diminish in proportion as the illuminated surface is placed inclined to the direction of the rays. 733. Photometers are instruments employed to measure the comparative intensity of different lights. The principle on which they are constructed is, to so place the lights that they will illu- minate a single surface, or two adjacent surfaces, with equal in- tensity. The relative intensities of the two lights are then as the square of their distances from the illuminated surfaces. Bunseris Photometer is the simplest and most convenient photom- eter yet invented. A disk of paper four or five inches in diameter, is rendered translucent by washing it with paraffine or stearine, dis- solved in oil of turpentine or naphtha, except a spot about an inch in diameter at the centre. When this disk is held between two lights, at a point where their intensity is unequal, the translucent part of the paper is easily distinguished from the central part, but when moved to a point where the two lights have equal intensity, all parts of the paper have a uniform appearance. . No light appears to shine through, because the illumination is equal on both sides. By means of a graduated bar, on which the light and disk are mounted, the distance of each light from the paper is determined, and their respec- tive intensities are calculated on the principles above mentioned. REFLECTION BY SPECULA AND MIRRORS. 734. Mirrors are solid bodies bounded by regular surfaces, highly polished, and capable of reflecting a considerable portion of the light which falls upon them. 732. What is said of the absolute intensity of light ? In what posi- tion with regard to the light will a plane surface be most strongly illu- minated ? 733. What are photometers? On what principle are they constructed ? Describe Bunsen's photometer, and the method of using it. 734. What are mirrors? 450 OPTICS. The term mirror is generally applied to reflectors made of glass and coated with an amalgam of tin and quicksilver. 735. Specula are metallic reflectors, having a highly pol- ished surface. The best speculum metal consists of 32 parts of copper and 15 parts of the purest tin. Specula are also made both of silver and of steel. In the use of glass mirrors, a portion of light reflected from the first surface, interferes with the perfection of the image; hence, where the most perfect instruments are required, metallic reflectors are employed. In treating of reflectors, we shall notice only the ac- tion of the principal reflecting surface, and use the term mirror to comprehend all regular reflectors. 736. Forms of mirrors. Mirrors are either plane or curved . Curved mirrors may be spherical, elliptical or paraboloid. The properties of elliptical and paraboloid reflectors have been men- tioned in sections 405 and 406. A concave spherical mirror is a portion of the surface of a sphere, reflecting from the internal side. A convex spherical mirror is a portion of the surface of a sphere, reflecting from the outside. Curved mirrors, whether concave or convex, may be regarded as made up of an infinite number of plane mirrors, each perpendicular to a radius drawn through it from the centre of the mirror. Fig. 395 shows a plane mirror, M A N, a concave mirror, m An, and a convex mirror, m' A ri, having a common point, A, and the line, P A C, perpendicular to each at the point A. If a ray of light, I A, is incident upon either mirror at the point A, the re- flected ray, A R, will make the same angle with the perpendicular as is made by the incident ray. At any other points, as t or t', the curved mirrors will act like little plane mirrors, perpendicular to the radii P t and Ct'. 735. "What is a speculum? What is the composition of speculum metal 1 "Why are metallic reflectors better than glass mirrors ? 736. What are the different regular forms of mirrors I How do concave and convex mirrors differ from each other? How may convex mir- rors be regarded ? How can plane concave and convex mirrors be placed so as to have a common perpendicular? What is the perpen- dicular to a concave or convex spherical mirror ? IMAGES FORMED BY PLANE MIRRORS. 451 737. Reflection by plane mirrors. Parallel rays of light, falling upon a plane mirror, will be parallel after reflection. If parallel rays of light, A D, A' D', fig. 396, fall upon the plane mirror, M N, they will each make equal an- 396 gles with the perpendiculars, E D, E D', and B N as the angles of incidence and reflection will be equal, the reflected rays, D B, D' B' , will make equal angles with the perpendiculars, and will consequently be parallel after reflection. If A D represent the upper side of the beam of light before reflec- tion, it will become, after reflection in D B, the lower side of the beam. Hence a beam of parallel light is inverted in one direction by reflection from a plane mirror. Diverging rays of light, falling upon a plane mirror, will con- tinue to diverge after reflection, and will appear to emanate from a point as much behind the mirror as the luminous point is be- fore it. Let A be a radiant point in front of the plane mirror M N, fig. 397. If the perpendicular, E D, E' D, E" D", be drawn, the reflected rays will make the same angles with the perpendiculars as the inci- dent rays, and hence the reflected rays will make the same angles with each other as they did before reflection, but they will ap- pear to diverge from the point -4', behind ^ : -%, / the mirror. Converging rays continue to converge after reflection from a plane mirror. After reflection they will converge towards a point as much in front of the mirror as the distance of the point behind the mirror, towards which they converged before reflection. This is easily seen by tracing the rays of light backward in the preceding figure. Reflection from a plane mirror changes the direc- tion of the rays of light, and removes the point of apparent conver- gence or divergence to the opposite side of the mirror. 738. Images formed by plane mirrors. Let M N\>Q an object placed in front of the plane mirror, A B, fig. 398, and E the place of the eye. From the great number of rays emitted in every direction from M 2T, and reflected from the mirror, a few only can enter the eye at E. These will be reflected from those por- 737. How are parallel rays reflected by a plain mirror ? How are diverging rays reflected ? How are converging rays reflected ? 452 OPTICS. tions, D F, G H, of the mirror, so situated with respect to the 398 eye and the points, M N, that the angles of incidence and reflection will be equal. If the rays, D E, F E, are continued backward, they will meet at m, and they will appear to the eye to radiate from that point. In the same manner the rays E,H E, will appear to ra- diate from n ; a virtual image of the object will therefore be formed between m and n. This is called a virtual image, because it is not formed of rays of light actually coming from the position of the image, but by rays so changed in their direction, that they appear to the eye as though originating from an object situated at m n, behind the mirror. If the eye is moved about, the image remains stationary, hence it is seen by means of rays reflected from other parts of the mir- ror. Two or more persons may see the image at the same time and in the same position, but by different rays of light. The position of the image behind the mirror may be found by drawing lines from prominent points in the object, perpendicular to the mirror, extending them as far behind the mirror as the points from which they are drawn are situated before it, then uniting the extremities of the lines, the outlines of the image will be delineated. The images of all objects seen in a plane mirror have the same form and distance from the mirror as the objects themselves. 739. Images multipled by glass mirrors. Glass mirrors pro- duce several images. This may be readily demonstrated by looking very obliquely at the image of a candle in a glass mirror. The first image, caused by partial reflection from the first sur- face of the glass, is comparatively faint. The second image is formed by reflection from the quicksilver, which covers the second surface, and is very clear and distinct. When rays of light from any object fall upon the first surface 738. How are images formed by a plane mirror? "What is meant by a virtual image ? How can the position of the image formed by a plane mirror be determined ? At what distance is the image formed by a plane mirror ? 739. Why does a glass mirror produce more than one image of an object ? From which surface of a glass mirror does the greatest amount of reflection take place ? KALEIDOSCOPE. 453 399 of a plate of glass, M N, fig. 399, a portion of the light being re- flected, forms the first image, a. The principal part of the light penetrates the glass, and is re- flected at c, by the silvering which covers the back of the mirror, and coming to the eye in the direction d H, produces the image, a', at a dis- tance from the first image equal to twice the thickness of the glass. This image is much brighter than the first, because the metallic coating of the mirror reflects a greater amount of light than the first surface of the glass. Other images, more and more obscure, are formed by rays which emerge from the glass after successive interior reflections from the two surfaces of the glass. As this multiplicity of im- ages diminishes the distinctness of vision, metallic reflectors are often employed in optical instruments. 740. Images repeated by inclined reflectors. "When an object is placed between two mirrors, which make with each other an angle of 90 or less, several images are produced, varying in numbers according to the inclination of the mirrors. If they are placed perpendicular to each other, three images will be seen, situated as in fig. 400. The rays O and D, from the point O, form, after a single re' flection, one, the image, 0', the other, the image 400 O" ; and the ray O A, which undergoes two re- flections at A and B, gives a third image, 0'". When the inclinations of mirrors is 60, five im. f " ages are formed ; and when they are placed at an angle of 45, seven images are produced. The number of images continue to increase as the inclination of the mirrors diminishes, and when the mirrors become parallel, the number of images is theoretically infinite, but as some of the light is lost at every reflection, and the successive images ap- pear more and more distant, only a moderate number of images are visible. 741. Kaleidoscope. This beautiful toy is formed by placing Explain fig. 399. Why is a glass mirror inferior to a metallic re- flector ? 740. How are images multiplied by two inclined mirrors 1 How many images are formed by two plane mirrors inclined to each other at an angle of 60 ? At 45 ? At what inclination should two plane mirrors be placed to produce the greatest number of images of a single object? 454 OPTICS. two mirrors, inclined at an angle of 45, in a paper tube, closed at one end by plain glass, and at the other by ground glass. In this tube, between the mirrors, are placed fragments of various objects, such as colored glass, tinsel, &c. Looking into the end covered with plain glass, seven images of every object are seen, symmetrically arranged. On moving the tube, so as to change the position of the objects, a series of beautiful changes take place, perfectly incomprehensible to those who do not understand the structure of the instrument. The mirrors in the kaleido- scope may be placed at other angles, when they will k give a dif- ferent number of images of objects within. 742. Intensity of reflected light. The amount or intensity of the light reflected regularly by any surface, increases with the degree of polish, and also with the enlargement of the angle of incidence. If we look very obliquely at a sheet of white paper, placed be- fore a candle, an image of the flame may be seen reflected from the surface of the paper, but the image disappears when the rays fall upon the paper nearer to the perpendicular. Different substances, polished with equal care, differ in their power of reflecting light. The amount of light reflected depends also upon the nature of the medium in which the reflecting body is placed. Bodies immersed in water reflect less light than in air. 743. Irregular reflection. Diffused light. The reflection from polished surfaces, which follows the two laws already announced, is called regular reflection; but only a part of the light is re- flected regularly from any surface, when the reflecting body is more dense than the surrounding medium. A part of the light is scattered in all directions, and is said to be irregularly reflected or diffused. This is the portion of light which renders an object visible. Light regularly reflected gives an image of the object which emits the light, while light irregularly reflected gives only an image of the body which reflects it. When a mirror becomes dim by the accumulation of light dust, or anything which tar- nishes its surface, the amount of regular reflection diminishes, 741. Explain the theory of the kaleidoscope ? 742. What circum- stances affect the intensity of light reflected from a polished surface ? 743. What is meant by irregular reflection? How does light render objects visible ? What effect is produced by dust accumulated on a polished surface ? FOCI OF CONCAVE MIRRORS. 455 and the irregular reflection increasing, all parts of the mirror be- come distinctly visible. 744. Concave and convex spherical mirrors. If an arc of a circle," M JV, fig. 401, is made to revolve around a line, A G L, drawn through its centre of figure A, and its centre of curva- ture (7, it will generate a curved surface, which will be a segment of the surface of a sphere. Internally, such a surface is called a concave mirror, and externally a convex mirror. The line, A C, is called the principal axis of the mirror, and any other line drawn through the centre of curvature, C, is called a secondary axis. The angle, M N is 401 called the angular aperture of the mirror. A section made by a plane passing through the principal axis, A C, is called the principal section, or a me- ridional section. The theory of reflection from curved mirrors is easily deduced from the laws of reflection by plane mirrors. Every point in the curved mirror may be regarded as a point in a plane mirror so situ- ated that its perpendicular, where the ray of light falls upon it, co- incides with the radius of the curved mirror at that point. A line drawn from any point in a spherical mirror to the cen- tre of curvature, will be perpendicular to the mirror at that point, and also perpendicular to any plane mirror touching the curved mirror at that point. 745. Foci of concave mirrors. The focus of a curved mirror is the point towards which the reflected rays converge. Parallel rays falling upon a concave mirror, fig. 401, converge, after reflection, to a point equi-distant between the mirror and the centre of the sphere, of which the mirror forms a part. This point is called the principal focus. Rays of light emanating from the principal focus of a concave mirror, will be reflected parallel to each other. 744. What are spherical mirrors 1 Explain the difference between concave and convex mirrors. What is the principal axis of a mirror? What is meant by the principal section of a mirror ? What is the perpendicular to a spherical mirror? How can the reflection from curved mirrors be explained by the laws of reflection from plane mirrors ? 745. What is the focus of a concave mirror 1 What is the principal focus of a concave mirror 1 456 OPTICS. Demonstration. The lines, CM, OB, C D, fig. 401, drawn from the centre of curvature of the mirror, M N, are perpendicular to the mirror at those points. The parallel rays, H B, G D, will converge, after reflection, to the point F. It is evident that the angle of re- flection, CDF, for any ray, will be equal to the angle of incidence, GDC; but G D (7 is equal to D C F, which is the alternate angle formed by a line, D C, meeting two parallel lines, G D, L A ; hence in the triangle, C F D, the angles, F C D and F D C, are equal, and therefore the sides, C F and jF D, are equal. If the point, D, gradu- ally approaches the point, A, C F -\- FD, will differ less and less from C A, till their sum will be sensibly equal to CA, or FA will be sensibly equal to one-half of C A, and the focus of parallel rays, after reflection from a concave mirror, will be equal to one-half the radius of curva- ture. If the point of incidence, D, recedes from A towards M, or N, the point, F, will gradually approach A, or the focal distance will diminish. A concave spherical mirror will therefore only reflect parallel rays to a single focal point when the diameter of the mirror is small. Practically it is found that the diameter of the mirror, or the angular aperture, M C N, should not exceed 8 or 10 degrees. Conjugate focus. If rays of light falling upon a concave mir- ror diverge from a point beyond the principal focus, they will converge, after reflection, to a point between the principal focus and the centre of curvature. This point of convergence is called the conjugate focus, because the distance of the radiant point and the focus to which the rays converge, after reflection, have a mutual relation to each other. Let rays diverging from a point, L, fig. 402, fall upon a concave 402 mirror, the angle of incidence, L K G, will be smaller than S K C, the angle of incidence for parallel rays falling upon the mirror at the same point. The angle of reflection, CKl, will also be smaller than CKF\ hence the ray, L K, will be so reflected as to cross the principal axis How are rays of light reflected which diverge from the principal focus of a concave mirror ? Explain these principles by reference to figure 421. What is the angular aperture of a concave mirror? What is meant by a conjugate focus of a concave mirror? Where should the radiant point be placed to have all the rays fall perpen- dicularly upon a concave mirror? Where is the conjugate focus when the radiant point is between the centre of curvature and the principal focus? SECONDARY AXES. 457 at a point, I, between jp, the principal focus, and C, the centre of curvature of the mirror. If the luminous point is removed to Z, the reflected rays will meet at L. If the luminous point is placed at the centre of cur- vature, C, all the rays will fall perpendicularly upon the mirror, and be reflected back to the point C, from whence they came. If the luminous point is situated between the centre of cur- vature and the principal focus, the conjugate focus will be re- moved beyond the centre of curvature, and become more and more distant as the luminous point approaches the principal focus. When the luminous point arrives at the principal focus, the con- jugate focus will be removed to an infinite distance, or, in other words, the reflected rays will become parallel. While the radiant point has removed from C to F, the conjugate focus has removed from (7, to an infinite distance. Virtual focus. If the radiant point passes from the principal focus, F, towards the 403 404 mirror, as in fig. 403, it is evident that the re- flected rays will di- verge, as though ema- nating from a point Z, behind the mirror, called the virtual focus. When the radiant point is near the principal focus, between it and the mirror, the virtual focus of the divergent reflected rays will be at a very great distance. As the radiant point continues to approach the mirror, the virtual focus also approaches it. While the radiant point passes from the principal focus to the mirror, the conjugate virtual focus, or point from which the re- flected rays appear to diverge, passes from an infinite distance be- hind the mirror, to the surface of the mirror, or to the radiant point itself. 746. Secondary axes. Oblique pencils. If the luminous point, L, fig. 404, is not situated in the principal axis of the mir- ror, a line drawn from the radiant point through the centre of curvature, as L C B, will constitute a secondary axis, and the ^ focus of the oblique pencil of rays diverging from L, will be Where is the conjugate focus when the luminous point is in the principal focus ? Explain the use of the term virtual focus. How does the position of the virtual focus vary with the movement of the radiant point? 746. What are the secondary axes 1 Howarethe foci of oblique pencils determined ? 458 OPTICS. found in this secondary axis. In the same manner we may draw secondary axes, and determine the foci, whether real or virtual, for any number of points in a luminous object. 747. Rule for conjugate foci of concave mirrors. Multiply the distance of the radiant point from the mirror, by the radius of curvature, and divide this product by twice the distance of the radiant point, minus the radius of curvature of the mirror, and the quotient will be the conjugate focus required. If the quotient given by this rule is negative, or if twice the dis- tance of the radiant point is less than the radius of curvature, the conjugate focus will be a virtual focus behind the mirror, and the re- flected rays will diverge. 748. Convex reflectors. The effects attending the reflection of diverging, converging, or parallel rays of light by convex re- flectors, are, in general, the opposite of the effects produced by concave reflectors. The foci of parallel and diverging rays of light, reflected by a convex reflector, are at the same distance as for concave mirrors, but they are situated behind the reflector, and are, hence, only virtual foci. Light converging towards any point behind a convex mirror, more distant than the principal focus, or focus of parallel rays, will diverge, after reflection, from a virtual focus nearer than the principal focus. Rays converging toward the principal, virtual focus, will be reflected parallel ; but rays converging towards a point nearer to the mirror than the principal focus, will be reflected to a real focus in front of the convex reflector. These phenomena will be readily understood by an examination of fig. 405. The ray S 7, is re- flected in the direction FIN; L ^,is reflected in the direction I E G, and reciprocally G E is re- flected in the direction G L, and M I in the direction / 8. 749. Images formed by concave mirrors The principles al- ready explained enable us to understand the formation of images by concave mirrors. Let A B, fig. 406, represent an object placed 747. State the rule for determining the conjugate focus of a con- cave mirror when the position of the radiant point is known. When is the conjugate focus real, and when is it only virtual? 748. How does the action of convex reflectors differ from concave reflectors ? Where is the principal focus of a convex mirror ? Explain fig. 405. VIRTUAL IMAGES, 459 before a concave mirror, beyond its centre of curvature. The lines, A and B C, 406 drawn through the cen- tre of curvature from the extremities of the object, are the secon- dary axes in which the extremities of the image, a 5, will be formed, at a distance from the mirror equal to the conjugate foci for the extreme points of the object. This image is real, inverted, smaller than the object, and placed between the centre of curvature and the principal focus. If a 5 is regarded as the object, placed between the centre of curvature and the principal focus, an enlarged image will be formed at A B. If the object is placed at the principal focus, no image will be formed, because the rays from each point of the object will be reflected parallel to an axis drawn through the centre of curvature from the points where they originate. If the object is placed entirely 407 On one side of the principal axis, as in fig. 407, it is evident that its image will be formed on the oppo- site side of the principal axis. 750. Virtual images. If the object, A B, fig. 408, is placed between the mirror and the principal focus, the incident rays, AD, AK, take, after reflection, the directions, D 7, K H, and their prolongations backward, form at 408 , a virtual image of the point A. In the same manner the image of B is ^~rrrr"j j f\" ~r formed at 5, so that the image of A B \ | is seen at a b. The image, in this case, 1 is a virtual image, erect, and larger ^ : '~ : --^::'.~.~J than the object From the preceding illustrations, it is evident, that, when an object is placed before a concave mirror, more distant than the centre of curvature, the image is real, but inverted, and smaller than the object ; as the object approaches the centre of curvature, 749. Explain the formation of images by concave mirrors. Why is the image formed by a concave mirror inverted ? 750. What is meant by a virtual image ? When is the image smaller, and when is it larger than the object ? Is a virtual image formed by a concave mirror erect, or is it inverted ? 460 OPTICS. the image enlarges and becomes equal to the object and coincides with it ; when the object approaches nearer to the mirror than the centre of curvature, the image becomes larger than the ob- ject, and more distant from the mirror. When the object arrives at the principal focus, the image becomes infinitely distant, and disappears entirely : when the object approaches nearer to the mirror than the principal focus, an erect virtual image, larger than the object, appears behind the mirror. 751. Formation of images by convex mirrors. Let A B, fig. 409, be an object placed before a convex mirror, at any distance 409 whatever. If we draw the secondary axes, A G, B C, it follows, from what ,,.. c h as keen said (748) concerning the con- struction of foci in convex mirrors, that all the rays emitted from the point, A, diverge after reflection, and that their prolongations backward converge to a point, a, which is a virtual image of the point, A. In the same manner, rays emitted from the point, B, form a vir- tual image of that point in &. Whatever may be the position of an object before a convex mirror, the image is always formed behind the mirror, erect and smaller than the object. 752. General rule for constructing images formed by mirrors. To construct the image of a point ; 1. Draw a secondary axis from, that point ; 2. Take from the given point any incident ray whatever ; 3. Join the point of incidence and the centre of cur- vature of the mirror by a right line ; this will ~be the perpen- dicular at that point, and will show the angle of incidence ; 4. Draw from the point of incidence, on the other side of the perpendicular, a right line, which shall make with it an angle equal to the angle of incidence. This last line represents the reflected ray, which being prolonged till it crosses the secondary axis, determines the place where the image of the given point is formed. 5. Determine the position of any other point in the ob- ject in the same manner. 753. Spherical aberration of mirrors. Caustics. The rays from any point of an object, placed before a spherical mirror, concave, or convex, do not converge sensibly to a single point, 751. What kind of images are formed by concave mirrors ? How does the size of an image formed by a convex mirror compare with the size of the real object 1 752. Describe the method of construct- ing the image of an object placed before a curved mirror. PRISMS AND LENSES. 461 unless the aperture of the mirror is limited to 8 or 10. If the aperture of the mirror is larger than this, the rays reflected from the borders of the mirror meet the axis nearer to the mirror than those which are reflected from portions of the mirror very near to the centre. There results, therefore, a want of clear- ness or distinctness in the image which is designated spherical aberration by reflection. The reflected rays cross each other sue- 410 cessively, two and two, and their points of intersection form in space a brilliant surface, called a caustic by reflexion, curving towards the axis, as shown in fig. 410, where G is the centre of curvature, F the principal focus, and d the centre of figure. The curve formed by the intersections of successive rays, is called a caustic by reflection. REFRACTION IN BODIES HAVING REGULAR FORMS. V54. Prisms and lenses, are bodies having certain regular forms, sections of which are shown in fig. 411. A prism is a solid having three or more plane faces, variously inclined to each other, as 411 shown at A, fig. 411. The an- gle formed by the faces, A R, A S, is the refracting angle of the prism. For some pur- poses prisms are used having more than three plane faces. A plane glass, B, is a plate of glass having two plane surfaces parallel to each other. A sphere, shown in section at C, has all parts of its surface equally distant from a certain point within, called the centre. A double convex lens, D, is a solid bounded by two convex surfaces, which are generally spherical. A piano convex lens, E, has one of its surfaces plane, and the the other convex. A double concave lens, F, has two concave surfaces opposite to each other. 753. What is meant by spherical Aberration of mirrors? How are caustic curves formed by reflection? 754. What is a prism? What is the reflecting angle f What is a plane glass ? What is a sphere? What is a double concave lens? 462 OPTICS. A piano concave lens, G, has one of its surfaces plane, and the other concave. A meniscus, shown at H, has one surface convex, and the other concave, their curvatures being such, that the two surfaces meet, if continued. As this lens is thicker in the centre than at its edges, it may be regarded as a convex lens. A concavo convex lens, shown at /, has one surface concave, and the other convex, but the curvatures are such that the sur- faces, if continued, would never meet. As therefore the concavity exceeds the convexity, it may be regarded as a concave lens. If the figures C, D, E, F, G, H, /, were revolved around the the axis, M N, they would severally describe the solid lenses they are intended to represent. In explaining the properties of lenses, and showing the pro- gress of light through them, we make use of such sections as shown in the figure, for every plane passing through the axis has the same form, and what is true of one section is true of all. Y55. Plane glass. If parallel rays of light are transmitted obliquely through glass or any other transparent medium bounded by parallel faces, as M N, fig. 412, the rays A B, A B, will be 412 refracted towards the perpendicular, on entering he medium, and emerging at C, C', they will be refracted from the perpendicular, and take the directions, C D, C' D', parallel to each other, and parallel to their directions before en- tering the medium. The displacement, A a-, A a', is the lateral aberration produced by transmission through a homogeneous medium bounded by parallel surfaces. The amount of lateral aberration increases with the thickness of the medium, and it also increases with the obliquity of the incident rays. Diverging rays, transmitted through a plane glass, appear, after refraction, to diverge from a point nearer to the glass, as shown in fig. 413. If the rays, C D, C' D', are continued back- ward, they meet in a point, &, nearer to the glass than the point, A, from which they originated, while rays in the glass appear to diverge from a point more distant than their real origin. What is a piano concave lens ? What is a meniscus ? What is a concavo convex lens 1 In treating of lenses why is it only necessary to consider a single section ? 755. How are parallel rays of light affected by transmission obliquely through plane glass? What change do diverging rays undergo ? How does the depth of water appear as pmrma^ed with its real depth ? REFRACTION BY PRISMS. 463 Objects seen in water will therefore appear to the observer nearer than they really are. Water is about 413 one-third deeper than it appears to be when the observer looks down into it, the bottom ap- pearing to be raised up. To an observer look- ***% ing from a dense to a rarer medium, objects ap- pear more distant than they really are. Converging rays, transmitted through a plane glass, or other dense medium bounded by parallel surfaces, will, for the same reason, converge to a point more distant than if the dense me- dium were not interposed. This will be evident by tracing the rays, D C, D C', fig. 413, in the opposite direction from what we have previously con- sidered. 756. Refraction by prisms. If a ray of light, I n, fig. 414, falls obliquely upon a transparent medium, whose opposite plane faces are not parallel, the ray will be re- 414 fracted at the first surface, and take a di- , ^- l rection nearer to the perpendicular. Now >^ -^ lens, will depend upon ~ the amount of curva- ture, and also upon the refractive power of the substance, of which the lens is com- posed. If the two surfaces of the lens have the same curvature, and the index of refraction, as for ordinary glass, is one and a half, the focus of parallel rays, called the principal focus, will be at a distance from the lens equal to the radius of curvature of either surface of the lens. Diverging rays. If the rays falling upon the lens come from a point, R, at a distance from the lens equal to twice the principal focus, they will converge to a point, 8, at an equal distance on the other side of the lens. It will be easily seen from the figure, that the angles, X and Z, are equal to each other, (being the alternate angles formed by the straight line, R A, meeting two parallel lines,) and also that the an- gles, X and 0, are equal. In the triangle, ASF, the sides, F A and FS, are equal, hence the angles, O and y, are equal, and y equals z, therefore if the incident ray is bent inward to a distance represented by the angle, Z, the refracted ray must be bent outward by an equal angle, y, by which means the radiant point is removed from F, the principal focus of parallel rays, to S, which is at double the dis- tance of F. 421 If the radiant point is taken more distant than , as at F, fig.- - "What is the index of refraction of common glass ? On what does the length of the focus of a lens depend? What is meant by the principal focus of a lens ? At what distance is the principal focus of a double convex lens? Explain the action of a lens upon diverging rays? RULES FOR DETERMINING THE FOCI OF LENSES. 467 421, the conjugate focus will be removed from S, to some point, T 7 , between 8 and the principal focus. If rays of light falling upon the lens, A B, fig. 422, converge towards a point, F, before re- 422 fraction, they will converge, after refraction, towards a point, T, between the principal focus, F, and the lens. Conversely, if rays of light diverge from a point, T 7 , between the lens and its principal forms, they will diverge after passing through the lens, from a virtual focus, F, more dis- tant than the principal focus. 760. Piano convex lenses. The action of a piano convex lens is in general the same as that of the double convex lens, but its foci are at double the distance, the principal focus being at a distance equal to twice the radius of the curved surface. 761. Concave lenses. A concave lens produces, upon rays of light transmitted through it, an effect the opposite of that pro- duced by a convex lens. Parallel rays of light, transmitted through a double concave lens, diverge from a virtual focus in 423 front of the lens, as shown in fig. 443 ; the virtual focus being at the centre of - the sphere of which the first surface forms a part. This is its principal focus. Diverging rays. If the radiant point is more distant than the principal focus, as at B, fig. 424, the virtual conjugate focus, A, will be between the principal focus, 424 F) and the surface of the lens, and the rays will diverge after refrac- tion. Converging rays, transmitted through a concave lens, will be rendered less convergent, parallel, or divergent, depending upon the distance of the point towards which they converge before entering the lens. 762. Rules for determining the foci of lenses. When lenses If the radiant point is more distant than the principal focus where will the conjugate focus be situated ? What is the action of a convex lens on converging rays? 760. Where is the principal focus of a piano convex lens 1 761. What is the effect of a concave lens upon parallel rays ? On diverging rayi? On converging rays? 468 OPTICS. are made of glass whose refractive index is one and a half, their foci may be determined by the following rules : RULE FOR THE PRINCIPAL FOCUS. Divide twice the product of the radii by their difference for the meniscus and concavo convex lenses, and by their sum for the double convex and double concave lenses. The quotient will give the focus for parallel rays. The focus of parallel rays, or principal focus, of the piano convex or piano concave lens, is double the radius of curvature. RULE FOR THE CONJUGATE FOCUS, WHEN THE FOCUS OF THE INCI- DENT RAYS IS GIVEN. Multiply the length of the principal focus by the focus of the incident rays, and divide the product by the difference between the principal focus and the focus of incident rays, and the quo- tient will be equal to the conjugate focus. If the distance of the focus of incident rays is less than the prin cipal focus, the value of the conjugate focus will be positive, and it will lie on the same side of the lens as the focus of incident rays ; but if the value of the focus of incident rays is greater than the prin- cipal focus, the value of the conjugate focus will be negative, and the focus of refracted rays will lie on the other side of the lens. 763. Combined lenses. If two convex lenses, A A, B B, are placed near together, as in fig. 425, their combined focus will be shorter than that of either lens used above. Let / be the length of the principal focus of the lens A A, and /' 425 the focus of the lens B B, and n the distance between the two lenses and /", the distance of the combined focus from the second /.f /__ If the distance between the lenses is nothing, then, /" = * , the focus of parallel rays. 762. What is the rule for determining the prin cipal focus of a lens ? What is the rule for the conjugate focus? When is the conjugate focus on the same side of the lens as the focus of incident rays ? When on the opposite side? 763. What is the effect of combining two lenses ? How is the principal focus of a combination of lenses de- termined 1 IMAGES FORMED BY LENSES. 469 764. Oblique pencils, when transmitted through lenses, have their foci in secondary axes, and their foci are determined by the same rules as the foci of direct pencils in the principal axis. It has been shown, in section 756, that a ray of light transmitted through a prism in a direction parallel to its base, suffers the least deviation possible ; hence in every other position the deviation is in- creased. From this principle it follows that the foci of oblique pen- cils transmitted through lenses will be somewhat shorter than the foci of direct pencils. This fact requires consideration in the forma- tion of the images of large objects. (See section 768.) 765. The optical centre of a lens is a point so situated that every ray of light passing through it will undergo equal and op- posite refraction on entering and leaving the lens. All rays of light passing through the optical centre emerge from the lens parallel to the incident rays. The position, form and foci, of all pencils of light passing through a lens are determined by their relation to some line, or secondary axis, passing through the optical centre of the lens, whether any ray of light from the radiant point actually passes through that centre or not. The optical centre of an equi-lateral double convex, or double concave lens, is at the centre of the lens. The optical centre of a piano convex, or piano concave lens, is at the centre of the curved surface. 766. Images formed by lenses. If an object is placed before a convex lens at a greater distance than the principal focus, an image of the object will be formed on the other side of the lens. If from the extremities of the object A B, fig. 426, the secondary axes, A a, B b, are drawn through 426 the optical centre of the lens, the image will be formed between these axes prolonged, at a distance equal to the conjugate focus of the lens, estimated separately for every point of the object. If the object is placed beyond the principal focus, and at less than twice this distance, the image will be mere distant 764. Where are the foci of oblique pencils found ? What effect is produced upon the foci of pencils of light by transmitting them obliquely through a lens ? What are secondary axes ? Where is the optical centre of a double convex or double concave lens of equal curvature on both sides ? Where is the optical centre of a piano convex or piano concave lens I 766. On which side of a lens are real images formed 1 Explain the formation of images by a convex lens. 470 OPTICS. and larger than the object. If the object recedes from the lens, the image will approach it. When the object is removed from the lens, more than twice the principal focus, the image will be smaller than the object, and it will gradually approach the lens, and diminish in size as the object recedes. The image can never approach nearer to the lens than the principal focus. The linear magnitude of the image as compared with the object will be proportional to their respective distances from the lens. If the object is placed nearer to the lens than the principal focus, 427 as A B, fig. 427, the rays will diverge after passing the lens, and a virtual image, a b, will be formed on the same side of the lens as the object. The virtual image formed by a convex lens is always larger than the object. If an object, A B, fig. 428, is placed before a concave lens, the rays from evejy point of the object will diverge after refraction more than 428 they did before entering the lens ; conse- quently a virtual image, smaller than the object, will be formed on the same side of -the lens. The size of the virtual image will be in proportion to its distance from the lens. 767. Spherical aberration of lenses. It has been assumed that spherical lenses bring rays of light issuing from a point to a sensible focus. For many purposes, however, greater accu- racy is required, and it becomes necessary to consider the im- perfections of spherical lenses. If the diameter of the lens V IF, fig. 429, is large in propor- 429 tion to its radius of curvature, rays of parallel light will not be brought to an accurate focus, but while the central rays cross the axis at F, the extreme rays will intersect the axis at #, and intermediate rays will in- tersect the axis at every possible point between F and G. The distance, F #, is called the lon- gitudinal spherical aberration of the lens. When is the image smaller, and when larger than the object ? When is a virtual image formed by a concave lens? Is a virtual im- age formed by a convex lens larger, or smaller than the object? What kind of images are formed by concave lenses] On what does the size of the virtual image depend ? 7 67. What is meant by spher- ical aberration of lenses ? ABERRATION OF SPHERICITY. 471 For lenses of small aperture, the aberration is in proportion to the square of the angular aperture of the lens, but for lenses of larger aperture, the aberration increases more rapidly than would be re- quired by this proportion. If the length of the principal focus be taken as unity, the longitudinal aberration for lenses of different an- gular apertures will be as follows : For 15 the aberration will be 0'025, " 22 " " " " 0-062, " 30 " " " " 0-150, " 45 " " " " 0-375. This effect of spherical lenses causes images to be formed at every point between F and G, the rays going from each image, more or less interfering with the distinctness of all the others. The amount of spherical aberration depends also on the form and position of lenses. If n = index of refraction, r the radius of the anterior surface, and R the radius of the posterior surface, then for parallel rays, the form of least aberration will be expressed by the following equation. _r _ 4 + Ti2 n a R ~ 2 n a +n If TI = !-, the form of least aberration will be a lens whose sur- faces have their radii in the proportion of 1 to 6, the side of deeper curvature being towards parallel rays. If the spherical aberration of such a lens, in its best position, is taken as unity, the aberration of other lenses will be as follows : Piano convex with plane surface towards distant objects, 4'2. Piano convex with convex surface towards distant objects, 1*081. Piano concave the same as piano convex. Double convex or double concave with both faces of the same cur- vature, the aberration will be 1*567. 768. Aberration of sphericity; distortion of images. When a straight object is placed before a lens, the extremities of the object not being in the principal axis, if the images of the ex- treme points are formed in the secondary axes at the same dis- tance from the optical centre of the lens, as the central portions of the image, the image will not be straight, but formed on a curve, the centre of which is at the optical centre of the lens, as a' &', fig. 50. But as an object recedes from the lens, the How does the sperical aberration of a lens compare with its angu- lar aperture? What is the form of a lens of least spherical aberra- tion ? In what position does a piano convex lens have the least ab- erration? 768. Explain the various causes which produce distortion of images. 4V2 OPTICS. 430 image will approach it, therefore as A and B are more distant from the lens than the centre of the object, the extremities of the image must be nearer than the centre, and instead of a' C ~b', we shall have the image a" C V, de- ?- scribed around a centre, somewhere between the lens and the centre of the image. Oblique pencils are also more strongly refracted than pencils which be- long to the principal axis ; hence this cause must tend to curve the image still more. This curvature, or distortion of images, is called aberration of sphericity. For ordinary purposes this im- perfection of lenses may be disregarded. The practical method of overcoming these difficulties will be best explained in connec- tion with the description of achromatic lenses. CHROMATICS. 76 9 . Analysis of light. Spectrum. Primary colors. A beam of sunlight, S H, fig. 431, admitted into a dark chamber, through a small opening in the shutter, E, forms a round white spot, P, upon a screen or any other ob- ject upon which it falls. If a triangular prism, JB A C, is in- terposed in its path as shown in the figure, the light will be re- fracted both on entering and leav- ing the prism, but instead of forming only a circular white spot on the screen, M N, it will be spread over a considerable space from S to K, called the solar spectrum, in which will be seen all the colors of the rainbow. Beginning with the color most refracted, they are violet, indigo, ~blue, green, yellow, orange, and red. If an opening is made in the screen so as to permit only the rays of a single color to pass, and we attempt to analyze this color by passing it through a second prism, we find it cannot be further decomposed by refraction ; 769. Describe the method of analyzing light by a prism. What are the primary colors obtained by this method? What color is most refracted? COMPLEMENTARY COLORS. 473 hence the colors of the solar spectrum produced by the refrac- tion of a triangular prism are generally called primary colors. 770. Recomposition of light. If a second prism, A B a, ex- actly similar to B A C, is placed behind the first, but in a re- versed position, as shown in the figure, the differently colored rays will be re-united and form white light at P, as though no prism had been used. Moreover, if, instead of the second prism, a double convex lens is so placed as to receive the colored rays and converge them to a focus, a round spot of white light will be again formed in the focus of the lens. If colored powders are mixed in the proportions that the several colors occupy in the solar spectrum, the color of the compound will be a grayish white. That the resulting color is not pure white is prob- ably owing to the fact that we cannot procure artificial colors that will accurately represent the colors of the solar spectrum. 771. Analysis of colors by absorption. Although the colors of the prismatic spectrum cannot be further divided by refrac- tion, Brewster has shown, that any of the colors may be still further decomposed by transmission through variously colored glass. He thus ascertained that red, yellow, and ~blue light are found in various proportions in all parts of the spectrum, and that any other color whatever may be formed by suitable combi- nations of these three. Brewster and other eminent philoso- phers have hence inferred that there are really only three pri- mary colors, red, yellow and l)lue. Dr. Young considered red, green and violet, primary colors. Ac- cording to Herschel, any three colors of the spectrum may be taken as primary, and all other colors may be compounded from them, with the addition of a certain amount of white. The distinction of colors into primary and secondary, should therefore be considered to a cer- tain extent as arbitrary, and as adopted principally for convenience of illustration. 772. Complementary colors. Any two colors which by their union would produce white light, are said to be complementary to each other. If we take away from the solar spectrum any color whatever, we may re-unite all the remaining colors, by means of a double convex lens, or by a second prism, and the 770. How can several colored rays be so combined as to produce white light? 771. How may light be analyzed by absorption I How many primary colors are recognized by Sir David Brewster 1 474 OPTICS. resulting color will obviously be complementary to the first, be- cause it is just what the first wants to make white light. In this manner it is found that, Red is complementary to Green. Violet red " " Yellowish green. Violet " " Yellow. Violet blue " " Orange yellow. Blue " " Orange. Greenish blue " " Reddish orange. Black " " White. The subject of harmony and contrast of colors, will be treated in connection with the phenomena of vision. W3. Properties of the solar spectrum. In the solar spectrum there are found three distinct properties which exist in various degrees of intensity in the differently colored rays. See fig. 434. (a) Luminous rays. According to Herschel, Fraunhofer and others, it is found that the maximum illuminating power resides in the yellow rays, and the minimum in the violet. (J) Calorific, or heating rays. The position of greatest inten- sity for the calorific rays varies with the nature of the material of the prism with which the spectrum has been produced. In the spectrum produced by a prism of crown glass, the greatest heat- ing power is found in the pale red. If a prism, filled with water is used, the greatest heating power is found connected with the yellow rays. If the prism is filled with alcohol, the greatest heat is connected with the orange yellow. With prisms, formed of highly refracting gems, the maximum heating power is found beyond the red ray. Flint glass resembles the gems in this respect. (c) Chemical rays. In a great variety of phenomena, solar light acts as a chemical agent. Under the influence of solar light, plants decompose carbonic acid, evolving pure oxygen and most vegetable colors are destroyed ; phosphorus is changed to its red or amorphous state, and loses its power of emitting light ; chlorine and hydrogen may be safely mixed in the dark, but combine with an explosion when exposed to the sun's light ; the green color of plants disappears in the dark, and the nature of the vegetable juices is changed when withdrawn from the 772. What is meant by complementary colors? Name the several colors which are complementary to each other. 773. What three remarkable properties are found in solar light ? DARK LINES IN THE SOLAR SPECTBUM. 475 chemical action of light ; and the wonderful phenomena of pho- tography depend upon the action of light upon sensitive chem- ical substances. The maximum chemical effect, produced by solar light, appears to be connected with the violet rays, or with rays between the violet and the blue. Some chemical effect is produced by rays refracted entirely beyond the extreme border of the visible violet rays. The lavender light of Herschel re- sults from the concentration of the so-called invisible rays, be- yond the border of the violet, where the greatest chemical power resides. A large convex lens gathers these otherwise invisible rays into a faint beam of lavender colored light. 774. Fraunhofer's dark lines in the solar spectrum. In 1802, Dr. Wollaston first discovered the existence of dark lines in the solar spectrum, but the discovery excited no special attention, and was applied to no practical purpose. Unacquainted with Wollaston's observations, the late cele- brated Fraunhofer, of Munich, re-discovered the dark lines of the spectrum, now distinguished as Fraunhofer 1 s dark lines. View- ing through a telescope the spectrum formed from a narrow line of solar light, by the finest prisms of flint glass, he noticed that its surface was crossed by dark lines of various breadths. None of these lines coincide with the boundaries of the colored spaces. From the distinctness and ease with which they may be found and identified, seven of these lines have been distinguished by Fraunhofer by the letters B, 0, D, E, F, G, H. Numerous other lines varying from 600 to 2,000 in number, according to the power of the telescope with which they are viewed have since been counted in the solar spectrum. To view these lines with the naked eye, a ray of sunlight is ad- 432 433 1 1! 