NRLF A REESE LIBRARY OP THK UNIVERSITY OF CALIFORNIA. > ' THE FORCES OF NATURE A POPULAR INTRODUCTION TO THE STUDY OF PHYSICAL PHENOMENA. BY AMEDEE GUILLEMIN. TRANSLATED FROM THE FRENCH BY MRS. NORMAN LOCKYER; AND EDITED, WITH ADDITIONS AND NOTES, BY J. NORMAN LOCKYER, F.R.S. OF TWO COLOURED PLATES, A PHOTOGRAPH, AND FOUR HUNDRED AND FIFTY- SIX WOODCUTS. THIRD EDITION. MACMILLAN AND CO. 1877. LONDON : R CI-AY, SONS, AND TAYLOR, BREAD STREET HII.L. PREFACE. "HI ROM time immemorial the mind of man has felt a strong desire to fathom the laws which govern the various phenomena of Nature, and to understand her in her most secret work in short, to make itself master of her forces, in order to render them as useful to material as to intellectual and moral life ; such is the noble undertaking to which the greatest minds have devoted themselves. For too long did man wander in this eager and often dangerous pursuit of truth : beginning with fanciful interpretations in his infancy, he by degrees substituted hypothesis for fable ; and then, at length, understanding the true method, that of experimental observation, he has been able, after innumerable efforts, to give in imperishable formulae, the most general idea of the principal phenomena of the physical world. In order thus to place itself in communion with Nature, our intelligence draws from two springs, both bright and pure, arid equally fruitful Art and Science : but it is by different, we may say even by opposite, methods that these springs at which man may satisfy his thirst for the ideals, which constitute his nobleness and greatness, the love of the beautiful, truth and justice, have been reached. The artist abstains from dulling the brilliancy of his impressions by a PREFACE. cold analysis ; the man of science, on the contrary, in pre- sence of Nature, endeavours only to strip off the magnificent and poetical surroundings, to dissect it, so to speak, in order to dive into all the hidden secrets ; but his enjoyment is not less than that of the artist, when he has succeeded in recon- structing, in its intelligible whole, this world of pheno- mena of which his power of abstraction has enabled him to investigate the laws. We must not seek then in the study of physical pheno- mena, from a purely scientific point of view, the fascination of poetical or picturesque description ; on the other hand, such a study is eminently fit to satisfy that invincible tendency of our minds, which urges us on to understand the reason of things that fatality which dominates us, but which it is possible for us to make use of to the free and legitimate satisfaction of our faculties. Gravity, Sound. Heat, Electricity, and Light are the divisions under which are arranged the phenomena the description of which forms the object of this work. The programme has not been confined to a simple explanation of the facts : but an attempt has been made to grasp their relative bearings, or, in other words, their laws ; a slightly difficult task, perhaps, when we cannot use the clear and simple language of mathematics. It may be added that the present work has been carried out in the same spirit as the astronomical one, " The Heavens ; " which is sufficient to show that there has been neither the thought nor the intention to compile a Treatise on Physics ; I have been content to smooth the way for those who desire to extend their studies, and likewise to present to general readers a sufficiently exact and just idea of this branch of science. PREFACE. vii In this attempt at a description of physical phenomena T have drawn from numerous sources, too long to enumerate, science having developed so much during the last two cen- turies ; but I should fail in a simple act of justice, if I did not express my gratitude to one of our most learned physicists, M. le Eoux, who was kind enough to read over most of the proofs of the work, and whose judicious advice has been of so much use to me. I must acknowledge the valuable aid of the artists, especially of MM. Bonnafoux and Laplante, Digeon and Rapine, who have designed or engraved the coloured plates and