1 1 1 ! HI pr B c M b DE * fr H FLIOT GLASS WWN GLASS sir I ' 1 It f. BC D E B. C tt III Ill 1 1 IJWATER mitted into a dark chamber through narrow openings in two screens, one placed behind the other, as shown in fig. 432, and is then re- 774. What are Fraunhofer's dark lines? How may they be ob- served ? In what respect are their positions the same in spectra ob- tained by prisms of different materials 1 How do they differ ? 476 OPTICS. fracted by a prism of the purest flint glass. The! lines, or some of them, will then be seen on the screen. The positions of these lines in the colored spaces of the spectrum is perfectly definite, but their distances from each other vary with the substance of which the prism is formed. Fig. 433 shows the arrangement of the dark lines in the spectrum, formed by prisms of flint and crown glass, and also by a prism filled with water. These dark lines answer the important pur- pose of landmarks for determining the indices of refraction for various substances. The exact limits of the several colors in the spectrum are not well defined, but the dark lines establish definite points from which the practical optician estimates the refractive power of any medium, and also the comparative refrangibility of the differently colored rays in which the dark lines occupy fixed positions. In the spectrum produced by the light of the sun, whether re- flected by the moon or planets, or from the clouds or any terrestrial object, the position of the dark lines is invariable. But the light of the stars differs from that of the sun, and the light of one star dif- fers from other stars in regard to the number and position of the dark lines in the spectrum. Electrical light, and the light of flames produced by any burning body whatever, give bright lines instead of the dark lines in the spectrum formed by solar or stellar light. The relation of the dark lines to the colors of the spectrum is shown in fig. 434. B lies in the red portion near the end ; C is farther advanced in the red ; D in the orange is a strong double line easily recognized ; E in the green ; j^in the blue ; G in the indigo ; and H in the violet. Besides these, there are also others very remarkable ; thus I is a triple line in the green, between E and F, consisting of three strong lines, of which two are nearer each other than the third ; A is in the extreme border of the red, and a is a band of delicate lines between A and B. 775. Intensity of luminous, calorific, and chemical rays. 434 Red. Orange. Yellow. Green. Blue. Indigo. Violet. Fig. 434 also shows how the in tensity of the luminous, calorific, and How does the light of the stars differ from sunlight ? What re- markable peculiarity in the light of flames and in electrical light ? CHROMATIC ABERRATION. 477 chemical rays, varies in different parts of the spectrum. The greatest illuminating power resides in the yellow part of the spectrum. The heating power is almost entirely absent in the violet and the blue, where the chemical agency is greatest, and it is greatest beyond the red, and extends a considerable distance, where no illuminating or chemical power is ordinarily manifest. The relative positions of the maximum illuminating, chemical, and heating powers of the solar spectrum, vary somewhat with the nature of the substance composing the prism with which the spectrum has been produced. 776. Refraction and dispersion of the solar spectrum. Kaly- chromatics. If a glass tube, retort neck, drinking glass, or any similar instrument of glass be held in the path of the colored rays from a triangular prism in a dark chamber, a beautiful sys- tem of colored rings will be formed, varying their form, position and color, with every change in the position or form of the glass interposed. This experiment exhibits, in the most surprising and agreeable manner, the wonderful resources of color contained in the solar beam. Language fails to express the exquisite and wonderful beauty of this simple experiment, involving only the refraction and dispersion of the solar spectrum. Kalycromatics^ (from the Greek for beautiful colors,) has been suggested as a word to distinguish these phenomena. 777. Chromatic aberration. When rays of ordinary white light are refracted by a lens of any form, consisting of a single transparent substance like glass, or a transparent gem, the rays are each acted upon as by a prism, and dispersed into all the co- lors of the solar spectrum. This 435 effect is shown by fig. 435, where V is the focus of the violet rays which are most refracted, and R is the fo- cus of red rays which are least re- fracted. A violet image is formed at F, and a red image at R, and as the other colors are situated between the violet and the red, all the space between Fand J2, is occupied by other images of intermediate colors. If an image of a point or line is formed at F, its color will be violet, but it 775. How does the intensity of the luminous calorific and chem- ical rays differ in different parts of the spectrum? 776. How can magnificent exhibitions of colored light be produced in connection with the solar spectrum ? 777. What is chromatic aberration ? 4:78 OPTICS. will be surrounded by fringes composed of all the colors of the spec- trum, the outer border of the fringe being red. This defect of all single lenses, formed of whatever substance, is called chro- matic aberration. 778. Achromatism. We have seen, section 774, fig. 433, that the spectrum formed by flint glass is nearly twice as long as that formed by crown glass. If therefore we take a prism of crown glass, A, fig. 436, and another prism of flint glass, B, having a 436 refractive angle so much smaller than the re- fractive angle of A, that the solar spectrum formed by it, will exactly equal in extent the spectrum formed by the first prism, we may place the two prsims in opposition, as shown in the figure, and the colored rays separated by trans- mission through one prism, will be exactly re- united by the other. The light transmitted through the two prisms, thus placed, will therefore be of the same color as before transmission. But while the color of the transmitted light is unaltered, its direction will be changed by about one-half the re- fractive power of the prism A ; for while the prism, B, has neu- tralized all the dispersion of color produced by A, it has neu- tralized only about half of its refractive power. Applying these principles to lenses, a double convex lens of 437 crown glass, A -4, fig. 437, may be united with a piano iconcave lens of flint glass, B B, having a focus about double the focus of the convex lens. These two lenses will act like the prisms in the preceding figure. The con- cave lens of flint glass will correct the chromatic aberration of the double convex lens of crown glass, and leave about one-half of the refractive power of the convex lens as the 1 effective refracting power of the compound lens. An achro- matic lens, formed of a double convex lens of crown glass, equally convex on both sides, joined with a piano concave lens of flint glass, having its concave side ground to fit one side of the double convex lens, will have the focus of a simple piano convex lens, with its con- vexity equal to one side of the double convex lens.* The forms of * As there is considerable difference in the refractive and disper- sive powers of different specimens of both flint and crown glass, these results are to be regarded only as illustrations of the principle of achromatism, the proportions of the several curves varying for different kinds of glass. 778. What is an achromatic prism? Explain the structure of an achromatic lens. STRUCTURE OF THE HUMAN EYE. 479 the convex lens of crown glass and the concave lens of flint glass, may be varied to any extent, provided their separate foci are inversely as the dispersive power of the substance of which each lens is made. / VISION. 779. Structure of the human eye. The human eye is the most perfect of all optical instruments. By means of this organ, stimulated by the light reflected or refracted from external ob- jects, we recognize their presence, nearness, color and form. Some knowledge of the structure and action of the eye is essen- tial to a proper understanding of the uses of other optical in- struments. The eye, situated in its bony cavity called the orbit, is main- tained in its position by the optic nerve and its sheath, by mus- cles which serve to move it or hold it steady in any required po- sition, and by the delicate membrane called the conjunctiva, which covers its anterior surface and lines the eyelids. The eye- lids serve to protect the organ from external injuries, and also to shut out light which might otherwise be troublesome or injurious by its excess, or too long continued action. Fig. 438 shows a horizontal section of the eye, the lower part of the figure representing the 438 side of the eye towards the nose. The globe, or ball of the eye, is nearly spherical, though the anterior portion is more convex than the other portions, as shown in the figure. The principal portions of the eye which require conside- ration, are the sclerotic coat, j,\ the cornea, the choroid coat, the retina and optic nerve, the iris, the pupil, the crystalline lens, the aqueous humor, the vitreous humor, and the- hyaloid membrane. The sclerotic, coat, i, is a strong opaque structure, composed of bundles of strong white fibres, interlacing each other in all di- rections. This membrane covers about four-fifths of the eyeball, and more than any other structure, serves to preserve the glob- 779. What is the organ of vision? Describe the structure of the eye. 480 OPTICS. ular form of eye. It has a posterior sieve-like opening, for the transmission of the fibres of the optic nerve, n; anteriorly, a transparent membrane called the cornea, a, is set into a groove in the sclerotic coat, as a watch crystal is set in the case, but these two membranes are so firmly united that they are separated only with considerable difficulty. The cornea is more convex than the sclerotic coat. The choroid coat, k, is a strong vascular membrane, lining the sclerotic coat, and covered internally by a dark pigment, the pig - mentum nigrum, which prevents any reflection of light from the internal parts of the eye. The third, or inner membrane of the eye, is the retina, m, which is merely an expansion of the optic nerve, n, uniting it to the brain. It is on this delicate lining membrane, (the retina,) that the images of external objects are formed. The iris, d, which forms the colored part of the eye, is a dark annular curtain or diaphragm, adherent at its outer margin, with a central opening which, in man, is circular ; in cats and the fe- line tribe generally it is elongated vertically ; in the ox and other ruminating animals, in a horizontal direction. The central open- ing of the iris, e, which allows light to penetrate the eye, is called the pupil. It varies from one-eighth to one-quarter of an inch in diameter. In a strong light the pupil contracts, but where the light is diminished it expands. Every one knows the sensation produced by entering a house after spending hours in the open air exposed to the light of the sun re- flected from snow. In this case the pupil becomes so contracted, and the eye so accustomed to a strong light, that objects within doors are almost invisible until the pupil expands and the eye recovers its sensitiveness in ordinary light. The movements of the iris are in- voluntary. The pupil of the owl is so very large that it sees distinctly at night, while in the day-time the pupil cannot contract enough to protect the eye from the blinding effect of the solar rays, and hence the owl is nearly blind by day. The crystalline lens, f, fig. 438, is a transparent body, placed behid the iris and very near to it ; it is enveloped in a transpa- rent membrane or capsule, which adheres by its borders to the ciliary process, g. The posterior surface of the crystalline lens, is more convex than the anterior. The crystalline lens is made What is the use of the iris 1 How does the crystalline lens act upon light ? ACTION OF THE EYE UPON LIGHT. 481 up of serrated fibres, arranged in layers which increase in den- sity from the circumference to the centre of the lens. Aqueous humor. The space between the cornea and the crys- talline lens is filled with a transparent liquid called the aqueous humor. The iris divides this space into two chambers, the ante- rior chamber, 5, between the cornea and the iris, and the poste- rior chamber, c, between the iris and the crystalline lens. These two chambers communicate freely with each other through the pupil, e. The free edge of the iris floats in the aqueous humor. Vitreous humor. The posterior compartment of the eye, h, behind the crystalline lens, constitutes by far the larger part of the internal cavity of this organ, and is filled with a transparent gelatinous fluid, inclosed in exceedingly delicate cellular tissue, which is condensed externally, and forms a delicate hyaloid mem- brane, everywhere covering the retina and the posterior surface of the crystalline lens. The vitreous humor, inclosed in its cel- lular tissue, and enveloped by the hyaloid membrane, is called the vitreous body. 780. Action of the eye upon light. The eye may be compared to a dark chamber, the pupil being the opening to admit the light, the crystalline lens being a converging lens to collect the light, and the retina a screen upon which is spread out the image of external objects. The effect is the same as when a double convex lens forms, at its conjugate focus, an image of any object placed in the other focus. Let A B, fig. 439, be an object placed before the eye, and consider that rays are emitted 439 from any point, as A, in all directions ; only those rays which are di- rected towards the pu- pil can penetrate the eye, or contribute to the phenomena of vision, The rays, on enter- ing the aqueous humor, are refracted towards the axis, O o, drawn through the optical centre of the crystalline lens ; but on entering the lens, which is more dense than the aqueous humor, they are still fur- ther refracted, and undergoing yet another refraction on leaving the crystalline lens, they converge towards a point, a, where they form an image of the point, A. The rays of light emitted from B, form its image in the point b, and in the same manner every part of the ob- 780. In what part of the eye, and how are images of external objects formed 1 21 482 OPTICS. ject A B, is delineated in the very small image a b, which is a real image, inverted, and formed exactly upon the retina. *I81. Inversion of the image formed in the eye. To prove that the image formed in the eye is really inverted, take the eye of an ox, cut away the posterior part of the sclerotic arid choroid coats; fix the eye thus prepared in an opening in the shutter of a dark chamber, and look at it with the aid of a mag- nifying glass, when external objects will be seen beautifully de- lineated in an inverted position, on the retina of the posterior part of the eye. Philosophers and physiologists have proposed various theories to explain how we come to perceive objects erect, Avhen their images in the eye are actually inverted. The most rational of these theories are the two following : 1st. That we judge of the relative position of objects, or of different parts of the same object, by the direction in which the rays come to the eye, the mind tracing them back from the eye towards the object. 2d. That the image formed on the ret- ina, gives correct ideas of the relation of external objects to each other, up and down being, in reference to impressions on the retina or brain, merely the relative directions of the sky and earth ; and we see all bodies, including our own persons, occupying the same rela- tions to these fixed directions as our other senses demonstrate that they really occupy. V82. Optic axis. Optic angle. The principal axis of the eye, called the optic axis, is its axis of figure, or the right line passing through the eye in such a position that the eye is symmetrical on all sides of it. In a well formed eye this is a right line, pass- ing through the centre of the cornea, the centre of the pupil and the centre of the crystalline lens, as 0, fig. 439. The lines A a, B 5, which are sensibly right lines, are secondary axes. Objects are seen most distinctly in the principal optic axis.- "When both eyes are directed towards the same object, the angle formed by lines drawn from the two eyes to the object, is called the optic angle, or the binocular parallax. To appreciate this difference of direction, look at two objects that are situated in a line with one eye, the other being closed ; then, without moving the head, look at the same objects with the other eye, and the objects will not both appear in the same line, but will 781. Why is the image formed upon the retina inverted ? How can an inverted image on the retina give to the mind a correct idea of the relation and position of external objects? 782. What is meant by the optic axis 1 What is binocular parallax ? CONDITIONS OF DISTINCT VISION. 483 seem suddenly to change their positions. By such experiments it will readily be found that some persons see principally with the right, and others chiefly with the left eye, when both eyes are open. Oth- ers will find that a part of the time the direction of objects is deter- mined by one eye, and part of the time by the other. 783. Visual angle. The angle formed between two lines drawn from the eye to the two extremities of an object, is called the visual angle, as A B, fig. 440. If the object is removed to twice the distance, the visual angle A' B' will be only one-half as great as A OB, and the breadth of the image formed on the retina will be proportionally decreased. The apparent linear magnitude 440 of an object is in in verse proportion ^^ ~{ X to its distance from the eye, or in di- / |)^^^^^^lJl rect proportion to the visual angle. ~a The apparent superficial magnitude is always the square of the appa- rent linear magnitude, and is in inverse proportion to the square of the distance. 784. The brightness of the ocular image of any object will be in direct proportion to the intensity of the light emanating from each point in the object. The amount of light received by the eye from any point in the object, or from the entire object, will be inversely as the square of the distance, and directly as the intensity of the light from each point. (732.) But the superficial magnitude of the image will diminish as the square of the distance increases ; hence, the apparent brightness of the image will remain constant, whatever may be the distance of the object. As the object recedes from the eye, the size of the image formed on the retina diminishes, the details of the various parts become crowded ^together, and only the bolder outlines occupy sufficient space to make a sensible impression, or to be clearly discerned. 785. Conditions of distinct vision. It may be stated in gen- eral, that two conditions are essential to distinct vision. 1st. That an object should be situated at such a distance as to form on the retina an image of some appreciable magnitude. 2d. 783. What is the visual angle ? How is the apparent linear mag- nitude of an object determined 1 How is the apparent superficial magnitude of an object determined ? 784. On what does the bright- ness of an image depend 1 Explain why the apparent brightness of an image is the same whether the object is near or remote. 484 OPTICS. That the object shall be sufficiently illuminated to produce a dis- tinct impression upon the retina, The distance at which an object can be seen varies with the color of the object, and the amount of illumination. A white object illumi- nated by the light of the sun can be seen at a distance of 17,250 times its own diameter. A red object illuminated by the direct light of the sun can be seen only about half as far as though it were white, and blue at a distance somewhat less. Objects illuminated by ordi- nary day-light can be seen only about half as great a distance as when illuminated by the direct rays of the sun. The smallest visual angle under which an object can be seen with the naked eye, is esti- mated at twelve seconds. All these calculations will vary for diffe- rent eyes. Persons having dark colored eyes can generally see much farther than those who have light colored eyes. Those whose eyes are trained to view distant objects, as sailors and surveyors, will see objects that are far too distant to be seen by the eyes of inexperi- enced persons. 786. Background. The distance at which the outline of any object can be distinguished, depends very much upon the color of adjacent objects, or of the background on which the object appears projected. Objects are most distinctly seen when the color of adjacent objects, or the background, presents a strong contrast to the colors of the object we wish to see. Colored signals. For signal flags used at sea, the colors red, yellow, blue and white are employed, because they are readily distinguished, and are easily seen, with the water or the sky for a background. For railroad signals, the colors red, white and black are mostly used. 787. Sufficiency of illumination. It is not enough for distinct vision, that a well denned image of the object shall be formed on the retina. This image must be sufficiently illuminated to affect the senses, and at the same time not so intensely illumi- nated as to overpower the organ. An image may be so faint as to produce no sensation, or it may be so intensely brilliant as to dazzle the eye, destroy the distinctness of vision, and produce absolute pain. When we look at the meridian sun, its light is so brilliant as to 785. What are the conditions of distinct vision ? At what distance can an object be seen under the most favorable circumstances ? What color can be distinguished at the greatest distance '? What is the smallest visual angle under which an object can be seen ? 786. What colors are usually used for signals? 787. Explain the effect of dif- ferent kinds of illumination upon objects. ADAPTATION OF THE EYE TO DIFFERENT DISTANCES. 485 overpower the eye and render it impossible even to see distinctly the solar disc, but if a sufficient stratum of vapor, or a colored or smoked glass is interposed, we see a well-defined image of the sun. Many stars are so distant that the rays which enter the pupil, when converged to a point on the retina, produce no appreciable sensation, but when the amount of light from the same stars falling upon a large lens is concentrated upon the retina, it produces sensation, and the stars become visible. On passing from a dark room to one brilliantly illuminated, or on going out into the open air at night from a well-illuminated room, the sensations experienced are owing partly to the contraction and expansion of the iris, as explained in section 779, and also to the fact that the sensibility of the retina is diminished by long exposure to intense light, and increased by remaining a long time in feeble light. 788. Distance of distinct vision. Though the human eye is capable of seeing objects at both great and small distances, most persons, when they wish to see the minute structure of an ob- j ect clearly, instinctively place it at a distance of from six to ten inches from the eye. This point, called the limit of distinct vision, sometimes varies for the two eyes of the same person. Persons who see objects at very short distances are called near- sighted, while those who see objects distinctly only at greater distances, are said to be long-sighted. 789. Visual rays nearly parallel. When we consider that the diameter of the pupil, when the eye is adjusted for viewing near objects, is only about one-tenth of an inch, if we take the limit of distinct vision at six inches, it will be found that the cone of rays entering the eye, from any single point, is included within an angle of one degree. If we take the limit of distinct vision at ten inches, the angular divergence of the cone of rays entering the eye from a single point will be little more than half a degree. In either case, therefore, the rays differ but slightly from parallel rays. For all objects more remote, the rays may properly be considered as parallel. Distinct vision is therefore obtained only by rays that are sensibly parallel or very slightly divergent. 790. Adaptation of the eye to different distances. Although there is a definite distance at which minute objects are most dis- How is the sensitiveness of the eye affected by a strong light] 788. What is the limit of most distinct vision ? When are persons said to be near-sighted ? When longsighted ? 789, By what rays \& distinct vision obtained ? 4:86 OPTICS. tinctly seen, the eye has a wonderful facility of adapting itself to viewing objects at different distances. Let two similar objects be placed, one three feet from the eye and the other at a distance of six feet. If the eye is fixed steadily upon the nearer object for a few moments, it will be distinctly seen, while the more remote object will appear indistinct, but if the eye is stead- ily fixed upon the the remote object, that 'object will soon be clearly seen, and the nearer object will appear indistinct. We thus see that either the converging power of the eye is subject to rapid variation, or that the distance of the crystalline lens from the retina is change- able. The means by which the e} 7 e thus rapidly adapts itself to viewing objects at different distances, have not been satisfactorily determined. 791. Appreciation of distance and magnitude aerial per- spective. The appreciation of the distance and magnitude of objects is entirely a matter of unconscious training, or education, and depends upon a variety of circumstances, as the visual angle, optic angle, comparison with familiar objects, and distinctness or dimness of the image, caused by intervening air or vapor. When the magnitude of an object is known, as the height of a man, a house, or a tree, the visual angle under which it is seen ena- bles us to appreciate its distance. If its magnitude is unknown, we judge of its size by comparing it with other familiar objects situated at the same distance. In viewing a range of buildings, or a row of trees, the visual angle decreases as the distance increases, and the objects decrease in appa- rent size in the same proportion, but the habit of viewing the houses or trees, and their known altitude, causes us to correct the impres- sion produced by the visual angle, so that they do not appear to de- crease in size as fast as their distance increases. Thus, when distant mountains are seen under a very small visual angle, occupying but a small space in the field of view, being accus- tomed to aerial perspective, we unconsciously restore to some extent their real magnitude. The optic angle, or binocular parallax, is an essential element in appreciating distances. This angle increases or diminishes inversely as the distance; the movement of the eyes required, to cause the op- tic axes of the two eyes to converge upon any object which we are viewing, gives us an idea of its distance. It is only by habit that 790. Can the eye distinguish distant and near objects with equal clearness at the same time ? What changes are probably required to adapt the eye to different distances? 791. How does the eye judge of distances? DOUBLE VISION. 487 we appreciate the relation between the distance of an object and the corresponding movement of the eyes, required to direct both eyes upon it. When persons blind from birth have obtained their sight by an operation for cataract, all objects appear to them to be situated at the same distance, until experience enables them to judge cor- rectly of distances. Infants plainly have no notion of relative distances and magnitudes, and vainly grasp at vacancy. 792. Single vision with two eyes. When both eyes are di- rected to the same object, similar images are produced in both eyes, and the inquiry is most natural why all objects thus seen do not appear double ? Passing by much learning bestowed on this subject, the simplest and most satisfactory explanation of the phenomenon is deduced from the anatomical structure of the optic nerves, and their relations to each other, and to the brain. The eyes may be compared to two branches issuing from a single root, of which every minute portion bifurcates, so as to send a twig to each eye. (Muller.) The optic nerve from the right lobe of the brain sends a portion of its fibres to each eye, and also sends some branches across and backward to the left lobe of the brain. A portion of the optic nerve from the right eye, instead of proceeding to the brain, curves around and enters the optic nerve and the retina of the left eye. In the same manner the optic nerve arising from the left lobe of the brain is connected with the right eye, and sends branches also to the left eye. Branches of the same nerve fibres which go to the external side of the retina of one eye, go to the internal side of the retina in the other eye. It is thus that a perfect sympathy and correspondence is established between similar parts of both eyes. Hence whatever object is observed, if the optic axes of both eyes are directed towards it, the image is formed on corresponding portions of the retina in both eyes, and the mind re- ceives the impression of a single object ; but the impression is more vivid than if the same object were' seen with only one eye. So per- fect is this sympathy between the two eyes, that if one eye only is exposed to a strong light, the pupils of both eyes contract. If one eye is diseased and protected from the light, it suffers pain from light entering only the sound eye. 793. Double vision. If both eyes are fixed steadily upon one object, any other object which may be seen at the same time will appear double. 792. "Why do not objects seen with two eyes appear double ? 488 OPTICS. Fix both eyes steadily upon the flame of a lamp or candle, and a finger held between the eyes and the light will appear double. Drunken persons, or persons about falling asleep, often see objects double, owing to the inability to direct both eyes steadily upon the same object. The same phenomena may occur when, from any cause, the nerves which control the eye become diseased. 794. Near-sightedness. Many persons are unable to see mi- nute objects distinctly unless they are placed within three or four inches of the eye. Such persons are often unable to see ordinary objects distinctly in a large room or across the street; they are therefore said to be near-sighted. (788.) This defect is owing to a too great convergent power, the eye bringing parallel or slightly divergent rays to a focus before they reach the retina. To secure distinct vision in such cases, it is necessary to bring the object so near the eye as to render the rays entering the eye, consid- erably divergent, when the image will be formed on the retina. The same object may be accomplished by placing a concave lens before the eye, when the rays from distant objects will be rendered diver- gent, and the strong convergent power of the eye will form the im- age on the retina. Concave lenses for near-sighted persons should be such as have a focus a little longer than the distance at which they see objects most distinctly. 795. Long-sightedness commonly occurs in old people, when the eye becomes flattened by diminution of its fluids, or some structural change in the crystalline lens occurs, by which its con- vergent power is diminished. In such cases the image is formed behind the retina, and vision is most distinct when the object, as a book when reading, is held at a considerable distance from the eyes, so as to allow the image to be formed on the retina. This defect of the eyes, when not accompanied by disease, may be entirely remedied by using convex glasses, which make up for the diminished converging power of the eyes, and bring the rays to such a condition, that the eye is enabled to bring the light from near ob- jects to a distinct focus upon the retina. In such cases, however, the power of accommodating the eye to different distances is often not as great as in younger persons ; hence many people in advanced life find it necessary to use one set of glasses for near, and another for distant objects. 796. Duration of the impression upon the retina. Every one 793. How can we see objects double? Why do drunken persons often see objects double ? 794. What kind of glasses are most useful to near-sighted persons 1 APPRECIATION OF COLORS. 489 knows that a lighted stick whirled rapidly around a circle ap- pears like a ring of fire. The rapidity of revolution required to produce this impression is one-third of a second in a dark room, and one-sixth of a second by daylight. When a meteor darts across the heavens, it appears to leave a lu- minous track behind it, because the impression produced upon the retina remains after the meteor has passed a considerable distance on its way. The zigzag course of the lightning appears, for the same reason, as a continuous track. Winking does not interfere with distinct vision, because the continuance of the impression of external objects on the retina, preserves the sense of continuous vision. 797. Optical toys. Thaumatrope. A great number of optical toys and pyrotechnic exhibitions owe their effect to the continu- ance of the impression upon the retina, when the object has changed its place. If a horse is painted on one side of a card and a rider on the other side, the rapid revolution of the card causes the rider to appear seated on the horse. In the same manner, if any object which takes a va- riety of positions in moving is painted in successive positions, at equal distances on a revolving wheel, so arranged that one only of the figures shall be seen at a time, the object is seen performing all the motions of real life. In this manner a horse may be made to ap- pear leaping a gate, or boys playing at leap-frog. These toys are called thaumatropes. Other toys called phenakistoscopes and phanlascopes, are variations of the same thing, combined with mirrors and other ingenious arrangements on the same principle. 798. Time required to produce visual impressions. If an ob- ject moves with sufficient velocity, it is entirely invisible, its im- age upon the retina not remaining long enough to produce any impression. This is the case with a cannon ball or rifle ball, viewed at right angles to the direction of its flight. But if the projectile is going from us, or coming towards us, it preserves the same direction long enough to allow of an impression. Motions describing less than one minute of arc in a second of time are not appreciable to us. Hence we do not see the move- ments of the hour hand of a clock, or of the heavenly bodies}. 799. Appreciation of colors. Color blindness. The power of the eye to distinguish colors, varies greatly in different per- 795. Explain the cause of long-sightedness 1 What glasses do such persons require ? 796. How can it be shown that the im- pression of light is not instantly perceived by the eye? 797. What is the thaumatrope 1 798. What is the time of a visual impression? 490 OPTICS. sons. Some eyes fail entirely in this particular, while in every other respect they are perfect. Such eyes are said to be color blind. Some confound certain colors, as red and green, while they distinguish others, or while they recognize all the colors of the spectrum, they cannot appreciate delicate shades of the same color. Colors are greatly modified by proper contrast with other colors. Thus the complementary colors mutually enhance, while those not complementary, diminish each other's beauty when contrasted. The sensibility of the eye is much diminished by long inspec- tion of any color, and its power of perceiving the complemen- tary color is proportionally increased. This principle is the key to harmony of colors in nature and art, and serves to explain the modification of color by contrast, and proximity of two or more colors. 800. Chevreul's classification of colors, and chromatic dia- gram. The chromatic diagram, of Chevreul, fig. 441, greatly VIOLET YELLOWISH GREHf ENISH BLUE facilitates the study of complementary colors, and the modifica- tions produced by their mutual proximity. 799. What is color blindness ? How are colors modified by mutual proximity ? How is sensibility of the eye affected by protracted ob- servation of a single color? 800. Describe the chromatic diagram. THE STUDY OF COLORS. 491 Three radii of a circle represent Brewster's three cardinal colors, red, yellow and blue; between these are placed orange, green and violet. Between these six colors are placed reddish orange, orange yellow, yellowish green, greenish blue, violet blue, and violet red. "We thus obtain twelve principal colors, each of which may be again divided into five scales or hues, which gradually approach the suc- ceeding color. We thus have the circumference of the circle, which represents the prismatic spectrum, divided into sixty scales of pure colors. Each radius representing a scale of colors is divided into twenty tones, to represent the intensity of each color in its own scale. The tone of any color may be lowered by the addition of white, when it will remain in the same radius or scale, but take a position at a lower tone, or nearer the centre of the circle. A color modified by black, is called a broken color, but as the color is deeper, the tone is carried towards the circumference of the circle. To represent the modifi- cations produced by black, Chevreul employs a movable quadrant, not easily introduced in our illustration. When two complementary colors are mixed, their combination pro- duces white, if the colors are pure. The combination of two colors not complementary produces a certain quantity of white, but prin- cipally a color which will be found in the diagram intermediate be- tween the two colors, if they are of the same tone, or nearer to the color of deeper tone, when their tones or intensities are different. The complementary color in the diagram is found at the opposite ex- tremity of the diameter of the circle. This diagram thus explains the effect which two colors produce upon each other by their mutual proximity. When two colors are placed near each other, each color appears modified as though mixed with a small portion of the complement to the color which is near it. Examples. (a) Suppose blue and yellow to be placed side by side ; at one extremity of a diameter we read yellow, and at the opposite violet, hence the proximity of yellow gives to the blue a shade of violet, or makes it approach violet blue. In the same manner we find orange complementary to blue ; hence the blue gives a shade of orange to the yellow, or makes it approach orange yellow. (6) Let green and yellow be contiguous, the yellow will receive red, the complement of green, and will become orange yellow, How many scales of color in Chevreul's classification ? What is meant by tones of color ? What are broken colors ? How is the tone of any color modified by white? Show by the diagram what color will be produced by mixing any two colors of the same tone. Explain how blue and yellow will be modified when seen together. 4:92 OPTICS. while the green will receive from the yellow its complementary violet. A part of the yellow in the green will thus be neutralized, and the green will appear bluer or less yellow, in fact, greenish blue. 801. The study of colors upon the principles here laid down is of great importance to the artist and manufacturer, whether in reproducing the beauties of nature, or in architectural deco- ration ; also in weaving, embroidery and costume. The skillful .salesman knows how to enhance the brilliancy or beauty of his goods by artfully contrasting the pieces which he hopes to sell by others having complementary colors. Good taste in dress never violates these principles, regarding with care the complexion of the wearer in contrast to the colors selected. Florid skins can bear dark hues in dress, while delicate complexions are made pallid by heavy colors. A green dress or wreath increases the freshness of a rosy complexion. A crimson dress and scarlet shawl worn together appear mutually dull and heavy, while either, with the contrast of an appropriate shade of green, would be attractive and tasteful. These topics will be found fully considered in ' Chevreul on colors.' OPTICAL INSTRUMENTS. 802. Magnifying glasses. Single lenses, used for magnifying small objects, occupy an important place in the arts. They are used by watch-makers, jewelers, engravers, and other arti- sans, whose labors are performed upon minute structures. These instruments occupy a middle place between spectacles and the regular microscope, composed of a variety of parts. A thorough knowledge of the uses and powers of simple lenses forms the basis of all calculations of the powers and uses of more complex instruments, like the compound microscope and the telescope. The eye takes no cognizance of real magnitude, which it can only estimate by inference, but notices directly only apparent magnitude, which is determined in all cases by the visual angle under which ob- jects are seen. (791.) We have seen (789) that it is essential to distinct vision that the rays entering the pupil from any one point of an object should be parallel, or slightly divergent, the distance of most distinct vision being generally from five to teu inches; for near-sighted persons, as 801. To what practical purposes may the study of colors be ap- plied 1 What is the effect of a green dress or wreath on a rosy com- plexion? 802. For what purposes are magnifying glasses used? How is apparent magnitude determined ? MAGNIFYING POWER OF LENSES. 498 small, sometimes, as two or three inches, and for eyes enfeebled by age, extending from fifteen even to thirty inches. 803. The magnifying power of a lens is found by dividing the limit of distinct vision, (ten inches,) by the principal focus of the lens. Let A B, fig. 442, be an object placed before a convex lens, so much nearer to the lens than the focus, F, that the rays, after refraction by the lens, shall be in that state of slight divergence best adapted to produce distinct vision, that is, diverging as though emanating from a point at a distance of ten inches, or the limit of distinct vision ; let a 5 represent the virtual image, formed where the refracted rays would meet if extended back- ward, then a b will be as much greater 442 ' than A B, as its distance from the lens is greater than the distance of the ob- ject, A B, from the lens. The diver- gence of rays of light entering the small opening of the pupil, from a point ten inches distant, is so small that we may consider them parallel, and then the object, AB, will be nearly at jFJ the principal focus of the lens. It is commonly supposed, that inasmuch as the distance of most dis- tinct vision differs for different eyes, that therefore the magnifying power of a lens varies for different eyes. If the magnifying power of a lens were alwaj-s equal to the distance of distinct vision, divided by the principal focus of a lens, it would be variable for different eyes, being two or three times as much for some eyes as for others. But this is not the case. If the eye is placed close to the lens, the distance between the lens and the object will be much less for near- sighted persons than for others, because their eyes are fitted to receive rays of light much more divergent than can be brought to a focus in ordinary eyes. So also persons who see most distinctly at a dis- tance greater than ten inches, require a lens to be placed proportion- ally more distant from the object. Hence the rule given above, taking ten inches as the distance of most distinct vision, and dividing by the principal, or solar focus of the lens, gives a result for the mag- nifying power, which is very nearly accurate for every variety of eyes. The superficial magnifying power is equal to the square of the 803. How is the magnifying power of a single lens determined ? Show how the magnifying power of a lens remains nearly the same for all eyes. How is the superficial magnifing power determined ? 494 OPTICS. linear magnifying power given by the rule stated above ; but the linear magnifying power is alone commonly used in scientific treatises. 804. The simple microscope acts in the same manner as the single lens or magnifying glass. Instead of a single lens, a doub- let or triplet, acting as a single lens, is often used. Easpail's dissecting microscope, shown in fig. 443, is the most complete simple miscroscope. The magnifying lens, o, mounted in a dark cup, 443 A, to protect the eye from extraneous light, is fixed in the end of a movable arm which can be rotated on its support, ele- vated and depressed by the milled head, JE, or lengthened by turning the milled head, (7. Below the lens is the stage B, which supports the object to be examined. The concave mirror, M, can be so adjusted as to illuminate the object by a concen- trated pencil of transmitted light. In using this microscope, the eye is placed over the lens o, which may be elevated or depressed till the focus is adjusted to give the most distinct view of the object on the stage. Opaque objects are illuminated by a bull's eye lens. By using lenses of different foci, magnifying powers may be ob- tained with this instrument, varying from two to one hundred and tAventy diameters. 805. The compound microscope consists, essentially, of two lenses, so arranged that when an object is placed a little be- yond the principal focus of the first lens, its image may be formed in the principal focus of the second lens, by which it is viewed as an object is viewed by a common magnifier. The arrangement of the lenses m the compound microscope is shown in fig. 444, and also the position of the object, and the images both real and virtual. The object, * r, being placed near the first lens, a b, called the ob- ject-glass, an image, inverted and much enlarged, is formed at 72 S, in the focus of the second lens, d c, called the eye-glass. By this lens, the rays are transmitted slightly divergent, and in the exact condition to produce distinct vision when viewed by the eye. The 804. Describe Raspail's dissecting microscope. 805. What are the essential parts of a compound microscope 1 Describe the action of the compound microscope. THE GALILEAN TELESCOPE. 495 rays transmitted through the eye-glass, if traced backward to the distance of distinct vision, form a virtual 444 image at E' S', much larger than the real image H S, formed by the action of the first lens. Such a compound microscope as the one shown in this figure, is subject to chromatic and spherical aberration, and the image viewed by the eye is not straight as shown in the figure, but curved so as to appear convex towards the eye. These imperfec- t ions are almost entirely corrected in the achromatic compound microscope described in 819. 806. The telescope is an instrument constructed for viewing distant objects. Telescopes are of two kinds. Refracting telescopes are con- structed of lenses. Reflecting telescopes contain one or more metallic reflectors. 807. The telescope used by Galileo in 1 609, is the oldest form of which we have any definite description. The Galilean telescope consists of a convex lens, of long focus, and a concave lens of short focus placed at a distance apart, equal to the difference of their principal foci. The light from distant objects collected by the large surface of the convex field lens, is brought to such a state of divergence by the concave eye-lens as to produce distinct vision in the eye. The magnifying power of the Galilean telescope is found by dividing the principal focus of the convex lens by the prin- cipal focus of the concave lens. The convex lens, M N, fig. 445, tends to form an image of a distant object, A By very near its principal focus, as at a b. The concave 445 lens, E F, being placed between the convex lens and the image, a b, 806. What is a telescope? How do refracting telescopes differ from reflecting telescopes? 807. How is the Galilean telescope con- structed ? Explain the action of this telescope by reference to fig. 445. 496 OPTICS. renders the rays which were converging to a, slightly divergent, as though emanating from a point, a', at the distance of the distinct vision, about ten inches. The same effect is produced on the rays converging to 6. The direction of the oblique pencils is changed, and the extremities of the image appear in the secondary axes a O' 6', and b O' b', drawn from a and b through 0', the optical centre of the lens E F. It is especially to be noticed, that while the rays from any one point in the object are rendered parallel, or slightly divergent by the concave lens, the pencils from the extreme points converge at O' much more than at 0, making the visual angle a' 0' b', under which the object is seen by the telescope, much greater than the visual angle a b, under which the object would appear without the tele- scope. Since the angle A B is equal to a O b, and a' O' b' is equal to a O' b, the visual angle a' O' b' is to the angle A O B as F is to 0' F, and the image a' b' appears as much greater than the object as the focus O F of the convex lens exceeds the focus 0' F, of the con- cave lens. The opera-glass consists generally of two Galilean telescopes, placed near together, to allow of distinct vision by both eyes. Niglit-glasses, used by seamen, are constructed like large op- era-glasses. They serve to concentrate a large amount of light in such a condition as to allow of distinct vision, and thus enable the eye to see objects distinctly in the night. They have a low magnifying power. With the Galilean telescope in all its forms the object appears erect. 808. The astronomical telescope may be constructed with a convex lens placed beyond the image formed by the field lens. The second lens then magnifies the image formed by the first lens. The object appears inverted, but this occasions very little inconvenience in astronomical observations. 809. Eye-pieces for both microscopes and telescopes consist of two or more lenses, so arranged as to magnify the image formed by the object-glass, with somewhat less spherical and chromatic aberration than if a single lens only were used. (a) The positive eye-piece, invented by Ramsden, consists of two piano convex lenses, with their convex surfaces turned towards each other, and placed at such a distance that the object or image What is the structure of the common opera-glass? What are night glasses? 808. Describe the astronomical telescope. 809. What are eye-pieces? Describe the positive eye-piece. Why does it produce less chromatic aberration than a single lens ? EYE-PIECES. 497 to be viewed by it is seen distinctly when brought very nearly in contact with the first lens. The spherical aberration produced by this eye-piece is only about one-fourth as much as if a single lens were used. The chromatic aberration also is less than with a single lens. Let F F, fig. 446, be the field lens, and E E the eye lens of the positive eye-piece. Let m n 446 be an image formed by the object glass either of a telescope or a microscope, then each ray from the image on passing the lens F F becomes colored, c 0, 5 v, representing the violet rays, and c r, & r, representing the red rays. The red rays, which are least refracted by the first lens, fall near the borders of the second lens, where the refractive power is greater than where the more refrangible violet rays fall ; hence the second lens tends to correct the chromatic dispersion of the first, and the violet and red rays enter the eye very nearly as though emanating from a common point. This is an import- ant excellence of the positive eye-piece ; but a yet more important advantage of this eye-piece is, that the image is less distorted than when only a single lens is used. (&) The negative eye-piece, which was invented by Huyghens, consists generally of two piano convex lenses, having the convex surfaces of both turned towards the object glass. The two lenses are placed at a distance from each other equal to one-half the sum of their foci. The image is formed between the lenses. This arrangement considerably enlarges the fields of view, and besides diminishing the spherical aberration, the chromatic aberration is less, and is more equalized in all parts of the field than in other eye-pieces. The action of the negative eye-piece will be more fully explained in connection with the compound achromatic microscope. (819.) In the most perfect form of the negative eye -piece, according to Prof. Airy, the first, or field lens, is a meniscus whose radii are as four to eleven, with the convex side toward the object, and an eye-lens hav- ing the form of least spherical aberration (767) with the more convex side towards the object. Describe the negative eye-piece. What is said to be the best form of the negative eye-piece I How many lenses in the terrestrial eye- piece? What is the structure of the common spy-glass? 498 OPTICS. (c) The terrestrial eye-piece consists of four lenses, two of them being added solely to produce an erect* image. Fig. 447 shows a section of the common spy-glass or terrestrial tel- escope, with the erecting eye-piece. The several tubes which shut 447 one within another, allow the instrument to be reduced to a con- venient length when not in use. 810. Reflecting telescopes are extensively used for astronom- ical observations. A variety of forms have been invented by different observers, but in all a metallic speculum is employed to form an image of distant objects, and an eye-piece is used to mag- nify the image. 811. Sir William Herschel's telescope, shown in fig. 448, con- sists of a speculum, S S, set in a tube somewhat larger than the diameter of the speculum, and an eye-piece, ef, placed at one side of the open end of the tube. The axis of the speculum, 448 represented by the dotted line a N, is so inclined that parallel rays, falling on every part of the speculum, will be reflected, conver- ging to the side of the tube where the eye-piece is placed to re- ceive them. The size of the tube, and the inclination of the axis of the speculum, is so adjusted that the eye of the observer may be placed at E without intercepting any part of the light which can fall upon the speculum in such a direction as to be re- flected to the eye-piece. Sir William Herschel's great telescope had a speculum four feet in diameter, three and a half inches thick, weighing two thousand one 811. Describe the structure and action of Herschel's telescope. "What were the dimensions of Sir William Herschel's great telescope ? ACHROMATIC TELESCOPES. 499 hundred and eighteen pounds. Its focal length was forty feet, and it was set in a sheet-iron tube thirty-nine and a half feet') long, and four feet ten inches in diameter. When directed to the fixed stars it would bear a magnifying power of six thousand four hundred and fifty diameters. This is called the front view telescope, because the observer sits with his back to the object and looks into the front end of the tele- scope. 812. Lord Rosse's telescope. Ry far the largest reflecting telescope ever constructed was made by the Earl of Rosse. It was commenced in 1842, and was so far completed as to be used for the first time in Feb. 1845. The great speculum is six feet in diameter, has a focal length of fifty-four feet, and weighs four tons. An additional speculum to be used in the same instrument weighs three and a half tons. The tube is of wood, hooped with iron, and is seven feet in diam- eter, and fifty -two feet in length. This telescope has fittings to mount the eye-pieces either for front view, as in Herschel's telescope, or at the side of the telescope, as in the Newtonian form, a small speculum placed at an angle of 45, reflect- ing the rays at a right angle through an orifice in the side of the tube, where the eye-piece is placed. The base of the instrument is supported upon a universal joint ; and by chains and windlasses this mammoth telescope is moved with ease, between two lofty walls supporting movable galleries, which enable the observer to follow the instrument in any required position. The amount of light on any surface being as the square of the di- ameter, if we reckon the pupil of the human eye at one-tenth of an inch in diameter, this telescope will be seven hundred and twenty times as broad as the pupil, or have an area five hundred and eight- een thousand and four hundred times as great as the unaided eye. If one-half the light is lost by reflection from the mirror, we shall still have two hundred and fifty thousand times as much light as commonly enters the eye. We need not wonder therefore at the marvellous power with which this instrument penetrates the re- moter regions of celestial space. 813. Achromatic telescopes The principle of achromatism has been briefly explained in section 778, where it' has been shown that a convex lens of crown glass may be combined with a concave lens of longer focus, made of flint glass, which 812. What are the dimensions of Rosse's telescope? 813. What forms of lenses are used in achromatic telescopes ? 500 OPTICS. has a higher refractive and dispersive power, the combination producing refraction without dispersion, and consequently form- ing an image free from the primary prismatic colors. The common form of achromatic compound lens is a piano con- cave lens of flint glass, united with a double convex lens of crown -glass. Such lenses are found in opera-glasses and spy-glasses, called achromatic, used both on land and at sea. This form of lens is also often employed in the smaller astronomical telescopes. But in such glasses a certain amount of spherical aberration remains uncor- rected. To secure perfect correction of spherical and chromatic aberration at the same time, a double concave lens of flint glass has been placed between two double convex lenses of crown glass, the curved sur- faces of the several lenses being carefully estimated in view of the refractive and dispersive powers of the two kinds of glass employed. The refractive and dispersive powers of glass are so variable, that the optician is obliged to determine them anew for every new speci- men of glass, and estimate again, by the formulae already given, the proportional curvatures of the lenses to be constructed from it. Sir John Herschel found that an achromatic object-glass of the form shown in fig. 449, will be nearly free from spherical aber- 449 ration, if the exterior surface of the crown lens is 6 '72, and the exterior surface of the flint lens 14-20, the focal length of the combination being 10-00, and the interior surfaces of the two lenses being computed from these data to destroy the chromatic aberration by making the focal lengths of the two glasses in the direct ratio of their dispersive powers. The two interior surfaces that come in contact may be cemented together if the lenses are small. Until quite recently, almost insuperable obstacles interfered with the manufacture of flint glass in large pieces of uniform density, free from veins and imperfections. In 1828, an achromatic lens fourteen inches in diameter was consid- ered a true marvel of optical art. The object glass in the great achro- matic refracting telescope at Cambridge, Mass., (one of the largest in use,) is about sixteen inches in diameter, with a clear aperture of fif- teen inches, and it cost, unmounted, about $15,000. M. Boutemps, a French artist, employed in the glass works of Messrs. Chance, Broth- ers & Co., Birmingham, Eng., has succeeded in producing a disk of What is the best form of achromatic lens? 814. How are equa- torial mountings for telescopes constructed 1 THE CAMBRIDGE TELESCOPE. 501 flint glass twenty-nine inches in diameter, two and a half inches thick, weighing two hundred pounds, and pronounced by the most skillful opticians very nearly faultless. 814. Equatorial mountings for telescopes. "With telescopes of great power, the diurnal motion of the earth causes a celestial object to pass out of the field of view too rapidly to allow of sat- isfactory observation. To obviate this difficulty, a system of machinery called an equatorial mounting, has been devised, to give to the telescope such a uniform motion as to keep any celes- tial object constantly in the field of view. An axis firmly sup- ported is placed parallel to the axis of the earth, and is caused to revolve by clock-work with a motion exactly equal to the siderial motion of the heavens. A second axis, across which the tele- scope is mounted, is mounted upon the first axis, and at right angles with it. The telescope can be elevated or depressed in declination by motion of the second axis, and it can be moved in right ascension by motion on the first axis. When the telescope has been thus directed to any celestial object, it may be clamped on both axes, and thejmovement of the clock-work will cause it to follow the motion of the object in the heavens. 815. The Cambridge telescope with equatorial mountings is shown in fig. 450, copied from a figure by Prof. Loomis. It stands on a granite pier surmounted by a single block of granite ten feet in height, to which the metallic bed-plate of the telescope is secured by bolts and screws. It is covered by a dome moving on a circular railway, which is easily rotated so as to allow the great telescope, twenty-three feet in length, to be directed to any part of the heavens. A narrow window, closed by shutters moved by chains, is opened when the telescope is in use. The hour circle attached to the equatorial axis is eighteen inches in diameter, divided on silver, and reads by two verniers to one second of time. The declination circle is twenty-six inches in diameter, divided on silver, and reads by four verniers to four seconds of arc. The movable portion of the telescope and machinery is estimated to weigh about three tons, but it is so perfectly counterpoised and adjusted that the observer can direct the instrument to. any part of the heavens by a very slight pressure of the hand upon the balance rods. This great achromatic telescope has eighteen different eye- 815. Describe the Cambridge telescope and its mounting. What is its range of magnifying power ? 502 OPTICS. pieces, giving to the instrument magnifying powers varj T ing from 103 to 2000 diameters. 450 816. Achromatic object glasses for microscopes, if constructed of the forms used in telescopes, are very unsatisfactory.. In the first place it is found exceedingly difficult to construct such lenses sufficiently small for the high magnifying powers required in the microscope. Secondly, the largest achromatic lenses for telescopes have but a small diameter in proportion to the length of their foci, and if lenses for the microscope have a diameter equally small in proportion to their foci, they admit too little light to be of much practical utility. But if their diameter is in- creased, the light admitted through the borders of the lenses 816. What difficulties are encountered in applying achromatic lenses to the microscope ? LISTER'S APLANATIC FOCI AND COMPOUND OBJECTIVES. 503 produces fringes, with colors in the inverse order of the solar spectrum, showing that while the color is perfectly corrected in the centre, the correction effected by the concave lens is too great at the margin. 817. Lister's aplanatic foci, and compound objectives. The discoveries of Joseph Jackson Lister, Esq., read before the Royal Society in 1830, have proved of the utmost value in perfecting the compound achromatic microscope. His preliminary principles are 1st, that piano convex achromatic lenses, shown in fig. 437, are most easily constructed. 2d, that if the convex and concave lenses have their inner surfaces of the same curvature, and are cemented together, much less light is lost by reflection than if the lenses are not cemented. Mr. Lister discovered that every such piano convex achrpmatic combination as A A, fig. 451, has some point, as f, not far from its principal focus, from which radiant light falling upon the lens will be trans- mittedfree also from spherical ab- erration. This point is therefore called an aplanatic focus. The incident ray, / d, makes with the perpendicular, i d, an angle considerably less than the emergent ray, eg, makes with e h, the perpendicular at the point of emer- gence. The angle of emergence is nearly three times as great as the angle of incidence, and the rays emerge from the lens nearly parallel, or converging towards a focus at a moderate distance from the lens. If the radiant point is now made to approach, the lens, so that the ray/ d e g becomes more divergent from the axis, as the angles of incidence and emergence become more nearly equal to each other, the spherical aberration becomes negative or over-corrected. But if the radiant point, /, continues to approach the glass, the angle of incidence increases, and the angle of emergence diminishes, and be- comes less than the angle of incidence, and the negative spherical aberration produced by the outer curves of the compound lens, be- comes again equal to the opposing positive aberrations produced by the inner curves which are cemented together. When the radiant has reached this point, /', (at which the angle of incidence does not exceed that of emergence so much as it had at first come short of it,) the rays again pass the glass, free from spherical aberration. The point/' is called the shorter aplanatic focus. 817. Whose discoveries have principally conduced to obviate these difficulties ? State Mr. Lister's two preliminary principles. Explain the phenomena of aplanatic foci of achromatic lenses. 504 OPTICS. For all points between the two aplanatic foci /and/' the spherical aberration is over-corrected, or negative ; and for all radiant points more distant than the longer aplanatic focus /, or less distant than the shorter aplanatic focus f, the spherical aberration is under- corrected, or positive. These aplanatic foci have another singu- lar property. If a radiant point in an oblique or secondary axis is situated at the distance of the longer aplanatic focus, the image situated in the corresponding conjugate focus will not be sharply defined, but will have a coma extending outwards, distorting the image. If the shorter aplanatic focus is used, the image of a point in the secondary axis will have a coma extending towards the centre of the field. These peculiarities of the coma produced by oblique pencils are found to be inseparable attendants on the two aplanatic foci. These principles furnish the means of entirely correcting both chromatic and spherical aberration, and of destroying the coma of oblique pencils, and also of transmitting a large angular pencil of light free from every species of error. Two piano convex achromatic lenses, A M, fig. 452, are so ar- ranged that the light radiating from the shorter aplanatic focus of the anterior combination, is received by the second lens in the direction of f*\ its longer aplanatic focus. If the two compound lenses are fixed in this position, the ra 452 diant point may be moved backwards or forwards -within moderate limits, .and the opposite errors the two compound len - ses will balance each other. Achromatic lenses of other forms have similar properties. It is found in practice that larger pencils free from errors can be 453 transmitted by employing three compound lenses, the middle and posterior combinations being so united as to act as a single lens, together balancing the aberrations of the more powerful anterior com- binations. Fig. 453 shows a common form of the triple aplanatic and achromatic objective, used for the compound microscope. What is the character of the aberration for radiant points between the aplanatic foci 1 What phenomena are observed with oblique pencils? How are two achromatic lenses combined to produce the best effect? What advantage is obtained by combining three com- pound lenses ? THE COMPOUND ACHROMATIC MICROSCOPE. 505 818. Aberration of glass cover corrected. If an object viewed with an achromatic microscope, which has all its aberra- tions corrected for an uncovered object, is covered with even a thin film of glass or mica, spherical aberration is again produced, thus sensibly impairing the distinctness of vision when a high power is used. Let abed, fig. 454, be a film of glass or mica bounded by parallel surfaces. If rays of light, diverging from O, pass through this film, the ray, O T' R E will suffer greater displacement than the ray O T R E, which makes a smaller angle with the perpendicular P. If R E and R E' are extended backward, they will cross the axis or perpendicular at the points JTand F. This separation of the points X and F is exactly similar to the spherical aberration of a concave lens, and is therefore called negative spherical aberration. Chro- matic aberration is also produced by the same means. The effect observed by the eye in such cases is, that lines are not so sharply defined, and the outline of an object appears bordered with broader fringes, with colors of the secondary spectrum upon the borders of the object. These errors are easily corrected by diminishing the dis- tance between the anterior and posterior com- binations of the compound objective, which is furnished with an adjusting screw for this purpose. 819. The compound achromatic microscope is composed of the triple achromatic objective, A M P, fig. 455, and the negative 455. T' P.V 454 M p eye-piece, formed of the field lens FF, and the eye lens E E. 818. "What effect is produced by covering an object with thin glass 1 Explain how a plate of glass produces spherical aberration of diverging rays? Why is this called negative aberration 1 How is this aberration corrected in the compound achromatic objective? 819. What are the essential parts of a compound achromatic mi- croscope ? 506 OPTICS. The section shown in the figure, shows how the light is acted upon in passing through the different parts of the instrument. Pencils of rays from all parts of the objects t, pass through the compound ob- jective AMP, and tend to form a red image at R R, and a violet image at V V, the object-glass being slightly over-corrected, so as to project the violet rays as far beyond the red as may be necessary to make up for the want of absolute achromatism in the eye-piece. The converging pencils S C T, being intercepted by the field lens F, are foreshortened, and at the same time the lateral pencils are bent inward, so that the images v v, r r, are smaller, nearer together than V V, R R, and curved in an opposite direction. The reversion of the curvature of the images is produced by the form of the field lens, which meets the central pencil, C, much farther from the images V V, R R, than where it meets the lateral pencils S T; thus the focus of the central pencil is more shortened than the others. The field lens of the negative eye-piece does not reverse the curvature, in every variety of instrument, but it always changes the form of the images so as to improve the definition. The violet rays 8n, T n, fall upon the eye-lens nearer its axis, than the red rays S m, T m, which are less refrangible, and hence the eye lens counteracts the divergence of the colored rays which were separated by the field lens, and causes them to pass to the eye so nearly parallel, that they appear to di- verge from the same point of the virtual image S T, formed at the distance of distinct vision. The distance between the red and violet images r r, v v, is just equal to the difference between the red and violet foci of the lens, and these images being curved just enough to bring every part into exact focus for the eye lens, the eye sees the image at S' T, spread out in its true form on a flat field. By means of this beautiful system of compensations, for the various errors of chromatic and spherical aberration and curvature of the im- age, which interfere with the performance of a single lens, the com- pound achromatic microscope has been brought to a degree of per- fection unsurpassed by any instrument employed in practical physics. 820. Angular aperture. The amount of light by which any point of an object appears illuminated, depends on the angular breadth of the pencil of light by which it is viewed. The an- gular breadth of the pencil of light which a lens transmits, is called its angular aperture. The minute details of an object viewed by a microscope, are seen with greater distinctness, in proportion to the angular aperture of the object glass employed. For what purpose is the object glass over- corrected ? Explain the action of the negative eye- piece in connection with the achromatic objective. 820. "What is meant by angular aperture ? MECHANICAL ARRANGEMENT OP THE MICROSCOPE. 507 In fig. 456, A, B, C, D, show the successive appearances of a trans- verse section of wood, by regular enlargements of the angular aperture 456 ABC D of the microscope with which it was viewed. The available angular aperture of a single lens seldom exceeds fifteen or twenty degrees. In the triple achromatic objective, the aperture for ordinary observa- tions has been extended to 100. With the highest powers used for viewing infusoria, both English and American opticians have ad- vanced the angular aperture to 150, and in some glasses to 175. 821. The mechanical arrangement of the microscope is well exhibited in fig. 457, 457 which has been engra. ved from a very excel- lent instrument, manu- factured by J. & W. Grunow, New Haven, Conn. The instrument is mounted on trunnions, which allow it to be in- clined at any angle. The body of the microscope is moved in a grooved support, by a rack and pinion motion for adjust- ing the focus. The stage has a fine, delicate move- ment, by a screw and milled head, acting upon a lever at the back ofi the instrument, by which movement the focus can be adjusted with the ut- most delicacy. The stage itself can be moved freely in any di- How is the definition of an object affected by the angular aperture of an object glass? How large angular aperture has-been obtained in the best microscopes? 821. Describe the mechanical structure of the compound microscope. 508 OPTICS, rection by a lever at the right. A mirror, concave on one side and plane on the other, is so mounted below the stage as to give a con- densed pencil of light for illuminating the object. Polarizing apparatus, and other accessories, are fitted to the stage, and to the body of the microscope. 822. The magic lantern is an instrument for projecting upon a screen, images of transparent pictures painted on glass. A lamp is placed in a dark box, before a parabolic reflector, M IV, fig. 458, which throws the light upon a convex lens, A, by which it is strongly condensed upon the object painted on the glass slide, inserted at G D. The magnifying lens, JB, forms an image of the illuminated picture upon a screen, placed at its conjugate focus. The picture is placed in an inverted position, to produce an erect image upon the screen. 458 A great variety of objects painted on glass can thus be exhibited either for amusement or instruction. The magnifying power of the magic lantern is equal to the distance of the screen from the lens, jB, divided by the distance of the lens from the object. 823. The solar microscope is a species of magic lantern illu- minated by the sun. It is however much more perfect in its structure, and it is commonly employed for viewing on a screen images of natural objects, very highly magnified. The structure and arrangement of the solar microscope are shown in fig. 459. It is mounted over an opening in the shutter of a dark room, on the side towards the sun. A plane mirror, M, is so arranged outside the shutter as to reflect the rays of sunlight, S, through the condensing lens, A, into the microscope. By turning the screw, B, the mirror may be elevated or depressed, and by means of another 822. What is the magic lantern ? Describe ite construction and the method of using it. How is the magnifying power of the magic lantern determined ? 823. What is the solar microscope ? THE CAMERA OBSCURA. 509 screw, T, it can be rotated on the axis of the microscope, so as to follow the motions of the sun. A small lens, E, moved by the rack 459 M and pinion with the milled head C, serves to condense the light upon the object slide, O, The slide O, which carries the object, is secured between the brass plates K K, by the screws H H. The object, strongly illuminated, is adjusted to the focus of the small lens, L, (which may be either a small globule of glass, or a compound achromatic objective, of short focus,) and an image, a 6, greatly enlarged, formed in the conjugate focus of the lens, is re- ceived upon a white screen placed in a convenient position. By di- minishing the distance between the object and the lens, L, the con- jugate focus will be increased, the screen may be placed at a greater distance from the lens, and the magnifying power will be propor- tionally increased. Instead of employing the light of the sun, the solar microscope may be illuminated by the electric, or by the oxhydrogen light. 824. The camera obscura consists of a dark chamber in which external objects are formed by the aid of a mirror, and a concave lens. This instrument affords a convenient method of sketch- ing natural scenery. A plane mirror, m, fig. 460, placed at an angle of 45 with the ho- rizon, reflects the light downward, through a converging lens, placed in the top of the dark chamber. A sheet of paper placed on the table in the focus of the lens, receives the image of a landscape or other object, which can be traced with a pencil by the artist, sitting, as shown in the figure, with his head and shoulders protected from extraneous light by a dark curtain. The student can easily prepare an instrument of this kind, by in- serting a spectacle glass in an orifice in the top of a box about two Describe its construction and the method of using it. 824. De- scribe the camera obscura, 510 OPTICS. 460 feet high, and placing a common mirror at the required angle above it. The paper on the table can be placed on a drawing board, and fixed at such a distance from the lens as gives the most distinct image. A cloak thrown over the side of the box where the ob- server sits, will darken the 'chamber so as to permit sketches to be made with great facility. Instead of the mirror and lens shown in fig. 460, a rectangular prism is often used as a reflector, and if one side of the prism is ground in the form of a lens, the two parts of the instrument are combined in one. 825. Wollaston's camera lucida is another instrument used for sketching from nature. It consists of a prism, a ~b c d, fig. 461, of which the angle, 5, is a right angle, the angle, d, is 135, and the angles at a and c are each 6Y|. It is mounted on a suitable stand, and the eye, P P', placed as 461 shown in the figure, sees the image of a distant object as though projected upon the paper M N, . where the outline may be traced by the pencil $,the eye seeing the image and the pencil at the same time. The light from a distant object entering the prism nearly at right angles with the face, b c, twice suffers total reflection, and emerges perpendic- ular to the face a b, when it enters the eye, and ap- pears as if coming from the paper, M N. The image projected upon the paper is as much smaller than the object as its distance from the prism is less than the distance of the object. The image can be made to assume any required dimensions by varying the relative dis- tances of the paper and the object. This instrument is principally employed by artists for sketching landscapes. A number of other forms of camera lucida are employed to suit dif- ferent purposes, but in all of them, either the object, or the pencil and paper, are viewed by reflected light, made to coincide in direc- tion with the direct light. 826. Photography is the art of producing pictures by the chemical action of light. The daguerreotype, ambrotype, crys- talotype, and photo-lithograph, are all produced by modified ap- For what purpose is it used ? 825. Describe Wollaston's camera lucida. How is this instrument used? RAILWAY ILLUMINATION. 5ll plications of the camera obscura. Instead of the plain paper and pencil used by the artist for sketching with the camera, a surface of silver or collodion, made sensitive by iodine, bromine, or some other chemical preparation, is placed in the camera and subjected to the action of the light of the image projected there by the lens. A camera employed for photography in any of its forms, requires to be achromatic, and also that the chemical rays shall be brought to a focus at the same point as the visual rays, or at a well clefined dis- tance from them. As objects copied by photography are seldom flat, the objective of the camera requires to be so constructed as not only to give perfect definition of all objects situated in the focal plane, but also it should be adapted to give tolerably good definition of parts of an object that are situated a little anterior or posterior to the focal plane. The usual form of the camera employed in photography, is shown in fig. 462. The achromatic compound 462 lens, A, is attached to the box C, andean be moved backwards or forwards by turning the milled bead, D. The se- cond box, B, slides within the first. A plate of ground glass set in the frame, E, is inserted in B, and when the focus is so adjusted as to give a perfect image on the ground glass, this is removed, and the sensitive plate cove red by a dark screen is inserted in its place. The dark screen is then re- moved, and the light produces a chemical change where the ima ge is projected. This image is then made permanent by vapor of mercury or other chemical applications. 827. Railway illumination. For illuminating railroads, it is important to throw upon the track a powerful beam of light, con- sisting of rays nearly parallel. When the track is thus illumi- nated, objects upon it are more readily distinguished by contrast with surrounding darkness ; it is therefore desirable to limit the light to the immediate vicinity of the track . The common method of effecting this object is to place an Argand lamp in the focus of a large parabolic reflector, (406,) situated in front of the locomotive. The light is thus thrown forward in parallel 826. What is photography ? By what instrument are the v arious kinds of photographic pictures obtained ? Describe the earner a em- ployed in photograph}'. 8:47. What, kind of illumination is req uired upon railways ? What instrumeut is employed for this purpos e 1 512 OPTICS. lines, and the lateral illumination produced by light radiated directly from the lamp is comparatively small. 828. The Presnel lens, a section of which is shown at o A g, fig. 463, is also employed for projecting a powerful beam of par- allel light upon objects to be illuminated at a distance. This form of lens, invented and first applied to practical purposes by Fresnel, consists of a central piano convex lens, surrounded by segmentary rings, with curvatures successively diminishing as much as is necessary to avoid the spherical aberration of a single 463 lens, the central lens, and all the angular segments having their curves so adjusted as to have a com- mon focus. The segmentary rings are some- _: times made entire, but generally } when the size is considerable, each ring is composed of several parts, e central lens and lateral segments are all cemented to a plate of glass, as shown in the figure. For most purposes, where the Fresnel lens is employed, it is neces- sary to give the illuminating beam of light a slight degree of diver- gence. It will be easily seen from the figure, that if the center of the lamp is placed at F, the principal focus of the lens, the diver- gence of the beam, after passing the lens, will be equal to the angle b A b, which the flame of the lamp subtends at the surface of the lens. A concave mirror is also placed behind the lamp, to throw forward the light in a condition to be refracted nearly parallel by the lens in front of the lamp. A much more brilliant beam of light is obtained in this manner than by the parabolic reflectors alone. This lens is also used in France for railway illumination. 829. Sea-lights, designed as beacons to the mariner upon dan- gerous coasts, or for lighting harbors, are usually placed in towers, called liglit houses. The great elevation of the light, permits it to be seen far out at sea. It is evident that all light thrown out above or below the plane of the horizon, is of no avail to the mariner. By an ingenious application of the principles of the Fresnel lens, a sheet of light is thrown out in every direction in the plane of the horizon. If fig. 464 is revolved about the central perpendicular line, as an axis, it will generate the apparatus known as the Fresnel 828. What is the pecular construction of the Fresnel lens ? 829. Where are sea-lights usually placed > REVOLVING LIGHTS. 518 465 fixed light. The central zone will consist of 464 a series of hoops whose perpendicular section is^ every where the same as a section of the Fresnel lens. This zone will therefore so act - upon the light of a lamp placed at the centre, as to project a sheet of light in every direc- ,, tion in the plane of the horizon. Above and below the central zone, are series of triangu- lar hoops. A section of one of these hoops, and its action upon light radiating from the central lamp, is shown in fig. 465 ; A C and' B C are plane faces, while A B is a convex"" surface. Light from the focus, F, is refracted on entering the face B C, it undergoes total reflection at the surface A B, and a second refraction at A C, from which it emerges in lines par - ^^ all el to the horizon. The focus of each prismatic hoop is carefully calculated for the place it is to occupy, so that every part of the appa- ratus throws out the light that falls upon it in a horizontal direction. 830. Revolving lights. To distin- guish one light-house on the coast from another, the Fresnel light is so modified as to give a steady light, and also revolving flashes of light of very great intensity. In the revolving Fresnel light, the triangular prismatic hoops above and below the central zone are the same as for the fixed light, but the central zone is made of eight Fresnel lenses, fig. 466, set as shown in the lower part of figure. The upper part of the same figure shows a front view of the central zone. While the entire apparatus revolves as shown by the direction of the arrows, each of the eight lenses gives a very intense light in certain directions, and between any two there is no light from the central zone of lenses. The light seen from any position appears gradually to increase to very great brilliancy, and then to fade away to much less than half its maximum intensity, Describe the Fresnel fixed light used in light-houses. Describe fig. 465. 830. Describe the Fresnel apparatus for a revolving light. 22* 466 514 OPTICS. after which it again increases to its former brilliancy. These changes are repeated at regular intervals. The lamp used for the Fresnel light is an Argand burner, with four concentric wicks, with currents of air passing up between them. The wicks are defended from the excessive heat of their united flames by a superabundant supply of oil, which is thrown up from below by a clock-work movement, and constantly overflows the wicks. A very tall chimney is required to supply a sufficiently strong current of air to support the combustion. The dimensions of the Fresnel light, and the number of lenses and hoops of which it consists, are varied to suit the purposes for which it is used ; the light produced varying in intensity from twenty-five to three thousand Argand lamps of common size. 831. The telestereoscope is an instrument which causes distant objects to appear in relief. The image upon the retina of every human eye represents a perspective projection of the objects sit- uated in the field of view. As the positions from which these projections are taken are somewhat different for the two eyes of the same individual, the perspective images themselves are not iden- tical, and we make use of their difference to obtain an idea of the distances from the eye of the different objects in the field of view. The images of the same object on the two retinae are more different from each other as the object is brought nearer to the eyes. In the case of very distant objects, the difference be- tween the pictures on the retinae of the two eyes becomes imper- ceptible, and we lose the aid just spoken of in estimating their distance and bodily figure. The telestereoscope increases the binocular parallax of distant objects, and by presenting to each eye such a view as would be obtained if the distance be- tween the two eves were greatly increas- appearance of relief, as if the objects were brought near to the observer. What kind of a lamp is used for the Fresnel light ? 831. Why are the pictures formed on the retinse of the two eyes different ? How 4o.es this difference vary in different positions 1 THE STEREOSCOPE. 515 ' Let b and V, fig. 467, be two plane mirrors placed at angles of 45 with the line of vision ; let c and c' be two smaller mirrors placed parallel to b and b', and let d and d' represent the position of the two eyes of the observer. It is evident that the light from distant objects falling upon the mirrors in the direction a b and a' &', will be reflected to the small mirrors c and c', where it will be again reflected to the eyes at d and d'. The two views seen by the eyes will evidently be the same as if the eyes were separated to the positions m and m'. The relief with which objects will be seen by this instrument, will obviously be increased as much as the distance b b', exceeds the dis- tance between the eyes d and d'. But while the perspective difference of the images seen by the two eyes has been increased, the visual angle under which each object is seen remains unchanged, and hence, as the apparent distance of the objects is diminished, their dimensions appear diminished in the same proportion. If the small mirrors are made to rotate on perpendicu- lar axes, while the large mirrors are fixed, the distortion of figure may be easily corrected by turning the small mirrors until objects ap- pear in their true proportions. If the lenses of an opera glass are inserted in the instrument, the convex field glasses being inserted at /and/', between the large and small mirrors, and the concave eye glasses between the eyes and small mirrors, the effect will be to in- crease the visual angle of every object in the field of view. If the glasses magnify as many diameters as the distance between the large mirrors exceeds the distance between the eyes, every object will ap- pear in its due proportions, and the effect will be surprising. The appearance will be as though the observer had been actually trans- ported to the immediate vicinity of the objects themselves. The dis- tance between the large mirrors of the telestereoscope should not ex- ceed the breadth of an ordinary window, unless it is to be used in the open air, when it may be made of any dimensions that are de- sired, and the effect produced will be in proportion to its magnitude. 832. The stereoscope is an instrument by which two pictures of an object give the appearance of a solid structure. If two pho- tographs of distant objects are taken from positions at such a dis- tance as to give an appropriate difference of perspective, they may be viewed in an instrument called a stereoscope, which will give them all the relief and solid appearance of real objects. If two pictures of an octahedron, as A and B, fig. 468, such as What is the design of the telestereoscope ? Explain its construc- tion. What effect is produced by inserting the lenses of an opera-glass in the telestereoscope? 832. How may pictures be made to show the objects in relief { 516 OPTICS. would be formed on the retinee of two eyes, are placed in the stereo- 468 scope, fig. 469, they give to the observer the idea of real solid octahedron, instead of the ordi- nary picture, C. Photographs of natural scenery, taken from two positions, when viewed in X this instrument, appear in relief like real objects. The construction and action of the stereoscope will be readily un- derstood by reference to figs. 470, and 471. From a double concave 469 470 471 lens, A B A' D, two eccentric lenses, represented by the smaller circles, are formed. E A e, in the lower part of the figure, repre- sents a transverse section of one of these eccentric lenses, and E A e the other. Each lens is equivalent to a triangular prism E A e, with a piano convex lens cemented to each refracting face of the prism. Fig. 471 shows a section of the stereoscope, the eccentric eye- lenses A E, A' E', being placed at the ordinary distance of the eyes, with their thin edges towards each other. Let P and P' represent two corresponding points in the stere- oscopic photographs which are to be examined. The rays of light, diverging from the point P, falling upon the eye-lens, are refracted nearly parallel, and by the pris- matic form of the lens are deflected from their course, and emerge from the lens in the same direction as if emanating from the point 0. In the same manner the rays from the point, P, also appear to diverge from the point 0. The same is true of all similar parts of the two pictures; thus the pictures appear Describe the lenses used in the stereoscope 1 How do these lenses act in the stereoscope to cause two pictures to appear as one ? Why does the stereoscope giv the appearance of relief? STEREOMONOSCOPE. 51T superimposed upon each other, and together produce the appear- ance of relief, for which the stereoscope is so much admired. The eccentric lenses of the stereoscope are sometimes fixed in po- sition, but they are often inserted in tubes, as in fig. 469, which can be extended to adapt the focus to different eyes, or separated to a greater or less distance, to suit the distance between the eyes of dif- ferent persons. If stereoscopic photographs are taken from positions too widely separated from each other, objects stand out with a boldness of relief that is quite unnatural, and the objects appear like very reduced models. In taking stereoscopic miniatures especially, great care is required to preserve a natural appearance. In general, a difference of a few inches in the two positions of the cameras, gives suffi- cient relief to the pictures when seen in the stereoscope. For public buildings and landscapes, two cameras are usually em- ployed, placed on a stand three or four feet from each other. If it is desired to show a great extent of a distant landscape, or to exhibit in miniature the grouping and form of distant monntains, two stations should be selected that are widely separated ; but in such cases, care should be taken that no near objects are admitted into the picture. 833. The stereomonoscope, (lately described by Mr. Claudet, of London,) is an instrument by which a single picture is made to present the appearance of relief commonly seen in the stereo- scope, and by means of which several individuals can observe these effects at the same time. Let A, fig. 472, be an object placed before a large convex lens, L, an image of the object will be formed at a, in the conjugate focus of 472 the lens, and from the image a, the rays of light will diverge as from a real object, which will be seen by the eyes placed at e e, e' e', or any other position, in the cone of rays b a c. Thus several persons may at the same time see the image suspended in the air. If a screen What precautions are necessary in taking stereoscopic photographs 1 833. What is the stereomonoscope ? Explain its structure and use. How does this instrument enable several persons to see the same ob- ject simultaneously 1 518 OPTICS. of ground glass is placed at S S, the image will appear spread out upon the glass, but it will appear with all the perspective relief of a real object. An image thus formed on ground glass can be seen only in the direction of the incident rays. This is not the case with an im- age formed on paper, which radiates the light in all directions, and is hence incapable of giving a stereoscopic effect in such circumstances. The stereomoscope consists of a screen of ground glass, 5 S, fig, 473, and two convex lenses, A L, B L, so placed as to form images of two stereoscopic pictures, M and 2V, at the same point on the screen 473 where the vibrations must meet in the same phase, is inconsistent with the undulatory theory of light. It appears that light is so modified in passing through haze, or at an opaque edge of a small hole, as to acquire an anatropy or inver- sion of properties.* 836. Interference colors of thin plates are seen in thin films of varnish, cracks in glass, films of mica, various crystals, and in other transparent substances, as in soap bubbles. The colors of such thin films are due to the interference of light twice reflected by the surfaces of the film. Two surfaces of glass, pressed together, furnish a thin plate of air between two reflecting surfaces. Let G A D B, fig. 475, be a trans- parent film, such as a thin blown bulb of glass, or a soap bubble ; let SAB T be the transmitted ray, 8 A R the ray reflected at the first surface, S A B A' R' the portion reflected from the second surface, and emergent at the first surface, S A B A' B' T' the portion emerging 475 from the second surface, after the two in- ternal reflections, then the ray A' R will be retarded behind the ray A JR, by the interval n m, owing to the increased length of path it has to travel in twice traversing the film, and B' T will, in a similar manner, fall behind the ray B T, by the interval p q. If these retarda- tions equal the interval of an odd number of half vibrations, they will interfere, as they originated from a common wave, in the ray 5" A. The reflected rays do not differ greatly in intensity, which is for each about one-thirtieth that of the incident light for glass, and therefore their interference produces blackness where they destroy each other. The transmitted light has the principal beam of little less intensity than the incident beam, having lost only about one- thirtieth part by reflection at each of the points A and B ; but the intensity of the twice reflected beam which interferes with it is about one-thirtieth of one-thirtieth, or one nine-hundredth of that of the incident beam ; hence the difference of the intensities of the bright * Potter's Physical Optics. How does the central band vary with different kinds of light? 836. Explain the production of colors by % thin plates. LENGTH OF LUMINOUS WAVES. 521 and dark bands formed by transmitted light is never as great as in the reflected beams. But the difference between the bright and dark bands is different for different colors of the spectrum, being least for violet light, and greatest for red. This fact is thought to be contrary to what should have been expected, according to the undu- latory theory. 837. Newton's rings. If a plane plate of polished glass is pressed against a piano concave lens whose radius of curvature is known, the interference bands become colored rings, and the exact thickness of the film of air by which each color is pro- duced is easily estimated. The form of this apparatus is shown in fig. 476. The letters and explanation of the figure are similar to the preceding. When the two glasses are pressed sufficiently near 476 together, the centres appear black by re- flected light, and bright by transmitted light. The thickness of the film of air where the first color appears, is equal to | A V L' o "] one-half the retardation producing that color, hence the length of the wave, or vibration, for any color, is estimated as equal to twice the thickness of the film of air where the color ap- pears. The colors succeed each other in the order of the length of the vibrations required to produce them. A second, third, and fourth series of colored rings will be found, where the thickness of the film is an exact multiple of the thickness required to produce the first se- ries of colors. The distance between the first and second series de- pends on the rapidity with which the thickness of the film increases. In the case of a lens pressed against a plate of glass, the distance be- tween the glasses, or the thickness of the film, increases as the square of the distance from the centre. The diameters of the bright rings will therefore be as the square roots of the numbers 1, 2, 3, .) A round rod may be taken to represent a small beam of common light, and the radii shown in fig. 485 may represent the transverse vibrations by which light is propagated in or- dinary media. Fig. 486 will then represent a transverse section of a polarized beam, with vibra- tions in planes parallel to each other. 850. Resolution of vibrations. The principle of resolution of forces, (110,) will enable us to understand how vibrations, in an in- finite number of planes passing through the general direction of a beam of light, may be resolved into vibrations in two planes, making with each other any required angle. If E, fig. 487, 487 represents the direction and intensity of a vibration it will be equivalent to a and c, in axes, at right angles to each other. Vibrations represent- ed by F, G-, and H, may, in the same manner, be resolved into vi- brations in the axes A B and G D. Then a + a' -f Z> -f ft', will represent the intensity of the result- ing vibrations in the axis A B, and c -f- c' + d + d', will rep- resent the intensity of the resulting vibrations in the axis C D. If we thus resolve vibrations in an infinite number of planes into vibrations in the axes A B and C D, the sum of the result- ing intensities in the axis A B, will be exactly equal to the sum of the intensities in the axis G D. A ray of common light may therefore be considered as consisting of vibrations moving in two planes at right angles to each other. Any medium that will, either by its position or internal constitution, separate light into 850. On what principle can we explain the resolution of vibrations in any number of planes into vibrations in two planes at right angles with each other ? To what may the vibrations of a ray of ordinary light be considered equivalent ? When is a medium said to polarize POLARIZATION BY REFLECTION. 531 two parts, vibrating in planes at right angles to each other, will produce that change denominated polarization of light. 851. Light polarized by absorption. Certain crystals have the remarkable property of polarizing all the light which passes through them in particular directions. They appear to absorb part of the light, and cause the remainder to vibrate in a single direction only. If a transparent tourmaline is cut into plates one thirtieth of an inch thick and polished, the plane of section being parallel to the vertical axis of the hexagonal prism in which this mineral crystallizes, the light transmitted through such a plate will be polarized. If a second plate is placed parallel to the first, as shown in fig. 488, the light trans- mitted through the first 488 489 plate, will also be trans- mitted through the second plate ; but the light will be entirely obstructed if the axis of the second plate is placed at right angles with that of the first, as shown in fig. 489. A plate of tourmaline becomes, therefore, a convenient means of polarizing light, and also an instrument for determining whether a ray of light has been polarized by other means. A tourma- line plate so used, is called an analyzer. Crystalline plates of sulphate of iodo-quinine, (called Herapathite, from the name of their discov- erer, Mr. Herapath,) act in all respects like plates of tourmaline. 852. Polarization by reflection. When light falls upon a transparent medium, at any angle of incidence whatever, some portion of the light is reflected. When the incident light falls upon the medium at a particular angle, which varies with the nature of the substance, all the reflected light is polarized. Let G, G, fig. 490, be a plate of glass, or any other transparent medium, and let a ray of light, a b, fall upon it at such an angle that the reflected ray 6 c, shall make an angle of 90 with the re- fracted ray, b d, then the reflected ray b c, which represents but a small portion of the incident light, will be polarized. If the me- dium is bounded by parallel surfaces, the portion of the light reflected from the second surface, will also be polarized. 851. How are plates of tourmaline prepared for polarizing light? How does light transmitted through a plate of tourmaline differ from common light ? What is meant 4 by an analyzer ? 852. How may light be polarized by reflection ? 532 OPTICS. The angle of polarization by reflection may be determined by 490 the followinglaw. The tanget of the angle of incidence for which the reflected ray is polarized, is equal to the index of refraction for the reflecting medium. This law sup- poses the reflecting substance more dense >than the surrounding medium. If the light is reflected from the second surface, as when passing from glass or water into air ; the index of refraction equals the cotangent of the angle of polari- zation. The polarizing angle for reflection from glass, is 56 25', reckoned from the perpendicular. The polarizing angle for water, is 53 11'. As the index of refraction varies for different colors, the polarizing angle varies in the same manner. If a polarized ray falls upon a reflecting surface at the angle of polarization, and the reflecting surface is rotated around the polar- ized ray as an axis, when it is so placed that the plane of incidence corresponds with the plane in which the ray was polarized, the po- larized light will be reflected just as if it were not polarized ; but when the plane of incidence makes an angle of 90 with the plane of polarization, the light is entirely intercepted. In this respect a reflecting surface, at the proper angle of incidence, serves the purpose of an analyzer, just like a plate of tourmaline. 853. Polarization by refraction. When light is polarized by reflection from either the first or the second surface of a trans- parent medium, a portion of the transmitted light is polarized by refraction. The amount of light polarized by refraction is just equal to the amount polarized by reflection, but as the amount of light transmitted by transparent substances, very much exceeds the amount reflected from their surfaces, only a small portion of the transmitted rays are polarized, or, more properly, the light transmitted through a single plate is but par- tially polarized. 854. Polarization by successive refractions. If a ray of light, E E' is transmitted obliquely through a number of parallel trans- parent plates, as shown in fig. 491, a portion of the light is polar- ized at every refraction, and after a sufficient number of refrac- tions, the whole of the transmitted light is polarized. Light polarized by refraction, is polarized in a plane at right an- What is the rule for determining the angle of polarization by re- flection from the first surface? What is the rule for the second sur- face? What is the polarizing angle for glass? For wiiter? In what circumstances can a ray of light polarized by reflection be again reflected ? 853. How is light polarized by refraction ? DOUBLE REFRACTION. 633 gles with the plane of polarization by reflection. Light polarized by reflection vibrates at right angles with its plane of polarization, or its plane of reflection, as shown at B, fig. 492. 491 492 Light polarized by refraction, vibrates also at right angles with its plane of polarization, but parallel to its plane of refraction, as shown at C, fig. 492. Light not polarized, though vibrating in an infinite number of planes, is equivalent to a system of vibrations in two planes at right angles to each other, as chown at A, fig. 492. 