woodcuts. AMEDEE GUILLEMIN. CONTENTS. BOOK I. G R A V I T 7. CHAPTER I. PHENOMENA OF GRAVITY ON THE SURFACE OF THE EARTH. Manifestation of weight by motion : fall of bodies, flowing of liquids, ascent of gas Pressure of bodies in equilibrium ; stability of the various solid, liquid, and gaseous strata which constitute the terrestrial globe Crumbling away of mountains ; fall of avalanches and of blocks of ice in the polar regions Air and sea currents Page 3 CHAPTER II. WEIGHT AND UNIVERSAL GRAVITATION. Common tendency of heavy bodies to fall towards the centre of the earth Weight is a particular case of the force of universal gravitation All the particles of the globe act on a falling stone as if they were all situated in the centre of the earth The force of gravity acts beyond the atmosphere even in the celestial spaces : the sun, planets, stars all bodies gravitate towards each other Page 10 CHAPTER III. LAWS OF ATTRACTION. FALLING BODIES. First experiments of Galileo on falling bodies Equal velocity of bodies falling in vacua Vertical direction of gravity Deviation from the vertical due to the rotation of the earth Galileo's inclined plane ; Attwood's machine ; Morin's machine ; laws of falling bodies Influence of the resistance of the air on the velocity of bodies falling through the atmosphere ; experiments of Desagulier Page 16 CONTENTS. CHAPTER IV. LAWS OF GRAVITY. THE PENDULUM. The Pendulum Galileo's observations Definition of the simple pendulum Iso- chronism of oscillations of small amplitude Relation between the time of the oscillations and the length of the pendulum Variations of the force of gravity in different latitudes Borda's pendulum Lengths of the pendulums which beat seconds in London, at the equator, and at the poles Calculation of the oblateness of the earth Experiments proving that the density of the earth increases from the surface to the centre Page 34 CHAPTER V. WEIGHT OF BODIES. EQUILIBRIUM OF HEAVY BODIES. CENTRE OF GRAVITY. THE BALANCE. Distinction between the weight of a body and its mass Loss of weight which a body undergoes when it is taken from the poles to the equator Centre of gravity, in bodies of geometric form ; in bodies of irregular form The Balance ; conditions of accuracy and sensibility Balance of precision Method of double weighing Specific gravity and density of bodies . Page. 45 CHAPTER VI. WEIGHT OF LIQUIDS. PHENOMENA AND LAWS OF EQUILIBRIUM: HYDROSTATICS. Difference of constitution of solids and liquids ; molecular cohesion Flowing of sand and powders Mobility of the molecules of liquid bodies Experiments of the Florentine Academicians ; experiments of modern philosophers Pascal's law of equal pressures Horizontality of the surface of a liquid in equilibria Pressure on the bottom of vessels ; pressures normal to the sides ; hydraulic screw Hydrostatic paradox ; Pascal's bursting-cask Equilibrium of super- posed liquids ; communicating vessels Page 58 CHAPTER VII. EQUILIBRIUM OF BODIES IMMERSED IN LIQUIDS. PRINCIPLE OF ARCHIMEDES. Pressure or loss of weight of immersed bodies Principle of Archimedes Experi- mental demonstration of this principle Equilibrium of immersed and floating bodies Densities of solid and liquid bodies ; Areometers .... Page 73 CHAPTER VIII. WEIGHT OF THE AIR AND OF GASES. THE BAROMETER. The air a heavy body Elasticity and compressibility of air and other gases Pneumatic or fire syringe Discovery made by Florentine workmen Nature abhors a vacuum Experiments of Torricelli and Pascal Invention of the barometer Description of the principal barometers . . . . . Page 84 CONTENTS. CHAPTER IX. WEIGHT OF THE AIR AND OF GASES (continued). PUMPS. MARIOTTfi's LAW. THE AIR-PUMP. Principle of the ascent of liquids in pumps Suction and force pumps The siphon Air-pump ; principle of its construction Double and single barrel air-pumps Condensing pumps Mariotte's law Page 102 BOOK II. SOUND. CHAPTER I. THE PHENOMENA OF SOUND Poge 123 CHAPTER II. PRODUCTION AND PROPAGATION OF SOUND. REFLECTION OF SOUND. VELOCITY OF SOUND IN DIFFERENT MEDIA. Production of sound by a blow or percussion, and by friction, in solids, liquids, and gases Production of sound by the contact of two bodies at different tem- peratures ; Trevelyan's instrument Chemical harmonicon The air a vehicle of sound ; transmission of sound by other gases, by solids and liquids Pro- pagation of sound at great distances through the intervention of the ground Velocity of sound through air ; influence of temperature ; experiments of Villejuif and Montlhery Velocity of sound in water ; experiments made on the Lake of Geneva, by Colladon and Sturm Velocity of sound through different solid, liquid, and gaseous bodies Page 126 CHAPTER III. PROPAGATION OF SOUND. PHENOMENA OF THE REFLECTION AND REFRACTION OF SOUND. Echoes and resonances Simple and multiple echoes ; explanation of these phenomena Laws of the reflection of sound : experimental verification- Phenomena of reflection at the surface of elliptical vaults Experiments which prove the refraction of sonorous impulses Page 138 CHAPTER IV. SONOROUS VIBRATIONS. Experiments which prove that sound is produced by the vibratory movement of the particles of solid, liquid, and gaseous bodies Vibrations of a cord, rod, or bell Trevelyan's instrument Vibrations of water and of a column of air Nature xii CONTENTS. of sound : pitch, intensity, and clang-tint The pitch depends on the number of vibrations of the sounding body ; Savart's toothed wheel ; Cagniard-Latour's and Seebeck's syrens Graphic method Variable intensity of sound during the day and night Limit of perceptible sounds ... ... Page 145 CHAPTER V. LAWS OF SONOROUS VIBRATIONS, IN STRINGS, RODS, PIPES, AND PLATES. Experimental study of the laws which govern the vibration of strings Monochord or Sonometer Nodes and ventral segments ; harmonics Laws of the vibra- tions of sonorous pipes Vibrations in rods and plates Nodal lines of square, round, and polygonal plates Page 163 CHAPTER VI. PROPAGATION OF SOUND IN AIR. SOUND WATES. Nature of sound waves ; their propagation in a tube The wave of condensation and the wave of rarefaction Length of sonorous undulations Propagation through an unlimited medium ; spherical waves ; diminution of their amplitude with the distance Direction of sound waves Co-existence of undulations Perception of simultaneous sounds ; Weber's experiments .... Page 178 .CHAPTER VII. MUSICAL SOUNDS. THE GAMUT, OR MUSICAL SCALE. Distinction between noises and musical sounds Definition of the gamut ; intervals which compose it The scale of the musical gamut is unlimited ; convention which limits it in practice Names and values of the intervals of the natural major scale Modulations ; constitution of the major scales proceeding by sharps and flats Minor scale Page 185 CHAPTER VIII. OPTICAL STUDY OF SOUNDS. Vibrations of a tuning-fork ; the sinuous curve by which they are represented Appreciation of the comparative pitch of two notes by the optical method of M. Lissajous Optical curves of the different intervals of the scale ; differences of phase Determination of the concord of two tuning-forks Vibrations of columns of air in tubes ; manometric flames, M. Koenig's method Comparative study of the sounds given out by two tubes ; the nodes and ventral segments of columns of air Page 193 CHAPTER IX. QUALITY OF MUSICAL NOTES. Simple and compound notes Co-existence of harmonics with the fundamental notes The quality (clang-tint) of a note depends on the number of the harmonics and their relative intensity : M. Helmholtz's theory Harmonic resonant chambers (resonnateurs) ; experimental study of the quality of musical notes Quality of vowels Page 204 CONTENTS. CHAPTEK X. HEARING AND THE VOICE. Organ of hearing in man ; anatomical description of the ear The external ear ; the orifice and auditory meatus The intermediate ear; the drum and its membrane; chain of small bones The internal ear or labyrinth ; semicircular canals, the cochlea and fibres of Corti ; auditory nerve Role of these different organs in hearing ; the difference between hearing and listening The organ of the voice in man ; larynx, vocal cords Clang-tint of voices Page 208 BOOK III. LIGHT. CHAPTER I. SOURCES OF LIGHT ON THE SURFACE OF THE