855. Partial polarization. Light reflected or refracted at any oblique angle is, in general, partially polarized, and by repeated reflections or refractions, the degree of polarization is increased, until, after a sufficient number of reflections or refractions, it is apparently completely polarized. Let M N, fig. 493, represent the plane of refraction, and AS, CD, the axes of vibration for common light, 493 then by repeated refractions these axes will be gradually made to approach each other, until they sensibly coincide, as shown in the figure, when the light is said to be completely polarized. The portion of light reflected, un- dergoes a similar series of changes, until the axes of vibration sensibly coincide, in a plane at right angles to their position in light polar- ized by refraction. 856. Double refraction is a property in certain crystals that causes the light passing through them in particular directions, to be separated into two portions, which pursue different paths, 854. How is light polarized by successive refractions ? How do the vibrations of light polarized by reflection differ from the vibra- tions of light polarized by refraction at the same surface? 855. What is meant by partial polarization ? 856. What is meant by double refraction ? What is the major axis in a crystal of Iceland epar? 534 OPTICS. and which causes objects seen through the crystals to appear double. The most remarkable substance of this kind with which we are familiar, is Iceland spar, or carbonate of lime, which crystallizes in 494 the rhombic system, as shown in fig. 494. The line a b, about which all its faces are symmetrically ar- ranged, is called the major axis of the crystal, and the plane a c b d, passing through the axis, and through the obtuse lateral edges, is called the plane of princi- pal section. (59.) If a crystal of Iceland spar, from half an inch, upwards, in thick- ness, is laid upon a sheet of paper, on which are drawn various lines, they will appear double, as shown in fig. 495. A B, C D, E F, G H, are the real lines, seen in their true positions. The dotted lines show the position of the additional lines, caused by extraordinary refraction. The line A B, in the plane of principal section, is not doubled. Any line parallel to A B, will also appear single. The index of refraction for the ordinary ray remains constant, in whatever direc- tion light passes through the crystal The index of refraction for the extraordinary ray, when parallel to the axis, is the same as that of the ordinary ray, and differs most from the ordinary ray when it passes through the crystal at right angles with the axis. The index of refraction for the ordinary ray in Iceland spar is constantly 1,6543 = m. The index of refraction for the ordinary ray, when it makes an angle of 90 with the major axis, is 1,4833 = n. Let x = the angle which the extraordinary ray makes with the major axis in any other position ; and let N = the cor- responding index of refraction for the extraordinary ray, its value may be determined by the following formula : ft = \fm* -f (n* m s ) sin' x - \/2,T367 0.5365 sin a x. 857. Positive and negative crystals. Positive crystals are those in which the index of refraction for the extraordinary ray How do lines appear when seen through a natural face in a crystal of Iceland spar? In what position will a line appear single ? What is meant by the extraordinary ray ? In what direction must the extraordinary ray pass through the crystal, to diverge most widely from the ordinary ray ? 535 is greater than for the ordinary ray, and the extraordinary ray is refracted nearer to the axis than the ordinary ray. Quartz and ice are examples of this class. Negative crystals are such as have the index of refraction for the extraordinary ray less than for the ordinary ray, the extra- ordinary ray being refracted farther from the axis than the ordi- nary ray. Iceland spar, tourmaline, corundum, sapphire, and mica, are examples of negative crystals. Some crystals have two axes of double refraction, as nitrate of potash, sulphate of barytes, and some varieties of mica, 858. Polarization by double refraction. When the light transmitted through a doubly refracting substance is examined with an analyzer, it is found that both the ordinary and extraor- dinary rays are completely polarized, whatever be the color of the light employed. The tourmaline plate, or other analyzer, will, in one position, transmit the ordinary image and wholly in- tercept the other, but when the tourmaline has been rotated 90, the ordinary ray is intercepted, and the extraordinary ray is transmitted. 859. Nicol's single image prism is an instrument formed of Iceland spar, by which the ordinary image, produced by double refraction, is thrown out of the field, and only a single image, (the extraordinary,) is transmitted. An elongated prism of Iceland spar is cut through by a plane, E F, at right angles with the principal section, from 496 the obtuse solid angle E, fig. 496, making an angle of 22, with the obtuse lateral edge K. The terminal face, P, is ground away, so as to make an angle of 68 with the obtuse lateral edge, and the opposite face, P', is ground in the same manner. All the new faces are carefully polished, and the two parts are cemented to- gether again with Canada balsam, in the same position they previously occupied. The lateral faces of this compound prism are all painted black, leaving only the terminal faces for the transmission of light. "When a ray of light, a b, fig. 497, falls upon this prism, it is re- fracted into the ordinary ray b c, and the extraordinary ray b d. The 857. Explain the difference between positive and negative crystals. What substances have two axes of double refraction ? 858. How do the two rays of light polarized by double refraction differ from each other ] 859. How is Nicol's prism constructed ? Explain the action of Nicol's prism. 536 OPTICS. index of refraction of Iceland spar, for the ordinary ray, being 1.654, 497 and that of balsam only 1.586, the ordinary ray cannot pass through the balsam, unless the incident ray di- verges widely from the axis of the prism, but it suffers total reflection, and is absorbed by the blackened side of the prism The extraordinary ray has a refractive index in the Iceland spar generally less than in the bal- sam, varying,, for Nicol's prism, between 1'5 and 1'56; therefore it passes through the balsam into the lower part of the prism, and emerges in the direction g h, par- allel to the incident ray. \ These prisms are capable of transmitting a colorless pencil of light, perfectly polarized, from 20 to 27 in breadth. 860. Polarizing instruments are made in a variety of forms, to suit particular purposes. A simple instrument, and yet one of the most convenient in use for exhibiting the phenomena of po- larized light, is shown in fig 498. A mirror, M, made of plate glass, covered with black varnish or cloth on the back, or, better, a bundle of ten to twenty thin plates of polished glass, is mounted on a mahogany support at the polar- 498 izing angle. A Mcol's prism, or a tourmaline plate, at E, serves as an an- alyzer. The objects to be examined are mounted in discs of wood or cork, and supported at A or B, where they are most distinctly seen by the eye, looking through the analyzer. The student who has not a tourmaline, or a Nicol's prism, can use as an analyzer a small piece of plate glass, mounted so as to rotate on an axis parallel to the base of the instrument. Polarized light may be applied to the microscope, by mounting a Nicol's prism beneath the stage as a polarizer, and another for an analyzer, in the body of the microscope, above the object glass. 861. Colored polarization. When a thin plate of selenite, mica, or any other doubly refracting substance is placed between the polarizer and the analyzer in the polariscope, the light is 860. How can a simple and convenient polarizing instrument be constructed? How can polarized light be applied to investigations with the microscope ? 861. Describe the phenomena of colored po- larization. ROTATORY POLARIZATION. 537 separated into two beams, which follow different paths, and as the vibrations of one ray are more retarded than those of the other, when they are reunited, they interfere, and produce the most beautiful colors, varying with the thickness of the plates, and the position of their axes with reference to the axes of the polarizer and the analyzer. If the film is rotated, while the polarizer and analyzer remain fixed, the color "will appear at every quadrant of revolution, and dis- appear in intermediate positions. If the film and the polarizer re- main fixed, and the analyzer is rotated, the color will change to the complementary at every quadrant of revolution ; that is, the same color will be seen in positions of the analyzer differing 180, and the complementary color will be seen at 90 and 270, from the first po- sition. Films of selenite, varying between ,00124 and ,01818 of an inch in thickness, will give all the colors between the white of Newton's first order, and white resulting from the mixture of all the colors. If two films of selenite are placed over each other, with their axes parallel, the color produced will be that which belongs to the sum of their thicknesses. But when the two films are placed with their axes at right angles, the resulting tint is that which belongs to the differ- ence of their thicknesses. 862. Rotatory polarization is a property which some substan- ces possess of changing the plane of vibration in a ray of polarized light, even when it falls perpendicularly upon it. The entire amount of rotation depends upon the thickness of the medium. Quartz, cut transversely to its major axis, solution of sugar, camphor in the solid state, and most of the essential oils, possess the power of rotating the plane of polarization of a ray passing through them. Different substances, and sometimes different specimens of the same substance, rotate the plane of polarization in contrary directions. When the rotation takes place in the direction of the motion of the hands of a watch, the medium is said to have right-handed polariza- tion. Thus we have right-handed quartz, and left-handed quartz. In a beam of white light, the vibrations which produce red have their plane of polarization rotated much more than the colors of greater refrangibility. This property varies inversely as the squares of the lengths of the luminous waves which produce the several co- How is the color affected by rotating the film of selenite, while the polarizer and analyzer remain fixed? How does the color change by rotating only the analyzer ? What effect is produced by placing one film of selenite over another 1 862. Explain the phenomena called rotatory polarization. 23* 538 OPTICS. lors. The power of rotating the plane of polarization becomes a valuable test for speedily determining the nature of various chemical substances, or the strength of a solution of any substance having this power. Solid's saccharimiter, for measuring the relative amount of cane and grape sugar in solutions or syrups, is constructed on this principle. Such an instrument affords also a ready method of detect- ing the presence of sugar in diabetic urine. 863. Colored rings in crystals. Colored rings, with a black cross of great beauty, are seen in thin plates of doubly refracting crystals, when viewed in certain directions, with polarized light. Figs. 499, and 500, show the appearance of the rings and cross in thick plates of quartz, in positions at 90 from each other. Other uniaxial crystals show a similar system of rings beautifully colored. 499 500 501 502 Figs. 501, and 502, show the form of the colored rings in biaxial crystals ; e. g. some micas. Every doubly refracting crystal presents some peculiarity in the form and arrangement of the colored rings seen, in its thin sections. This subject is of great interest to the'mineralogist. 864. Polarization by heat, and by compression. Glass irreg- ularly heated, or heated and irregularly cooled, possesses the power of double refraction, and when viewed by polarized light, it exhibits dark crosses, bands, or rings, varying with the form of the glass, and difference of density in different parts. Similar phenomena may be produced by compression, or by bending rods or plates of glass. 865. Magnetic rotatory polarization. If a thick plate of glass i& applied to tjie poles of a powerful electro-magnet, the glass is neither attracted nor repelled ; but if a ray of polarized light is transmitted through the plate in a certain direction, the plane of polarization is rotated as by a plate of quartz, or other rotatory To what practical purposes may rotatory polarization be applied t 863. What phenomena are seen in certain crystals when viewed by polarized light \ APPLICATION OF POLARIZED LIGHT. 539 polarizer, showing that light and magnetism have some intimate relation to each other. This rotatory effect may depend upon change in the tension of the molecules of the glass by the magnetic force, and not upon any direct relation between light and magnetism. 866. Atmospheric polarization of light The light of the sun reflected by the atmosphere is more or less polarized, depending upon the angular distance from the sun. If the earth had no atmosphere, the sky would every where appear perfectly black. The color of the sky is produced by light reflected by the atmosphere. If we look at the sky through a Nicol's prism, we shall find, on rotating the prism, that light from some parts of the sky is polarized to a very appreciable extent. There are several points in the sky where no polarization is perceptible. The point in the heavens directly opposite to the sun. is called the anti-solar point. At a distance above the anti-solar point, varying from 11 to 18, there is a point of no polarization, and another neutral point at an equal distance below the and solar point. Another neutral point, or point of no polarization, is found from 12 to 18 above the sun, and a similar one below it, but the latter is observed with great dif- ficulty. When the sun is in the zenith, these two points coincide in the sun. At all other points in the sky, the light is more or less po- larized, the degree of polarization amounting sometimes to more than one-half as much as by reflection from glass at the angle of complete polarization. 867. The eye a polariscope The structure of the crystalline lens is such, that the unaided eye is capable of analyzing a beam of light polarized by reflection or by double refraction. A person accustomed to use his eyes in viewing the phenomena of polari- zation, can thus detect with ease facts of this nature, which are wholly inscrutible to one not familiar with such observations ; another of the numerous proofs we have that the eye is capable of very exact training ; but nevertheless it is a proof also of an imperfection in the eye itself. 868. The practical applications of polarized light are nume- rous. The water telescope consists of an ordinary marine tele- scope, with a Nicol's prism inserted in the eye-piece. 864. How may a polarizing structure be produced artificially? 865. How can magnetism 'be made to affect a ray of light? 866. How does the light of the sky differ from the direct light of the sun? What is the anti-solar point? What points in the sky ex- hibit no polarization of light f What is the maximum of atmos- pheric polarization ? 540 OPTICS. 503 The light reflected from the surface of the water is the principal obstruction to viewing objects beneath its surface. Nicol's priam, in a certain position, entirely cuts off the polarized portion of the re- flected light, and allows objects far below the surface to be seen in the telescope. A Nicol's prism, in the same manner, will enable the fisherman to direct his spear with greater certainty. Amateurs, in visiting galleries of paintings, find Nicol's prisms mounted as spectacles, of great service. Let the observer place himself in an oblique position, and look at an oil painting; when the sheen of reflected light renders the objects in the painting invisible, he has but to look through a Nicol's prism, set in a proper position, and the entire details of the painting at once become visible in all their proper colors. An opera-glass, provided with Nicol's prisms, would be a valuable instrument in examining a pic- ture gallery. Polarized light is also of great value in micros- copic inv estigations. Fig. 503 shows the appearanc e of a grain of starch, seen in the microscope with polarized light. The dark cross which changes its position by rotating the analyzer, distinguishes starch from every other substance. Different kinds of starch are also thus readily distinguished from each other. By means of polarized light, the chemist can detect one thir- teen-millionth of a grain of soda, and distinguish it from potassa or any other alkali. In physiological chemistry, especially in the examination of crystals found in various cavities and fluids of both animals and plants, the use of polarized light is especially* important. Instead of a few isolated facts, of interest only to the curious inquiirer, the polarization of light presents itself as a great fact in nature, meeting us with wonderful revelations in almost every department of natural science. By this marvelous property of light, the astronomer determines that the planets shine by re- flected light, and that the stars are self-luminous bodies. 86Y. What evidence is there that the human eye is a polariscope ? 868. What is the peculiarity of the water telescope ? What effect is produced by looking obliquely at an oil painting through a Ni- col's prism? What peculiar appearance is observed in grains of starch when examined in the microscope by polarized light? What facts in chemistry and astronomy show the practical application of polarized light ? ARTIFICIAL MAGNETS. 541 MAGNETISM. PROPERTIES OF MAGNETS. 869. Lodestone natural magnets. There is an ore of iron, called by mineralogists magnetite, or magnetic iron, some speci- mens of which possess the power of attracting to themselves small fragments of a like kind, or of metallic iron. This power has been called magnetism, from the name of the ancient city of Magnesia, in Lydia, (Asia Minor,) near which the ^04 ore spoken of was first found. It crystallizes in forms /T*\ of the monometric system, often modified octohedra, / / \ like fig. 504, and is a compound of one equivalent of \v~~ / peroxyd of iron with one of protoxyd. (Fe + ^\_y' Fe 2 3 = Fe 3 4 .) It is one of the best ores of this valuable metal. All magnets were originally lodestones, or natural magnets. 505 A fragment of this ore rolled in 506 iron filings or magnetic sand, becomes tufted, as in fig. 505, not alike in all parts, but chiefly at the ends. Fig. 506 shows the same mass mounted in a frame of soft iron, I Z, with poles, p p'. Thus mounted, the lodestone gains in strength, by sustaining a weight from the hook below, on a soft iron cross bar. 870. Artificial magnets are made by touch or influence from a lodestone, or from another magnet, or by an electrical current. Hardened steel is found to retain this influence permanently, while masses of soft iron become magnets only when in contact with, or within a certain distance of a permanent magnet. Arti- ficial magnets are more powerful than the lodestone, and possess properties entirely identical with it. Magnets attract at all dis- tances, but their power increases, like all forces acting from a cen- tre, inversely as the square of the distance. Heat diminishes the power of magnets, but if not heated beyond a certain degree, 1400 F., (full redness,) this power returns on cooling, and is increased at lower temperatures. Above that point, the coercive power, (881,) is destroyed, and they lose all sensibility to mag- netic influence. 869. What, is the lodestone 1 Whence the term magnetism ? What is said of natural magnets ? How is their power distributed 1 How are they mounted? 870. How are artificial magnets made I What-i^ said of the power of magneta ? 542 MAGNETISM. Various forms are given to magnets. The bar magnet is a simple straight bar of hardened steel. If curved so as to bring the ends near together, it is called a horse shoe magnet, and if several bars, straight or curved, are bound together into one, fig. 507, it is called a compound magnet, or magnetic batter} 7 . 508 Magnetic needlts are light bars, fig. 508, sus- pended on a central point so as to move in obedi- ence to terrestrial or artificial attractions. The mode of making magnets, and the circumstances influencing their power, are noticed hereafter. The most powerful artificial magnets can sustain only about twenty-eight or thirty times their own weight. Usually they sustain very much less. 871. Distribution of the magnetic force polarity. The mag- netic force is not equally distributed in all parts of a magnet, but is found concentrated chiefly about the ends, and diminishing toward the centre, which is neutral. The points of greatest at- traction are called poles. When a magnet is rolled in iron filings or magnetic sand, the position of the poles is seen as in the bar magnet, fig. 509, whose centre is found to be quite devoid of the attracted particles which cluster about the ends. The point of 509 no attraction is called the neutral point line of magnetic indiffer- ence, or equator of magnetism. Every magnet has at least two poles, and one neutral point. The magnetic poles are distin- guished as N or S, austral or boreal, (A and B,} or by the signs, (+) and minus, ( ) all these signs having reference to the earth's attraction, and to the antagonism between the poles of unlike How does heat affect it? Name the several sorts of artificial magnets? 871. How is the magnetic force distributed? What are the poles ? What is the neutral point ? How are poles marked ? MAGNETIC FIGURES. 543 name. The law regulating the distribution of magnetic force in a bar, was determined by Coulomb, by means of the torsion balance, to be very nearly as the squares of the distance of any given point, from the magnetic equator or neutral point. 872. Magnetic phantom magnetic curves. The distribution of the magnetic force about the poles of a magnet is beautifully shown by placing a sheet of stiff paper over the poles of a horse- shoe magnet, and scattering fine iron filings or magnetic sand from a seive or gauze bag over the paper. As they touch the surface of the paper, each filing assumes a certain position, marking the exact place of the magnetic poles and of the neutral line, as seen in fig. 510. The magnet may be laid horizontally, or a series of magnetic bars may be placed as in fig. 515, pro- 510 ducing very pleasing and instructive results. Tapping the edge of the paper gently with the nail, or a pen-stick, facilitates the ad- justment of the filings. The curves exhibited by the magnetic phantom have been mathematically investigated by De Haldat, who for that purpose transferred them to a glued paper. 873. Magnetic figures may be produced on the surface of a thin steel plate, by marking on it with one pole of a bar magnet. Magnetism is thus produced in the steel along the line of contact, which is afterwards made evident by magnetic sand, or iron filings sprinkled on the plate. These lines may be varied or multiplied at pleasure, with pleasing effects ; their polarity is always the reverse of that carried by the bar. They may be made even through paper or card board, and will remain for a long time. Blows, or heat, What law regulates the distribution of magnetism ? 872. What is the magnetic phantom? How are the magnetic curves shown and preserved? 873. What are magnetic figures, and how produced ? What is their polarity ? What shows them best ? 544 MAGNETISM. will remove them. Hard plate steel is best for this purpose, about one-twentieth to one-eighth of an inch thick, and six inches to twelve inches square. 874. Anomalous magnets are such as have more than two poles. Thus the bar seen in fig. 511, has a pair of similar poles. ) at the centre, and its ends are of course also similar, (+) while it has two neutral points at a and c. Fig. 512, shows a bar with three sets of poles, ar- ranged alternately and -f-, with three neutral points at w, 0, and n. Broken at these neutral points > every magnet becomes two or more separate magnets, with corresponding polarity. 875. Attraction and repulsion. The law of magnetic attrac- tion and repulsion is, that like poles repel, and unlike poles at- tract each other. If a piece of soft iron is presented to either pole of a magnetic needle, fig. 508, there is attraction, which is reciprocal between the needle and the iron ; for if the iron is suspended, and the needle ap- proached to it, the iron is attracted by either end of the needle. If, 513 512 however, a magnet is approached to the needle, -|- to there is at- traction ; if to or -f- to -f- there is repulsion. If the unlike poles of two equal magnetic bars, tufted with iron- filings, are approached, the tufts join in a festoon ; but if the poles are of the same name, most of the filings fall. For the same reason, if a magnetic bar, B, fig. 513, is slid upon another bar, A, of equal power to B, as the two opposite ends approach each other, the key, previously suspended, falls, because the two bars mutually neutralize each other by the opposing action of the austral and boreal magnetism. 874. What are anomalous magnets? Describe figs. 511 and 512. 875. What is the law of magnetic attraction and repulsion? How is it with soft iron ? Explain the experiment shown in fig. 513. MAGNETISM IN BODIES NOT FERRUGINOUS. 545 876. Magnetism by contact. When a mass of iron, or of any magnetizable body is placed in contact with a magnet, it 514 receives throughout its mass magnetism, of the same name as the pole with which it is in contact. Thus in fig. 514, the key is sustained by the north pole of a mag- netic bar ; a second key, a nail, a tack, and some iron- filings, are, in succession, also sustained by the magne- tism imparted by contact from the bar magnet through the soft iron. Tested by a delicate needle, every part of the sustained masses will manifest only north polarity, and we may regard them as only prolongations of the original pole. This is analogous to electrical conduction. Pure soft iron receives magnetism sooner and more powerfully than steel or cast-iron, and also parts with it sooner. Hardened steel and hard cast-iron, retain more or less of the magnetic force permanently. No other metals beside iron, nickel, cobalt, and possibly manga- nese, can receive or retain magnetism by contact. These are therefore called the magnetic metals. 877. Magnetism in bodies not ferruginous. Beside the magnetic metals, so-called, Cavallo has shown that the alloy, brass, becomes magnetic (slightly) by hammering, but loses that prop- erty again by heat. Some minerals are magnetic, particularly when they have been heated. The pure earths, and even silica, are found to have the same property. In the case of silica, and some other minerals containing oxyd of iron in combination, this is not so surprising. M. Biot determined in the case of two specimens of mica, one from Siberia, (muscovite,) and the other from Zinnwald, (lithia mica,) that their magnetic powers were, (by the method of oscillations,) as 6*8, to 20, and he remarked, if the oxyd of iron be the cause of their magnetic virtue, it should exist in the minerals in the above proportion ; and curiously enough, the result of Vauquelin's analyses, (then unknown to M. Biot,) corresponded, almost exactly, to these numbers. Some states of chemical combination, however, appear to destroy, or cloak, the magnetic virtues of iron; e. g. an alloy of iron, one part, 876. Illustrate magnetism by contact, from fig. 514. What is the polarity of the mass in contact? Compare soft iron and hardened steel in respect to magnetic power. What other metals receive mag- netism? 877. What other bodies does Cavallo state to be magnetic? What was Biot's observation on mica ? Where is the magnetic virtue of iron cloaked ? 546 MAGNETISM. with antimony four parts, was found by Seebeck to be utterly devoid of magnetic action; and the magnetic power of nickel is entirely concealed in the alloy called German silver. MAGNETIC INDUCTION OR INFLUENCE. 878. Induction. Every magnet is surrounded by a sphere of magnetic influence, which has been called its magnetic atmos- phere. Every magnetizable substance within this influence be- comes magnetic also, (without contact,) the parts contiguous to the magnet pole, having an opposite, and those remote from it, a similar name. This influence is called induction. Thus in fig. 515, the JVend of a bar magnet induces south polar- 515 ity in the contiguous ends of the five bars surrounding it, and N polarity in their remote enda If these bars are of hardened steel, they will retain a small portion of the mag- netic force induced from a powerful bar, but if they are of soft iron, they will part with it as soon as the source of magnetism is with- drawn. In this case, the magnetized bars have a tendency to move up to the magnet, and are prevented only by friction and gravity. The attraction is reciprocal, and we hence infer that there is induction in every case of magnetic attraction. In the iron-filings, arranged in magnetic curves, fig. 510, on a glass plate, or card board, the same law is observed. Small pieces of soft iron wire suspended from the ends of a thread near, and parallel to each other, when approached by a bar magnet, receive induced magnetism, the farther ends diverging by mutual re- pulsion. Two sewing needles thus suspended and influenced, become permanent magnets. The ingenuity of the teacher, aided by such familiar works as ' Davis' Manual of Magnetism,' or ' Harris' Rudiments,' will furnish many pleasing and instructive illustrations of magnetic induction. 879. Theoretical considerations. The real nature of the mag- netic force is unknown to us ; but the analogies offered by elec- tro-magnetism and magneto-electricity, lead to the conviction 878. What influence surrounds a magnet? What is this power called? Illustrate it by fig. 515. Give other illustrations. 879. What is said of the analogies of magnetic force ? How is it concen- trated with other forces? 880. What is the theory of two magnetic fluids ? THEORY OF TWO FLUIDS. 547 that it is but one mode of electrical excitement. Magnetism af- fords no phenomena immediately addressed to the senses, unlike the case of light, heat, and statical electricity. It is distinguished from statical electricity by its permanent character when once excited, and by the very limited number of substances capable of receiving and manifesting it. 880. Theory of two fluids. It may be assumed that there are two magnetic or electrical fluids, (the boreal or positive, and the austral or negative,) which are in a state of equilibrium or com- bination in all bodies ; that in iron, nickel, &c., these two forces are capable of separation, by virtue of the inductive influence of the earth, or of another magnet, while in other bodies, this per- manent separation cannot be effected. The two magnetic forces are never seen isolated from each other, but are always united in one bar. Hence we cannot have a boreal magnet, or an austral magnet, as we may in statical electricity produce, at pleasure, vitreous or resinous excitement over the whole surface of a body. Both names must co-exist, and if we break a magnetic bar at its neutral point, we have two magnets of diminished force, but each half has its two poles like the original bar, and its neutral point also. The anomalous magnets, figs. 511, 512, will render this statement intelligible. Every magnet must, in this view, be re- garded as an assemblage of numberless small magnets, every molecule of steel having its own poles, antagonistic to those of the next contiguous particle. This conception is rendered more evident by fig. 516. Hence the N and S poles of the several particles each point in one 516 way, and towards the JVand pjpcjcji=: 8 ends of the bar. Theseop--^ [| posing forces therefore COn- nans n s n s n s n s n n s stantly increase from the cen- tre or neutral point, where they are in equilibrium, to the ends, where they find their maximum. This arbitrary explanation enables us to conceive how such a body may excite similar man- ifestations of power in another, without itself being weakened, and how each part becomes a perfect magnet, if the bar is broken. The experiment shown in fig. 513, illustrates well the re-union of the two fluids, to form the neutral state of the undecomposed influence. What is said of the existence of these ? How may every magnet be regarded? Illustrate this from fig. 516. How do iron filings, the magnetic pastes, the attractions and repulsions are directly as the quantities of electricity possessed by the two bodies. The force of torsion, or resistance of wires to twisting, varies directly with the angle of torsion, inversely as the length of the wire, and directly as the square of its section. Coulomb happily applied these principles, first established by himself, to the meas- urement of electric forces in his 919. Torsion electrometer. This instrument, fig. 539, consists of an exterior glass cage, protecting a slender needle, n , insulated from the earth. The boiler is negative, and positive electricity is collected at D, provided the water is pure and free from grease. Turpen- tine and other volatile essences reverse the polarity, while grease or steam from acid, or saline water, destroy all excitement. If the nozzle of the jet ends in ivory or metal, there is also no ex- citement. A boiler, such as is described, will develop in a given time, as much electricity as four plate machines forty inches in di- ameter, making sixty turns a minute ; a truly surprising result. 938. Other sources of electrical excitement.!. The bands 937. Describe Armstrong's hydroelectric machine ? To what does Faraday attribute the excitement ? What name has the electricity 1 What circumstances affect this ? What of its power ? THEORY OF THE ELECTRICAL MACHINE. 591 of leather, India-rubber or gutta-percha, used to drive machine- ry, often become powerful sources of. resinous electrical excite- ment, giving sparks, sometimes over twenty inches in length, of negative electricity. In cotton mills, so much electricity is thus set free, that it becomes necessary to let steam into the carding and roving rooms, to avoid inconvenience from the repulsions and attractions of the cotton. A leathern band, mentioned by Mr. Bachelder, (Am. Jour. Sci. [2] in. 250,) gave sparks to the finger at three feet, and a luminous brush, to a steel point, at seven feet. The discharge from leather, as from all bad conductors, is local, or danger would attend it. Dr. Franklin, in a letter to Bowdoin, suggested for a portable elec- trical machine, a cross band of stuffed leather, moved by a winch over drums. 2. The friction of shoe-leather, on woolen carpets, in houses warmed by hot-air furnaces, or steam, in cold weather, is a fer- tile and curious source of negative electrical excitement. The young people in the author's house find an unfailing source of amusement in cold weather, in giving electrical shocks, by kisses and otherwise, to unwary people, or in lighting the gas by a spark from the finger or a key handle, after running briskly over the car- pet. Prof. Loomishas noticed these effects in the Am. Jour. Sci. [2] x 821, and xxvi, 586, in detail. They appear to be unknown in Eu- rope, owing probably to the fact that European houses are never warmed and dried by hot-air furnaces. 939. Theory of the electrical machine. The phenomena of the electrical machine may be explained, either on the theory of one or of two fluids. The explanations of induction (928) already given, apply equally to the development of free electricity, upon the prime conductors of electrical machines. When the machine is turned, the neutral electricity of the rubber is decomposed, the positive fluid follows the glass, until coming opposite the points on the prime conductor, the negative electricity of the con- ductor flows out, to unite with the positive of the glass, while the positive fluid of the conductor is repelled to the other end, thus leaving the prime conductor powerfully positive. Reaching the rubber, the neutral fluid of the glass is there decomposed, its neg- ative portion seeks the common reservoir, and the positive fol- lows the revolving glass to the points as before. The conduc- 938. What other sources of electrical excitement are named? What is said of electrical houses, and the cause ? 939. Explain the action of the electrical machine. What becomes of the negative fluid of the prime conductor ? How does it become positive ? What is said of the action of the amalgam ? 692 ELECTRICITY. tor does not acquire positive electricity from the plate, but gives its negative thereto, thus becoming itself positive. It is still an open question whether the action of the amalgam is chemical or mechanical. (934.) It is certain that an amalgam of silver, or gold, does not act to excite electricity, like amalgams of oxydizable metals, and Dr. "Wollaston demonstrated, that the latter did not act in an atmosphere of carbonic acid or nitrogen, free of oxygen. In all cases, the discharge of an electrical conductor by a spark or otherwise is accompanied by the induction of an opposite excitement in the body receiving the shock, whose opposite electricity, uniting with that of the conductor by a forcible disruption of the intervening dielectric, produces the sound and flash of the electric discharge. 940. Experimental illustrations of electrical attractions and repulsions. A multitude of instructive and amusing experiments may be made with the electrical machine, illustrating the law of attractio'n. A few must suffice. 1. THE INSULATING STOOL is a bench with glass legs, (aboard on four 553 black bottles answers perfectly,) on which a person may stand or sit, while in communication with the electrical machine. Being thus insulated, the free electricity can es- cape only through the surrounding air approaching the kunckle to any part of the person or dress of one so situa- ted, a strong spark is received. Except for the hair being *- repelled, the person charged is not conscious of any change from an ordinary state. A doll's head, with paper hair, set upon one of the conductors, is a common electrical toy. 2. HENLEY'S ELECTROSCOPE, fig. 553, serves to mark the de- gree of tension in the machine by the repulsion of a pith ball at the end of a straw ; it is mounted on one of the conductors, and in dry weather remains extended a long time, but in damp weather falls immediately, when the machine stops. 3. ELECTRICAL BELLS, fig. 554 ; the bells, A and B, are suspended 654 by a metallic thread, from the ends of a cross- bar of metal hung on the machine ; the bell, C, and the two clappers, are hung by insulating threads. G is connected with the earth ; and when the machine is worked, A and B become positive, and by induction C becomes negative, and the little clappers being alternately attracted and repelled, a constant ringing is kept up as long as the excitement lasts. If the machine is too act- ive, luminous sparks pass, and the bells remain still. \ 940. Explain the insulating stool and Henley's electroscope. Why do the electrical bells ring ? THE ELECTRICAL WHEEL. 593 4. VOLTA'S HAIL-STORM is a contrivance designed to show how (in Volta's view) hail might be produced. A 555 glass bell communicates with the machine, fig- 555, above, and rests on a metal plate in com" munication with the earth. When the machine is worked, the pith balls on the plate areviolent- ly agitated, being drawn up and repelled again actively, while the excitement lasts. A simple bell glass, or large tumbler, electrized by contact of its interior surface with the con- ductor of an electrical ' machine, answers quite as well, and may be placed over a heap of pith balls on the table ; they are violently thrown about as long as the excitement contin- ues. The dance of puppets is only a sub- stitution of little figures of dancing peasants, made of cork or pith, and placed between two metallic plates. 5. THE ELECTRICAL WHEEL is composed of several points fixed in a centre, so balanced as to rest on an up- 556 right, sustained on one of the conductors, fig. 556 ; as the machine is worked, the escape of the electricity from the points re-acts on the air with sufficient force to revolve the wheel with activity. The exis- tence of such a current of air, caused by the escape of electricity from points, is further shown 6. BY A CANDLE FLAME ; a candle, fig. 557, held before the point, has its flame blown aside by the rush of air accompa- nying the electricity. If the candle is placed as a conductor, and a point is held out to it, the direction of the flame is altered by the reverse fluid induced on the point, fig. 558. This experiment has been called the electrical How-pipe. The rush of air from the points may be so energetic from an active ma- chine, as to extinguish the flame. In the dark, all points on an elec- trical machine emit a stream of light, called the electrical brush. Of course no sparks can be drawn from points, but a Leyden jar may What is Volta's hail-storm? Why does the electrical fly revolve? How does a point affect a candle flame ? What other illustrations are named ? 594 ELECTRICITY. be silently charged from them. If the point is covered with a ball 557 an inch or two in diameter, 658 its peculiar action ceases, and the ball emits sparks. 7. Franklin's spider, Elli- cot's electrical water pot, the inclined plane, and the elec- trical planisphere, are other I well known forms of appa- ratus, designed to show the same principle. The cata- logues of all leading instru- ment-makers, contain numerous additional illustrations to the same end. ACCUMULATED ELECTRICITY AND ITS EFFECTS. 941. Disguised or latent electricity. The phenomena of induc- tion already explained, have a curious and most important exten- sion in the subject of this chapter. When two equal and in- sulated conductors, equally excited by the two opposite electri- cities, are separated from each other by only a thin plate of glass, or other dielectric material, no signs whatever of any electrical excitement are communicated by either to an electroscope con- nected with them. The dilectric prevents the union of the op- posing electricities, but not their mutual inductive action, where- by their presence is entirely masked to surrounded bodies. Kemoved to some distance from each other, each manifests free electricity, by the divergence of its electroscope. But if they are once more brought together, this evidence of excite- ment again disappears, and so on, until the imperfect insulation of the air gradually neutralizes all free electricity. When so situated, the electricities are said to be latent or dis- guised, paralyzed by their mutual attractions. 942. The condenser of JEpinus. The phenomena of disguised electricity are illustrated by the use of various condensers, con- sisting essentially of two extended metallic surfaces, and an in- sulating medium. They are sometimes adapted to accumulate electricity of high tension, and sometimes their aid is invoked to render sensible, quantities of electricity, otherwise insensible. 941. What is disguised electricity 1 942. What are electrical con- densers? THE .EPINUS CONDENSER. 595 The condenser of ^Epinus, fig. 559, 560, is designed for the for- mer purpose. Two polished me- 559 560 tallic surfaces, A C, with elec- troscopes, a, b, and an intermedi- ate thin glass plate, B, fig. 560, are all mounted on insulating' glass pillars, and slide in a groove cut in the base. In fig. 559, the two discs are placed in close contact with the intervening dielectric, B, while by the chain, n, positive electricity flows into A, from the excited conductor of an electrical machine. Did A stand alone, it could only receive so much electricity as would raise its surface to the same tension with the prime conductor of the machine. But this condition is wholly changed by the pres- ence of the second plate, C, cut off from actual contact with A by . the dielectric, B, but entirely within its inductive influence. A part of the natural fluid of C is at once decomposed by this influence of A, attracting its negative fluid to the inner surface of C, and holding it there, while the corresponding positive fluid from G is expelled by the conductor, m, to the earth. No free electricity would remain if it were possible for B to exist and act as a dielectric without thick- ness : but as this is evidently impossible, it happens that a little less negative fluid is drawn to the surface of C, than exists of positive on A, by reason of the thickness of B. Consequently the electroscope on A remains slightly elevated, (residual charge,) even after some time, while that on C continues wholly passive. But the neutralization of A's positive fluid by the decomposition of an equivalent of natural electricity in C, results in lowering the tension of A, to the low degree corresponding to its residual free electricity. Hence A can receive a fresh charge from the machine, raising its tension to its first condition, and inducing the decomposi- tion of a fresh portion of neutral electricity in C as before, and thus the action proceeds, until the whole of the natural fluid of both plates is decomposed and disguised, or rendered latent, excepting that small portion which at each instant constitutes the free electri- city, equivalent to the difference due to the thickness of B, and which, as we have seen, would be null, if B could be conceived of as having no thickness. It is this small residue which constitutes the residual charge in the Ley den jar. ' In performing this experiment, the knuckle may serve as a con- Describe that of .65 a glance that this arrangement is identical in principle with the condenser of JEpinus, and the electrical plates of Frank- lin. If the knob, b, of the Leyden jar, insulated upon a s,tand, fig. 566, is presented to the conductor, a, of the elec- trical machine in action, only a single spark or so, will enter it, unless a way is provided, as by the conductor, c, for the escape of the similar electricity from the exterior coating, while its opposite is then fixed as in C, fig. 560. The charg- ing of the jar then proceeds, and for every spark which darts from a to b, a corresponding one of similar electricity, is seen to escape from the outer coating to c. When it is held in the hand, the same effect follows through the arm, accompanied by a slight twinge in the nerves. Presently the point of sat- uration is reached, the two decomposed electrici- ties are latent, either coating may be fearlessly touched alone, but as soon as by the discharger or otherwise, communication made between them, a loud snap and brilliant spark follow with a violent shock. The invention of the Leyden jar, or vial, is commonly attributed to Cunaeus or Mushenbroek of Leyden, in 1746. Von Kleist, dean of the chapter at Comin, in Pomerania, also independently discovered this important instrument by a similar accident. With a view to fix electricity in some insulated substance, Cunce- us, in 1746, led electricity into a small vial containing water, by a bent nail thrust through the cork, and hung on the prime conduc- tor. Endeavoring, in one of these trials, to detach the vial and nail 945. What is said of the Leyden jar ? Describe it. THE ELECTRIC BATTERY. 599 from the electrical machine, Cunaeus,|to his great amazement, received a violent shock. Von Kleist, in the course of a valuable series of experiments (1745) on electricity, led the fluid by a brass wire or pin into a bottle containing mercury. ' As soon,' he says, ' as this little glass, with the pin, is removed from the electrical machine, a flaming pencil issues from it so long, that I have been able to walk sixty paces in the room with this little burning machine ; and if the finger or a piece of money be held againt the electrified pin, the stroke coming out is so strong that both arms and shoulders are shaken thereby.' This discovery of so wonderful a power in nature, before unsus- pected, created immense excitement over the civilized world, and it was precisely at this time that Franklin immortalized himself by his contributions to the new science. He explains the action of the Leyden vial by his single fluid hypothesis, in his 'observations and experiments on electricity,' in a manner which must ever win for him the reputation of a profound philosopher. 946. Electricity in the Leyden jar resides on the glass. In fig. 567, the jar, A r is composed of the 567 three separable pieces ; B, the glass, C, its outer, and D, its in- ner metallic coatings. When this jar is charged, and set on an insu- lating surface, it may be separated into its three parts without being discharged ; but and D will then be found by the electroscope entirely free from excitement, while B remains strongly excited. Putting the parts together again as in A, the jar will be found charged as at first, if the air is dry, and too much time has not passed. 947. The electric battery As the charge of the Leyden jar is, other things being equal, directly as its surface, large jars are plainly of more power than small ones. But a limit of size is soon reached, which the thickness of glass required for strength, and other circumstances, render it unprofitable to pass. Hence several coated jars, of moderate size, are united by joining all their inner coatings by metallic rods, and all their outer coatings by a common conducting base, as shown in fig. 568. Such an arrangement is called an electrical lattery. When charged from a common source, and discharged in the usual way, they all act as one great jar, the result being in not quite the ratio of the number of jars, but nearly so. Hence, the smaller the number, What is it like ? How is it charged suppose it to be insulated 1 What of its history ? What is said of Franklin's explanation 1 600 ELECTRICITY. the thinner the glass, and greater the size of the jars, the better, and several batteries of seven and nine jars, united to the charging rods of the central jars, are preferable to more extended single series. They are charged by connecting the interior with the prime conductor by , and the exterior with the earth. If the battery is extensive, and the machine powerful, great caution is requisite to avoid receiving its shock ; an accident which might be serious in its consequences. 568 The battery used by Von Marum, with the machine already noticed, (935,) embraced one hundred jars, I each thirteen inches in diameter and two feet high The coated surface was five hundred and fifty square feet, 5 (five and a half feet to each jar.) ?When fully charged, its force was ir- *resistible. A bar of steel nine inches long, half an inch wide, and one- twelfth of an inch thick, was rendered powerfully magnetic by the discharge. A small iron wire, twenty-five feet long, was deflagrated, and various metals were dissipated and raised in vapor, when placed in the circuit of discharge. A book of 200 pages was pierced by it, and blocks of hard wood, four inches square, split in fragments. 948. Discharge in cascade. A series of two or three Leyden jars may be placed horizontally upon insulating stands, so that the interior of each succeeding one may receive the spark from the outer coatings of the one preceding. This mode of charging cannot be carried beyond two or three jars, owing to the accumulated resistance soon vitiating the result But Mr. Boggs, of London, lias very ingeniously contrived an elec- tric battery, the jars of which are charged together, but are dis- charged consecutively. Each jar is supported in a horizontal posi- tion on a vertical spindle, their knobs, while being charged, pointing outward, like the radii of a circle, and when the battery is to be dis- charged, the knobs, by a quarter revolution, are brought opposite, each to the bottom of the next jar. In this way the disruptive power or intensity of the spark is multiplied as the jars, the quantity remain- ing the same. Mr. Boggs is said to have discharged his battery of twelve jars through a space of twelve feet. (Sill. Jour : [2] vii, 418.) 949. The diamond jar. To show that the coatings of the jar convey the electricity collected on the glass to the point where it 94. Where is the electricity of the Leyden jar resident ? Illus- trate it from fig. 567. 947. What is the electric battery ? How constructed and used ? Describe Von Marum's and its effects. 948. What is discharge in cascade ? What is Boggs' mode ? THE UNIVERSAL DISCHARGER. 601 meets the cause of discharge, ajar may be coated, like fig. 569, with metallic filings, or patches of tin-foil, cut in 669 lozenges, (a diamond jar,) the wire of which is bent over so as to bring the ball near the outer coating, which connects by a chain with the earth. When the machine, (on whose arm this jar is hung,) is worked, a brilliant spark is seen at intervals to dart from the knob to the outer coating, and thence to spread in zigzag courses over the whole surface. 950. The universal discharger. Various contrivances are in use for regulating or measuring the discharge of the electric bat- tery, and the single jar. Of these, Henley's universal discharger, fig. 570, is, perhaps, the most useful. By means of this simple appa- ratus, the electrical fluid may be made to pass through any substance placed upon the table, t. Two rods, sliding in the joints a a', end in balls, c d covering points which can be ex- posed by their removal. The rod, #', connects with the positive side of the battery, for example, while by the discharging rod, fig. 561, communication can be made at pleasure between a and the negative side of the battery, by a chain or metallic thread. The charge of the battery 570 may be prevented from pass- ing a given limit, by using the discharging electrometers of Lane or Cuthbertson, in which a ball is sustained at such a distance from the dis- charging knob of the battery, that when its charge reaches the proper tension, it dis-- charges itself. A beautiful illustration of the slow discharge of a charged jar is seen in fig. 571, where a charged Leyden jar, with a small bell in place of the knob, is set upon a board, near to a little brass ball, hung from a silken thread, upon a wire, carrying a second ball in connection with the earth by A JB. The effect is, that 949. What does the diamond jar show ? 950. Describe Henley'a universal discharger. How may the battery charge be limited] How is the slow discharge illustrated 1 26 602 ELECTRICITY. the -f electricity of the jar attracts the little ball, but after strik- ing the bell, the ball is repelled, until, coming in contact with the other bell, it is discharged, and so on for many hours, this little chime is rung by the electrical pendulum. 951. The electric light and spark result from the re-union of the two electricities. Every elec- trical discharge produces expan- sion of the air, and the form and color of the spark are materially influenced by the density and chemical composition of the gas- eous medium in which it passes. The character of the sparks depends on the form, area, and electrical intensity of the discharging surfaces, as also on the kind of electricity on the conductor in which the spark originates ; from the negative conductor the sparks are far less dense and powerful. In Kinersley's thermometer, fig. 572, the agitation and expansion of the air following an explosion is clearly seen. A portion of water in the larger vessel, which is air-tight, communicates freely with the small open tube, attached to the foot, and ending in a narrow glass tube. When an electrical discharge takes place through the appa- ratus, the consequent expansion of the air violently raises the column in the smaller tube, but after the commotion is over, the fluid gra- dually regains its original level, as the air in the larger vessel cools. The electrical mortar discharges its ball by the force of expanded air, at the moment of electrical discharge. The electrical egg. In a vacuum, the spark becomes an ovoidal tuft of light, uniting the conductors. The apparatus, fig. 573, is designed to show these effects. A large egg-shaped glass vessel is mounted at the lower extremity with a stop-cock, for attaching it to the air-pump, in order to remove the whole or a part of the air, or to replace it by vapor of alcohol, ether, or any other gas not acting on brass. By the rod, A, connection is established with the electrical ma- chine, while the distance between the electrical poles, B (7, may be adjusted by sliding the upper rod in its air-tight socket. This apparatus is called the electrical or philosophical egg. The 951. What is said of the electric spark ? Describe Kinersley's thermometer. How is the spark in vacuo ? Describe the fig. 573. COLOR OF THE ELECTRICAL SPARK. 603 rarer the air the more globular becomes the spheroid, and at the 572 same time less bril- liant. The auroral tube is only a modifi- cation of the same ap- paratus. This apparatus is also used with splendid ef_ feet with Ruhmkorff's induction coil. (Elec- tro Dynamics.) 952.' The color of the electrical spark varies with the nature and density of the gas- eous medium through which it passes. Far- aday observed that in air, oxygen, and dry chlorohydric acid gas, the spark was white, :With a light bluish shade, especially in air. In the heavy thunder-storms common in an American sum- mer, the light of a powerful flash of lightning is distinctly purple, and sometimes violet. In nitrogen it is blue or purple, and gives a remarkable sound ; in hy- 574 drogen it is crimson, and disappears when the gas is rarefied, in carbonic acid the color is green, and the form of spark very irregular ; in oxyd of carbon it is some- times green and sometimes red ; in chlorine it is green. The little apparatus, fig. 574,is well calculated to show these effects by contrast at one view. The three tubes, a a' a" are respectively filled with various gases and scaled. Each tube has two short platina wires, n n, soldered into its sides, through which the electric spark from b must pass on its way to the ground by c. 952. What is the color of the spark in different media 1 604 ELECTKICITY. 953. Difference between the positive and negative spark. 575 The tuft of light from positive electricity is far more beautiful than that from negative, as seen from the ends of two points. Thus while positive electri- city gives an opening sheaf of light, negative electricity _ gives only a small star, fig. 575. In rarefied air, these differences are much less apparent. Faraday suggests that they are due, chiefly, to the greater facility with which negative electricity escapes in air, than positive, as conductors, negatively charged, lose their ex- citement sooner than those positively charged. 954. Scintillating tube and magic squares. Every collection 676. of electrical apparatus contains these familiar pieces of appa- ratus, illustrative of the phenomena of the electric spark. The scintillating tube, fig. 576, has rows of lozenge-shaped pieces 577 of tin foil pasted on its interior, usually in a spi- ral, and when held by the hand, as shown in the fig- ure, the electricity flashes from point to point at the same apparent instant, producing a most agreea- ble effect. The magic squares are panes of glass on which arc interrupted strips of tin foil, cut to represent some de- sign, to be made visible only when a spark passes. These squares are mounted on a foot, in connection with the earth, and are set near the ball of the prime conductor. 953. What is the difference between the positive and negative spark ? To what has this been attributed 1 954. What are the scin- tilating tube and magic squares ? INFLAMMATION OF COMBUSTIBLES. 605 By scattering metallic filings over a varnished surface of glass, the same effect is produced as upon the jar, fig 569. 955. Effects of the electric discharge. The effects of the electric discharge are chiefly, 1st, physiological; 2d, physical; 3d, mechanical; 4th, chemical. The passage of the electricities through bodies, is sometimes impeded by their bad conducting power, or by want of proper dimensions ; and in either case, a powerful electric discharge manifests itself in one of those modes. 956. Physiological effects. These are seen in the shock ex- perienced by all living beings, in the passage of electricity through any of their members. Any number of persons joined hand to hand, will receive, at the same instant, the shock of an electric battery. Abbe Nollet, imparted it to over six hundred per- sons in his convent at one time those in the middle of the chain being little less affected than those near the conductors. A person charged on the insulating stool, feels a prickly heat and glow of the skin, resulting in perspiration. Many useful applications have been been devised of this agent in medicine, for which, consult Channing's medical electricity. It needs hardly to be said, that the full shock of a powerful battery will destroy life in man. Sparks, fifteen or eighteen inches long, begin to be unsafe, if from large sur- faces. Small animals, as birds, are easily killed by a moderate dis- charge, on the table of the universal discharger. Fig. 970. 957. Inflammation of combustibles. Although no sense of heat is felt when the knuckle receives 578 strong sparks from an active machine, yet the smallest spark serves to in- flame ether, whether from a Ley den jar, from the finger, or more stikingly, from an icicle held in the fingers of one mounted on an insulating stool. The ether is placed in a metallic cup,, and the spark should be drawn on its = edge, moist with ether. Gunpowder placed on the table of the universal discharger, over the points of the rods, a a', fig. 970, is simply thrown about, without being fired ; but if a wet string, in place of one of the conducting wires, forms part of the connection, its retarding power is such as to fire the powder. The lighting of gas from the finger of one charged by 965. Classify the effects of the electrical discharge. 956. What are its physiological effects 1 957. What is said of the inflammation of combustibles ? 606 ELECTKICITY. running on a carpet, has already been mentioned, (938, (2).) Lycopo- dium, alcohol, a newly extinguished candle, and many other combus- tibles, are also easily inflamed by the spark. A gold leaf confined between two glass plates with the edges hanging out, will burn with the explosion of the glass, and if held between cards, will stain them with purple oxyd of gold. Silhouette likenesses of Franklin are thus printed : a powerful current from a battery is needed for this. 958. Union of elements effected by electricity. A mixture of hydrogen, two volumes, and of oxygen one volume, or of hy- drogen, with several times its volume of common air, is exploded by a spark passing through the containing vessel, e. g. the tin air-pistol, called * Vol- 530 ta's pistol,' fig. 579, is provided with an insu- Llated conductor, end-< ing near the inner sur- j face of the pistol at B. Its mouth is closed tighly by a cork, and the spark caused to pass by holding it near the prime conductor, fig. 580, or to the electrophorus. The cork is then violently expelled, by the expansion of steam, with a loud explosion. 959. Volta's electrical lamp A self-regulating hydrogen ap- paratus is seen in fig. 581, similar in its action to that described in (354) In its base drawer is an elec- trophorus, T P, the plate, P, of which is always charged. A silk cord connects the upper plate, P, with the gas cock, J5, in such a way that when the gas in T is drawn, the communication is af- fected at 0, with the insulated wire t', and the electricity thus finds its way in a spark between the but- tons at 0, and escapes to the earth ^ by t. As the hydrogen is flowing at that moment from the jet, it is inflamed, and kindles a little candle 958. How is union of elements effected by electricity? 959. De- scribe Volta's electrical lamp. CHEMICAL EFFECTS OF STATICAL ELECTRICITY. 607 standing in its path. Every time the cock, R, is moved, the plate, P, rises, and communicates a spark. With care, this in- strument remains in action for weeks, from a single excitement. 960. The mechanical effects of the electrical discharge. Any thin non-conducting substance placed between the balls of the universal discharger, is either pierced or broken where the fluid passes. The phenomena attending these experiments are curious and instructive in point of theory. Glass is pierced when a thin piece of glass, v, is placed in the posi- tion seen in fig. 582, between the points of 582 the conductors, a b, a small hole will be made through the glass, as if with a drill, provided the effect of the fluid is concen- trated by placing a drop of oil at the point to be pierced. The hole is circular, starred, and its edges smooth, and sometimes it re- mains filled with the powdered glass in fine dust, easily removed. It requires a power-, ful battery to pierce glass one-twelfth of an inch thick. If a card is placed in the path of the fluid, it is pierced with a raised edge, (burr,) on both sides of the hole. When the card is placed obliquely, as seen in fig. 583, between the points, a c, of the insulating holder, the hole is made in the place and direction seen at o in the section; that is, nearer the negative pole, its 583 edges being raised, or thickened, a circumstance due, probably to the decomposition of the neutral fluid in the card,occasioning a rush of electricity in both direc- tions. This has been esteemed a fact inexplicable, on the single fluid hypothesis, while its position, always near to the negative pole, indicates that the neg- ative fluid passes less readily through the air than the positive. Many other examples of the fracture } or dispersion of non-conducting bodies, maybe gath- ered from the larger treatises. 961. The chemical effects of statical electricity are generally feeble. Besides those before alluded to, (958,) Wol- laston, with very fine points of gold wire immersed in water, de- composed water in a very limited manner. A paper moistened with iodid or bromid of potassium, is stained brown by the electrical 960. What are the mechanical effects of the electrical discharge 1 Illustrate them from figs. 582 and 583. 961. Describe its chemical effects. 608 ELECTRICITY. discharge when it is laid upon the scintillating square, (fig. 577.) Olefiant gas, sulphuric acid, chlorohydric acid, ammonia, and ni- trous oxyd, are decomposed by the electric discharge, with the separation of their constituent elements, and carbonic acid is de- composed into oxygen, and oxyd of carbon. The elements of the air unite under a prolonged series of sparks, (Pristley,) to form nitric acid, (Cavendish,) and lightning in the atmosphere, forms the same compound, as the analysis of rain-water has shown. (Liebig.) Numerous other evidences of the chemical ef- fects of electricity have been recorded ; perhaps the most im- portant of these, is that atmospheric effect called 962. Ozone. This term is derived from the Greek, in allusion to the peculiar odor which is always perceived after an electrical discharge or excitation of a machine, and sometimes improperly compared to the odor of sulphur, which it does not all resemble. It is due to a remarkable state or condition induced in oxygen gas by electricity, (and by several other causes also.) Mr. Scon- bein, of Basle, has devoted himself to the study of the curious properties of this singular product, the record of which belongs rather to chemistry than to physics. Atmospheric Electricity. 963. Franklin's kite. We owe to Dr. Franklin the demonstra- tion that the phenomena of a thunder-storm arc due to electri- city, identical with that excited in electrical experiments. He proposed two modes, in 1749, by which he supposed electricity might be drawn from the clouds. Dalibard, at his suggestion, erected in the open air near Paris, in 1752, a pointed iron rod, 40 feet long, and insulated. On the 10th of May, 1752, electrical sparks were obtained from this rod, with the usual snapping sound. In June of the same year, Franklin, tired of waiting for the erection of a tall spire in Philadelphia on which to place his pointed conductor, conceived the idea of reaching the higher re- gions of the air by a kite. This he formed of a silk handker- chief stretched over two light cedar sticks. It had a pointed wire at top, and a silken cord insulated it from the hempen string, at the lower end of which he tied an iron key. Watching the approach of a thunder storm he raised the kite, and soon had the satisfaction of seeing the fibres of the hempen 962. What is ozone? 963. What was Franklin's experiment of the kite ? Give the dates and history. What is said further of Romas and Richmann? FREE ELECTRICITY OF THE ATMOSPHERE. 609 string bristle and repel each other, and finally when the rain had rendered the string sufficiently a conductor, he enjoyed the "unspeakable satisfaction of seeing long electrical sparks dart from the iron key. Thus was realized by actual experiment one of the boldest conceptions and most interesting discoveries in the history of science. Efforts have been made to rob Franklin of the honor of this dis- covery, but it is one thing to suggest that two phenomena may be identical, and quite another thing to prove it. Dalibard's experi- ments were undertaken at Franklin's suggestions and hardly pre- ceded his own in date. These experiments were everywhere repeated, and it soon became evident that they were far from being free from danger. Romas, in June, 1753, during a thunder storm in France, drew flashes of elec- trical fire ten feet long, from a kite raised by a string 550 feet long. The experiment was accompanied by every evidence of intense elec- trical tension in the attraction of straws, the sensation of spiders webs over the faces of the spectators, and in the loud reports and roaring sounds, similar to the noise of a large bellows. In August, 1753, Prof. Eichmann, of St. Petersburgh, lost Ms life while engaged in sim- ilar experiments. Cavallo, in 1777, in London, obtained enormous quantities of atmospheric electricity by an electrical kite, and no- ticed that it frequently changed its character as the kite passed through different layers of the air. In telegraph offices during a thunder storm, vivid sparks, often very inconvenient and not with- out danger, are constantly flowing from the receiving instruments, being induced on the telegraph wires from the atmosphere, during thunder storms. (Henry, Sill. Jour. [2] iii, 25,) 964. Free electricity in the atmosphere. That the atmos- phere, besides the combined electricity proper to it, contains also at all times free electricity, is proved by raising an insulated conductor a few feet into the air, as by a long fishing rod, and connecting it with the condenser of the electrometer, the leaves of which will diverge sensibly when there is no sign of any thun- der storm. Near the earth, (say within three or four feet,) no evidence of free electricity can be detected, and as we rise in the air, its force constantly increases. Becquerel and Breschet, sent up arrows, attached to a tinsel cord ninety yards long, from the top of the great St. Bernard, while the other end was connected What of the telegraph? 964. What is said of free atmospheric electricity ? How does height affect its developement 1 26* 610 ELECTRICITY. with the condenser of an electrometer ; they found that the gold leaves diverged in proportion as the arrow rose higher. This phenomenon is most striking during fogs and in cloudy weather, when no lightning is commonly seen. Crosse, of Eng- land, had over a mile of insulated wire sustained on poles one hundred feet high above the tall trees of his park, connecting pointed conductors with his laboratory, where he has frequently collected, during a heavy fog, electricity enough to charge and discharge a battery of fifty jars, and seventy-three square feet of coated surface, twenty times in a minute, with a report as loud as that of a cannon. It appears from experiments like these and others made chiefly by Ronald's, of Kew, that the atmospheric electricity increases and decreases daily, twice in twenty-four hours, and the following gene- ral results are established. 1st. The electricity of the air is always positive, is fullest at night, increases after sunrise, diminishes towards noon, increases again towards sunset, and then decreases towards night, after which it again increases. 2d. The electrical state of the apparatus is disturbed by fogs, rain, hail, sleet or snow. It is negative when these approach, and then changes frequently to positive, with subsequent continued changes every three or four minutes. 3d. Clouds also, as they approach, disturb the apparatus in a sim- ilar way, and produce sparks from the insulated conductor in rapid succession, so that an explosive stream of electricity rushes to the receiving pole, which should be passed off to the earth. Similarly powerful effects freqently attend a driving fog and heavy rain. The subject of atmospheric electricity, especially the descrip- tion of electric meteors, is more properly referred to meteorology. DYNAMICAL ELECTRICITY. GALVANISM OR VOLTAISM. 965. Discovery of galvanism. In 1786, Luigi Galvani, pro- fessor of anatomy in the University of Bologna, while engaged upon a long series of observations on the effects of atmospheric electricity upon animal organisms, noticed that the legs of some frogs, prepared for experiments, became convulsed, although dead and mutilated when the vertebrae, with portions of the lumbar What were Crosse's experiments? What general results follow? 965. Give the history of Galvini's discovery. DISCOVERT OP GALVANISM. 611 nerves, were pressed against the iron railing of the window bal- cony where they were placed, awaiting the use for which they had been designed. Repeating this novel and curious observa- tion in various ways, he soon found that 584 the convulsions were strongest when he made connection by means of two metals between the lumbar nerves, and the exte- rior muscles denuded of the skin, as shown in fig. 584, where rods of copper and zinc, being thus held, convulse the leg into the position shown by the dotted line. To repeat Galvinrs experiment, strip the skin from the legs of a vigorous frog, and cut the animal in two, an inch above the thighs. Ex- pose the lumbar nerves within and on either side of the back bone, by pushing aside the muscles with the finger, so that the point of an arc of the two metals may touch the nerves ; then bring the other metal rod into contact with any portion of the outer surface, and strong twitchings will be developed as if the animal was alive, both on touching and removing the rod, even some hours after death. Upon this fundamental observation a new science has grown up, that of dynamic electricity, or galvanism. It is true, Galvani, Avho was an anatomist and physiologist, and not a chemist or physicist, did not work out all the teachings of his own discovery, being more interested in demonstrating, as he did, the existence of a true ani- mal electricity, developed between the outer surface and the nerves, while he left to others, and chiefly to VOLTA, the physical branch of the subject, devoting the few remaining years of his life to the study of animal electricity, never indeed accepting Volta's doctrines ; and dying in 1798, before his pile was given to the world. In this de- partment of vital electricity, his labors have been justly appreciated only in our time, having been naturally eclipsed in his own by the splendid discovery of the voltaic pile, and the crowd of wonders fol- lowing in its train. Galvani regarded the convulsions of the frog as excited by a nervous or vital fluid, (the galvanic fluid,} which passed from the nerves to the muscles by way of the exterior communication estab- lished between them : this fluid, in his view, existed in the nerves, it traversed the metallic arc, and falling on the muscles, it contracted them, like the electric discharge. The story usually found in text books, of the accidental discovery, How is his experiments repeated ? Compare what is said of Volta and Galvani. What was Galvani's vital fluid? Give other facts in this history. 612 ELECTRICITY. in 1790, of the new science by the twitching of frog's legs, prepared for the repast of Madame Galvani, is a fabrication of Alibert, an Italian writer of no repute. Galvani had then been for eleven years engaged upon a laborious series of electro-physiological experiments on this subject, using frog's legs as electroscopes. JSTo great truth was ever discovered by accident. Years of laboriousVesearch had prepared the way to this discovery. It is undoubtedly true that what we find is often more important than what we seek, but it is research and not accident which makes the discovery. Every hypothesis is good which bears fruit in discovery; but to accept the discovery and reject the hypothesis when no longer fruitful, requires all the self-denial of the highest philosophy, and is the peculiar attribute of the greatest minds. 966. Origin of Volta's discovery. Adopting at the outset with the greatest enthusiasm the vitalist hypothesis of Galvani, Volta came, after no long time, to the conviction that the electrical ef- fects attributed by Galvani to the animal electricity of the frog, were really due to the contact of dissimilar substances, and that the frogs limbs were only the sensitive electroscope, adapted to in- dicate the electrical current developed by the two unlike metals. Thus originated his celebrated ' contact theory ;' a view of the source of dynamic electricity, that long held almost universal sway over scientific opinion until gradually supplanted by the electro chemical theory, which refers the phenomena to chemical action. By the use of his condensing electrometer, (944,) Volta sought to establish the contact theory by a great number of well-devised ex- periments. Being assured of the passive state of the electrometer, he established communication between the earth and the upper plate by the moistened fingers, while at the same time a bit of zinc plate held also in the moistened fingers of the other hand is placed in con- tact with the lower plate ; after a single instant, contact is broken, and on raising the upper plate, the gold leaves diverge. Whence the electricity ? Volta replied, ' from the contact of the two unlike sub- stances,' overlooking the fact that there was a chemical action, due to the effect of the moist fingers on the zinc. As the plate touched by the zinc became positive, and the copper negative, he assumed that there was an ' electromotive force 1 capable of developing these electrical states in the two metals as a result of simple contact. This experiment was repeated with conductors of every sort, and always, What is said of discovery by accident 1 966. "What was Volta's hypothesis ] How did Volta seek to establish the contact theory 1 Whence did he derive the electricity 1 How did he classify con- ductors ? 613 when one of them was an alterable substance, with the same results. He divided conducting bodies into two classes ; the first class, in- cluding the metals, metallic ores and carbon, he calls electrometers ; the second class contains liquids, saline solutions, animal tissues, tfcc. He found that a double combination of three elements, so ar- ranged that their order was reversed, neutralized each other, and produced no spasm in the frogs legs, which he uniformly used as an electroscope. This was in 1796, four years in advance of the date usually assigned as that of the invention of the pile. Passing over the long controversy between Volta and his cotempo- raries, we come to the essential fundamental fact of Volta's discovery, viz : that certain metqls, and 'particularly the oxydizable metals, disen- gage electricity and charge the condenser, when placed in the conditions just described. This discovery immediately led to the second, and by far the most celebrated of Volta's discoveries, viz., the voltaic pile, or battery. 967. Volta's pile, or the voltaic battery. Every form of ap- paratus designed to produce a current of dynamic electricity is called a battery or pile. Volta's original apparatus was, as its name implies, a pile of alternate silver and zinc discs, laid up as in fig. 585, with discs of paper or cloth between them, moistened with brine, or acid water. This arrangement was more commonly made with alternate discs of copper, (C,) and zinc, (Z,) care being taken always to observe the order, copper cloth zinc. The terminal discs were provided with ears for the convenient at- tachment of wires. Thus arranged, the following character- istic results are observed. 1st. The pile being insulated by glass or resin, touch z with the plate of the condenser, (cov- ered with silk,) while the finger rests on c, and then apply the plate to the condenser ; the gold leaves will indicate strong vit- reous electricity. 2d. Reverse this order, touching c with the plate while the finger is on z, and a strong charge of resinous electricity is received. The pile may be regarded as a Ley den jar, or electrical battery, perpetually charged, and capable of re-charging itself as long as the given conditions are maintained. These results may be repeated an indefinite number of times, What is the essential fact of Volta's discovery ? To what did this lead 1 967. What is a pile or battery ? Describe Volta's pile. 614 ELECTRICITY. as long as the cloths remain moist, and the intensity of the ac- tion is directly as the number of plates in the pile. Each touching couplet of copper and zinc may be soldered togeth- 585 er and is then called a couple, pair, or vol- taic element. Any two metals of unlike properties may be substituted for the zinc and copper, with the same results. The end of the pile which yields vit- reous electricity is called its positive pole, and that which yields resinous electrici- ty is called the negative pole ; a name also applied to the wires or conductors connecting the two poles. Arranged as in fig. 585, the pile, when its poles are joined, gives a decided shock, similar to, but less intense, than that from statical electricity ; and on breaking contact between the poles, a brilliant spark of voltaic electricity is seen ; and lastly, if these wires end in points of gold or platina, and are inserted in water, a flow of gas bubbles from them, announ- ces the decomposition of the water ; thus grouping the classification of the effects of the pile into physiological, physical, and chemical phenomena. The discovery of the pile, Volta announ- ced in March, 1800, to Sir Joseph Banks, both in the form just described and also the crown of cnps, (Couronne des tasses,) a se- ries of twenty glass goblets arranged in a circle, with wires connect- ing the -f- and elements of each cup to the opposites of the next. This is the type of all modern batteries with separate cells. He classifies its effects, but makes no mention of its power of chemical decomposition. This last power was immediatel yd is covered by Nich- olson and Carlisle, in London, on the 2d of May, 1800. Aside from Volta's theoretical notions, history will ever assign him What effects are noticed by the condenser? How is the pile to be regarded? Explain the terms couple Voltaic element and poles. How are the effects of the pile classified? When and how did he announce this discovery ? What other apparatus did he also de- scribe at the same time? Who discovered the chemical effects, and when 1 What is said of Volta ? SIMPLE VOLTAIC COUPLE. 615 a high place as a philosopher, and as having by his genius blessed the world by one of the greatest and most fruitful discoveries in science. 968. Quantity and intensity. There is a very marked differ- ence between the tension of the electricity of the Voltaic pile, and that of friction. No sensation follows the touch of either pole of a Voltaic battery alone : both poles must be touched simul- taneously in order to perceive the shock. The projectile force, in voltaic electricity is so nearly null, that in the most energetic and extensive series of cells, the terminal points must be brought in- definitely near, or into actual contact, before any current is estab- lished. The intensity of the battery is however increased by re- duplicating the number of couples of a given size, while the quantity remains unchanged. The quantity of electricity set in motion in the Voltaic battery depends not on the number of the series, but entirely on the extent of surface brought into action in each pair, and also upon the conducting power of the interposed liquid. 969. Simple Voltaic couple. Whenever two unlike sub- stances, moistened by, or immersed in, an acid or saline fluid are brought into contact, a Voltaic circuit is established. The earli- est recorded observation on this subject, (Sulzer's,) was the fa- miliar experiment of a silver and copper coin, or bit of zinc, placed on the opposite sides of the tongue, and the edges brought together, when a sharp, prickly sensation and twinge is felt, and if the eyes are closed, a mild flash of light is also seen. In this case, the saliva is the saline fluid, exciting a Voltaic current due to its chemical effect on the zinc or copper, and the nerves of sense are the eletroscope. The action depends on contact, and ceases as often as this is broken. In fig. 586, we have the simplest form of Voltaic 586 battery, a slip of amalgamated zinc, Z, and another c me of copper, C, immersed in a glass of water, acidu- lated by sulphuric acid. When these strips touch, (either within or without the fluid,) an electrical cur- rent sets up, passing from the zinc to the copper in the fluid, and from the copper to the zinc in the air as shown by the arrows. The polarity of the ends in the air is the reverse of that in the acid, as shown by the signs plus and minus. This is in analogy to the decomposi- 968. What is said of the tension of the Voltaic pile ? What of its projectile force ? What of quantity and intensity? 969. What is essential to a Voltaic circuit ? What was the first observation \ 616 ELECTRICITY.. tion of neutral electricity in a rod of glass or of wax. While contact is maintained, either directly or by conducting wires, evi- dence of chemical action is seen in the constant flow of gas bubbles (hydrogen) from the zinc to the copper, from the surface of which they are given off. This action ceases at any moment when con- tact ceases, and if the separation of the metals takes place in the dark, a minute spark is seen at the moment of breaking contact. The direction of the Voltaic current depends entirely on the nature of the chemical action producing it. Thus if in the ar- rangement just described, strong ammonia water was used in place of the dilute acid, all the electrical relations of the metals and the fluid would be reversed. Since, then, the action would be on the side of the copper, and the zinc would be relatively the electro-negative metal. 970. Electro-positive and electro-negative are relative terms, designed to express the mutual relations of two or more elements in relation to each other. Thus zinc, being a metal very easily acted on by all acid and many saline solutions, becomes electro- positive to whatever other element it may be associated with, unless, as in the last section, the other element is acted on, and the zinc is not, when it becomes electro-negative. Oxygen is an element which acts upon every other, and is therefore the type of electro-negative substances ; gold, platinum, and silver, being among the least easily oxydized metals, become electro-negative substances to all others more easily acted on than themselves, and therefore are fit substances for the negative element of vol- taic couples. In chemical works, tables will be found in which all the elements are grouped in this relative order of electro-pos- itive and electro-negative power. 971. Amalgamation. Commercial zinc is never pure, and the foreign substances which it contains, (carbon, iron, cadmium, &c,) are such as to stand in an electro-negative relation to the zinc. A slip of common rolled zinc, immersed in dilute sulphuric acid, is actively corroded with the escape of abundance of hy- drogen, while if a strip of chemically pure zinc was used, no ac- tion would happen. (De la Rive.) This action of common zinc is called a local action, implying the existence of as many small local Voltaic circuits as there are particles of foreign electro-neg- Explain the simple voltaic circuit from fig. 586. Give the polar- ities in and out of the fluid. What determines the direction of the current? 970. Explain the use of the terms electro-positive and electro-negative. 971. How is commercial zinc affected by acids? TROUGH BATTERIES. 617 ative substances on its surface ; each of which constitutes, with the contiguous particles of zinc, a minute battery, and thus the whole surface is presently corroded and roughened, and the power of the whole couple reduced just in proportion to the ex- tent of this local action. Rub the freshly corroded surface of such a piece of commercial zinc with a little mercury, when instantly it combines with and brightens the whole surface, covering it with a uniform coating of zinc amalgam. This perfectly protects the zinc from local action by covering up the electro-negative points, and makes the whole surface of one electrical name. Zinc, thus amalgamated, may be left indefi- nitely long in acid water, without injury, and when brought in con- tact with the electro-negative element of a Voltaic couple, it becomes a much more energetic source of electricity than before. The discovery of this property, (due to Mr. Kempt,; is hardly less important than the discovery of the battery, for without it, sustained and manageable batteries are impossible. BATTERIES WITH ONE FLUID. 972. Voltaic batteries are constructed for use either with one or with two fluids. The first embraces the original crown of cups, (967,) and all batte- ries with one fluid and a single cell. The batteries with two fluids and two cells, of whatever name, involve a double chemical decom- position, and are, hence, more complicated, but also generally more efficient ; we will consider these separately, remarking, that the inter- est attached to the first class, with a single exception, is now chiefly historical. 973. Trough batteries. The inconvenience of Yolta's original form of the pile, fig. 584, led to placing the elements in a trough, as seen in fig. 587, called, from the inventor, Cruickshank's troughs. Each compound 587 couple of zinc and copper was cemented water tight into a groove, all the zincs facing in one direction. The filling of these cells with dilute acid was a tedious operation, with extended series, Is pure zinc affected ? Why this difference ? How is zinc amalga- mated, and why ? 972. How are batteries classified ? 973. Describe the trough batteries, fig. 587 and 588. 618 ELECTRICITY. and as the zincs were not amalgamated, the best force of the ap- paratus was spent before it could be filled. Davy and Nicholson greatly improved the trough by attaching the couples to a bar of wood by straps c o n m, as in fig. 588, and Dr. Wollaston surround- ed each zinc, z, with the copper, on both sides, thus doubling the effective surface. Thus arranged, the whole series could be plunged at one move- ment into glass cells, a a, or into a porcelain trough divided into cells. It was with a series of 2000 couples r so arranged, each plate hav- ing an effective surface of twenty-two square inches, that Davy, in 1806-8, made a series of experiments remarkable in the history of science. This battery was placed in the vaults under the Royal Institution, where its hydrogen and acid vapors did not annoy the experimenter, and its power was led up by conductors to the laboratory. Hare's ' calorimotor consisted of twenty plates each, of copper and zinc, nineteen inches square, and so constructed in a cubical box as to form but two large elements of fifty square feet each, or two hundred square feet of active surface in both members, all plunged by one movement in a vat of acid. The deflagrators of Dr. Hare as originally constructed were formed of spirals of copper and zinc, rolled with a narrow space between them, and the opposing metals held from contact by wooden strips. Each zinc was 9" X 6", and each copper 14" x 6" ; so that every part of the zinc was opposed to the copper surface ; eighty of these coils were so arranged on bars of wood as to plunge by an easy mechan- ism into glass cylinders containing the acid. The facility of immer- sion and removal of these coils in contact of the acid liquor, made Hare's deflagrators as much superior to the early trough batteries as the batteries of two fluids are superior to Hare's. In a very efficient form of Hare's deflagrator, the members were connected in a box, suspended, to revolve on an axle having another box placed at right angles to the first, so that a quarter revolution of the appara- tus, turned on or off the exciting acid at pleasure, without deranging the connections. A battery constructed for Prof. Silliman, in Boston, in 1836, on the "What is said of Davy's battery ? What are Hare's deflagrators ? What other large single cell batteries are named ? SMEE'S BATTERY. G19 plan of Wollaston and Hare combined, contained nine hundred cou- ples of copper and zinc (10" x 4" each) exposing five hundred and six square feet of available surface, arranged in twelve parallel se- ries, capable of being used consecutively as nine hundred couples, or in three series of three hundred each. One plunge immersed the whole battery, and when new, the arch of flame between its poles measured over six inches. Mr. Crosse, and also Mr. Gassiot, have constructed very extended series of trough batteries for physiological experiments; the former had twenty-four hundred pairs of plates, the cells well in- sulated ; the latter put up three thousand five hundred and twenty cylindrical pairs, placed in cells of varnished glass, and insulated by glass pillars varnished. The batteries were excited by water only. Except for the purposes of low intensity and long continued action, batteries of this description are now no longer constructed. The want of sustained and regular action in all batteries of the original form, has led to the contrivance of other and more scientific batteries ; some of the most valuable of which we will now describe. 974. Smee's battery is formed of amalgamatic zinc and silver, and needs but one cell and one fluid to excite it. The silver plate, fy fig. 589, is prepared by washing in nitric acid to roughen it, and then coating its surface with platinum, thrown down on it by a voltaic current, in that state of fine di- 589 vision, known as platinum-black. This is to prevent the adhesion of the liberated hy- drogen to the polished silver. Any surface of polished metal retains a film of gas with singu- lar obstinacy, thus preventing in a measure the contact between the fluid and the plate. The roughened surface produced from the de- posit of platinum-black entirely prevents this. The zinc plates z z in this battery are well amalgamated, and face both sides of the silver. The three plates are held in position by a clamp &, at top, while the interposition of a bar of dry wood, w, prevents the passage of a current from plate to plate. Water acidulated with one-seventh its bulk of oil of vitriol, or, for less activity, with one-sixteenth, is the exciting fluid. The quantity of electricity excited in this battery is very great, but the intensity is not so great as in the compound batteries pres- ently to be described. This battery is nearly constant, does not 974. Describe Smee's battery. What is said of its value ? 620 ELECTRICITY. act until the poles are joined, and, without any attention, will main- tain a uniform flow of power for days together. A plate of lead, well silvered, and then coated with platinum-black, will answer equally well, and indeed better than a thin plate of pure silver. This battery is recommended over every other for the student, as comprising the great requisites of cheapness, simplicity, and con- stancy. This is the battery generally employed in electro-metal- lurgy. Chester has patented an improved form of this "battery, much used by tne telegraph companies. It is the only single fluid battery now much used in physical experiments. 975. The sulphate of copper battery is designed to use a so- 590 lution of sulphate of copper in dilute sulphuric acid, the copper element being made to contain the exciting fluid. This battery has been a good deal used for electro-magnetic experiments, but it soon becomes incumbered with a pulp of metallic copper thrown down on the zinc. BATTERIES WITH TWO FLUIDS. 976. Daniell's constant battery. This truly philosophical in- strument was invented in 1836 ; up to which time the improve- ments in the original voltaic pile had been only mechanical. Prof. J. F. Daniells, of London, first discovered and applied an effec- tual means of preserving the power and continuing the action of the apparatus for a length of time. All other batteries with two fluids are only modifications of his. It consists of an exterior circular cell of copper, (7, fig. 591, which serves both as a containing vessel and as a negative ele- ment ; a porous cylindrical cup of earthenware, P, (or the gullet of an ox tied into a bag,) is placed within the copper cell, and a solid cylinder of amal- gamated zinc, Z^ within the porous cup. The outer cell, C, is charged by a mixture of eight parts of water and one of oil of vitriol, saturated with blue vitriol, (sulphate of copper.) Some of the solid sulphate is also suspended on a perforated shelf, or in a gauze bag,' to keep up the saturation. The in- ner cell is filled with the same acid water, but with- out the copper salt. For the most constant results, he used saturated solution of blue vitriol, made slightly acid for the outer cell, and for the zinc, 976. What is the sulphate of copper battery ? 976. Describe Dan> iells' constant battery. GROVE'S BATTERY. 621 twenty parts water to one acid. Eight or ten hours is about the limit of its constancy. Any number of cells so arranged are easily connected together by binding screws, the G of one pair to the Z of the next, and so on. The hydrogen from the decomposed water in this instrument is not given off in bubbles on the copper side, as it is in all forms of the simple circuit of zinc and copper ; because the sulphate of copper there present is decomposed in the circuit, atom for atom, with the decomposed water, and the hydrogen takes the atom of oxyd of copper, appropriating its oxygen to form water again, while metallic copper is deposited on the outer cell. No action of any sort results in this battery, if the zinc is well amalgamated, until the poles are joined, and it gives oif no fumes. Ten or twelve such cells form a very active, constant, and economical battery, and two dozen of such are ample for ordinary uses. Hot solutions increase its power, and the ex- tent of zinc surface, and not the diameter of the copper, limits the amount of electrical effect. 977. Grove's nitric acid battery. Mr. Grove, of London, has successfully applied the principle of Daniell's battery, to produce 592 the most powerful and in- tense sustaining battery known. The fluids used are strong nitric acid and dilute sulphuric acid, kept apart by a porous jar. The metals are amalgamated zinc, placed in the sulphu- ric acid of the outer vessel, and platina in the porous vessel : fig. 593, shows this arrangement as complete. The platinum element is seen isolated in fig. 592. The cover, c, upon the vase, V, fig. 593, tends to keep down the strong vapors of nitrous acid evolved when the battery is in action. The binding screws, , 5, serve to unite the 'elements of separate pairs. The zinc here surrounds the platinum, because both that metal and the nitric acid are to be economized as much as possible, being the On -what does its efficacy depend 1 Describe its action and theory. 977. What is Grove's battery ? 622 ELECTRICITY. costly parts of the arrangement. From six to ten parts of water are used in &, to one of acid. The action of this battery is intense and splendid. The hy- drogen is immediately engaged by the nitrous acid which it de- composes very readily. There is therefore a double chemical ac- tion, and an increased flow of electricity, since no part of the power is lost in combination. The fumes of nitrous acid are partly ab- sorbed by the nitric acid, turning it at last intensely green ; but enough are evolved to render it important to set the apparatus in a clear space, or good draught. Four cells, with platinum three inches long by half inch wide, decomposes water rapidly ; and twenty such cells form a battery giving intense effects of light. Platinum, in the nitric acid battery, is estimated as sixteen or eighteen times more powerful than copper in Danielle' battery ; that is, six square inches of platinum is as efficacious as one hundred square inches of copper ; and Peschell found three hundred and forty times as much surface of copper was needed, in a spiral battery on Hare's construction, as of platinum to insure equal effects. A Grove's battery, constructed by Jacobi, of St. Petersburgh, con- tains sixty-four platinum plates, each thirty-six square inches surface, or combined, sixteen square feet. This would be by comparison equal to a Daniells' battery of two hundred and sixty-six square feet, or a Hare's battery of about five thousand five hundred square feet. Grove's battery is rather costly, and very troublesome to manage, as are all batteries with double cells and porous cups. 978. Carbon battery. The great cost of large members and extensive series of Grove's platinum battery led Prof. Bunsen, of 594 Marburg, to use the carbon of gas coke as a substitute for the platinum. Prof. Silliman, jr. in 1842, described a battery (see Sill. Jour. [1] xliii, 393, and xliv, 180) in which natural plumbago was used in place of the platina of Grove's arrangement. This was before Bun- sen's apparatus was known of in this country. Fig. 594 shows the original form of Bunsen's cells. "Where the carbon, C, is contained in an exterior vase, V, of nitric acid, the amalgamated zinc is in a porous cup, P, of dilute sulphuric acid. The ob- jection to this arrangement is the large consurnpion of nitric acid and smallness of the zinc. In the au- Compare the efficiency of platinum and copper. DRY PILES. 623 thor's plan, afterwards adopted essentially by M. Deleuil, the car- bon was in the porous cup surrounded by the zinc. In fig. 595, this arrangement is shown in de- 595 tail. P, is the pile complete. F, is the jar of hard pottery to contain the zinc, Z, and the dilute sulphuric acid ; V is the porous vase, to contain the carbon, G, with its nitric acid. The attachment of a conductor to the carbon is accomplished by a conical hole in the centre, into which a plug of hammered copper is crowded with a wrenching motion. If the hard carbon of the gas retorts is used, (it is unquestionably superior,) a copper band is attached to its top by electro-galvanic soldering. The carbon of Bunsen's cells is prepared by pulverizing, and baking in moulds, the coke of bituminous coal. Fig. 596 shows a series of ten cups of the carbon battery arranged for use, the alternate members be- 596 ing joined by binding screws, as made by Deleuil, of Paris, each zinc being twenty-two centime- tres, (eight and three-quarter inches) high. As the electro-mo- tive energy of the battery de- pends on size as well as number,! these large members have great advantages. The author demonstrated, in 1842, (loc. cit.) that car- bon was nearly if not quite as good as platinum surface for sur- face. A battery of fifty cells, like fig. 596, costs fifty-five dollars in Paris, and with such a series, all the most splendid effects of the elec- tric light, deflagrations, and chemical decompositions can be very sa- tisfactorily shown. 979. Dry piles of Zamboni and DeLuc. These are constructed of discs of metallic paper, as of copper and zinc, (called gold and silver papers,) placed back to back, and alternating as in the pile of Volta, (966,) all the coppers facing in one direction. Sometimes paper gilded on one side and zinc on the other ; or zinc paper smeared with black oxyd of manganese and honey on the other side, is used, and with more marked effects. Some hundreds and even thousands of these discs, as large as a quarter dollar, are crowded into a glass tube varnished within 978. "What is the carbon battery 1 Describe it from fig. 594. De- scribe the arrangement in fig. 595. What is said of its size, power, and cost 1 624 ELECTRICITY. and without, just large enough to receive them. Screw caps of metal compress and retain the discs, forming at the same time metallic connections with the outer pairs to propagate the elec- trical effect. A feeble current is thus set up, which may last for years ; but if the paper has been artificially dried so as to free it from all absorbed moisture, no current exists. Zamboni, (1812,) and DeLuc, (1810.) who first constructed piles of this sort, arranged them in pairs to ring bells by the vibration of a small electric pendulum, (fig. 571,) alternately attracted and repelled between the columns, which are in the condition of a perpetually charged Leyden jar of low tension. A set of these bells rang in Yale College laboratory for six or eight years unceasingly. BOHNENBERGER'S ELECTROSCOPE is constructed on this principle. B and C, fig. 597, are the poles of two dry piles, between which hangs a single gold leaf, ending in the knob, D. When any feebly electric body is approached to D, the gold leaf at once declares its electrical name, by being attracted to its opposite. This is undoubtedly one of the most delicate electroscopes known. 980. Other voltaic batteries exist in great va- riety, but involving no principle not already ex- plained. Some have special adaptation to a partic- ular use, like Chester's form of Smee's battery for telegraphic use ; Farmer's copper battery ; the bat- tery of Bagration, of zinc and copper in moist earth ; or Grove's oxygen and hydrogen gas battery, so instructive theoretically. But further descrip- tions are excluded by want of space. 598 FOLAKITY, RETARDING POWER, AND NOMENCLATURE OF THE VOL- TAIC PILE. 980. Polarity of the compound circuit. In batteries of two or more couples, connection is formed, not as in the sin- gle couple, (969,) between members of the same cell, but between those of dif- ferent names in contiguous cells, as in fig. 598, where 979. How are dry piles constructed ? What of their endurance ? How did Zamboni arrange them ? "What is Bohnenberger's electro- scope ? 980. What is said of other piles ? GROUPING OF ELEMENTS. 625 the copper of 1 joins the zinc of 2, and so on. The current flows from the zinc to the copper in the fluid, but from the cop- per to the zinc in the air, (fig. 586,) both in simple and compound circuits. This is important to 599 be remembered, since the zinc is called the electro-positive ele- ment of the series, although out of the fluid it is negative- Consequently, in voltaic decom- positions, the element which goes to the zinc pole is called the electro-positive, and for the same reason, that which goes to the copperjs the electro-negative element. The terminal plates, Zand C, in 1 and 5, fig. 598, are not concerned in the electrical effect, being in fact only con- 600 ductors of the electricity, and hence they may be removed as in fig. 599, without alter- ing the power or nature of the battery. They serve, in fact, merely as a convenient 1 2 "3 f mode of joining the poles, as in fig. 600. The apparent polarity of the simple circuit is therefore the reverse of that of the com- pound circuit ; but an attentive observation of these explana- tions, and of the figures, will avoid all confusion on this point. 