EARTH. Sources of cosmical light : the sun, planets, and stars Terrestrial, natural, and artificial luminous sources Lightning ; Polar aurorse : electric light ; volcanic fires ; light obtained by combustion Page 219 CHAPTER II. THE PROPAGATION OF LIGHT IN HOMOGENEOUS MEDIA. Light is propagated in vacuo Transparent, solid, liquid, and gaseous bodies ; transparency of the air Translucid bodies Light is propagated in a right line in homogeneous media ; rays, luminous pencils, and bundles of rays Cone of shadow, broad shadow, cone of penumbra The camera obscura Light is not propagated instantaneously Measure of the velocity of light by the eclipse of Jupiter's satellites Methods of MM. Fizeau and Foucault . . . Page 221 CHAPTER III. PHOTOMETRY. MEASURING THE INTENSITY OF LIGHT SOURCES. Luminous intensity of light sources, illuminating power Principles of photometry Law of distances Law of cosines Rumford's photometer Bouguer's photo- meter Determination of the illuminating power of the Sun and the full Moon Stellar photometer ' . Page 238 CONTENTS. CHAPTER IV. REFLECTION OF LIGHT. Phenomena of reflection of light Light reflected by mirrors ; diffused light ; why we see things Path of incident and reflected rays ; laws of reflection Images in plane mirrors Multiple images between two parallel or inclined surfaces ; kaleidoscope Polemoscope ; magic lantern Spherical curved mirrors ; foci and images in concave and convex mirrors Caustics by reflection Conical and cylindrical mirrors Luminous spectres . ." Page 247 CHAPTER V. REFRACTION OF LIGHT. Bent stick in water ; elevation of the bottoms of vessels Laws of the refraction of light ; experimental verification Index of refraction Total reflection Atmospheric refraction ; distortion of the sun at the horizon . . . Page 275 CHAPTER VI. REFRACTION OF LIGHT. PRISMS AND LENSES. Transparent plates with parallel faces ; deviation of luminous rays Multiple images in a silvered mirror Prisms Phenomena of refraction in prisms Converging and diverging lenses Real and virtual foci of converging lenses ; real and virtual images Foci and images of diverging lenses Dark chamber Megascope Magic lantern and phantascope Solar microscope . . Page 286 CHAPTER VII. COLOURS : THE COLOURS IN LIGHT SOURCES, AND IN NON-LUMINOUS BODIES. DISPERSION OF COLOURED RAYS. White colour of the sun's light Decomposition of white light into seven simple colours ; solar spectrum Reconiposition of white light by the mixture of the coloured rays of the spectrum Newton's experimenl ; unequal refrangibility of simple rays Colours of non-luminous bodies Page 306 CHAPTER VIII. COLOURS. Classification of colours Tones and scale of the colours of the solar spectrum, after the method of M. Chevreul Chromatic circles of pure and subdued colours ; tones and scales Complementary colours Page 317 CHAPTER IX. LINES OF THE SOLAR SPFCTRUM. The discoveries of Wollaston and Fraunhofer ; dark lines distributed through the different parts of the solar spectrum Spectral lines of other luminous sources Spectrum analysis ; spectrum of metals ; inversion of the spectra of flames Chemical analysis of the atmosphere of the sun, of the light of stars, nebuke, and comets Page 323 CONTENTS. CHAPTER X. SOLAR RADIATIONS. CALORIFIC, LUMINOUS, AND CHEMICAL. Divisions of the spectrum ; maximum luminous intensity of the spectrum Obscure or dark rays ; heat rays ; chemical rays Fluorescence, calorescence. Page 336 CHAPTER XI. PHOSPHORESCENCE. Phenomena of spontaneous phosphorescence Animal and vegetable phosphores- cence Glow-worms and fulgurse ; infusoria and medusae Different conditions which determine the phosphorescence of bodies Phosphoresence by inso- lation Becquerel's phosphoroscope . . . Page 341 CHAPTER XII. WHAT IS LIGHT? Hypotheses concerning the nature of light Newton's emission theory Huyghens' undulatory theory ; vibrations of the ether Propagation of luminous waves ; wave-lengths of the different rays of the spectrum ...... Page 348 CHAPTER XIII. INTERFERENCE OF LUMINOUS WAVES. PHENOMENA OF DIFFRACTION. GRATINGS. Dark and bright fringes due to very small apertures