982. Grouping the elements of a pile in various numerical re- lations, is an important means of modifying its power, and the character of its effects, already ex- 601 plained in 968. Take, for example, six cups, as in fig. 601, arranged in consecutive or- der, and we have, owing to the resist- ance to the electric now, the maxim- um intense effects possible with such number. Changed to 2 groups of 3 each, and the quantity is doubled, with half of the intensity, fig. 602. In fig. 603, are three groups of two cups each, so arranged as to present three times the surface in 601, with a proportionate loss of intensity. Lastly, in -fig. 604, each zinc, and each copper, joins one conmon conductor, each on its own side, 981. Explain the polarity of the simple and compound circuit 27 626 ELECTRICITY. throwing the six couples into one surface of six-fold extent to 601. The arrangement may be expressed, assuming the resistance of a single cup as unity, thus, 1. = 1'5. | = 0'666. -l = 0'166, and so for any number of couples. 983. Electrical retarding power of the battery. Ohm's law. A certain resistance to the passage of a voltaic current is offered by every additional element placed in the circuit as well as by increased length of conductor. The new properties thus acquired by the compound circuit, have been already alluded to. (908.) Ohm, of Berlin, in 1827, first demonstrated mathematically the law regulating the flow of electricity in the compound bat- tery. As the apparatus is composed solely of conductors of dif- ferent retarding power, the electric current must proceed, not only along the connecting wire, from pole to pole, but also through the whole apparatus ; the resistance offered to the passage of the current consists therefore of two parts, one exterior to, and one within, the apparatus. Let the ring, a b c, in fig. 605, represent a homogeneous conductor, 605 and let a source of electricity exist at A. From this source the electricity will diffuse itself over both halves of the ring, the positive passing in the direction a, the negative in b, and both fluids meeting at c. Now it fol- lows, if the ring is homogeneous, that equal quantities of X- ^s electricity pass through all sections of the ring in the same time. Assuming that the passage of the fluid from one cross section of the ring to another, is due to the difference of electrical tension at these points, and that the quantity which passes is proportional to this difference, of tension, the consequence is, that the two fluids proceeding from A, must decrease in tension the farther they recede from the starting point. This decreasing tension may be represented by a diagram. Sup- 606 pose the ring in fig. 606, to be stretched out to the line A A'. Let the ordinate A B rep- j^^v resent the tension of positive electricity at ^v j A, and A' B 1 the negative tension at A', then the line B B' will express the tension for all parts of the circuit by the varying lengths of A B, A B', at every point of A c E c A. Hence Ohm's formula F = , where F represents the R 982. How may the elements be grouped, and with what effects ? 983. What is said of the retarding power of the battery ? n H I ' FARADAY'S NOMENCLATURE. \ ^ 627 strength of the current JS, the electromotive force of the battery, and R, the resistance. Therefore the greater the length of the cir- cuit, the less will be the amount of electricity which passes through any cross section in a given time. In exact terms, this law states that the strength of the current is inversely proportional to the resist- ance of the circuit, and directly as the electromotive force. But in the simplest voltaic current, we have not a homogeneous conductor, but several of various powers. To illustrate this, let the conductor A A\ fig. 589, consist of two portions having different cross sections. For example, let the cross sec- tion A d be n tunes that of d A ; then, if equal quantities pass through all sections in equal times, if through a given length of the thicker wire no more fluid passes than through the thinner wire, the difference of tension at both ends of this unit of length of the thicker wire must be only th of what it is in the latter. Thus, " the electric fall," as Ohm ft calls it, will be less in the case of the thick wire than of the thinner, as shown by the line B c in the figure. The result is expressed in the law that the " electric fall" is directly as the specific resistances of the conductors, and inversely as their cross sections. Hence, the greater the resistance offered by the conductor, the greater the fall. The very simplest circuit must therefore present a series of gradients expressive of the tension of its various points as one for the con- necting wire, one for the zinc, one for the fluid, and one for the cop- per. The electro-motive force of a voltaic couple (" E " of Ohm's formula) may be experimentally determined, and is proportional to the electric tension at the ends of the newly broken circuit. 984. Faraday's nomenclature. Dr. Faraday has introduced certain terms into the language of electrical science, which are generally adopted for their convenience, and their absence of as- sumed, or theoretical notions. Electrode is used in place of pole, to which latter term, mean- ing the terminal wires of a battery, Davy and others seemed to attach a sense as if it possessed a certain attractive force, like the pole of a magnet. Electrode, (from electron, and odos, a way,) means simply the way or door by which a Voltaic current en- ters or leaves a substance. Anode is that surface of a body receiving the current, or the Explain Ohm's theory from figs. 605, 606. State the law. State it for the battery from fig. 607. 984. What is said of Faraday's no- menclature 1 628 ELECTRICITY. positive side of the series, from ana, upwards, (as the sun rises,) and odos, a way. Cathode, is that surface of a body from which a current flows out towards the negative side of the series : (from Jcata, downwards, as the sun sets, and odos, a way.) The observer is supposed to face the north, with the positive of the battery on his right hand, and its negative on his left. Electrolyte,, is any substance capable of separation into its constituents by the influence of a Voltaic series, (from electron and luo, to set loose.) Electrolysis, the act of decomposition. Electrolyzed, and electrolyzable, are obvious derivatives from the same words. Ions, are the elements into which an electrolyte is resolved by tho current. These are either anions, elements formed at the positive electrode, or cations, ions found at the negative electrode. Hereafter we shall employ these terms when they are appropriate. THE EFFECTS OF THE VOLTAIC PILE. 985. The Voltaic spark and arch. In 1808, Davy, with the extensive series of two thousand couples at the Royal Institu- tion, first demonstrated the full splendors of the Voltaic arch between electrodes of well-burned charcoal. However powerful 608 the series may be, no eifect is in the air seen until the points of the carbon elec- trodes are brought into actual contact, or at least insensibly near. Herschel noticed that an electrical spark from a Ley den jar, sent through the carbon points, when near each other, established the flow of the voltaic current, by pro- jection no doubt of material particles. When the spark passes, then the electrodes may be withdrawn, as in fig. 608, and the arch of electric flame connects them with a white and violet light of intolerable brightness ; several inches in length if the pile is very powerful. This arch of seeming flame is not pro- duced by the combustion of the carbon electrodes, since it exists, with even greater brilliancy, in a vacuum, or in an atmosphere of nitrogen or carbonic acid. M. Despretz states that in vacuo with a powerful pile, the voltaic arch may be formed at some centimeters distance, without contact. Fig. 609, shows a con- Explain Faraday's nomenclature. 985. What is said of the Vol- taic arch ? At what distance does the spark pass? Describe the Vol- taic arch. What is said of its constitution ? What origin has it secured ? REGULATORS OF ELECTRIC LIGHT. 629 venient apparatus for this experiment in vacuo, or in various gases, as in Davy's original experiments. The Voltaic arch is accompanied by a loud hissing or rushing sound, 609 due to the mechanical removal and transportation of particles of carbon from the positive to the neg- ative electrode by which the former is diminished in length, or made cup-shaped, while the latter is sensibly elongated, as first noticed and described by Prof. Silliman, in 1822, (Sill. Jour. [1] v. 108,) in the use of a powerful deflagrator constructed by Dr. Hare. Through colored glasses, these particles of carbon 610 can be conveniently observed, apparently moving slowly from pole to pole, and giving unquestionably that oval form to the arch, seen in fig. 609, when the electrodes are vertical, and the negative carbon is appa- rent. There is also distinctly to be seen, a "* certain structure in zones, or bands of dif- ferent brilliancy. When the image of the carbon electrodes is projected on a screen, as was first done by Foucault with the electric lantern, the growth of the negative and the decrease of the positive electrode is easily observed, without injury to the eyes. The negative carbon is seen 612 to glow first, as if the light 611 originated there, but as the experiment advances, the positive carbon becomes the most brilliant, and maintains this superiority during the experiment. The Voltaic arch is magnetic, or capa- ble of influencing the magnet, by the ap- proach of which it is deflected, as in fig. 612, or even made to revolve with a loud hissing noise ; a fact first observed by Davy, but since carefully stu- died by De la Rive, Quet, and Despretz. 986. Regulators of the electric light. Since the introduction of powerful constant batteries, it has been possible to use the electric light for scientific and economical purposes. For this purpose regulators have been devised to render the light "What of the transfer of matter between the electrodes ? How may the points be safely observed ? Describe the phenomena on a screen ? How does the magnet affect the arch ? 630 ELECTRICITY. constant, by approaching the electrodes in proportion as they are 613 consumed. In fig. 613, is shown that of Deleuil, of Paris, and its details, in fig. 613. The two carbon points, P and JV, are held in position by two vertical rods, of which the lower one, P, is moved upwards by the mechanism in fig. 614, while the upper one, N, passes through the ball, D, with friction. The flow of the current is shown by the arrows arriving at G, and departing at H. The frame of the apparatus is of cast iron. The slightly concave mirror, S, is for cer- tain purposes replaced by a large parabolic mirror. When the zinc electrode is con- nected with G, and the carbon with H, communication is established by depressing JV with the hand. As the current in its cir- cuit passes through a coil of wire sur- rounding the electro-magnet, E, fig. 614 ; the soft iron am- ature, m, on the lever A, is drawn up to E, so long as the current flows, but if it is in- terrupted, then m falls and the i lever A is drawn upwards by the spring, B, acting against the fulcrum, L : the effect of that motionTs to raise the electrode, P, by a tooth I, catching in notches on the upright, J?. In this way connection is again estab- lished ; and when this simple mechanism is once adjusted, 614 it will act for hours with great certainty, maintaining the light constant. In Silliman's Chemistry, p. 126, Duboscq's regulator is figured and described, a form of the instrument, well adapted to optical purposes, and called the photo-elec- tric microscope. 987. Properties of the electric light. Like the solar light, it is unpolar- ized. It explodes a mix- ture of hydrogen and chlo- rine, and acts on chloride of silver, and other pho- tographic preparations, like the sun. Bodies made phosphores- 986. Describe the regulator of Deleuil and its action. Figs. 613, 614. HEAT OP THE VOLTAIC ARCH. 631 cent by the sun, are similarly affected by the electric light In 1842, Silliman took Daguerreotypes with it, and it it is now used in preference to solar light, for the purpose of taking microscopic photographs. (Duboscq.) Fizeau and Foucault, have compared, by photometric measure- ment, the light from ninety-two carbon couples, arranged in two se- ries of forty-six, (601,) with the solar beam, and also with the oxyhy- drogen or Drummond light. In a clear August day, with the sun two hours high, the electric light, assuming the sun as unity, bore to it the ratio of 1 : 2'59, i. e., the sun was twice and a half more pow- erful, while the Drummond light was only one one hundred and forty-sixth that of the sun. Bunsen found the light from forty-eight elements of carbon, equal to five hundred and seventy-two candles. The intensity of the electric light depends far more on the size of the individual members of the pile than on their number. The ef- fect from forty couples was found by Fizeau and Foucault to be about the same as that from double the number, when the eighty were ar- ranged consecutively, as in fig. 601, while, with the same elements in two parallel series, there was a very great increase of effect. Fraun- hofer showed that the spectrum of the electric light was distinguish- ed from that of the sun by a very bright line in the green, and a somewhat less luminous one in the orange. (744.) Dove has lately shown, (Poggendorff's Annalen, 1857, N"o. 6,) that this light has two distinct sources: 1st, the ignition or incandescence of the trans- lated particles, passing in the course of the discharge : 2d, the proper electric light itself. Draper has shown that the spectrum from a glowing platinum wire heated by the battery, contains no lines, BO that it is strictly white. (Sill. Jour. [2] viii, 340.) It is not only par- ticles of carbon which pass in the Voltaic arch, but of whatever conductor may form the positive electrode, as platinum, or any metal, and the light varies in its optical properties with every change of the elect-rode. (Wheatstone.) 988. Heat of the Voltaic arch. Deflagration. When the positive electrode is fashioned into a small crucible of 615 carbon, as in fig. 615, gold, silver, platinum, mercury, and other substances, are speedily fused, deflagrated, or volatized, with various colored lights. The fusion of platinum (like wax in a candle) before the Voltaic arch is significant of its intense heat, and still more the volatilization and fusion of carbon, a result first announced by Silliman in 1822, and since confirmed by Despretz, 987. What are the properties of the electric light ? "What is the comparison with the sun, and drummond light ? On what does the intensity depend ? What is said of the electric spectrum 1 What are Dove's and Draper's results ? 082 ELECTRICITY. who, by the union of the heat of six hundred carbon couples ar- ranged in numerous parallel series, and conjoined with the jet of an oxyhydrogen blow-pipe, and the heat of the midday sun, focalized by a poweriul burning glass, succeeded in volatilizing the diamond, fusing magnesia and silica, and softening anthracite. The diamond is also softened, and converted into a black spongy mass resembling coke, or more nearly, the black diamond found in the Brazilian mines. A delicate stream of mercury being allowed to flow from a narrow elongated funnel, (the negative electrode,) upon a surface of mer- cury in a glass vase forming the positive electrode, is deflagrated with transcendent splendor. Many yards of number twenty plati- num wire, held between the electrodes, may be kept in the full glow of white heat for a long time. The teacher can devise many pleas- ing additional experiments, as drawing the arch beneath water, oil, and other liquids, from points of carbon, or from platinum and steel wires. When a* fine platinum wire is made the positive electrode, and a solution of chloride of calcium, or any other metallic chloride, is made the negative electrode, on touching the surface of the liquid with the point of the fine wire, if the series is powerful the wire is fused on the surface of the liquid, evolving a light of surpassing beauty, whose color is that appropriate to the metal in solution ; e. g., from calcium salts, violet-red, from sodium, yellow, from barium, reddish-yellow, from potassium, violet, from strontium, red, &c. These beautiful facts were first noticed by Dr. Hare. Dr. Page has described a singular motion imparted by the current to globules of pure mercury, placed in a shallow dish, and covered by acidulated water, the globules elongate to ovoida and move act- ively about, one end, being that towards the -f- pole, clouded by es- caping gas bubbles. If the mercury contains zinc, the position of the clouded end is reversed. (SHI. Jour. [2] xi 192.) 989. Measurement of the heat of the Voltaic current. By means of a long wire coiled into a close spiral, and inclosed in a calorimeter (594,) of glass, containing water, Becquerel and oth- ers have established the laws regulating the flow of heat in the electric current, by its effect in elevating the temperature of the water. A coil of platinum wire contained in the bulb of a Sanc- torio's thermometer, (507,) becomes a means of estimating the heat of currents too feeble to be otherwise measured. The re- sults are, that when a voltaic current traverses a homogeneous wire, the quantity of heat in a unit of time is proportional What varies the light ? 988. How are the heating effects of the arch shown ? What evidences of its heat are given 1 What hap- pens when a fine platinum wire is deflagrated from liquid surfaces ? What of Voltaic motions ? 989. How is the heat of the Voltaic arch measured ? ELECTROLYSIS OP WATER. 633 1. To the resistance which the wire opposes to the passage of the electricity : 2. To the square of the intensity of the current. The inten- sity of a current is measured by the quantity of water which it will decompose in a given time. For a given quantity of electricity, the elevation of tempera- ture at different points on a conducting wire, is in the inverse ra- tio of the fourth power of its diameter. Draper has applied the co-efficient of expansion to determine the degree of heat corresponding to a particular color. (519.) 990. The chemical effects of the pile are most wonderful, and the present advanced state of chemical science is largely attrib- utable to the flood of light shed by the researches of Davy and Faraday upon the electrical relations of the elements and the decomposition of compounds by the Voltaic circuit. * In 1800, immediately after Yolta's announcement to Sir Joseph Bank's (967) of his discovery of the pile, Messrs. Nicholson and Car- lisle, constructed the first pile in England, consisting of thirty-six half crowns, with as many discs of zinc and pasteboard, soaked in salt water. Observing gas bubbles arise when the wires of this pile were immersed in water, Nicholson covered them with a glass tube filled with water, and on the second of May, 1800, completed the splendid discovery, that the Voltaic current had the power to decompose wa- ter and other chemical compounds. Stimulated by so fine a result, chemists and physicists everywhere repeated the experiment, per- fecting the methods of obtaining both the oxygen and the hydrogen gases in a separate condition. The chemical theory of the pile, ori- ginally advanced by Fabbroni, a countryman of Volta's, some years before, was taken up and ardently advocated by Davy, who, in 1801, had succeeded to a place in the laboratory of the Royal Institution : where, on the 6th of October, 1807, he made, by the Voltaic pile, the memorable discovery of potassium, the metallic base of potassa, before regarded as a simple substance ; and soon after established the startling truth that all the earths and alkalies, until then esteemed simple substances the whole crust of the globe in fact were oxyds of metals, whose existence had hitherto been unsuspected. 991. Electrolysis of water. Voltameter. The Voltaic de- composition, or electrolysis (984) of water is the finest possible illustration of the chemical power of the pile. Water is a com- pound of oxygen and hydrogen gases, in the proportions of one Give the resulting laws ? 990. What is said of its chemical effects? Who first observed them ? What is said of Davy's results ? 27* 634 ELECTRICITY. measure of the former to two of the latter. When two gold or platinum wires are connected with the opposite ends of the bat- tery, and held a short distance asunder in a cup of water, a train of gas-bubbles will be seen rising from each and escaping at the 616 surface. If the electrodes are not of gold or platinum, the oxy- gen combines with them, and only hydrogen escapes, as in Nicholson's original experiment. With two glass tubes placed over the platinum poles, fig. 616, we can collect these bubbles as they rise. The gas (hydrogen) given i off from the negative electrode is twice the volume of that obtain- ed from the positive. When the tubes are of the same size, this difference becomes at once evident to the eye. By exam- ining these gases, we shall find them, respect- ively, pure hydrogen and oxygen, in the pro- portion of two volumes of the former to one of the latter. Agree- ably to principles already explained, (981,) the oxygen (electro- negative) appears at the + electrode, and the hydrogen (electro- positive) appears at the electrode. The rapidity of the de- composition is greater when the water is made a better conduc- tor, by adding a few drops of sulphuric acid ; and for rapid elec- trolyses the number of couples in the series should be increased to overcome, by superior tension, the low conducting power and chemical affinity of the electrolyte. If a single tube only covers both electrodes, as in fig. 617, the total electrical effect is easily measured by the graduation of the tube, the quantity of gases given off in a unit of time being directly as the current. 618 The contents of this tube will explode if a light- ed match is applied to them, or if an electric spark passes through them. Such an instrument is a Voltameter. A convenient form of this instru- ment is seen in fig. 618, made of a common bottle filled with acid water ; the platina electrodes pass ^through the cork and end in two plates of platina, I while a bent gas tube of glass conveys off the ^accumulating gases as fast as they are evolved by 'the electrolysis. 990. Describe the electrolysis of water. What is a Voltameter? ELECTROLYSIS OF SALTS. 635 992. Laws of electrolysis. From a great number elaborate experiments, the accuracy of which remains unshaken, Faraday has deduced the following general laws of electrolysis. 1st. The quantity of any given electrolyte, resolved into its constituents by a current of electricity, depends solely on the amount of electricity passing through it, and is independent of the form of apparatus used, the size or dimensions of the elec- trodes, the strength of the solution, or any other circumstance. Hence, the amount of water decomposed in a given time in the Voltameter, is an exact measure of the quantity of electricity set in motion. 2d. In every case of electrolysis, the elements are separated in equivalent or atomic proportions, and when the same current passes in succession through several electrolytes in the same cir- cuit, the whole series of elements set free are also in atomic pro- portions to each other. Faraday hence infers that the amount of electricity required to resolve a chemical combination, is in constant proportion to the force of chemical affinity by which its elements are united, 3d. The oxydation of an atom of zinc in the battery, generates exactly so much electricity as is required to resolve an atom of water into its elements. Thus 8*45 grains of zinc dissolved in the battery, occasions the electrolysis of 2 -35 grains of water. But these numbers are in the ratio of 32 -5 : 9 the equivalents, respectively, of zinc and of water. Hence follow these corollaries : First, that the source of Voltaic electricity in the pile is chemical action solely. Secondly, that the forces termed chemical affinity and electricity, are one and the same. One or two additional illustrations of these laws will be in- structive here. 993. Electrolysis of salts. In the bent tube, B A, fig. 619, put a solution of any neutral salt ; i, e., sulphate of soda, and diffuse the blue tincture of a purple cabbage in the liquid. Let the cur- rent of a Voltaic pile communicate with this saline solution by two platinum wires, dipping into the legs of the tube presently the blue color of the solution is changed on the positive side for red, and the negative for green, indicating the presence of an acid set free in A, and of an alkali in B. If the action is kept up, the whole of the blue liquid is changed to red and green. 992 Who established the laws of electrolysis? W-hat is the first law ? What is the 2d law ? What the 3d ? Illustrate these. What corollaries follow ? 993. Describe the electrolysis of salts. 636 ELECTRICITY. Transpose, then, the -f and wires, so as to reverse the direc- tion of the current ; presently the red and green change back to 619 blue, and in a short time that which was red becomes green, and vice versa. This is a case of electro- lysis in which the electrolyte (sul- phate of soda) is changed, not into its ultimate elements, but only into the acfH and alkali, which may be called its proximate constituents ; any other saline fluid may be sub- stituted with similar results. If an alkaline chloride is used, i. e. t common salt, the free chlorine re- volved on the -f- side, discharges all color, while the soda produces on the side its appropriate green tint. If a metallic salt, e. g., sulphate of copper, or ace- tate of lead, is used in A B, then on the side, metallic cop- per or lead is evolved, while on the -{- side is the free acid before in combination in the salt. A more surprising example of the apparent transfer of elements 620 under the power of the Voltaio current is illustrated in fig. 620, where in the center glass, B, of the three wine glasses, ABC, is a solution of sulphate of soda, while A and C contain only pure water, blued with cabbage tincture. Filaments of moist cotton wick connect the three glasses, and the electrodes are introduced into A and C, when the same series of changes, already described in fig. 619, take place, with the same reversals when the electrodes are transferred. B remains apparently unchanged while C is reddened and A becomes green, or vice versa. There is in fact nothing more wonderful in this case than in the last, only the dissection of the process into three parts, makes the result still more striking. In place of A, B, C, any number of glasses, with different salts and compounds, may be substituted, with results conformable to the law in 992. 994 Electro-metallurgy. The electrotype. The cold cast- ing of metals by the Voltaic current, is a fine example of the rich gifts made by abstract science to the practical arts of life. Give a more surprising example with three glasses, fig. 620. ELECTRO-METALLURGY. 637 Every Daniell's battery is in fact an electro-metallic bath, in which metallic copper is constantly thrown down from solution, of a firm and flexible texture. The very simple apparatus required to show these results experi- mentally, is represented in the fig. 621. It is noth- 621 ing, in fact, but a single cell of Daniell's battery. A glass tumbler, S, a common lamp-chimney, P, with a bladder-skin tied over the lower end and filled with dilute sulphuric acid, is all the appara- tus required. A strong solution of sulphate of copper is put in the tumbler, and a zinc rod, Z, is inserted in P ; the moulds, or casts, m m, are sus- pended by wires attached to the binding screw of Z. Thus arranged, the copper solution is slowly decomposed, and the metal is evenly and firmly deposited on m, m. A perfect reverse copy of m is thus obtained in solid, malleable copper. The back of m is protected by varnish, to prevent the adhesion of the me- tallic copper to it. In this manner the most elaborate and costly medals are easily multiplied, and in the most accurate manner. In practice,reverse casts are made in fusible metal or wax of the object to be copied,and the operation is conducted in a separate cell, containing only the sulphate of copper, one of Smee's batteries supplying the power. The art is now extensively applied to plating in gold and silver from their solutions ; the metals thus deposited adhering per- fectly to the metallic surface on which they are deposited, provided these be quite clean and bright Even alloys, as bronze, brass, and German silver, may be deposited according to electrolytic law. The positive electrodes should be of the same metal as that in so- lution, and as large as the surfaces to be coated, and these should not be larger than the plates of the battery furnishing the current. Wood cuts and printers' types are thus copiedln copper, the moulds taken in wax from them being made conductors by dusting over the surface with extremely fine plumbago. All the copper-plates of the charts of the Coast Survey are reproduced by the electrotype the originals are never used in the press, but only the copies, and any re- quired number of these may be produced at small expense. For an instructive account of these extensive electrotype operations, the student is referred to an elaborate paper by the Electrotypist of the Coast Survey, Mr. G. Mathiot, (Sill. Jour. [2] xv, 305,) in which the law of Ohm (983) is applied to determine the electrical condi- tions of this important practical problem. 994. Describe electro-metallurgy, or the electrotype. 995. What 13 said of the deposit of metals by other metals ? Give the examples. 638 ELECTRICITY. 995. Metals deposited from solution by the presence of another metal. It was known to the alchemists, very early in chemical history, that certain metals, as gold, silver, copper, lead, tin, &c., were deposited in a pure, or ' reguline 1 condition, from their solutions, when another metal was present, or even sometimes without that condition. Thus the lead tree, (arbor Saturna,*) the tin tree, (arbor Jovis,} the silver tree, (arbor Diance^ were so called by the alchemists, from the apparent growth of these metals out of their solutions, and in tree-like forms. This growth we now know to be Voltaic deposition. A solution of chlorid of gold in ether, by slow change, de- posits spontaneously, crystals of fine gold, in elegant moss-like growths ; and Liebig has shown us how to prepare a silver solution, which,by the aid of an essential oil as a reducing agent, will coat glass with a film of silver so thin as to be transparent, and still so brilliant as to reflect light more perfectly than the best mercurial mirrors. A dilute solution of acetate of lead, (half an ounce to a quart of rain water,) surrenders all its lead to a strip of zinc hung in the con- taining bottle, in elegant crystalline plates ; (the arbor Saturna ;) this, and the next case, are true Voltaic circuits, while in the two first cases, hydrogen appears to supply the want of the second ele- ment of Voltaic couple. In like manner, a dilute solution of nitrate of silver, placed over mercury, soon deposits all its silver in an ar- borescent form (arbor Diana) on the mercury. But the most instructive case of this kind is when a bar of pure tin is placed upright in a tall vessel, the lower half of which is tilled with a saturated solution of protochlorid of tin, while above it rests a dilute solution of the same salt. The bar is therefore in two solu- tions chemically identical, but physically unlike. The result is a Voltaic current, by which metallic tin, in beautiful brilliant plates, is deposited upon the upper part of the bar, while the lower part is correspondingly dissolved by the free electro-negative element of this electrolysis. 996. Deposit of metallic oxyds and Nobili's rings. E. Bec- querel has shown that oxyd of lead and oxyd of iron may be deposited in a thin film on the surface of oxydizable metals by using an alkaline solution of the metallic oxyd, and making the plate to be oxydized the negative electrode of a con- stant battery ; a deep brown coating of the oxyd is thus depos- ited in a few minutes so firmly as to withstand the action of the burnisher, and perfectly protect the iron or steel from atmos- pheric action. 996. What is said of the deposit of metallic oxyds Nobili's rings? PHYSIOLOGICAL EFFECTS OP THE VOLTAIC PILE. 639 If the film of oxyd of lead is very thin, it presents, over a surface of polished silver or steel, a most pleasing exhibition of colored rings, analogous to the colored rings of Newton from thin plates, (837). For this purpose the negative electrode is .made of a thin platinum wire, protected from the solution by a glass tube, except at the extremity, where a mere point is presented. A rim of wax on the edges of the plate retains the solution of potassa, saturated with oxyd of lead, while it is connected on the positive pole, and the neg- ative point is held for a few seconds within a line of the polished sur- face. These colored rings were first noticed by Mr. Nobili, whence their name. 997. The physiological effects of the Voltaic pile. Galvani's original experiment, (9 65,) and the earlier observations of Swam- medam and Sulzer, of two metals on the tongue, (969,) deserve to be remembered as being our earliest knowledge of this sub- ject. From a small number of pairs, the dry hand grasping the electrodes, receives no sensation ; number, and not size of elements, is requisite [for the physiological effect. But from a column of fifty elements, (966,) or still more from fifty cups of Bunsen, a smart twinge is felt, reaching to the elbows, or if the hands are moistened with saline or acid water, the shock will be felt in the shoulders. This shock is unlike the sharp and sudden commo- tion from statical electricity, being a more continued sensation, accompanied, during the continuance of the current, by a sense of prickly heat on the surface. But it is only at the making and breaking of contact that a sTioclc is felt. If the battery contains some hundreds of couples actively excited, the shock becomes painful, or even fatal. It may be passed through any number of persons whose moistened hands are firmly joined, but it is sen- sibly less acute at the middle of such a circuit than to those at the electrodes. Even after death, this power produces spasmodic muscular contractions, efforts to rise, and contortions of the fea- tures frightful to behold. Persons in whom animation was sus- pended, have been restored by the influence of the hydro-electric current on the nervous system. When the current follows the ramifications of the nerves, the effect is greater than when it is reversed, an important circumstance in the medical application of this power, for which subject, reference may be had to the works Dr. Wm. F. Channing, and of Dr. G. Bird. The senses of sight, hearing, and taste, are all effected by a Vol- 997. What are the physiological effects of the pile ? How after death ? What senses does it affect 1 Has it an effect on vegetables ? 640 ELECTRICITY. taic current ; a flash of light, a roaring sound, and a sub-metallic savor being received when the shock of a small battery is passed, successively, through the eyes, the ears and the tongue. From the experiments of E. Becquerel, it appears that seeds sub- jected to a gentle electric current, germinate sooner than otherwise. Von Marum, observed that plants with a milky juice, like the Eu- phorbiacea, do not bleed after a powerful electrical shock, owing, he suggests, to the loss of contractile power in the plant. Certain animals, as the Surinam eel, (Gymnotus electricus,) and the torpedo, or numb-fish, found on our coast, possess, in their organiza- tion, a high electrical power, and are perpetually charged electrical batteries. 998. The magnetic and electrical effects of the pile, belong to the subject of electro-dynamics, presently to be considered sepa- rately. It is sufficient now to state the fundamental fact of elec- tro-magnetism ; namely, that a conductor over which a Voltaic 622 current is passing, affects a freely suspended needle, as another magnet would do. If the current flows from the -\- to the of the bat- tery, (i. e. from S. to N.,) over a magnetic needle, the austral or N. pole of the magnet invariably turns to the left, as in fig. 622. The further consideration of this important and deeply interesting subject is reserved for the chapter on electro-dynamics. The electrical effects of the pile have been alluded to in sec- tions 966, 967, and 979. THEORY OF THE PILE. 999. Three views. a. It has already been stated, (966 ) that Volta and his school ascribed the effects of the pile to the simple contact of unlike metals, each decomposing the neutral elec- tricity of the other, and arguing that the chemical action of the battery was requisite only to afford conductors for the electricity, while the metallic substances remain in every way unchanged, "they are supposed to discharge into each other. According to this hypothesis, the two metals are in opposite electrical states, one being positive, the other negative, these states becoming at once destroyed by the intervening fluid. This theory assumed 998. What are its magnetic and electrical effects? 999. What three rules of the pile are here named ? VOLT A' S CONTACT THEORY. 641 that the whole effect of the apparatus, is but a disturbance and reproduction of electrical equilibrium. It cannot be maintained in this sense, for otherwise, there must be assumed the produc- tion of a continual current, flowing on against a constant resist- ance without any consumption of the generating force. 5. On the other hand Fabbroni, Davy, Wollaston, and above all in our day, Faraday, De la Rive and Becquerel, have sought to establish that the Voltaic excitement was only the reciprocal of the chemical action and as this was more intense, and porperly directed, so was the pile more powerful. In addition to the statements and arguments already adduced, it is proper here to consider the ground of these two views, and somewhat more in detail. c. A third view or theory of the pile has been advanced by M. Peschell, which he calls the molecular theory, and which rests on a sort of middle ground between the contact and the chem- ical theories. 1000. Volta's contact theory. The advocates of this mode of explaining the action of the pile, (embracing nearly the whole body of the German physicits,) contend that they have experi- mentally established the following points in support of Volta's theory, viz: 1st, that Volta's original experiments demonstrate the fact beyond question, that the simple contact of heterogeneous metals does produce an electrical current. (966.) 2d, that in some cases when a purely chemical action exists between a fluid and one of the two metals immersed in it, that the contact of the metals arrests this action, and an opposite action commences. 3d, that there are even cases of hydro-electric combinations, in which electrical action exists, without any chemical action what- ever on the electromotors. 4th, the advocates of this view fur- ther contend that chemical action is never the primitive cause of electrical excitement ; although some do not question the influ- ence of chemical action in promoting and increasing the excite- ment originally due to contact. Since scarcely any chemical action, or none at all, occurs in a constant battery without contact, it is, with reason, urged that contact of the heterogeneous metals is the one indispensible prior cause of the Voltaic current. Hence the real difficulty seems to be, to decide what share chemical influence really has in exciting the eletrical action. Want of space prevents our 1000. State the claims of Volta's theory. 642 ELECTRICITY. giving the evidence in detail upon which the advocates of the contact theory rely for the support of the above propositions. 1001. The chemical theory assumes the electrical current to be the reciprocal of the chemical action in the cells of the battery, and that chemical action is essential to the production of such a current. M. De la Rive demonstrated this latter point in the following man- ner. A pair, formed of two plates, one of gold, the other of plati- num, was plunged into pure nitric acid, without the development of any current ; by the addition to the nitric acid of a single drop of clorohydric acid, a very decided current was obtained from the gold to the platinum through the liquid. In the first case there was no chemical action, in the second case, the gold was attacked, and the platinum was not, or was less attacked. The laws of electrolysis, first demonstrated by Faraday, as al- ready stated, (992,) lend the evidence of mathematical certainty to the chemical theory of the pile. Since we thus reach the unavoidable conclusion that an equivalent of electricity is a chem- ical equivalent, and so bring the discussion down to the rigid test of the balance, the ultima ratio of chemists and physicists. In addition to the laws of Faraday, already rehearsed, are the following 1002. Laws of the disengagement of electricity by chemi- cal action, first stated by M. Becquerel. 1st. In the combination of oxygen with other bodies, the oxygen takes the electro-positive substance, and the combustible the electro- negative. 2d. In the combination of an acid with a base, or with bodies that act as such, the first takes the positive electricity, and the second the negative electricity. 3d. When an acid acts chemically on a metal, the acid is electri- fied positively, and the metal negatively : this is a consequence of the second law. 4th. In decompositions, the electrical effects are the reverse of the preceding. 6th. In double decompositions, the equilibrium of the electrical forces is not disturbed. 1003. The quantity of electricity required to produce chem- ical action is enormous, compared with the amount of statical 1001. What does the chemical theory assume ? What is De la Rive's demonstration ? What basis do Faraday's results give ? 1002. Give Becquerel's five laws. POLARIZATION OP THE ELEMENTS OP A LIQUID. 643 electricity disturbed by the common frictional machine. Fara- day has, in his masterly way, demonstrated this fact by a simple experiment. He has shown that the quantity of voltaic electricity requisite for decomposing one grain of water, would be sufficient to maintain at a red heat, (during three minutes forty-five seconds, the time requi- site to effect the perfect decomposition of the grain of water,) a wire of platinum one one hundredth of an inch in diameter. The quan- tity of frictional electricity required to produce the same effect, would be that furnished by eight hundred thousand discharges of a battery of Ley den jai*s, exposing three thousand five hundred square inches of surface, charged with thirty turns of a powerful electrical machine. M. Becquerel, by a different mode of experiment, arrived at nearly the same results. Therefore, to decompose a grain of water, requires an amount of electricity equal to that furnished by the discharge of an electric pane having a surface of thirty-two acres. ' Equal to a very powerful flash of lightning'. ' This view of the subject gives an almost overwhelming idea of the extraordinary quantity of elec- tric power which naturally belongs to the particles of matter*. (Far- aday Expt. Res., 853 861.) 1004. Polarization and transfer of the elements of a liquid. The electro-chemical theory has been much expanded by the re- searches of H. De la Rive ; he explains the phenomena of polariza- tion and the transfer of the elements of a liquid in the following manner. His theory assumes that every atom has two poles, contrary, but of the same force. The different kinds of atoms differ from each other in that some have a more powerful polarity than others. When two insulated atoms are brought near each other, they attract each other by their opposite poles; the positive pole of that which has the strongest polarity unites with the negative pole of that which has the feeblest polarity. A compound atom, when insulated, has there- fore two contrary polarities between the poles of a pile ; for example, the atom is so arranged that its -4- pole is turned to the platinum, (or side,) of the pile, and the pole is turned to the zinc, (or -f- side,) of the pile. This same action occurs with other atoms, so that there is pro- duced a chain of polarized particles between the poles of the pile. 1003. Illustrate the quantity of electricity required to produce chemical action. 1004, What is said of the polarization of the ele- ments of a liquid ? 644 ELECTRICITY. The oxygen of the particle of water nearest the zinc, becomes negative, because of its affinity for the zinc, and the hydrogen be- comes positive. The other particles of water become similarly elec- trified by induction, but the platinum has become negative by in- duction from the zinc, and therefore is in a condition to take up the positive electricity from the zinc of the contiguous hydrogen. The action now rises high enough for the zinc and the oxygen to combine chemically with each other. The oxyd of zinc thus formed dissolves in the liquid, (dilute sulphuric acid,) and is thus removed. But the particle of hydrogen nearest the zinc, now seizes the oppositely elec- trified oxygen of the adjacent particle, producing a fresh atom of water. The particle of hydrogen which terminates the flow is elec- trically neutralized by the platinum, to which it imparts its excess of positive electricity, and escapes in the form of gas ; and other particles of water are continually produced, to supply the place of those decomposed, and thus continuous action is maintained. These changes, continually taking place, furnish an uninterrupted flow of electricity, which is conveniently termed a Voltaic current. Other instances of electrolysis are explained in a similar way. 1005. Chemical affinity and molecular attraction distinguished. According to De la Rive, and in support of the view of the polarity of atoms, the distinction between chemical affinity and molecular at- traction is as follows : chemical affinity is the attraction of atoms, operating by their contrary electric poles, which come into contact, while physical attraction results from the mutual attractive action that the atoms exercise over each other in virtue of their masses. This last attraction is never able to produce contact, because of the repulsive force of the ether which envelops the atom, and which in- creases in proportion as the sphere which separates the attracted at- oms diminishes. 1006. Theory of Grotthuss for electro-chemical decomposi- tions. Grotthuss, who wrote on the pile in 1805, in accordance with the then prevailing notions of the electrodes being poles of attraction and repulsion, like that of a magnet, conceived the pole from whence resinous electricity issues, as attracting hy- drogen and repelling oxygen, while that from which vitreous electricity issues, attracts oxygen and repels hydrogen. So when the force of a battery reaches a point adequate to the electrolysis of water, the particle of water, a, fig. 623, has its oxy- gen attracted towards the -f- pole, while its two atoms of hydrogen 1005. Distinguish chemical affinity and molecular attraction. 1006. What was the theory of Grotthuss ? PESCHELL'S MOLECULAR THEORY OF THE PILE. 645 are repelled towards those whose oxygen parts under this electrical attraction from its own atoms of hydrogen, to join the oxygen of a, producing a new atom of water, while c in its turn sends its oxygen to join the hydrogen of b, and so on to the end of the series, when, finally, arriving at the other electrode, the hydrogen having no new atom of oxygen to join, 623 it is given off at the anode, while the oxy- gen appears at the ca- thode. He conceives a /] similar succession of decompositions and re-compositions to occur in every electrolyte, me- tallic salts, and oxyds, and thus explains why, in the decomposition of salts, the middle glass (993) is neither reddened or made green. 1007. Peschell's molecular theory of the pile. Resting upon the opinion long held by many chemists, that those forces which lie at the basis of adhesion, and those which cause chemical af- finity are not essentially different, Peschell holds that when electricity is generated in any Voltaic arrangement, it results from a molecular change, brought about in the touching bodies by the adhesive force which subsists between them. This theory possesses the advantage, that no new power need be assumed to exist, whereas the contact theory demands the existence of an ' electromotive force,' of which we know nothing. It also accounts for the production of electricity, apart from any chemical action. In common with the chemical hypothesis, it deduces the phenomena of the single battery from the molecular forces ; it con- siders the fluid not merely as a conductor of electricity, but as en- gaged in its production, and that the elements of the battery, by the physical changes which they undergo, are the actual sources of elec- tricity ; that their contact renders this change possible, and it is, therefore, the occasion,and not the generating cause,by which the elec- tricity is produced. By this view, the chemical hypothesis is only a special case of the molecular. The simultaneous commencement of chemical action with the development of electricity, and the circum- stance that the chemical intensity of a simple Yoltaic arrangement in- creases and decreases as the chemical action on the fluid conductor, and on the elements of the battery is greater or less, fully accords with the statements of this theory. It follows, hence, that the electrical and molecular force are one and the same, and that the latter ap- pears as electricity whenever it passes from one mode of operation 100T. Give Peschell's molecular theory. In what respect does it sustain the chemical view ? 646 ELECTRICITY. into the other, as, . g., when it ceases to hold the elements of the water, and so oxydizes the zinc. ELECTRO-DYNAMICS, OR ELECTRO-MAGNETISM AND MAGNETO-ELEC- TRICITY. 1008. General laws. Electro-dynamics is that department of physics devoted to the mutual action of electric currents, which are wholly unlike the phenomena of static electricity. The phenomena of electro-dynamics may all be arranged under the following general propositions. 1. Every conductor, conveying a current of electricity, affects a free needle as a magnet would do. 2. Electric currents affect each other like magnets. 3. A magnet acts upon an electric current as a second current would have done. 4. Electric currents in conductors excite similar currents in other conductors within their influence. 5. Magnets excite electric currents, and all the electrical effects depending upon them. Hence, when magnetism is excited by electric currents, it is called electro-magnetism : and inversely, when electrical cur- rents result from magnetism, they are called magneto-electrical currents. It is impossible, in our narrow limits of space, to consider each of these heads in detail. We shall endeavor, however, to present those phenomena and their applications which are of most general interest. 1009. CErsted's discovery. In 1819-20, Prof. Hans Christ- ian (Ersted, of Copenhagen, in a course of researches upon the relation of the Voltaic apparatus to the magnet, made discovery of the fundamental fact of the electro-magnetism, already noticed (996.) Many physicists had before sought to evolve the phenom- ena of magnetism from the battery ; but in vain, because they proceeded without connecting the poles by a conductor, in which case, of course, (as we now clearly see,) the power of the appa- ratus is dormant, like stagnant statical electricity in an unexcited conductor. (Ersted closed the battery circuit by a conductor, and therein exactly rests Ms discovery. He found when such 1008. What is electro-dynamics'? What are its general laws? What two sub-divisions are named ? 1009. What was (Ersted's dis- covery ? On what did it depend ? (ERSTED'S DISCOVERY. 647 a conjunctive wire was approached to a free needle, that the needle was influenced by it, as if he had used a second magnet : in other words, the conducting wire, of whatsoever metal it might happen to be, had itself become a magnet. If positive electricity flows from south to north over a hori- zontal conducting wire, 624 placed in the magnetic meridian, then a free mag- netic needle, 5 B the wire a solenoid. The effect of the helix thus wound, is reduced solely to the influence of a series of equal and parallel circular currents. By winding the silk covered wire in the manner shown in fig. 636, the two ends of the coil are re- 636 turned to the center of gravity, and being pointed with steel, the whole system can be con- veniently suspended, as in fig. 637, upon what is called an (A Ampere's frame, in which the arrows show the course of the current from the battery thus suspended ; the axis of the solenoid, A B, swings into the magnetic meridian, while its several spires are in the plane of the magnetic equator. This position it assumes in obedience 637 to the solicitation of terres- trial magnetism ; consequent- ly it simulates in all respects the character of a magnetic needle, although possessing not a particle of iron or steel 'in its structure. If a second helix, 5, through which also a current passes, is presented to the^first7as"Tn ngT637, all the phenomena of attraction and repulsion will be seen, the action of the two helices or solenoids being to each other exactly like those of two magnets. 1018. DeLa Rive's floating current, al- ready explained in section 1015, is also well adapted to illustrate the attractive and re- pulsive influence of a magnet on a free con- junctive wire, as well also as its obedience to the solicitations of terrestrial magnet- ism. For this purpose the conjunctive wire is wound, as in fig. 638, into a helix. Left to itself, this apparatus will act just 638 1017. What results if the wire is wound as in fig. 635 ? What is such an apparatus called 1 If wound as in fig. 636, how does it act in fig. 637 ? How is it affected by a second helix ? 1018. How does fig. 638 illustrate these principles 1 MAGNETIZING BY THE HELIX. 655 as the selenoid on the frame, fig. 637, and will obey the impulses of a magnetic bar, or of another solenoid. 1019. Directive-action of the earth. These effects are ex- pressed in the following law : Terrestrial magnetism acts upon electric currents just as if the entire globe was encircled witJi electric currents from E. to W. in lines parallel to the magnetic equator. The direction in which these currents are supposed to move is the same with the apparent motion of the sun, and the one in which the earth's surface receives its advancing rays ; and since it is now known that electrical currents generated by heat exert precisely the same influence on the magnetic needle as Voltaic currents do, therefore it has been inferred that the thermal ac- tion of the sun is the generating and maintaining cause of the currents of terrestrial magnetism. (896.) 1020. Magnetizing by the helix. We have already (901) de- scribed a mode of producing magnets from an electrical current. The explanation of this, after all that has been said, is easy. As each volute of the helix, causing an electric current, is an active magnet, it is easy to conceive that under the united influence of a great number of such circular and parallel currents, the coer- cive force of a steel bar, or bar of soft iron, should be decom- posed, and active magnetism be thus induced, permanent or tran- sient, according as steel or iron is the subject of experiment. Even a series of sparks from an excited electrical machine, passed through a helix, will magnetize a steel needle. The position of the poles in a bar so situated will depend on the right-handed or left- 639 handed twist of the spire. If the current fiows from -f- to , and the wire, as in fig. 639, turns from left to . _ _ _ , A r\ n /v A Q . /*\ n r\~ r\~r\ ~\ .. right, (like the hands of a watch,) then the v^j^&zF< ^-^Jss*^*^pa north pole of the mag- 640 net is toward the left ; but if the spire turns, as in fig. 640, from right to left, or opposite to the hands of a watch, then the poles are 1019. "What is the law of the earth's action on electric currents? What is the direction of the terrestrial currents ? What general conclusion follows 1 1020. Explain the magnetizing power of the helix. What determines the position of the poles in a helix 1 656 ELECTRICITY. reversed. "Let a person," observes Faraday, "imagine that lie is looking down upon the dipping needle, or north magnetic pole of the earth, and then let him think upon the direction of the motion of the hand of a watch, or of a screw moving direct; currents in that direction would create such a magnet as the dipping needle." If the helix is wound on a tube of glass, paper, or wood, these 641 substances offer no resistance to the passage of the power ; but if a tube of copper or lead were em- 1 ployed, the magnetizing power of the current on the inclosed bar would be destroyed. If the same helix is wound in two opposite di- rections, as in fig 641, then, according to the di- rection curent, there will be a pair of north poles at the point of reversal in the centre? (or a pair of south ones,) and the two ends will have the same name. A bar of steel placed in such a helix will remain permanently an anomalous magnet, (874.) Reversing the position of the bar in the helix, or re- versing the position of the electrodes in the binding cups, will reverse its polarity. ARAGO'S ORIGINAL EXPERIMENT. If a short conjunctive wire of cop- per, or any non-conducting metal, is strewn with iron filings, they 642 will arrange themselves as seen in fig. 642, not bristling as in the magnetic phantom, with opposite polarities, (872,) but in close concentric rings, disposed over the whole length of the conductor. This fact was observed by Arago, in 1824, and by others, before the application of the helix to the induction of magnetism in soft iron. When the helix is closely wound with many turns of insulated 643 wire, and excited by a battery of considerable quan- tity, a cylinder of soft iron, as a b, in fig. 643, will be drawn into it from the position seen in the figure, with great power, and after several oscillations, will come to rest in the middle of its length, in opposi- tion to gravity, realizing the fable of Mahomet's coffin, suspended in mid air without visible support. , This fact is embraced in Dr. Page's electro-magnetic ~ engine, fig 664. 1021. Electro-magnets. Sturgeon, of England, in 1825, ap- pears to have been the first to produce soft iron electro-magnets. How does Faraday illustrate the cause of the current ? How is it if the helix is wound, as in fig. 641 ? What was Arago's experi- ment 1 How does the helix affect an iron bar 1 ELECTRO-MAGNETS. 657 644 Prof. Henry, and Dr. Ten Eyck, in 1830, produced electro-mag- nets of enormous power by a new mode of winding the inducing coil. (Sill. Jour, [1] xix, 400.) Electro-magnets are wound with coils of closely packed and insu- lated copper wire, vary- ing in size and length, according to the use to be made of them ; fig. 644, shows the usual form of those designed to sustain great weights. The spools at B, are vir- tually continuations of one spool, and the direc- tion of the whorl is ap- parently reversed by the bend of the horse-shoe. If a lever of the third order (198) is used as a steelyard, the lumber of heavy weights is avoid- ed, and the power of the apparatus easily tested. Prof. Henry, on a bar of fifty-nine Ibs. weight, used twenty-six coils of wire, thirteen on each leg, all joined to a common conductor by their opposite ends, and having an ag- gregate length of seven hnndred and twenty-eight feet. This ap- paratus, with a battery of four and seven-ninths feet of surface, sustained two thousand and sixty-three pounds avoirdupois : with a little larger battery surface it sustained twenty -five hundred Ibs. Electro-magnets develop their surprising power only when the armature is in contact with the poles, a fact due to induction ; without their armatures, they sustain not a tenth part of their maximum load. They are capable of over saturation by an ex- cess of battery power, and retain a remarkable residual force 1021. Who made the first electro-magnets ? How are these wound ? What is said of Henry's? When is their power developed 1 What of their polarity ? What circumstances affect their po\ver ? What laws has Dub established ? 28* 658 ELECTRICITY. (due to induction) after that has been cut off, so long as the keeper is in place, but as soon as the armature is detached, the whole of this magnetism is lost. Their polarity is instantaneously reversed by reversing the poles of the battery. This complete and imme- diate paralysis and reversal of power, renders these magnets of inestimable value in d3mamical electricity. The chief circumstances affecting the production of electro-mag- nets are, 1st, the quality of the iron, which should be the softest and purest possible, and the bar, if bent and hammered, should after- wards be most carefully annealed for a long time. 2d, the form of the bar. Dub has shown, that other things being equal, the power of an electro-magnet is proportional to the square root of the diam- eter of the cylinder, and consequently for magnets destined to lift great weights, short and thick cylinders are preferable. 3d, with a given battery power, Henry, (loc. '*.) demonstrated that a series of short coils of thick wire produced the greatest effect. But in case of feeble currents, as in the electro-magnetic telegraph, long and fine copper wire produces, on the principle of the galvanometer, the best results; the effect being as the square of the number of windings. The latest researches on this most important subject are by Dr. Dub, abstracts of whose results can be seen in Silliman's Jour- nal, (2; vol xvii, 424. Dr. Page, in his experiments on electro-magnetism as a moving power, constructed coils which raised cylinders of iron weighing over six hundred pounds each. On the poles of a horse-shoe mag- net, with an armature, such coils could lift an incredible weight. 1022. Vibrations and musical tones from indued magnetism. Dr. Page, in 1837, noticed the production of a musical sound from a magnet, between the poles of which a flat spiral was placed. The sound was heard whenever contact Avas made or broken between the coil and the battery. Two notes were distinguished, one the proper musical tone of the magnet, and the other an octave higher. De La Rive, Delezenne, and others, have confirmed and extended these cu- rious observations. The existence of molecular disturbance in re- ceiving and parting with magnetic induction, has been farther illus- trated by the same ingenious observer, by the vibrations imparted to Trevellyan's bars by the current from two or three cells of Grove's battery. (Sill. Jour. [2] ix, 105.) Trevellyan's bars are pris- matic bars of brass, hollow on one side, so as to rest by sharp edges on blocks of lead. When these are gently warmed, and then laid upon the leaden blocks, the unequal expansion and contraction of the 1022. What is said of the vibrations of magnets ? What other example of electro magnetic vibrations is given ? ELECROMAGNETIC MOTIONS. 659 two metals, gives the brass bars a slight motion of vibration, due to molecular disturbance by heat. A voltaic current,'according to Dr. Page's observation, produces the same effect as heat, but more re- markably. 1023. Electro-magnetic motions and mechanical power. The facility with which masses of soft iron may be endued with enor- mous magnetic power by currents of Voltaic electricity, and again discharged, or reversed in polarity, has led to numberless contrivances to use this power as a mechanical agent. A great variety of pleasing and instructive models of such machines, with the use both of permanent magnets and of electro magnetic armatures, or of electro-magnets only, are described in Davis' s Manual of Magnetism. We annex a figure of an electro-magnetic engine, contrived by Dr. Page, similar to one by which he obtained a useful effect of ten horse-power, in driving machinery and transporting a railway train. A and B, fig. 645, are two very powerful helices of insu- 645 lated copper wire, within which are two heavy cylinders of soft iron, CD, counter-balanced on the ends of a beam, G FT, like the working beam of a steam engine. By the movement of an eccentric, Z, on the main shaft of the fly wheel, the poles are changed, at the moment, to magnetize and de-magnetize, alter- nately, the two helices, drawing into them the two soft iron cyl- inders, by a force of many hundred pounds. Prof. W. R. John- son tested the force of an engine of this kind built by Dr. Page 1023. What is said of the adaptation of electro-magnets to me- chanical power 1 Describe Dr. Page's electro-magnetic engine, fig. 645. 660 ELECTRICITY. in 1850, and found it to give about six and a half horse power. (Sill. Jour. [2] x, 472.) M. Jacobi, of St. Petersburg, lias studied this subject very care- fully, and has contrived an effective form of rotating machine, very similar to that of Cook and Davenport, so well known in the U. S. in 1837. Froment, of Paris, has also constructed a powerful appa- ratus of this sort, in which armatures of soft iron on the periphery of a wheel are drawn towards electro-magnets placed radially. In all these machines it is heat developed by chemical action that is transformed, in the form of magnetic-attraction, into mechan- ical work. (707.) As the result of a great many experiments, Mr. Joule has shown that the best theoretical result from the heat, equiv- alent to the solution of a grain of zinc in a battery, is eighty Ibs. raised one foot high. But a grain of coal burned in a Cornish boiler, raises one hundred and forty-three Ibs. one foot, and the price of the coal is to that of the zinc as 9d per cwt., to 216d per cwt. There- fore, under the best conditions, (which are never reached in practice,) the magnetic force is 25 times dearer than that of steam. Until, therefore, zinc is cheaper than coal, in the proportion of 80 to 143, coal will probably be burned in atmospheric air, preferably to the combustion of zinc in sulphuric acid, to produce mechanical work. 1024. Action of magnetism on light. Fig. 646 shows the ap- 646 M paratus designed by Ruhmkorff, in illustration of Faraday's mag- netic rotatory polarization of light already spoken of under Optics, What is said of the mechanical equivalents of electro-magnetism ? DIAMAGNETISM. 661 (865.) Two powerful inducing coils, JVand Jf, surround two hollow cylinders of soft iron, , buried in the gun powder, produces its combustion, even at a distance of many miles, and in many distinct mines, or blast holes, at the same instant. This mode of blasting was lately ap- plied on an extended scale in the construction of the great forti- fications at Cherbourg, by Napoleon III. 1042. Clarke's magneto-electric apparatus.~This apparatus con- sists of a powerful magnetic battery, A, fig. 662, clamped on the 662 upright board, R, by the clamp C. The wheel, F, puts in mo- tion two helices, H G, wound upon a rotating armature of soft iron. The electrical cur- rent induced in the coils is in- terrupted by the spring, or hook, Q, which rubs on the in- terrupted back piece, H, while the circuit is completed by the hook, 0, passing upon the con- tinuous part of the spindle, R- A stout wire, T, movable at pleasure, connects the two sides, M and JVJ otherwise in- sulated by the piece of dry wood, L. When the coils are rapidly rotated before the poles of the magnet, the current is interrupted twice in every revolu- tion by the hook, Q, with the production of a brilliant spark. If the coils are composed of a long and fine wire, then powerful shocks will be experienced by one holding the handles R and S, but capable of a great graduation, by changing the position of the break piece, H, with reference to the point of the revolution when it leaves Q. These shocks may be made quite intolerable. 1042. Describe Clarke's magneto-electric apparatus, and its effects 1 UNIVERSALITY OF ELECTRICAL EXCITEMENT. C81 If the conducting wires of the intensity coil terminate in a decora- posing apparatus, fig. 663, 663 minute trains of gas bubbles are seen to rise from the platinum points under the tubes, showing the produc- tion of dynamic from mag- netic electricity. Other ef- fects of the intense class, as the decomposition of iodid of potassium, may also be produced with it. Substituting a coil of large wire, not over two hundred feet long, for the small long wire, the quantity armature is produced, from which brilliant sparks, 664 the deflagi*ation of mercury, and seting fire to ether, as in fig. 664, may be pro- duced ; mercury, in a copper spoon, B, is touched by the revolving points, A, on the end of the axis, d, and with every disruption of the circuit, the ex- tra current discharges with splendid B< effect. A platinum wire may also be ignited, and electro-magnets charged by the same armatures. Thus we see all the effects of electricity, physical and physiological, coming from a mag- net. OTHER SOURCES OF ELECTRICAL EXCITEMENT INCLUDING THERMO- ELECTRICITY AND ANIMAL ELECTRICITY. 1043. Universality of electrical excitement. Every change in the physical or chemical condition of matter, seems to be at- tended with electrical excitement. This is evident from the phe- nomena attending the cleavage, or pulverizing, of many minerals and crystallized substances, as mica, sugar, zinc-blende, and nu- merous other substances which evolve light when suddenly cleaved. If precautions are taken to insulate these, as with mica it is easy to do, by sealing wax, they also show the effects of electrical excitement by the condenser. The production of crystals is often also accompanied by electrical light. 1043. What is said of the causes of electrical excitement ? 29* 682 ELECTRICITY. Combustion, evaporation, the escape of gas attending chemical transformations, chemical decompositions and combinations, have all been known to evolve electricity when properly observed ; but in most such cases, the phenomena are too complicated to render it clear to which, if indeed to any single action of those enumerated, the excitement is due. The electrical currents set up by heat, (thermo-electricity,) and those arising from the phenomena of life, (animal electricity,) are the most important of all sources of electricity not before dwelt on, and to them we will now briefly advert. 1044. Thermo-electricity. The discovery of this source of electrical currents is due to Seebeck, of Berlin, in 1822. He found that if two metals of unlike crystalline texture and con- ducting power are united by solder, and the point of junction is either heated or cooled, an electrical current is excited, which flows from the point of junction to that metal which is the poorer 665 conductor. Fig. 665 shows such an arrangement of two little bars of bismuth and antimony. When the junction, , to the antimony, a. If the form of a rectangle is given to this arrange- ment, as in fig. 666, an instrument resembling Schweigger's multiplier is formed, (1010,) by which the magnetic needle is deflected. The thermo- electric multiplier of Nobili and Melloni, or thermoscope, (521, 543,) is formed of about fifty minute bars of antimony and bismuth, soldered together at their al- ternate ends. Degrees of temperature otherwise inappreciable are accurately measured by the influence of the ther- mo-electric current excited in this appa- ratus, and multiplied in the galvanome- . (fig. 628.) A twisted wire also pro- duces a thermo-electric current when the twisted portion is gently heated, and other solids, besides metals and even fluids, give rise to this species of electricity. The order in which the metals stand in reference to this power is wholly un- like the Voltaic series, and appears related to no other known prop- In what physical and chemical changes does electrical excitement show itself 'I 1044. What is thermo-electricity 1 Who discovered it, and when 1 How is its existence demonstrated ? What is NobiJi's thermoscope 1 How do the metals take rank in this respect 1 666 ANIMAL ELECTRICITY. 683 erty of these elements. The rank of the principal metals in the thermo-electric series is as follows, beginning with the positive : bismuth, mercury, platinum, tin, lead, gold, silver, zinc, iron, antimony. When the junction of any pair of these is heated, the current passes from that which is highest to that which is lowest in the list, the extremes affording the most powerful com- bination. If we pass a feeble current of electricity through a pair of an- timony and bismuth, the temperature of the system rises, if the current passes from the former to the latter ; but if from the bismuth to the antimony, cold is produced in the compound bar. If the reduction of temperature is slightly aided artifi- cially, water contained in a cavity in one of the bars may be frozen. Thus we see that as change of temperature disturbs the electrical equilibrium, so conversely the disturbance of the latter produces the former. 1045. Animal electricity. The researches of Galvani early established the existence of currents of electricity in the animal organism, flowing from the external, or cutaneous, to the inter- nal, or mucous, surfaces of the body. Aldini, who was a zeal- ous advocate of Galvani's claims, du- ring the controversy between the fol- lowers of Galvani and Volta, demon- strated the existence of such a cur- rent by the legs of a frog, the lumbar nerve being brought in contact with the tongue of an ox lately killed, while the hand of the operator, fig. 667, wet with salt water, grasps an ear of the animal, to complete the circuit The legs are then convulsed. as often as the nerves touch the mu- cous surface of the tongue. The same delicate electroscope also shows similar excitement when its pen- dulous ischiatic nerves touch the human tongue, the toe of the frog being held between the moistened thumb and finger of the experimenter. Or, when, as Aldini showed, contact is made be- tween the muscles of the thigh and the lumbar nerves by bend- ing the legs of a vigorous frog, contractions immediately follow. How may water be frozen by a reversed current ? 1045. What is animal electricity ? Give Aldini's experiments. 684 ELECTRICITY. Mattcucci, of Pisa, in 1837, (forty years after Galvani's re- sult was obtained,) has the merit of reviving Galvani's original and correct opinion as to the vital source of this electricity. He demonstrated, that a current of positive electricity is always cir- culating from the interior to the exterior of a muscle, and that although the quantity is exceedingly small, yet by arranging a series of muscles, having their exterior and interior surfaces al- ternately connected, he produced sufficient electricity to cause 668 decided effects. By a series of half thighs of frogs, arranged as in fig. 668, he decomposed the iodid of potassium, deflect- ed a galvanometer needle to 90, and by a condenser caused the gold leaves of an electroscope to diverge. The irritable muscles of the frog's legs form an elec- troscope fifty-six thousand times more delicate than the most delicate gold leaf electrometer. Du Bois Raymond, of Vienna, has demonstrated the existence of those currents in his own per- son by the use of the galvanometer. 1046. Electrical animals. In some marine and fresh water animals, a special apparatus exists, adapted to produce at pleasure powerful currents of statical electricity, either as a means of defence, or of capturing their prey. Of these, the electrical eel of Surinam, first described by Humboldt, and the cramp-fish, or torpedo, a flat fish found on our own coast, are the most remarkable. They have an alternate arrangement of cellu- lar tissue and nervous matter in thin plates of a polygonal form, constituting a perpetually charged electrical battery, arranged in the manner of a pile. By touching their opposite surfaces, a very violent shock is received, such as to disable a very powerful man, or even a horse. Prof. Matteucci has shown us how to charge a Ley den jar, by placing the torpedo between two plates, arranged like the plates of a condenser ; and Faraday has pub- lished an interesting account of his experiments with the eels of Surinam, from which he not only obtained shocks, but made magnets, deflected the galvanometer, produced chemical decom- positions, evolved heat and electrical sparks. (Expt. Res., 1749- 1795.) The student is also referred to Prof. Matteucci's interest- ing ' Lectures on Living Beings,' for further details on this very Who revived Galvani's views 1 Give his results. 1046. What is said of electrical animals ] Who have investigated this subject ? METEOROLOGY. 685 interesting subject, and to a memoir, on the American Torpedo, (Dr. D. H. Storer, Sill. Jour. [1] xlv. 164.) METEOROLOGY. 1047. Meteorology is that branch of natural philosophy which treats of the atmosphere and its phenomena. The subject may properly be divided into three parts. 1st, Aerial phenomena, comprehending winds, hurricanes and water spouts. 2d, Aqueous phenomena, including fogs, clouds, rains, dew, snow and hail. 3d, Luminous and electrical phenomena, as lightning, aurora-borealis, rainbows : to which may be added meteorics tones and shooting stars. Before commencing the consideration of the phenomena above mentioned, a few words will be said of the distribution of tem- perature over the surface of the earth. 1048. Climates, seasons. By climate is meant the condition of a place in relation to the various phenomena of the atmosphere, as temperature, moisture, &c. Thus we speak of a warm climate, a dry climate, &c. A season is one of the four divisions of the year, spring, sum- mer, autumn and winter. Astronomical seasons are regulated according to the march of the sun. In meteorology it is sought to divide them according to the march of temperature. Winter being the most rigorous of seasons, it is so arranged that its coldest days (about January 15th) fall in the middle of the sea- son. Hence winter consists of December, January and February ; spring of March, April and May, &c. Few meteorologists have regard to the astronomical divisions, which make winter begin December 21st. 1049. Influence of the sun. The sun is the principal cause that regulates variations in temperature. In proportion as this luminary rises above the horizon, the heat increases; it dimin- ishes as soon as it sets. The temperature, also, depends on the time it remains above the horizon. The sun, in winter, sends its rays obliquely upon the earth, and at this season, therefore, less heat is received than in summer, when its rays are more nearly perpendicular, (572 ; 3d.) Mathematicians have in vain endeavored 1047. What is meteorology ? How is it divided ? 1048. What is climate and what the common significance of season '? 1049. How does the sun influence the climate ? 686 METEOROLOGY. to deduce the temperatures of days and seasons from the height of the sun above the horizon. This failure is owing to many accidental and local causes which modify the result. 1050. Means of temperature. The mean or average daily tem- perature is commonly obtained by observing the standard thermo- meter at stated times during the day, and then dividing the sum of these temperatures, respectively, by the number of observations. The lowest temperature of the day occurs shortly before sunrise, the highest a few hours after noon. The mean daily tempera- ture, at Philadelphia, is found to be one degree above the tem- perature at 9 A. M. By taking the average of all the mean daily temperatures throughout the year, the mean annual temperature is obtained. 1051. Variations of temperature in latitude. The average an- nual temperature of the atmosphere diminishes from the equator towards the poles. But the temperature is not the same for places in the same latitude in the two hemispheres, as is seen in the following table. Places. Latitude. Temp Places. Latitude. Temp. Falkland Isles, Buenos Ayres, Rio Janeiro. 51 S 34 36' S 22 56' S 47 23 62 6 73 96 London. Savannah, Calcutta, 51 31' N 32 05' N 22 35' N 50 '72 64 '58 78 -44l This variation is owing to a variety of local causes, such as the elevation and form of the land, proximity to large bodies of water, the general direction of winds, &c. 1052. Variation of temperature in altitude. The temperature of the air diminishes with the altitude. As a general rule, it may be stated that there is a diminution in temperature of 1 F. for every 343 feet of elevation. On rising from near the level of the sea, the rate of decrease is more rapid; after a certain height is reached, it proceeds more slowly ; but in very elevated regions, it again increases. 1053. Limit of perpetual snow. It follows from what has just been stated, that in every latitude, at a certain elevation, there must be a point where moisture once frozen must ever remain congealed. The lowest point at which this is attained is called the limit of perpetual snow, or the snow-line. This point is 1050. "What are means of temperature? Give examples. 1051. Does temperature vary with latitude ? 1052. How with altitude ? CAUSE OF WINDS. 687 highest near the equator, and sinks towards either pole, as is shown in the table below. Places. Latitude. fnow lines. Straits of Magellan, Chili, Quito, Mexico, ^Etna, Kamtschatka. 54 S 41 S 00 19 N 37 30' N" 56 40' N" 3,760 feet 6,009 15,807 14,763 9,531 5,248 1054. Isothermal lines. If all the points whose mean temper- ature is the same are connected by lines, a series of curves are obtained, which Humboldt was the first to trace on charts, and which he has named isothermes, or isothermal lines, (from isos equal and thermos heat). The latitude and longitude are the principal conditions which determine the temperature of any point upon the earth's surface, but the influence of these conditions is greatly modified by numerous accidental and local influences : hence, the isothermal lines present numerous sinuosities instead of passing around the earth parallel to any degree of latitude. The introduction of isothermes formed an important epoch in meteo- rological science, for by it have been established the great laws of the distribution of heat over the surface of the earth for the four seasons. The chart of isoclinal lines, fig. 525, serves to illustrate also the general direction and place of isothermal lines, (896.) AERIAL PHENOMENA. 1055. Cause of winds. Wind is air in motion. Winds are generally caused by variations in the temperature of the earth, produced in part by the alternation of day and night, and the change of the seasons. The air, in contact with the hotter por- tion of the earth becomes heated, and being lighter than before, rises, while the surrounding air rushes in below to supply its place. The revolution of the earth, on its axis, also comes in as an important modifying cause of the thermal conditions. Winds are also, sometimes, caused by the sudden displacement of large volumes of air, as in the fall of an avalanche, and by a rapidly moving railway train. 1053. Give the limits of perpetual snow in the table. 1054. What are isothermal lines? To what are these related? 1055. What causes produce winds? 688 METEOROLOGY. Winds are divided into three classes, viz., regular, periodical and variable. 1056. Regular winds are those which blow continuously in a nearly constant direction, as the trade winds. Trade winds occur in the equatorial regions, on both sides of the equator to about the 30 of latitude. Those in the northern hemisphere blow from the north-east to the south-west ; those in the southern hemisphere from the south-east to the north-west. These winds are produced by the unequal distribution of heat upon the surface of the earth, and by the rotation of the earth on its axis. From the vertical position of the sun, the equatorial regions are in- tensely heated, the temperature gradually diminishing towards the poles. The heated air, above the equator, rises and blows off in the upper regions of the atmosphere towards either pole. At the same time, currents are established on the surface of the earth to supply to the equatorial regions the air which the upper currents have car- ried off. If the earth was at rest, these winds would blow due north and south. But the earth is revolving on its axis, from west to east, at the equator ; therefore, the eastern velocity is greatest, but ti gradually diminishes towards the poles. In consequence of this, the wind blowing from the north pole, towards the equator, ac- quires a westerly direction, and seems to come from the north-west, and for the same reason, the wind blowing from the north pole towards the equator, acquires an easterly direction, and seems to come from the south-east. 1057. Periodical winds are those which blow regularly in the same direction, at the same seasons of the year, or hours of the day. The most interesting winds of this class, are the monsoons, and the land and the sea breezes. The monsoons occur within, or near the tropics ; they blow from a certain quarter, one half of the year, and from an opposite point during the other half The cause of the monsoon is found in the effect produced by the sun in his annual progress from one tropic to another, successively heating the land on either side of the equator. The simoon is a periodical wind which blows over the deserts of Asia and Africa; it is noted for its high temperature, and the sand which it raises in the atmosphere, and carries along with it. This wind from the Great Sahara desert blows over Algeria and Italy, and reaches even the north shores of the Mediterranean where it re- ceives the name of sirocco. 1056. What are regular winds 1 Name them. How are they produced? 1057. What are periodical winds? What are the mon- soons and wrocco ? TORNADOES. 689 On the coasts and islands within the tropics, and to some ex- tent in temperate regions, a sea breeze daily occurs flowing from the sea to the land during the day ; as it gradually subsides, it is succeeded by a land breeze, flowing from the land to the sea. In some places these breezes are scarcely perceptible beyond the shore ; in others, they extend inland for miles. The causes of the land and sea breezes are very apparent. During the day, while the sun shines, the land acquires a higher temperature than the water of the surrounding ocean. The air, above the land, becomes heated, and rises. To supply the place of that which has risen, air flows in from the sea, constituting the sea breeze. But when the sun descends, the land rapidly loses its heat, by radiation, while the temperature of the ocean is scarcely changed. In conse- quence of this, the air above the land becomes cooled, and therefore more dense, and flows towards the water, constituting the land breeze. At the same time, in the higher regions of the atmosphere, air flows in from the sea to the land. 1058. Variable winds are those which blow sometimes in one direction, sometimes in another. The direction of winds is influ- enced by numerous causes, as the nature and form of the sur- face of the earth, the proximity of large bodies of water, &c. In these latitudes, the direction of the prevailing winds is from the north-west to the south-east. 1059. Hurricanes are terrific storms often attended by thunde 1 " and lightning ; they are distinguished from every other tempest by their extent, their power, and the sudden changes in their direction. From numerous observations, u it appears that hur- ricanes are storms of wind, which revolve around an axis, up- right or inclined to the horizon, while at the same time the body of the storm has a progressive motion over the surface of the earth." This law has been established by Redfield and Reid. Their progressive velocity varies from ten to thirty miles per hour; the rotatory velocity is sometimes as much as a hundred miles per hour. The diameter of a hurricane is from a hundred to five hundred miles, though sometimes, as in the Cuban hurricanes, it is much more. 1060. Tornadoes or whirlwinds are distinguished from hurri- canes, chiefly in their extent and continuance. They are rarely more than a few hundred rods in breadth, and their whole track is seldom more than twenty-five miles in length. The continu- What causes land and sea breezes ? 1058. What are variable winds ] 1059. Describe hurricanes. What is their extent and ve- locity ? 1060. What are tornadoes, their limits and duration 1 690 METEOROLOGY. ance of tornadoes is but a few seconds at any one place. They are oftentimes of great energy, uprooting trees, overturning buildings, and destroying crops. 1061. Waterspouts differ from whirlwinds in no other respect than that water is subjected to their action, instead of bodies, upon the surface of the land. Waterspouts first appear as an inverted cone, extending down- ward from a dark cloud. As the cone approaches the water, the latter becomes agitated, the spray rises higher and higher, and finally both uniting, there is formed a continuous column from the cloud to the water, usually bent as in fig. 669, but sometimes erect. After a little time, the column breaks, and the phenomena disappear. As to 669 the origin of waterspouts, philosophers are divided. Kaemtz, a distinguished German meteorologist, assumes that they are princi- pally due to two opposite winds, which pass side by side, or when a very brisk wind prevails in the higher regions of the atmosphere, while it is clear below. Peltier, and other physicists, ascribe water- spouts to an electrical cause. Waterspouts are in great part formed of atmospheric water, as is shown by the fact, that the water escaping from them, is not salt even in the open sea. If the atmosphere is not moist, there is no condensation of vapor, and the only noticeable phenomena is the vi- olence of the wind and its rotatory motion. 1062. Anemometers are instruments designed to measure the velocity of winds. Waltmann's anemometer is one of the best. 1061. What are waterspouts ? To what causes ascribed 1 HUMIDITY OF THE AIR. 691 It consists essentially of a small wind-mill, to which is attach- ed an index marking the number of revolutions per minute. The stronger the wind, the greater the number of revolutions made. The necessary data for ascertaining correctly with this instrument the velocities of winds, are easily obtained as follows. Nothing more is necessary, than on a calm day, to travel with the apparatus on a carriage or rail car, observing the number of revolutions made in going any known distance in a given time. The effect will be the same as if the air was in motion. A table is then constructed, indicating the velocity of a wind which turns the sails forty, fifty, sixty, or more times per minute. 1063. The velocity of winds varies from that which scarcely moves a leaf, to that which overthrows the staunchest oak. Smeaton has classified winds as follows, according to their velocity and power. Velocity of the wind. Miles per hour. Perpendicular force on one sq. ft. in Ibs. avoirdupois Common appellation of sunh winds. 1 .005 Hardly perceptible. A (V7Q \ ^r 5 Ui y .123 > Gentle wind. 10 4-Q9 15 .*\J 1.107 > Pleasant brisk gale 20 25 1.968 3.075 [very brisk. 30 35 4.429 6.027 > High wind. 40 7.873 Very high. 50 12.300 Storm. 60 17.715 Great storm. 80 31.490 Hurricane. 100 49.200 Violent hurricane. AQUEOUS PHENOMENA. 1064. Humidity of the air. Vapor of water is always con- tained in the air. This may be demonstrated by placing a vessel filled with ice or a freezing mixture in the atmosphere ; in a little time the vapor from the air will be condensed on the walls of the vessel, in the form of minute drops of water, (626.) Air is said to be saturated with moisture when it contains as much of the vapor of water as it is capable of holding up at a given tem- 1062. "What are anemometers ? How are they graduated ? 1063 What is the velocity of various winds enumerated in the table ? 1064. What is said of the humidity of the air ? 692 METEOROLOGY. perature. That the capacity for moisture is greater as the tempera- ture increases, is shown in the following table. A body of air can absorb At 32 F. the 160th part of its own weight of watery vapor. " 59 " " 80th " " " 86 " " 40th "113 " " 20th " " " " It will be noticed that for every 27 of temperature above 32, the capacity of air for moisture is doubled. From this it follows that, while the temperature of the air advances in an arithmetical series, its capacity for moisture is accelerated in a geometrical series. 1065. Absolute humidity ; relative humidity. The term abso- lute humidity of the air has reference to the quantity of moisture contained in a given volume. The absolute humidity is greatest in the equinoctial regions, and diminishes towards either pole ; it diminishes, also, with the altitude, but the true ratio is not fully known. The absolute humidity is also greater on coasts than inland, in summer than in winter, and less in the morning than about midday. The term relative humidity has reference to the dampness of the atmosphere, or its proximity to saturation. This state is dependent upon the mutual influence of absolute humidity and temperature. The atmosphere is considered dry when water rapidly evaporates, or a wet substance quickly dries. The expressions wet and dry convey simply an idea of the relative humidity of the atmosphere, and have no reference to the absolute quantity present, for a damp air is rendered dry by raising its temperature, and a dry air damp by cooling it. 1066. Hygrometers are instruments by which the humidity of the atmosphere is determined. They are of various kinds, and may be classified as follows : chemical hygrometers, absorption hygrometers, condensation hygrometers and psychrometers. All hygroscopic substances (viz., those which have an affinity for water) are chemical hygrometers. The amount of moisture in the air is determined with these subtances, by filling a tube with chlorid of calcium, for example, and passing a known volume of air through it ; the increase in weight of the tube, after the experiment, indicates the weight of moisture present in the air. This method yields the best results, but is difficult of execution. How much vapor of water can it absorb at different temperatures ? 1065. How are terms absolute and relative humidity to be under- stood ? 1066. What are hygrometers 1 What is the chemical mode of hygrometry ? HYGROMETERS. 693 Hygrometers of absorption are founded on the fact that certain organic substances elongate in a humid atmosphere, 670 and contract in a dry atmosphere. Saussure's hy- grometer, fig. 670, consists of a metal frame, in which is hung a hair, c. This hair is fastened at its upper end, d, to a screw, a b, the other end passes over a pulley, o, and is stretched tight by a silk thread, and a weight, p, also attached to the pulley. The axis of the pulley carries a needle, which moves over a graduated scale as the hair is lengthened or short- ened. The instrument is graduated by marking zero at that point on the scale at which the needle stops when the apparatus is placed in a perfectly dry atmosphere, and one hundred, at the point the needle marks in an atmosphere saturated with moisture. The interval between these two points is then divided into one hundred equal parts, which indicate different degrees of humidity. Founded on the same principle as the instru- ment above described, are hygroscopes; these show whether there is more or less moisture in the at- mosphere, but furnish no indication of its amount. They are usually made in the form of a human figure. If much moisture is present, a cord within the apparatus, increases in length, and draws up over the head of the figure an umbrella or hood ; as the air be- comes less humid, the cord contracts, and the covering falls. Some seed-vessels, as the capsules of a species of hibiscus, common in Asia Minor, act as sensitive hygroscopes, opening and closing with changes of moisture long after they have been removed from the plant. Of condensation hygrometers, the best 671 known is Daniell's, fig. 671. It consists of a glass tube bent twice at right angles, having a bulb at either extremity. The bulb, A, is partly filled with ether, into which is inserted the ball of a deli- cate thermometer inclosed in the stem of the instrument. The tube is filled with the vapor of ether, the air having been driven out. The bulb, B, is covered with fine muslin. Upon the supporting pillar, a second, thermometer is placed. In order to determine the dew point, or hygrometric state of the atmos- Describe Saussure's hygrometer 1 What are hygroscopes ? Give examples. 694 METEOROLOGY. 672 phere, by this instrument, a few drops of ether are allowed to fall upon the muslin-covered bulb, evaporation of the ether takes place, the bulb is cooled, and condenses the etherial vapor within. In con- seqence of this effect, the ether in A evaporates, causing a reduction of temperature indicated by the internal thermometer. At a certain point the atmospheric moisture begins to form in a ring of dew upon the bulb A. The difference at this moment between the degrees in- dicated by the two thermometers, denotes the relative humidity of the atmosphere ; the difference is greater, the dryer the air. Regnault's hygrometer depends on the same principle as Dan- iell's instrument ; but in place of the black and vacuous glass, he employs two thin tubes of polished silver. Psyckrometers, or hygrometers of evaporation, are founded on the rapidity of the evaporation of water in the air. August's psych rometer, fig. 672, is very commonly used ; it consists of two similar thermo- meters, t' t, placed side by side, supported on a frame. The bulb of t 1 is covered with fine muslin, the lower end of which dips into a small vessel, v, like a bird- glass, containing water ; by this arrangement the bulb is continually kept moist. Evaporation takes place from the moistened bulb, with a rapidity vary- ing with the humidity of the atmosphere, and a cor- responding depression in the temperature of the ther- mometer is produced. The hygrometric state of the at- mosphere is determined from the observed difference in the two thermometers by the use of a formula, for which reference may be had to the " Smithsonian In- structions for meteorological observations," or to ' " Boye's Pneumatics," p. 110. These instruments are made on the Smithsonian model by James Green, of New York, whose barometers have been before re- ferred to, (327.) 1067. Fogs, or mists, are visible vapors that float in the at- mosphere, near the surface of the earth. . Fogs are produced by the union of a body of cool air with one that is wanner and hu- mid. Many philosophers, as Saussure and Kratzenstein, consider that the globules, or vesicles, of which a fog is composed, are hollow, the water serving only as an envelope ; it is probable, if this is true, that the vesicles are mixed with a great quantity of drops of water. Describe Daniell's hygrometer, fig. 671. "What are psychrometers, and how used ? Describe August's psychrometer. CLOUDS. 695 1068. Clouds are masses of vapor that float in the upper re- gions of the atmosphere. They are distinguished from fogs only by their altitude ; they always result from the partial condensa- 673 Nimbus. Cumulus Stratus. Cirro-cumulus. Cirrus. tion of the vapors that rise from the earth. As clouds often float in regions whose temperature is many degrees below the freezing point, they are sometimes, no doubt, composed of frozen particles. 1069. Classification of clouds. Clouds are generally divided into four great classes, viz : the nimbus ; the cumulus ; the stra- tus, and the cirrus, as shown in the diagram, fig. 673. The nimbus, or rain cloud, (nimbus, storm,) has a characteristic storm-like form ; it is distinguished from others by its uniform grey, or blackish tint and its edges fringed with light. The cumulus, (cumulus, heap,) appears often in the form of a he- misphere resting on the horizon as a base ; oftentimes in detached masses, gathered in one vast cloud. When lighted up by the sun, they present the appearance of mountains of snow. The cumulus is the cloud of day ; in the fine days of summer it is most perfect. The stratus, (stratus, covering,) consists of sheets of cloud, or layers of vapor, stretching along and resting upon the horizon. It forms about sun- set, increases during the night, and disappears about sun- rise. It floats at a moderate elevation above the earth. The cirrus, (cirrus, curl,) usually resembles a distended lock of hair, being composed of streaks, or feathery filaments, assuming every 1067. What are fogs ? How does the vapor exist ? 1086. What are clouds ? 1069. Classify and describe them. 696 METEOROLOGY. variety of figure. The cirrus floats at a higher elevation than other clouds, and probably is often composed of snow flakes. Intermediate forms of clouds are distinguished by the names of cirro-stratus, cirro-cumulus, and cumulo-stratus. 1070. Rain is the vapor of clouds, or of the air precipitated to the earth in drops. Rain is generally produced by the rapid union of two or more volumes of humid air, differing considerably in temperature ; the several portions, when mingled, being inca- pable of absorbing the same amount of moisture that each would retain if they had not united. If the excess is great, it falls as rain, if it is of slight amount, it appears as cloud. The produc- tion of rain is the result of the law, that the capacity of air for moisture decreases in a higher ratio than the temperature. 1071. Rain-gauge. The quantity of rain that falls during a given time is measured by means of an instrument called a rain- gauge. One of the simplest rain-gauges consists of a cylindrical copper vessel, furnished with a float ; the rain falling into the vessel, the float rises. The stem of the float is accurately graduated, so that an increase in the depth of the water of one one-hundredth of an inch, is easily measured. Another rain gauge, a section of which is represented in fig. 674, 674 consists of a cylindrical copper vessel, M, closed by a cover, B, shaped like a funnel, with an ap- erture in the centre, through which the water passes into the interior. This cover prevents loss by evaporation. A lateral glass tube, A, ^carefully graduated, rises from the base of the vessel. The water rises in the tube to the same height as in the copper cylinder. If the appa- ratus has been placed in an exposed situation, for a certain time, as a month, and the gauge shows three inches of water ; this indicates that the rain that has fallen during the interval would cover the earth to the depth of three inches, if it were not diminished by evaporation, or infiltration. 1072. Distribution of rain. Rain is not equally distributed over the surface of the earth. As a general rule it may be stated 1070. What is rain, and how produced? 1071. Describe the rain guage and its use. SUBSTANCES UPON WHICH DEW FALLS. 697 that, the higher the average temperature of a country, the greater will be the amount of rain that falls upon it. Local causes, how- ever, produce remarkable departures from this rule. In the trop- ics the average yearly fall is ninety-five inches ; in the temperate zone it is thirty-five inches. Regions without rain are not unfrequent. In Egypt, it scarcely ever rains. Along the coast of Peru, is a long strip of land upon which no rain ever descends. A similar destitution of rain occurs on the coast of Africa and some parts of North America ; the inter- vals between the showers being six or seven years. In Guiana it rains during a great part of the year ; this is also the case, according to Davison, at the straits of Magellan. In the Island of Chiloe, (S. lat. 43,; there is a proverbial saying, that it rains six days of the week, and is cloudy on the seventh. 1073. Days of rain. The rainy days are more numerous in high than in low latitudes, as is seen in the following table, al- though the annual amount of rain which falls is smaller. Con- sequently, the ordinary rains of the tropical regions are more powerful than those of the temperate regions. N". latitude. Mean annual number of rainy days. From 12 to 43 78. .1 " 43 " 46 103. " 46 " 50 134. ,; " 60 " 60 161. In the northern part of the United States there are, on the average, about 134 rainy days in the year ; in the southern part, about 103. 1074. Annual depth of rain The greatest annual depth of rain occurs at San Luis, Maranham, 280 inches ; the next in order are Vera Cruz, 278 ; Grenada, 126 ; Cape Francois, 120 ; Cal- cutta, 81; Rome, 39; London, 25; Uttenberg, 'l2'5. In our country, the average annual fall is 39'23 inches; at Hanover, N. H., 38 ; New York state, 36 ; Ohio, 36 ; Missouri, 38-265. 1075. Dew is the moisture of the air condensed by coming in contact with bodies cooler than itself. The temperature at which this deposition of moisture commences, is called the dew point. (626.) The dew point varies according to the hygrometric state 1072. What is said of the distribution of rain in several places ? 1073. What is the mean annual number of rains as quoted 1 1074. What is the average annual depth of rain 1 1075. What is dew, and the dew point 1 30 698 METEOROLOGY. of the atmosphere ; being nearer the temperature of the air, the more completely the air is saturated with moisture. In this cli- mate, in summer, the dew point is often 30 or more below the temperature of the atmosphere. In India, it has been known to be as much as 61. 1076. Cause of dew. Dr. "Wells, an American, residing in England, determined by his researches the cause of dew. It may be given briefly as follows : During the day, the surface of the earth becomes heated by the sun, and the air is warmed by it. When the sun goes down, the earth continues to radiate heat without receiving any in return, and thus its temperature dimin- ishes. The air loses its heat more slowly, and is cooled only when it comes in contact with the cooler earth. If this cooling reaches the dew point of the air, moisture is condensed in the form of small drops upon cold objects, (good conductors,) as the soil or vegetation. 1077. Substances upon which dew falls. Dew does not fall upon all substances alike ; in consequence of differences in radi- ating power, certain substances cool quicker and more perfectly than others. The dusty road, the rocks and barren soil, cool slowly, and therefore on them but little dew falls. Trees, shrubs, grasses, and vegetation of every kind, radiate heat easily, and becoming cooler, abundance of dew is deposited upon them. 1078. Circumstances influencing production of dew. The most copious deposits of dew take place on cool clear nights. For when there are clouds, these radiate back the heat which has escaped from the earth, and thus prevent its cooling, and therefore no dew is deposited. The same effect results from the straw, mats, boards, &c., which gardeners use to cover delicate plants, to protect them from freezing. (See diagram 675-39.) On a windy night there is but little dew deposited, because the air is moved away from the cold surface of any body before it has become sufficiently cooled to deposit moisture. 