Grimaldi's experiment Interference of luminous waves ; experimental demonstration of the principle of interference Phenomena of diffraction produced by slits, apertures of different form and gratings Coloured and monochromatic fringes .... Page 357 CHAPTER XIV. COLOURS OF THIN PLATES. The soap-bubble Iridescent colours in thin plates Newton's experiment on coloured rings ; bright and dark rings Laws of diameters and thicknesses Coloured rings are phenomena of interference Analysis of the colours of the soap-bubble Page 367 CHAPTER XV. DOUBLE REFRACTION OF LIGHT. Discovery of double refraction by Bartholin Double images in crystals of Iceland spar Ordinary and extraordinary rays ; principal section and optic axis Positive and negative crystals Bi-refractive crystals with two axes, or bi-axial crystals Page 376 xvi CONTENTS. CHAPTER XVI. POLARIZATION OF LIGHT. Equal intensity of the ordinary and extraordinary images in a doubly refracting crystal Natural light Huyghens' experiments ; variations of intensity with four images ; polarized light Polarization of the ordinary ray ; polarization of the extraordinary ray : the two planes in which these polarizations take place Polarization by reflection Page 385 CHAPTER XVII. CHROMATIC POLARIZATION. Discovery of the colours of polarized light, by Arago Thin plates of doubly refractive substances ; variations of colours according to the thickness of the plates Colours shown by compressed and heated glass Coloured rings in crystals with one or with two axes Direction of luminous vibrations : they are perpendicular to the direction of propagation, or parallel to the surface of the waves Page 397 CHAPTER XVIII. THE EYE AND VISION. Description of the human eye Formation of - images on the retina Distinct vision of the normal eye Conformation of the eyes in Myopsis and Presbyopsis Page 406 BOOK IY. HEAT. CHAPTER I. DILATATION. THERMOMETERS. Sensations of heat and cold ; causes of error in the perception of the temperature of bodies General phenomena of dilatation and contraction in solids, liquids, and gases Temperature of bodies Thermometers based on dilatation and contraction The mercurial thermometer Alcohol thermometer Air ther- mometers ; metallic thermometers Page 415 CHAPTER II. MEASURE OF EXPANSION. Effects of variations of temperature in solids, liquids, and gases. Applications to the arts Rupert's drops Measure of the linear expansion of solids Expan- sion of crystals Contraction of iodide of silver Absolute and apparent ex- pansion of liquids All gases expand to the same extent between certain limits of temperature Page 432 CONTENTS. xvii CHAPTER III. EFFECTS OF VARIATIONS OF TEMPERATURE : CHANGES IN THE STATE OF BODIES. The passage of bodies from a solid to a liquid state : fusion Return of liquids to the solid state : solidification or congelation Equality of the temperatures of fusion and solidification Passage of liquids into gases : difference between evaporation and vaporization Phenomenon of ebullition : fixed temperature of the boiling-point of a liquid under a given pressure Return of vapours and gases into a liquid condition : liquefaction and congelation of carbonic acid and several other gases A permanent gas defined Page 443 CHAPTER IV. PROPAGATION OF HEAT. RADIANT HEAT. Heat is transmitted in two different ways, by conduction and by radiation Examples of these two modes of propagation Radiation of obscure heat in vacua Radiant heat is propagated in a straight line ; its velocity is the same as that of light Laws of the reflection of heat ; experiments with conjugate mirrors Apparent radiation of cold Burning mirrors Refraction of heat; burning glasses Similarity of radiant heat and of light Study of radiators, reflectors, absorbing and diathermanous bodies Thermo-electric pile ; experi- ments of Leslie and Melloni Page 457 CHAPTER V. TRANSMISSION OF HEAT BY CONDUCTION. Slow transmission of heat in the interior of bodies Unequal conductivity of solids Conductivity of metals, crystals, and non-homogeneous bodies Pro- pagation of heat in liquids and gases ; it is principally effected by transport or convection