1079. Frost is frozen dew. "When the temperature of the earth sinks in the night to the freezing point, the aqueous va- por then deposited congeals in the form of sparkling crystals, known as frost. Fig. 675, in which the arrows indicate the movements of heat, and the numerals the temperature of the air, 1076. What is the cause of dew ? 1077. Upon what substances does dew fall 1 1078 . What circumstances influence its fall ? 1079. What is frost? COLORED SNOWS. 699 will render the phenomena of dew and frost more intelligible. 675 1080. Snow is the frozen moisture that descends from the at- mospher%, when the temperature of the air at the surface of the earth is near, or below, the freezing point. The largest flakes of snow are produced when the atmosphere is loaded with moisture, and the temperature of the air is about 32 ; as the cold in- creases, the flakes become smaller. The bulk of recently fallen snow is ten or twelve times greater than that of the water obtained from it. Snow flakes are crystals of va- rious forms. Scoresby has enumerated six hundred forms, and fig- ured ninety-six. Kaemtz has met with at least twenty forms not figured by Scoresby. Crystals of 676 snow are not solid, else they would be transparent as ice ; they contain air. It is from the reflection of I light from the assemblage of crys- tals, that its brilliant whiteness is | due. Snow crystals are produced with most regularity during calm weather, without fog. Fig. 676 represents a few of the beautiful forms assumed by snow crystals. 1081. Colored snows. Captain Ross, in 1819, discovered a crimson snow clothing the sides of the mountains at Baffin's Bay. Raymond has observed it on the Pyrenees ; it has also been seen on the Italian Alps and Appenines. Certain French meteorologists at Spitzbergen, in 1838, passed over a field covered with snow, which appeared of a green hue whenever pressed upon by the foot. These hues, it has been found, are owing to Explain the diagram, fig. 675. 1080. What is snow ? What is Baid of its bulk, forms, and color? 1081. What is snow colored by 1 700 MEREOROLOGY. the presence of a certain class of microscopic plants, the differ- ent hues probably representing different stages of development. 1082. Hail is the moisture of the air frozen into globules of ice. Hail-stones are generally pear-shaped ; they are formed of alter- nate layers of ice and snow, around a white snowy nucleus. It is necessary for the production of hail, that a warm, humid body of air, mingle with another so extremely cold, that after uniting, the temperature shall be below the freezing point. The diffi- culty of explaining the phenomena of hail-storms consists in ac- counting for this great degree of cold. Hail-storms are most frequent in temperate climates. They rarely occur in the tropics, except near high mountains, whose summits are above the snow line. It is in great part during the summer, and in the hottest part of the day, that hail falls. Hail-storms rareiy occur at night. Hail-stones are often of considerable size; the largest are frequently an aggregation of several frozen together. Sleet is frozen rain ; it occurs only in cold weather ; it falls only during gales, and when the weather is variable. ELECTRICAL AND LUMINOUS PHENOMENA. Certain of the optical phenomena of the atmosphere have al- ready been considered in previous paragraphs, as the rainbow, mirage, &c. (840 and 845.) The general laws of atmospheric electricity are also given in section 964. We shall now speak briefly of some of the more important electrical phenomena. 1083. Origin of atmospheric electricity. The more prominent sources of atmospheric electricity are, 1st, evaporation. Elec- tricity is always produced where impure water is evaporating, and in which chemical decomposition is taking place. As ocean and other waters are generally in this condition, we have here a most abundant source of electricity. 2d, condensation. "When a va- por is condensed into a liquid, electricity is developed. Conden- sation is considered one of the most fruitful sources of electricity. 3d. Vegetation also furnishes electricity to the atmosphere. Pouillet has shown, that positive electricity is developed when seeds first sprout, and it escapes with the carbonic acid produced during the act of germination. The same results are probably 1082. What is hail, its origin [and mode of occurrence ? 1083. What is said of the origin of atmospheric electricity ? APPEARANCE OP AURORAS. T01 produced throughout the life of the plant. 4th, combustion. During the combustion of any substance, positive electricity escapes from it, while the substance itself is negatively elec- trified. 6th. Friction, it has already been shown is the most common cause of static electricity. Most probably, when large volumes of air encounter each other, electricity is developed by this cause, especially when the masses differ in humidity and temperature. 1084. Aurora borealis. Under this name are comprised the luminous phenomena seen in the northern sky, though occasion- ally they have been observed' also in the neighborhood of the south pole ; they are there called aurora australis. They present, when in full display, a spectacle of surpassing splendor and beauty. The cause of the aurora borealis is yet involved in ob- scurity. Although it is, evidently, intimately connected with mag- netic electricity, it is impossible to say what this connection is. (896.) It has been ascribed to the passage of electrical currents through the upper regions of the atmosphere, the different colors being manifested by the passage of the electricity through air of different densities. (1041.) 1085. Appearance of auroras. Before the aurora appears, the sky in the northern hemisphere assumes a darkish hue, which gradually deepens, until a circular segment of greater or less size is formed. This dark segment is bounded by a luminous arc, of a brilliant white color, approaching to blue. The lower edge of this arc is clearly defined ; its upper edge grad- ually blends with the sky. When this luminous arc is formed, it frequently remains visible for hours, but is always in perpetual mo- tion. It rises and falls, and breaks in various places. Clouds of light are suddenly disengaged, separating into rays, which stream up- wards like tongues of fire, moving backwards and forwards. When the luminous rays are numerous, and their palpitating lights pass to the zenith, they form a brilliant mass of light, called the corona or crown, whose centre is the point towards which the dipping needle at the place is directed. The aurora is then seen in its greatest splendor ; the sky resembles a fiery dome, supported by waving columns of different colors. When the rays are darted less visibly, the aurora soon dis- appears, the lights momentarily increase, then diminish, and finally disappear. It is asserted that sounds, like the rustling of silk, often accompany the display of auroras, but this is extremely problemat- 1084. What is said of the aurora 1 1085. What appearances precede the aurora f Describe the aurora. 1086. What is their extent and height ? What is said of that of November, 1848 ? 702 METEOROLOGY. ical ; the most celebrated polar navigators never heard any noises which they could certainly ascribe to the auroras. 1086. Extent and height of auroras. The aurora is not a 677 (Auroral display, seen at Bossekap, 70 N. 1838-9.) local phenomenon ; it is often beheld simultaneously in places far apart, as in Europe and America. In 1796, a beautiful aurora was observed simultaneously in Pennsyl- vania and France. The aurora of January 7th, 1831, was observed in all central and northern Europe, and at Lake Erie. The aurora of November 17, 1848, is probably the most remarkable hitherto re- corded. It was seen from Odessa, on the Black Sea, lat. 46 35' long. 30 35' E. to San Francisco, (California,) 38 N. lat 122 W. long, and as far south as Cuba. It seems everywhere to have had a pre- vailing red hue, mistaken in many places for a conflagration. (Sill. Jour. [2] vii. 203.) Many astronomers have endeavored to determine the height of auroras, but the results of their calculations are not cer- tain. Earlier philosophers computed their altitude at several hun- dred miles ; a lower limit is assigned by later observers. A brilliant auroral arch was observed in the northern and middle states, April 7th, 1847 ; from the observations made at Hartford and New Haven, Conn., its height was computed by Mr. E. C. Herrick, of the latter place, to be nearly one hundred and ten miles. 1087. What of the frequency of auroras ? What periods are named 1 What are Herrick's results at New Haven 1 LIGHTNING. 703 1087. Frequency of auroras. Auroras are more frequently seen in winter than in summer ; but this circumstance does not indicate that during the former season there are actually a greater number, for the increased length of night would render a greater number visible, even if they were equally distributed throughout the year. About the period of the equinoxes they appear to be more frequent than at other times. In addition to the annual period, there appears to be another, a secular period, extending through a number of years. One of these periods was comprised between 1717 and 1790 ; its maximum^was ob- tained in 1752. An increase in the frequency of auroras began again in 1820. Prof. Olmsted, in an important paper on this subject, in the Contrib. of Smithson. Inst. vol. 8, fixes one of these secular pe- riods between August 27, 1827, and November, 1848, or a little later. The number of auroras, observed for a period of twelve years, at New Haven, by Mr. E. C. Herrick, is given in the following table. Number of auroras. From May 1838 to May 1839, 35 " 1839 < 1840, 36 11 1840 t 1841, 36 " 1841 1 1842, 21 " 1842 t 1843, 7 " 1843 ' 1844, 7 " 1844 f 1845, 12 " 1845 1846, 20 " 1846 Dec. 1847, 44 January 1848 " 1848, 45 1849 " 1849, 17 1088. Disturbance of the magnetic needle. During an auro- ral display, the compass needle is often much disturbed. (885.) Sometimes it is deviated several minutes, or degrees, to the east ; then it is agitated and returns. The oscillations of the needle are as variable as the aurora ; when the arch is quiet, the needle is motionless; its disturbance com- mences when the streamers begin to fly. During the aurora of No- vember 14th, 1837, the entire range of the needle was observed by Messrs. Herrick and Haile to be nearly 6. According to Wilke, the position of the dipping needle is as variable as the compass needle ; the former rising and falling with the corona. 1089. Lightning. It has already been stated, that air sub- jected to compression, emits a spark; the production of light- 1088. How do they affect the needle? 1089. What is said of lightning ? 704 METEOROLOGY. ning is by some attributed to the same cause, viz : to the ener- getic condensation of the atmosphere before the electric fluid, in its rapid progress from point to point. When lightning is emitted near the earth, the flashes are of a brilliant white color ; when the storm is higher, and therefore in a rarefied atmosphere, their color approaches to violet. (952.) Clouds appear to collect and retain electricity. When a cloud overcharged with ' electricity approaches another less charged, the electric fluid rushes from the former to the latter. In the same manner the electric fluid may pass from the clouds to the earth. In such cases, elevated objects, as trees, high buildings, church steeples, &c., often gov- ern its direction. It is unnecessary to dwell upon the powerful and destructive effects of lightning. 1090. Classes of lightning. Lightning has been divided by Arago into three clas ses, viz : zig-zag or chain lightning, sheet lightning, and ball lightning. This classification is convenient, and is universally adopted. The form of zig-zag or chain lightning is supposed to be caused by the resistance of the air compressed before it The light- ning takes the path of least resistance ; then moves forward until it meets -with a like opposition, and so continues glancing from side to side until it meets the object it seeks. Sometimes the flashes divide into two, and sometimes into three branches ; it is then called forked lightning. Sheet lightning appears during a storm as a diffuse glow of light illuminating the borders of the clouds, and occasionally breaking out from the central part. Heat lightning, as it is called, appears often in serene weather du- ring summer, near the horizon ; it is generally, if not always, unat- tended with thunder ; heat lightning is the reflection in the atmos- phere of lightning very remote, or not distinctly visible. By many, this phenomenon is supposed to be occasioned by the feeble play of electricity when the air is rarefied, and the pressure upon the clouds is so much diminished that the electric fluid cannot accumulate upon their surface beyond a certain point, and escapes in noiseless flashes to the earth. Ball lightning appears in the form of globular masses, sometimes remaining stationary, often moving slowly, and which in a little time explode with great violence. This form of lightning is of very rare occurrence, and philosophers have not as yet been able to ac- count for it. 1090. How has Arago classified lightening 1 Describe the several sorts. LIGHTNING RODS. 705 Volcanic lightning. The clouds of dust, ashes, and vapor, that issue from active volcanoes, are often the scene of terrific lightning and thunder. Volcanic lightning is probably caused by rapid con- densation of the vast volumes "of heated vapor thrown into the air. The rapidity of lightning of the first two classes is probably not less than two hundred and fifty thousand miles per second. Arago has demonstrated that the duration of a flash of lightning does not exceed the millionth part of a second. The waving trees illuminated at night by a single flash of lightning during a storm, appear motionless ; the duration of the flash is so short, that, during its continuance, the trees have not sensibly moved. 1091. Return stroke. When a highly charged thunder cloud approaches the earth, it induces the opposite kind of electricity upon the ground below, and repels that of the same kind. If the cloud is extended, and comes within striking distance of the earth, or of another cloud, a flash at one extremity is often fol- lowed by a flash at the other. This latter is called the return stroke, and sometimes is of such violence as to prove fatal, even at a distance of several miles from the point of the first discharge. 1092. Thunder. As lightning passes through the air with amazing velocity, it leaves void a space behind it, into which the air rushes with a loud report ; this is thunder. The rolling of thunder is generally ascribed to the reverberation of the sound from clouds and adjacent mountains. It is also con- sidered that as the lightning darts to a great distance with immense velocity, that thunder must be produced at every point along its course, and the sounds not reaching the ear at the same time that elapses between lightning and its thunder, we are enabled to calcu- late the distance of the former. Sound travels at the rate of eleven hundred and eighteen feet per second. If the thunder reaches our ear five seconds after the flash, the distance is about a mile. 1093. Thunder storms are most frequent and violent in the torrid zone. They decrease in frequency towards either pole. Thunder storms are more frequent in the summer than in the winter months, and after mid-day than in the morning. They are produced in the same manner as ordinary storms ; but they differ from the last in the rapidity and extent of the condensation of the atmospheric vapor, and in the accumulation of electricity. Thunder storms are usually attended by an alteration in the di- 1091. What is the return stroke I 1092. What is said of thunder ? 1093. What is said of thunder storms? 1094. What is said of light- ning rods ? 30* 706 METEOROLOGY. rection of the wind. Of one hundred and sixteen thunder storms recorded in the Meteorological Register of the Connecticut Aca- demy, ninety-nine were either preceded or followed by an al- teration in the direction of the wind. 1094. Lightning rods were first introduced by Dr. Franklin. He was induced to recommend their adoption as a means of pro- tection to buildings, from the effects of lightning, by observing that electricity could be quietly and gradually withdrawn from an excited surface by means of a good conductor, pointed at its extremity. (925.) Lightning rods are ordinarily made of wrought iron ; but copper is preferable, being a better conductor of electricity, and less easily corroded. The size of the rod, if of iron, should not be less than three- quarter inch in diameter. The upper extremity of the rod should be pointed. Three points is the usual number used in the U. S., but one is sufficient. The points should be tipped with silver, gold, or plati- num, or copper gilded by electricity ; these metals being unaffected by the air, which would corrode the copper or iron, and render them poorer conductors. The rod should be continuous from top to bot- tom, and securely fastened to the building. Glass or wooden insu- lators are often recommended, but when once wet by a shower, there is but little advantage in them over metallic supports. When there are surfaces of metal about the building, as gutters, pipes, of curve on, 290. Capillary tubes, ascent of liquids in 293 ; depression of mercury in, 292 laws governing liquids in, 287 ; laws of liquids in, 291. Capstan, 202. Carbonic acid, 647 ; apparatus, Thil- orier's, 650 ; liquid and solid, 652. Cartesian devil, 259. Causes of pseudomorphism, 97. Caustics, 753. Central forces, 175 ; analysis of mo- tion produced by, 176. Centre of gravity, 142; determination of, 143 ; in bodies unequal in den- sity, 149 ; of regular figures, 144. Centre of oscillation, 165. Centrifugal forces, effect of, on yield- ing mass, 179 ; illustration of effects of ? 177. Chain pumps, 370. Change of volume during solidifica- tion, 617. Chemical affinity, 35. Chemical telegraphs, 1031. Chimneys, draught in, 689 ; smoky, 690. Chromatic aberration, 777. Chromatic scale, 458. Clarke's magneto-electric app't. 1042. Classification of machines, 197. Cleavage, 72. Clouds, 1068. Coercive force, 881. Cohesion, 32, measure of, in solids, 33 ; modified results of, 40. Color blindness, 799. Colored polarization, 861. Colored rings in crystals, 863. Colors, analysis of, 7"" by absorption, 771 ; appreciation 799; Chevreul's classification Compressing machine, Condenser, Liebeg's, 643. Condensing engine, 683. Conductibility for heat.deterniination of, of solids, 556 ; examples and illustrations of, 563 examples from the organic kingdoms, 564; of clothing, 566 ; of crystals, 559 ; of different bodies, 562 ; of gases, 561 ; of liquids, 560 ; of wood, 558 ; table of, ot solids, 557. Conductors of electricity, 910. Conjunctive wire, 1009. Conduction of heat, 555. Constant discharge of liquids, means for obtaining, 276. Convection, 567 ; in liquids, 568. Cooling by radiation, law of, 573. Coronas, 841. Coulomb's apparatus for rolling fric- tion, 225; for starting friction, 222. Coulomb's experiments on friction, results of, 223-226. Coulomb's laws of electrical attrac- tion and repulsion, 918. Crystalline forms, constancy of, 75 ; definitions of, 53. Crystalline molecules, equality of axes in, 78 ; shape of, 76. Crystalline structure, development of, 84} produced by vibration, 83. Crystalline systems, 54-69. Crystallization, by liquefaction, 80 ; conditions of, 79 ; development of heat during, 88 ; development of light during, 89 j from gaseous state, 81 ; separation of salts by, 85 ; sudden, 86. rystal'g, changes caused by, 87. Crystals, compound, 71 ; expansion of, 526; growth of, 52; modified 711 forms of, 60; positive and neg- ative, 857. Cubical expansion, 524. Currents produced by ice, 697. Currents induced by other currents, 1034; magnets, 1037. Curve, ballistic, 232. Curves, descent of bodies in, 160 ; of expansion of liquids, 541. Daniell s pyrometer, 518. Declination, 883. Decrease in temperature of atmos- phere by elevation, 602. Definition of electrical terms, 905. De La Eive's floating current, 1015, 1018. Demonstration of, first law of elec- trical attraction and repulsion, 920 ; laws of oscillation of the pendulum, 163 ; rotation of the earth, 164 ; second law of electrical EC attraction and repulsion, 921. Density, 260 ; of gases, 552-553 ; of liquids, 267-269 ; of solids, 261- 266 ; of the earth, estimation of, 141 ; of vapors, 657-658. Descent of bodies in curves, 160 ; on inclined planes, 159. Development during crystallization, of heat, 88 ; of light, 89. Development of crystalline struc- ture, 84. Dew, 1075 cause of, 1076 ; on which falls, 1077. Dew point, 626. Diapason, 460. Diamagnetism, 641. Diathermacy of bodies, applications of, 589. Diathermic power, causes which mo- dify, 587. Diffraction of light, : Diffusion of gases, 348 ; method of illustration, 349 ; table of, 350. Diffusion of motion requires time, 130. Dimetric system, 55 ; modified forms of, 63-64. Dimorphism, 91 ; temperature affect- ing, 92. Dipping needle, 886 j Blot's, 888. Direction of crystalline forces, 77. Direction of force of gravity, 140. Disappearance of heat during lique- faction, 607. t Discharger, universal, 950. Discord, 4566. Dispersion, epipolic, 846. Distillation, 641 ; fractional, 644. Divisibility, 22. Double refraction, 856. substance Electrical Draper's pyrometer, 519. Draught reversed, 690. Dry pile of Zamboni and De Luc, 979. Ductility, 44. Du Fay's electrical theory, 914. Dynamical theory of heat, 707 ; mo- tion of molecules by, 708. Dynamometers, 182, 183, 184. Ear, 478; external, 479; internal, 481 ; middle, 480 ; sensibility of, 461. Earth, a common electrical reser- voir, 911 ; demonstration of ro- tation of the, 164 ; estimation of the density of, 141. arth circuit, 1027. Earth's magnetism, action on dip- ping needle of, 887 ; inductive power of, 892 ; origin of, 896. j 434 ; repeated, 435. Elastic bodies, impact of, 132 ; strik- ing elastic planes, 133. Elastic fluids, 235. Elasticity, 26, 45 ; affected by tem- perature, 47 ; oscillation of, 46. Electrical attraction and repulsion, 908 : Coulomb's laws of, 918 ; illus- tration of, 940 ; of light bodies, 930. Electric battery, 947. Electrical bells, 940. currents, 916 ; paths and velocities of, 917 ; retarding power of batteries, 983 ; mutual action of, 1015. ' Electrical condenser, discharge of, 943 ;_ of ^Epinus, 942. Electrical discharge in induction, 927 ; laws of induction, 928 ; a cas- cade, 948 ; eel, 1046 ; effects, 907 ; egg, 951 ; excitement, sources of, 932, 933, 938 ; hail-storm, Volta's, 940 ; light, stratification of, 1041 ; spark, color of, 952. Electrical machines, care and man- anagement of, 936. Cuthbertson's, 935. Eamsden's, 935. Hare's, 935. Eitchie's double plate, 935; the cylinder, 933 ; theory of, 939. Electrical, animals, 1046; phenom- ena, atmospheric, 1083-1093 ; ten- sion, 915 ; terms, definition of, 905 j theories, 912 ; wheel, 940. Electric discharge, effects of, 955; physiological, 956 ; inflammation of combustibles, 957 ; mechanical effects of, 960 ; chemical effects 'of, 961. Electric sparks, difference between positive and negative, 958. 712 decompositions, Expansibility Electric light, 951 ; regulators of, 986. Electric light and spark, cause of, 951. Electricity, animal, 1045 ; ; atmos- pheric, 964 ; atmospheric, origin of ; 1083 ; conductors of, 910 ; dis- tribution of, 924; free in atmos- phere, 964 ; from steam, 937 ; iden- tity from whatever source, 1039 ; induction of, 927; latent, 941 ; loss of in excited bodies, 926 ; on sur- faces of excited bodies, 923 ; power of points in concentrating^ 925 ; quantity and intensity of, 968 ; thermo, 1044 ; vitreous and resin- ous, 909 ; voltaic, 967 ; voltaic, theories of, 999. Electro - chemical 990 ; conditions of, 1002 ; theory of, 1006. Electro-dynamic spiral, 1017. Electrolysis, laws of, 992 ; of salts, 993 ; of water, 991. Electrodes, 984. Electro-magnetic motions, 1023 ; dis- coveries, 1014. Electro-magnets, 1021. Electro-metallurgy, 994. Electrometers, 931. Bohnenberger's, 979 ; torsion, 919. Bennett's, 931. Cavallo's, 931. Volta's, 931. Electrophorus, 932. Electro-positive and electro-negative elements, 970. Electroscopes, 909 ; Bohnenberger's, 979 ; Henley's, 940 ; Volta's con- densing, 944. Electrotype, 994. Elements, 7 ; of a pile, grouping of the, 982. Emissive power for heat, 579 ; causes which modify, 580; of * bodies, 57. Endosmose, 298 ; materials for sep- tum in, 301 ; necessary conditions for, 300 ; of gases, 306 ; of, 305. Endosmotic action^ with inorganic solutions, 304 ; with organic solu- tions, 303. Endosmotic currents, direction of, 302. Engine, atmospheric, illustration oflFire principle of, 681 ; Branca's, 676 ; condensing, 683 ; fire, 376 ; Guer- Floating ick's, 677 ; high-pressure, 684 ; low-pressure, 683 ; Newcomen's, 680; Savary's, 679; Watts' im- ?rovements or, 682 ; Worcester's, 78. Eolipile, 674 ; Do Garay's, 675. Epipolic dispersion, 846. Equality of axes in crystalline mol- ecules, 78. Equator-magnetic, 886. Equilibrium, 105 ; of floating bodies, 258 ; of liquids between laminae, 294 ; of machines, 192; of oblique forces acting on lever, 199 ; of solids supported on an axis, 147 ; of solids supported on a horizontal surface, 148; of solids supported on points, 150. Evaporation, circumstances influ- encing, 625 ; mechanical force de- veloped during, 639 ; production of cold by, 636. Evaporative power of fuels, 687. ~ spansibility, 23 ; relation between, and compressibility, 550. Expansion, amount of force exerted by, 530 ; apparent and absolute, 538 ; applications of the, -of solids, 532 j cubical, 524 ; curves of the, of liquids, 541 ; effects and appli- cations of the, of gases, 551 ; ef- fects of unequal, of water, 543 ; in- crease of mean, by heat. 529 ; laws of the, of gases, 546 ; linear, 523 ; of crystals, 526 ; of liquids, 536 ; of mercury, 540 ; of solids, 522 ; of water, 542 ; phenomena produced by, 531 ; ratio of the, of gases, by heat, 547 ; table of the, of liquids, 539: table of the, of solids, 528 ; uniformity of, in solids, 527. Extra-current, 1096. Eye, action of ; on light, 780 ; adap- tion of, to distances, 790 ; human, structure of, 779 ; inversion of im- ages formed in, 781. fe-pieces, of microscopes, 809 ; of telescopes^ 809. Falling bodies, application of laws of, 158; table of laws of, 156. iraday's nomenclature, 984 ; laws of electro-chemical decomposition, 992. Faraday on condensation of gases, 653, 649; discoveries, 992-1024- 1034-1037, 1038. Fire engine,' 37 6. Fire, open, 701. Flats and sharps, 455. 'oating bodies, attraction and re- pulsion of, 296 ; equilibrium of, 258. Flow, theoretical and actual, 275. Fluids, elastic and non-elastic, 235 ; resistance of fluids, 230. Fluorescence, 846. Fog- bows, 841. heated Eye theories Faraday 713 Fogs, 1067. Foot-pound, 711. Force, coercive, 881 ; definition of 29 ; varieties of, 30. Forces, composition of, 109 ; paral- lelogram of, 108 ; resolution of 110; resultant of parallel, 112 system of, 107 ; transfer of, 123. Formation of vapors in a vacuxim, 620 Form of the earth, 138. Formula for projectile force, 129. Formulae to compute changes in volume of gases, 548, 549. Fortin's barometer, 327. Fountain, Hiero's, 377 ; intermittent 363. Franklin's electrical hypothesis, 913 Franklin's kite, 963. Freezing in red-hot crucibles, 668 mixtures, 610 ; of water ? 618. Friction, Babbage' s experiments on, 227 ; Coulomb's apparatus for de- termining, 222, 225 ; results of Cou- lomb's experiments on, 226 ; roll- ing, 224; sliding, 220; starting 221. Frost, 1079. Fuel, value of^ 687. Furnaces, Chilson's, 702 ; hot-air 702 ; hot- water, 703, 704. Galileo's telescope, 807. Galleries, whispering, 436. Galvanism, discovery of 965. Galvanometer, 1011 ; tangents, 1012. Galvano-plastic art, 994. Galvaiii's experiment, 965. Galvani's theory, 965. Gamut, 449. Gaseous state, crystal'n from, 81. Gas-jet, musical, 465. Gases, absortion of, by solids, 307, 353 ; conductibility for heat of, 561 ; density of, 552 ; diffusion of, 348 ; endosmose of, 306 ; escape of compressed, 358 ; expansion of, 545 ; identity of vapors and, 645 ; simple and compound, 311 ; table of densities of, 553 ; table of lique- faction and solidification of, 654 ; transpiration of, 351. General laws of matter, value of, 5. Glasses, burning, 593 ; magnifying, 802. Glottis, 471, Gold's steam heating apparatus, 705. Goniometers, Hatty's, 73 ; Wollas- ton's reflecting, 74. Gravitation, 135 ; examples of, 4 ; law of, 4. Gravity, a source of motion, 151 ; centre of, 142 ; direction of the force of, 140 ; local variations of, 139. Grooved plates, colors of, 845. Growth of crystals, 52 : organized beings, 52 ; unorganized beings, 52. Guerick's apparatus, 677. Gyroscope, 181. Hail storms, 1082. Haldat's pressure apparatus, 240. Halos, 841. Harmony, 448. Hare's calorimoter, 973 ; deflagrator, 973. Hatty's goniometer, 73. Heat, communication of, 554 ; con- duction of, 555 ; definition of terms of, 487 j development of, during crystallization, 88 ; dynamical theo- ry of, 707 ; elastic force of, 37 ; im- ponderable, 489 : latent, 606 ; na- ture of, 488 ; radiation of, 570 ; re- flection of, 576 ; refraction of, 592 ; relation of force to, 712, sources of, 491, 716 ; transmission of ra- diant, 583 ; what is, 486. Helix, 1017; magnetizing by, 1020. Henry's magnets,1021; currents, 1035. Hexagonal system, 59 ; modified forms of, 69, 70. Hiero's fountain, 377. High-pressure engine, 684. High-pressure steam, 635. Horse-power, 686 ; machines, 187. Humidity, absolute'and relative,1065. Hydraulic ram, 378. Hydrodynamics, 233. Hydrogen lamp, 354. Hydrostatic balance, 257 ; paradox, 253 ; press, 254. Hygrometers, 1066 ; August's, chem- ical, 1066 ; baniell's, 1066. Hygroscopes, 1066. Hypsometer, 634. [llumination, railway, 827. [llustration of effects of centrifugal forces, 177. [mages, distortion of, 768 ; virtual, 750. [mpact, 127 ; of elastic bodies, 132. [mpenetrability, 19 ; of air, 314. [nclination map, 889. Inclined plane, 208 ; application of power to, in different directions, 209-211 ; effect of power applied to, 212. ^dependence of light and heat, 590. Index of refraction, determination of, 757. nduction, 878 ; an act of contigiious particles, 929 ; laws of electrical, 928 ; from currents, 1034. 714 INDEX. Inductive philosophy, 1 ; origin of, 2 Inductive power of earth's magnet ism, 892. Inertia, 27 ; of air, 315 ; proportiona to quantity of matter, 28. Inorganic growth, 51. Insulators, 911. Insulating stool, 940. Intensity of sound, 445. Interference, colors of thin plates 836. Interval, 454. Inversion of electrical current pro- duced by change of liquid, 969. Isoclinal lines, 889. Isodynamic lines, 891. Isogonal lines, 884. Isomorphisnij 98. Joule's experiments on the mechan- ical equivalent of heat, 713 -results of, 714 ; conclusions from, 715. Kaleidoscope, 741. Lamp, hydrogen, 354. Lanterns, magic, 822. Larynx, 470. Latent heat, 606, and sensible heat of steam at different temperatures 638 ; of steam, 637 ; table of, 609 Lateral strength, 102 ; table of, 102 Law, Mariotte'js, 343. Laws, applications of, of falling bod- ies, 158 ; demonstration of, of os- cillation of the, pendulum, 163 ; of I electrical attractions and repul- sions, 918 ; of electrical induction, 928 : of electrolysis, 992 ; of falling bodies, 156; of fusion, 611; ol matter, value of, 5 ; of momentum, 126 ; of motion, Newton's, 134 ; oi oscillations of the pendulum, 162 ; of solidification, 615 ; of the vibra- tion of air in tubes, 467 ; of the vibration of cords, 389 ; verification of the, of falling bodies, 157. Lens, 593 ; double convex, 759 ; Fres- nel, 828 ; optical centre of, 765. Lenses, 754 ; combined, 763 ; con- cave, 761 ; images formed by, 766 ; magnifying power of, 803 ; plano- convex, 760. Le Kov's dynamometer, 183. Leslie s differential thermometer, 509. Level, spirit, 256 ; water, 255. Lever, 198 ; applications of, 201. Leyden jar, 945 ; electricity in, 946. Light, absolute intensity or, 732 ; ab- sorption of, 725 ; action of eye on, 780 ; amount of, increase with angle of incidence, 726 ; analogy between heat and, 591 ; analysis ofj 769 ; beams of, 720 ; determin- ation of the index of refraction of, 757 ; development of, during crystallization 89 ; diffused, 743 ; dispersion of, 725 ; emitted from all visible objects, 721 ; Foucault's experiments on velocity of, 723- images produced by, transmitted through small apertures, 730 ; in- dependence of heat and, 590 ; in- terference of, 834 ; internal reflec- tion of, 727 ; intensity of, at dif- ferent distances, 731 ; intensity of rays of, 775 ; intensity of reflected, 742 ; mirrors for, 734 ; nature of, 718 ; passage of, through different media, 758 ; pencils of, 720 ; polar- ization of, 849 ; properties of, 725 ; . propagation of, in a homogeneous medium, 722 ; rays of, 720 ; re- composition of, 770; reflection of 725 refraction of, 725 ; refraction of, by prisms, 756 ; relation of, bodies to, 719 ; theories of, 718 ; theories of, unsatisfactory, 724 ; total reflection of, 728 ; transmitted through plane glass, 755 ; velocity t Of, 723, 838. Light bodies, electrical attraction and repulsion of, 931. Lights, sea, 829 ; revolving, 830. "ightning, 1089; classes of, 1090; protective power of, rods, 1095 ; rods, 1094. Limits of magnitude, 103. Lines, isoclinal, 889; of magnetic force, 894. liquids, convection in, 568 ; curves of expansion of, 541 ; equilibrium of, of different densities in commu- nicating vessels, 252 ; equilibrium of, in communicating vessels, 250 ; equilibrium o/, in same vessel, 249 ; escape of, through capillary tubes, 281 ; escape of, through long tubes, 280 ;escape of,througn short tubes, 279 ; expansion of, 536 ; level sur- face of, 248 ; pressure of, on con- taining vessel, 271 ; specific gra- vity of, 268, 269 ; tables of the ex- pansion of, 539 ; transmit pressure in all directions, 238 ; velocity of sound in, 427. iquefaction, crystallization by. 80 ; of vapors, 646 ; table of solidifica- tion and, of gases, 654 ; theory of solidification and, of gases, 64U. ister's objectives, 817. _._ ocal variations of gravity, 139. analogy Lodestone, 869. ong-sightedness, 795. 715 Looming, 843. Lord Eosse's telescope, 812. Low-pressure engine, 683. Luminous rays, length of, 838. Luminous vibrations, nature of, 847 ; transmission of, 848. Machine, 191 ; Atwood's, 157 ; Boh- nenberger's, 180. Machines, classification of, 197 ; equi- librium of, 192 ; horse-power, 187 ; utility of, 193. / Magnetic attraction and repulsion, ' 875. Magnetic curves, 872 ; equator figures, 873 ; fluids, two, 880 ; force, distribution of, 871 ; intensity, 890 ; ^_ meridian. 883 ; observations, sys- tem of simultaneous, 893 ; phan- tom, 872. , Magnetic needle, 882 ; directive ten- dency of, 882 ; variations of, 885 ; Melody, 448. Men, strength of, 186. Metals, deposition of, by others, 995. Metallic oxyds, deposit of, 996. Metastatic thermometer, 514. Microscopes, achromatic object glass- es for, 816 ; compound, 805 ; com- pound achromatic, 819 : eye-pieces of, 809 ; mechanical arrangements of, 821 ; Easpail's dissecting, 804 ; simple, 804; solar, 823. Mirage, 844. Mirrors, 582 ; aberration of, 753 ; con- cave and convex spherical, 744; foci, of concave, 745; for light, 734 ; forms of, 736 ; images formed by concave, 749 ; images formed by plane, 738; images multiplied by glass, 739 ; reflection by plane, 737 ; rules for conjugate foci of concave, 747 ; secondary axes of, 746 ; spherical aberration of, 753. disturbance in auroral display, 1042. Magnetism, atmospheric, 895; ac- .LU.VUJ..UOVJ. wmio VL ^ijavu,**,. . tion of, on light, 1024 ; by contact, Moisture, capacity of air for, 1064. 876 877 :, on ngm, 1UZ4 ; oy contact, in non-ferruginous bodies, of steel by sun's rays, 903. Mists, 1067. Modified forms of crystals, 60. Molecular attraction, 31; repulsion, 36. CM I } V/J- OUGC-L tJJ DUJH O f*J&) VW Magnets, 869 ; anomalous, 874 ; ar- Momentum, 125. tificial, 870 ; by electro-magnetism, Monoclinic system, 57 ; modified 901 ; by touch, 899 ; circumstances affecting value of, 898 ; compound, forms of, 67. Monochord, 450. 902; horse-shoe, magnetism ofJMonometric system, 54; modified 900; natural, 869; production oil forms of, 61, 62. artificial, 897 ; to deprive of their Motion, 114 : common not interfering with particular, 122; composition of, 119 ; diffusion of, requires time, power, 904, Magneto electric appt., 1042 ; induc- tion, 1037. Magic lantern, 822; magic squares, 954. Magnitude, limits of, 103. Manometers, 345 ; with compressed air, 347 ; with free air, 346. Marcet's apparatus, 635. Mariner's compass, 882. Mariotte's law, 343; limits of, 344; variations from, 656. Material bodies, division of, 3. Matter, 6 ; essential properties of, 130 ; examples of composition of, 120; examples of resolution of, 121 ; gravity a source of, 151 ; Newton's laws of, 134; of power changed by machines, 196 ; resolu- tion of, 119 ; uniformly retarded or accelerated, 118 ; variable, 117 ; va- riations of, 115. Movement of drops between laminae, 295. Musical instruments, 466. Musical scale, 449. 17 ; indestructibility "of, "9 ; minutelMusic halls, 442. division of, 13,14; non-essentialjNatterer's experiments on gases, 655. properties of, 21; physical states of, Nature of heat, 488 5 of light, 718; 38. of luminous vibrations, 847. Maximum density of water, 542; of Near-sightedness, 794. different solutions, 544. Maximum tension of vapors, 621. Measure of time, 167. Measurers, stream, 284. Mechanical equivalent of heat, de- termination of, 713 ; Joule's exper- iments on, 713, 714. Needle, astatic, Negretti's and Zambra's maximum thermometer, 512. Newcomen's engine, 680. Newton's laws of motion, 134. Newton's rings, 837. Nichol's single image prism, 859. Nicholson's areometer, 264. 716 Nobili's rings, 996: Nodal figures 397. Nodal lines, 393 ; determination of 394 ; delineation of, " ' Nodal points^ 385. Oblique pencils of light transmittec through lenses, 764. Objectives, 817 ; aplanatie foci of, 817 compound, 817 ; Lister's, 817. Observation, 1. Obscura-camera, 824. Ocular images, brightness of, 784. (Ersted's compression apparatus 236 ; discovery, 1009. Ohm's law of electrical retarding power of battery, 983. Optical centre of a lens, 765 ; toys 797. Optic angle, 782 ; axis, 782. Opaque bodies, 719. Organic and inorganic growth, 51. Organized beings, growth of, 52. Origin of earth's magnetism, 896. Oscillation, centre of^ 165. Oscillations of elasticity, 46. Ozone, 962. Page's electro-magnetic machine 1023 ; vibrating armature, 1036. Papin's digester, 680. Parachute, 342. Paradox, culinary, 632 ; 253. Parallel forces, resultant of, 111-113. Parallelogram of forces, 108. Pascal's barometric experiments, 323. Pendulum, 161 ; applications of, 166 ; ballistic, 131 ; compensating, 534 ; demonstration of laws of oscil- lation of the, 163 ; laws of the os- cillation of the, 162; rotation ox the earth demonstrated by, 164. Penumbra, 729. Perkins' hot-water apparatus, 704. Perspective, aerial, 791. Phantascope, 797. Phenakistoscope, 797. Philosophy, inductive, 1. Photography, 826. Physics, subjects of, 4. Piles, dry, 979 ; theory of action of, 999 ; grouping of, 982. Piles, Voltaic, chemical theory of, 999 ; chemical effects of, 990. Pitch, 444. Plane, inclined, 208. Plumb'line near mountain, 141. Pneumatic experiments, 367. Pneumatic ink-bottle, 359. Polariscope, the eye a, 867. Polarity, 871 ; of the compound cir- cuit, 981. hydrostatic, Projectiles, Polarization of light, 847; atmos- pheric, 866 ; by absorption, 851 ; by compression, 864; by double refraction, 858 ; by heat, 864 ; by reflection, 852 ; by refraction, 853 ; by successive refraction, 854 ; col- ored, 861 ; magnetic rotatory, 865 ; partial, 855 ; rotatory, 862. Polarized light, applications of, 868. Polarizing instruments, 860. Polymorphism, 95. Porosity, 24; relation of, to weight and density, 25. Power, 191 ; horse, 189, 686 ; steam, 189. Positive and negative crystals. 857 ; electricity, 909. Press, hydrostatic, 254 ; screw, 216. Pressure, apparatus, Haldat's, 240 ; centre of, 247 ; equality of liquid, 238 ; lateral, increases with depth, 243 ; of liquids downwards, 239 ; of liquids, on containing vessel, 271 ; of liquids, on walls, 243 ; resistance to, 101 : table of water, 246 ; total, on walls, 244; total, on walls and bottom, 245 ; upward, 241. Primary colors, 769. Prismsj 754 ; Nichol's, 859. Projectile force, formula for, 129. ~rojectiles, 168; time of flight of, 173. Projection of a body in a direction other than vertical, 171 ; vertically downwards, 169 ; vertically up- wards, 170. Proof plane, 922. Pseudomorphism, 96; causes of, 97. ulley, compound, 207 ; fixed, 205 ; movable, 206. Pumps, 371; air, 364; chain, 370; forcing, 374 ; rotary, 375 ; suction, 372 ; suction and lifting, 373 ; Tates' air, 365. Quantity and intensity, 968. Sadiant heat, absorption of, by dif- ferent media, 571 ; intensity of, 572. Radiation, apparent, of cold. 575 ; law of cooling by, 573 ; or heat, 570 ; of heat universal, 574. Rainbows, 840. Kain, 1070; annual depth of, 1074; distribution of, 1072 ; regions with- out, 1072. Sain-gange, 1071. > Railway illumination, 827. ilamsden's plate electrical machine, 935. Jaspail's dissecting microscope, 804. iays length of luminous, 838 ; length of sonorous, 453. 717 Reflected light, intensity of, 742. Sensibility of ear, 461 ; of thermome- Reflecting telescope, 810. ters, 504. Reflection of heat, 576 ; light, 725 ; Separation of salts by crystallization, internal, 727 ; irregular, 743 ; total,! 85. 728. Shadow, acoustic, 430. Reflective power for heat, causes I Shape of crystalline molecules, 76. which modify 580; determination | Sine compass, 1012. of, 577. Single vision with two eyes, 792. Reflectors, 582; convex, 748; images Siren, 440. repeated by inclined, 740. Sliding friction, 220. Refraction of light, 725 ; atmospheric, Smoky chimneys, 690. 842 ; by prisms, 756 ; determinationjSnow, 1080 ; colored, 1081 ; limit of of index of, 757 ; double, 856. perpetual, 1053. Refrigerators, 697. Soda-water apparatus, 648. Regular figures, centre of gravity of, 'Solar microscopes, 823. 144. (Solid bodies, 49. Relation of power to weight, 194. (Solenoid, 1017. Repulsion molecular, 36 ; relation (Solid carbonic acid, 652. between attraction and, 39. Resistance, 219 ; to pressure^ 101. _ Resolution of forces, 110 ; of motion, 119 ; of motion, examples of, 121 ; of vibrations, 850. Respiration, products of, 691. Retina, duration of impressions on, 796. Retorts, 643. Return stroke, 1091. Revolution about an axis, 178. Reynier's dynamometer, 184. Rheostat, 1013. Ritchie's double plate machine, 935 ; Ruhmkorff's coil, 1140. Roget's vibrating spiral, 1015. Rolling friction, 224 ; Coulomb's ap- paratus for, 225. Ropes, rigidity of, 219. Rosse's telescope, 812. Rotascope, 181. Rotation of the earth demonstrated by the pendulum, 164. Rules for determining foci of lenses, 762. Ruhmkorff's coil, 1040; effects of, 1041. Rumford's thennoscope, 510. Rutherford's maximum and minim- um thermometer, 511. Safety tubes, 379. Saturated space, 621. Saturation, 614. Saturn, tree of, 995. Savart's toothed wheel, 441. Savary's engine, 679. Saxton's deep sea thermometer, 516 ; reflecting pyrometer, 520. Scale, chromatic, 458; musical, 449. OA-I Scintillating tube, 954. Screw, 216 : applications of, 218 ; Ar- chimedes , 369 ; mechanical efficien- cy of the, 217. Solidification, change of volume dur- ing, 617 ; elevation of temperature during, 616 ; laws of, 615. Solids, equilibrium of, supported on an axis, 147 ; supported on a hori- zontal surface, 148. .Solids, symmetry of, 50. Solution, 614. Sonometer, 450. Sonorous vibrations in tubes, 462; waves, length of, 453. Sound, 417 ; calculation of distances by, 426 ; distance, is propagated, 432 ; distance, is propagated in air ; 423 ; distance, is propagated in gases, 425 ; intensity of, 445 ; New- ton's formula for velocity of, in air, 424; reflection of ? 433; refraction of, in mixed media, 431 ; velocity of, in air, 423 ;. velocity of, in gases, 425 ; in liquids, 427 ; velocity of, in solids, 428. Sounding bodies are in vibration, 418. Sounds, interference of, 429 ; musical qualities of, 443 ; not propagated in a vacuum, 419 ; of inferior an- imals, 475-477 ; propagated in elas- tic bodies, 420. Sources of atmospheric electricity, 1083; of electricity, 1043; of heat, 491. Spaces described by falling bodies, 153. Speaking tubes, 437. Specific gravity bottles, 265. Specific gravity of gases, determina- tion of the, 552 ; table of the, 553. Specific gravity of liquids, determined by flasks, 269 ; by areometers, 268. Specific gravity of solids, determined by balance, 257 ; determined by by flask, 266 ; determined by Nich- olson's areometer, 264; heavier 718 than water, 261 ; lighter than water, " " ~! ; soluble in water, 263. of animals, 185 ; of men, 186 ; table ~~, v/j.uis.i u ^ T.uuv4, ~^. of absolute, 100; transverse, 102. Specific gravity of vapors, determined Strength of materials, definition of, by Dumas' method, 658 ; Gay Lus- sac's method, 657. Specific heat, 595 ; affected by com- pression, 601 ; of a body in different Stuttering, 474. states, 603; of gases, 599; Reg- nault's law of atomic weight and, Suction pumps, 372; lifting and, 373. 605 ; relation between atomic Sudden crystallization, 86. weight and, 604-605 ; table of, 600. Spectrum, 769 ; dark lines in solar, 774; dispersion of solar, 776 ; prop- erties of, 773. Specula, 735. Spherical aberration of lenses, 767. Sphericity, aberration of, 768^. Spheroidal form, causes which pro- duce the, 667. Spheroid, rate of evaporation from 663 ; repulsive action between sur- face and, 666 ; temperature of va- por from, 664. Spneroidal state, applications of, 672 ; connection of certain phenomena with, 669 ; explosions produced by, 670, 671 ; illustrations of, 660 ; on liquid surfaces, 662. Spirit level, 256. Spirit thermometers, 506. Springs intermittent, 362. Standard points in thermometers, 496. Starting friction, 221 ; Coulomb's ap- paratus for, 222. Statical forces, 106. Stationary waves, 402 Structure of human eye, 779. Study of colors, 801. Sublimation, 81. Support of a triangular mass on its angles, 145. Syphon, 360 ; intermittent, 361. Svstem of forces, 107. Tables, expressing laws of falling bodies, 156 ; of absolute strength, 100 ; of absorptive power for heat, 578 ; of boiling points, 628 ; of boiling points at different E laces, 634; of conductibility for eat of solids, 557 ; of density of gases, 553 ; of diffusion of gases, 350 ; of expansion of gases, 547 ; of expansing liquids, 539 ; of ex- pansion of solids, 528 ; of heat transmitted through screens, 585- 586 ; of latent heat, 609 ; of lumin- ous vibrations, 838 ; of length of sonorous waves, 453 ; of liquefac- tion and solidification of gases, 654 ; of specific heat, 600 ; of spher- ical aberration of lenses, 767 ; of strength of men and other animals, 188 ; of water pressure, 246. Tangents compass, 1012. j Tantalus' vase, 361. Tate's air-pump, 365. Steam apparatus, Branca's,676 ; Guer- Telegraph, electric, Bain's, 1031; ick's. 677. Steam-boat, first, 675. Steam boilers, 685 ; explosions, 671. Steam cylinder, Papin's, 680. Steam engine, atmospheric, 681; high-pressure, 684 ; history of, 673 ; low-pressure. 683; Newcomen's, 680; Savary's, 679; Watt's im- provements in, 682 ; "Worcester's, 678. Steam heaters, boiler for Gold's, 706 ; Gold's, 705. Steam, high pressure, 635 ; latent heat of, 637 ; mechanical power of, 686 ; cable, 1032. Variations of, 1028. Gauss and Weber's, 1026. House's, 1030. Morse's, 1029. . Sommering's, 1026. Steinheil's, 1026. Wheatstone's, 1028. Telescope, 806 ; achromatic, 813 ; as- tronomical, 808 ; Cambridge, 815 ; equatorial mountings for, 814 ; eye pieces of, 809 ; Galileo's, 807 ; Her- schel's, 811 ; object glass of Cam- bridge, 813 ; reflecting, 810 ; Eosse's. 812. sensible and latent heat of, at dif-jTelestereoscope, 831. ferent temperatures, 638 Steel-yards, 201. Stereomonoscope, 833. Stereoscope, 832. Still and worm, 642. Stone's ventilating shaft, 696. Streams, velocities of, 283. Strength, absolute, 100 ; lateral, 102 ; Temperature, artificial, how pro- duced, 700 ; means of atmosphere decreasing by elevation, 602. Terrestrial gravity, 137. Thaumatrope, 797. Theories Of electricity, 912 ; of light, 718. Theories of the pile, 999. 719 Theoretical considerations of mag netism, 879. Thermochrosy, 588. Thermo-electricity, 1044. Thermo-electric pile, 521. Thermoscope, Kumford's, 510. Thermometer, 492 ; air, 507 ; Breg net's metallic, 515; filling, 495 fixing standard points of, 497 ; gra duation of, 500; history of, 508 indications furnished by, 493 ; Les lie's diiferential, 509 ; limits of mer curial, 505 ; metastatic, 514 ; mount ing of, 501 ; Negretti and Zambra'i maximum, 512 ; Kutherford's max and min., 511 ; Saxton's deep sea 516 ; sensibility of, 504 ; spirit, 506 506 ; tubes, 494 ; Walferden's max imum, 513. Thermo-metric scales, 498 ; conver- sion of different into each other 499. Thunder, 1092 ; storms, 1093. Thilorier's carbonic acid apparatus 650. Timbre, 446. Time, measure of, 167. Tone, 444. Toothed-wheel, Savart's, 441. Tornadoes, 1060. Torricelli's theorem, 273 ; from, 274 ; tube, 320. Torsion, 48 ; electrometer, 919. Trains of wheel work, 203. Transfer of force, 123. Translucent bodies, 719. Transmission of luminous vibrations 848. Transmission of radiant heat, 583 : influence of the nature of the screens on the, 585 ; influence of the nature of the source on the 586. Transparent bodies, 719. Transpiration of gases, 351. Transverse strength, 102. Triangular mass supported on its angles, 145. Trichnic system, 58 ; modified forms of, 65, 66. Trimorphism, 94. Truck, 201. Trumpet, hearing, 439 ; speaking, Tubes, speaking, 437 ; vibrations in, 462-465. Tuning forks, 460. Tympanum, 480. Umbra, 729. Undulations, circular, 400; of air, 411; of a sphere of air, 412; of the waters of the globe, 410 ; ori- gin of, 380; phases of, 384; pro- gressive, 381 ; progressive in li- quids, 401. Uniformly accelerated and retarded motion, 118. Unison, 447. Unorganized beings, growth of, 52. Utility of machines, 193. Vacuum limited, 366 ; pans, 633. Value of fuel, 687. Vaporization, 619, 709 ; temperature and limits of, 624. Vapor, quantity of, given off by the the body, 692. Vapors, liquefaction of, 640 ; maxim- um tension of, 621. Variable motion, 117. Variation chart, 884; magnetic, 883. Variations of motion, 115. Veins, constitution of, 277 ; contrac- tions of, 278. Velocity, 116. 125 ; of falling bodies, 152 ; of light, 723, 838 ; relation of, to quantity of matter, 124. Ventilating shaft, Stone's, 696. Ventilation of buildings, 695 ; quan- tity of air required for, 693 ; sup- ply of fresh air for, 699. Ventilators, Emerson's, 698. , 474. Vibrations corresponding to notes, 451, 452 ; forms of, 387 ; isochron- ous, 383 ; of air in tubes, laws of, 467 ; of air in tubes, results of experiments, 468 ; of cords, 388 ; of cords, laws of, 389 ; of elastic plates, 392 ; of membranes, 398 ; of planes, laws of, 395 ; of rods, 390 ; of solids, 386 ; paths of, 391. Virtual velocities, principles of, 190. Vision, conditions of distinct, 785 ; distance of distinct, 788 ; double, 793 ; single with two eyes, 792. Visual angle, 783 ; impressions, time required to produce, 798 ; rays nearly parallel, 789. is- viva, 128. itreous and resinous electricity, 909. ocal apparatus of man, 469. /"oice, 469 ; mechanism of, 472 ; range of human, 473. [olume of bodies, change in the, 710. oltaic action, chemical theory of, 1001 ; arch, heat of, 988 ; contact theory of, 1000; polarization and transfer of elements in, 1004. oltaic circle, difference between simple and compound, 969, 981. /"oltaic couple, simple, 969. T oltaic current, direction of, depends deductions Ventriloquism, 720 INDEX. on direction of chemical activity, 969 ; energy of, proportional to chemical activity, 1001 j measure- ment of heat of, 989 ; resistances to, ogical Wh Voltaic decomposition, 991; law of chemical equivalents in, 992. Voltaic electricity, 966 ; chemical ac- tion necessary for production of, 1001 ; laws of the disengagement of, 1002; quantity of, to produce chemical decomposition, 1003. Voltaic piles, 967 ; Volta's, 967 ; Wol- laston's, 973 ; effects, physiologica" effects of, 997 ; magnetic and elec trical effects, 998 ; spark, 985 ; arch, 984, 985. Voltameter, 991 ; Volta's pile, 967. Volta's discovery, origin of, 966 ; con- tact theory of the pile, 1000. Walferdin's maximum thermometer, 513. Water, freezing of, 618; jets, 282; level, 255; maximum density of, 542 ; spouts, 1061 ; wheels, 285. Watt's improvements in engines, 682. Waves, circular reflected from a plane, 407 ; combination of, 408 ; depth of, 403 ; intensity and velo- city of aerial, 413 ; intensity of ae- rial expanding freely, 415 ; inter- ference of aerial, 413 ; interference of, in an ellipse, 409 ; length of sonorous, 453 ; production of, 399 ; reflection of, from foci of an ellipse, 405 ; reflection of, from foci of a parabola, 406. Wedge, 213; applications of, 215; resistance to be overcome, 214. Wedgewood's pyrometer, 517. Weighing machine, 201. Wells, Artesian, 251. Wheel and axle, 202. Wheel, barometer, 329. Wheel work, analysis of trains of, 204; trains of, 203. Whirlwinds, 1060. Whole space described by falling bodies, 154. Winds, cause of, 1055; periodical, 1057 ; regular, 1056 : trade, 1056 ; variable, 1058 ; velocity of, 1063. Zamboni's dry pile, 979. Zero-point, displacement of in ther- mometer, 502. a Zinc, amalgamated, 971 ; local ac- tion of, 971. 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