Slight conductivity of liquid and gaseous bodies . . Page 477 CHAPTER VI. CALORIMETRY. SPP:CIFIC HEAT OF BODIES. Definition of a unit of heat Heat absorbed or disengaged by bodies during varia- tions in their temperature Specific heat of solids Latent heat of fusion Ice-calorimeter Latent heat of vaporization of water .... Page 484 CHAPTER VII. SOURCES OF HEAT. Solar heat ; measure of its intensity at the surface of the earth, and at the limits of the atmosphere ; total heat radiated by the sun Temperature of space Internal heat of the globe Heat disengaged by chemical combinations ; combustion Heat of combustion of various simple bodies Production of high temperatures by the use of the oxyhydrogen blowpipe Generation of heat by mechanical means ; friction, percussion, compression , Page 492 xviii CONTENTS. CHAPTER VIII. HEAT A SPECIES OF MOTION. What we understand by the mechanical equivalent of heat Joule's experiments for determining this equivalent Reciprocal transformation of heat into mechanical force, and of mechanical force into heat Heat is a particular kind of motion . Page 504 BOOK Y. MAGNETISM. CHAPTER I. MAGNETS. Phenomena of magnetic attraction and repulsion Natural and artificial magnets ; magnetic substances Poles and neutral line in magnets Action of magnets on magnetic substances ; action of magnets on magnets Law of magnetic attraction and repulsion Direction of the magnetic needle : declination and inclination; influence of the terrestrial magnet Process of magnetization Attractive force of magnets Page 511 BOOK VI. ELECTRICITY. CHAPTER I. ELECTRICAL ATTRACTION AND REPULSION. Attraction of amber for light bodies Gilbert's discoveries ; electricity developed by the friction of a number of bodies Study of electrical attraction and repul- sion ; insulators, or bad conductors ; good conductors Electrical pendulum Resinous and vitreous, positive and negative electricity Laws of electrical attraction and repulsion Distribution of electricity on the surface of bodies Influence of points \* ' ' Pa 9 e 5 ' 31 CHAPTER II. ELECTRICAL MACHINES. Electrification at a distance ; development of electricity by induction Distribution of electricity on a body electrified by induction Hypothesis as to the normal condition of bodies ; neutral electricity proceeding from the combination of CONTENTS. positive and negative electricities Electroscopes ; electric pendulum ; dial and gold-leaf electroscopes Electrical machines : Otto von Guericke's machine ; Ramsden, or plate-glass machines ; machines of Nairne and Armstrong The electrophorus Page 545 CHAPTEE III. LEYDEN JAR. ELECTRICAL CONDENSERS. The experiments of Cuneus and Muschenbroeck ; discovery of the Leyden jar Theory of electrical condensation ; the condenser of ^Epinus Jar with moveable coatings Instantaneous and successive discharges Leichtenberg's figures Electric batteries The universal discharger Apparatus for piercing a card and glass Transport and volatilization of metals; portrait of Franklin Chemical effects of the discharge ; Volta's pistol Fulminating pane. Page 567 CHAPTER IV. THE PILE OR BATTERY. ELECTRICITY DEVELOPED BY CHEMICAL ACTION. Experiments of Galvani and discoveries of Volta ; condensing electrometer Description of the upright pile Electricity developed by chemical actions Theory of the pile ; electro-motive force ; voltaic current Electricities of high and low tension Couronne de tasses ; Wollaston's pile ; helical pile Constant- current piles ; Daniell, Bunsen, and Grove elements Physical, chemical, and physiological effects of the pile Experiments with dead and living animals. Page 585 CHAPTER V. ELECTRO-MAGNETISM. Action of a current on the magnetic needle ; Oersted and Ampere Schweigger's multiplier ; construction and use of the galvanometer Action of magnets on currents Action of currents on currents Influence of the terrestrial magnetic f orc e Ampere's discoveries ; solenoids ; the electrical helix ; theory of magnets Magnetism of soft iron or steel discovered by Arago ; magnetization by means of helices The electro-magnet ; its magnetic power ; its effects . Page 604 CHAPTER VI. PHEONMENA OF INDUCTION. Discovery of induction by Faraday Induction by a current ; inducing coil and induced coil Induction by a magnet Machines founded on the production of induced currents Clarke's machine Ruhmkorff's machine Commutator Effects of the induction coil Page 620 b 2 xs CONTENTS. CHAPTER VIT. THE ELECTRIC LIGHT. Sparks obtained by static electrical discharges ; luminous tufts Light in rarefied g ases Voltaic arc ; phenomena of transport ; form of the carbon points Intensity of the electric light Electric light of induction currents Stratifi- cations ; experiments with Geissler's tubes Phosphorescence of sulphate of quinine Page 631 BOOK VII. ATMOSPHERIC METEORS. Optical meteors ; mirage, rainbow Tension of aqueous vapour in the atmosphere ; hygrometry Clouds and fogs Dew, rain, snow Crystals of snow and ice Variations of barometric pressure Measure of maxima and minima tempe- ratures Electrical meteors ; thunderbolts, thunder and lightning Aurora boreales Page 645 APPENDIX. DISCOVERY OF OXYGEN IN THE SUN BY PHOTOGRAPHY, AND A NEW THEORY OF THE SOLAR SPECTRUM Page 673 INDEX " Page 685 COLOURED PLATES. PAGE I. POLAR AURORA BOREALIS (Front.) 521 II. SPECTRA OF DIFFERENT LIGHT SOURCES ... 352 III. SPECTRUM SHOWING OXYGEN AND NITROGFN IN THE SUN 673 LIST OF ILLUSTRATIONS ON WOOD. FIG. PAOF 1. Action of weight shown by the tension of a spring 4 2. Convergence of the verticals towards the centre of the earth .... 11 3. Tke Leaning Tower at Pisa 17 4. Experiment showing the equal velocity of bodies falling in vacuo ... 10 5. The direction of gravity is perpendicular to the surface of liquids at rest 21 6. Eastern deviation in the fall of bodies 23 7. Movement of heavy bodies on an inclined plane 24 8. Pulley of Attwood's machine 25 9. Experimental study of the laws of falling bodies. Attwood's machine . 26 10. Experimental study of falling bodies. Law of spaces described ... 27 11. Experimental study of falling bodies. Law of velocity 29 12. M. Morin's machine 30 13. Parabola described by the weight in its fall 31 14. Oscillatory movement of a simple pendulum 36 15. Compound pendulum 38 16. Effect of centrifugal force 40 17. Borda's pendulum. Platinum sphere and knife-edge 41 18. Borda's pendulum. Measurement of the time of an oscillation by the method of coincidences 42 19. Weight of a body ; centre of gravity 45 20. Centres of gravity of parallelograms, a triangle, a circle, a circular ring, and an ellipse 47 21. Centres of gravity of a prism, pyramid, cylinder, and cone 48 22. Centres of gravity of an ellipsoid and a sphere of revolution .... 48 23. Experimental determination of the centre of gravity of a body of irregular form or non-homogeneous structure 49 24. Equilibrium of a body supported on a plane by one or more points . . 50 25. Equilibrium of a body resting on a plane by three supports 50 26. Positions of equilibrium of persons carrying loads 51 27. Equilibrium on an inclined plane 51 28. Stable, neutral, and unstable equilibrium 52 29.- Scales 53 3D. Chemical balance : the beam 54 31. Chemical balance 55 32. Flowing of sand 59 xxiv LIST OF ILLUSTRATIONS. FTQ. 33. Cohesion of liquid molecules 60 34. Spherical form of dew-drops 60 35. Cohesion of liquid molecules ; drops of mercury 61 36. Principle of the hydraulic press ; 62 27. The pressure exercised on one point of a liquid is transmitted equally in every direction 63 38. The surface of liquids in repose is horizontal 63 39. Pressure of a liquid on the bottom of the vessel which contains it . . 64 40. Pressure of a liquid on the bottom of a vessel : Haldat's instrument . . 66 41. Pressure of a liquid on a horizontal stratum 67 42. The pressures of liquids are normal to the walls of the containing vessel 67 43. Hydraulic tourniquet 68 44. Hydrostatic paradox 68 45. Hydrostatic paradox. Pascal's experiment 69 46. Equilibrium of superposed liquids of different densities 70 47. Equality of height of the same liquid in communicating vessels ... 71 48. Communicating vessels. Heights of two liquids of different densities . 72 49. Experimental demonstration of the principle of Archimedes .... 74 50. Principle of Archimedes. Reaction of one immersed body on the liquid which contains it .*.....,,... 75 51. Equilibrium of a body immersed in a liquid of the same density as its own 78 52. Density of solid bodies. Method of the hydrostatic balance .... 79 53. Density of solid bodies. Charles' or Nicholson's areometer 80 54. Density of solid bodies. Method of the specific gravity bottle ... 81 55. Density of liquids. Hydrostatic balance 81 56. Specific gravity of liquids. Fahrenheit's areometer 82 57. Specific gravity of liquids. Method of the specific gravity bottle . . 82 58. Experimental demonstration of the weight of air and other gases ... 86 59. Elasticity and compressibility of gases 87 60. Pneumatic syringe 88 61. Torricelli's experiment 90 62. Torricelli's experiment. Effect of the weight of the atmosphere ... 90 63. Magdeburg hemispheres 92 64. Bursting a bladder by exhausting the air underneath it 92 65. Jet of water in vacua 93 66. Normal or standard barometer 95 67. An ordinary cistern barometer 95 68. Cistern of Fortin's barometer 96 69. Fortin's barometer as arranged for travelling 97 70. Gay-Lussac's barometer, modified by Bunten 98 71. Pial or wheel barometer 99 72. Bourdon's aneroid barometer 100 73. Vidi's aneroid barometer 101 74. Principle of the suction-pump 103 75. Suction-pump 104 76. Force-pump 105 77. Combined suction- and force-pump 105 LIST OF ILLUSTRATIONS. XX v *' PAGE 78. The siphon 106 79. Action of the piston and valves in the air-pump 108 80. Detail of the piston and its valves * .... 109 81. Air-pump with two cylinders. Transverse section 109 82. Plan of the air-pump with two cylinders 110 83. Exterior view of the air-pump Ill 84. Bianchi's air-pump. Interior view of the cylinder 112 85. Bianchi's air-pump. General view 113 86. The baroscope 115 87. Condensing machine. Interior view of the piston 115 88. Silbermann's condensing pump. Exterior view 116 89. Silbermann's condensing pump. Section 116 90. Connected condensing pumps 117 91. Experimental proof of Mariotte's law 118 92. Philosophical lamp or chemical harmonicon 128 93. Sound is not propagated in a vacuum 129 94. Measure of the velocity of sound through air, between Villejuif and Montlhery, in 1822 132 95. Experimental determination of the velocity of sound through water . 135 96. Experiments made on the Lake of Geneva, by Colladon and Sturm . 136 97. Reflection of sound. Phenomena of resonance 139 98. Property of the parabola 141 99. Experimental study of the laws of the reflection of sound 142 100. Reflection of sound from the surface of an elliptical roof 143 101. Sonorous refraction. M. Sondhauss's instrument 144 102. Vibrations of stretched string 146 103. Vibrations of a metal rod 147 104. Proof of the vibration of a glass bell 148 105. Vibrations of a metal clock-bell 149 106. Trevelyan's instrument 149 107. Trevelyan's instrument. Cause of vibratory movements 150 108. Vibrations of liquid molecules 150 109. Vibrations of a gaseous column 151 110. Savart's toothed wheel. Study of the number of vibrations producing sounds of a given pitch 152 111. Cagniard-Latour's Syren 153 112. Interior view of the Syren 153 113. Seebeck's Syren 154 114. Graphic study of the sonorous vibrations. Phonautography .... 155 115. Combination of two parallel vibratory movements ........ 156 116. Combination of two rectangular vibratory movements 157 117. Sonometer 164 118. Harmonic sounds. Nodes and ventral segments of a vibrating string . 167 119. Harmonics. Nodes and ventral segments of a vibrating string . . . 168 120. Vibrations of compound sounds 169 121. Prismatic sonorous pipes 170 122. Cylindrical sonorous pipes 170 123. Tubes of similar forms . , 171 LIST OF ILLUSTKATIONS. FIG. 124. Sonorous tubes. Laws of the vibrations of open and closed tubes of different lengths 172 125. Longitudinal vibrations of rods 174 126. Vibrations of a plate 1*75 127. Nodal lines of vibrating square plates, according to Savart .... 176 128. Nodal lines of vibrating circular or polygonal plates, according to Chladni and Savart 177 129. Nodes and segments of a vibrating bell 177 130. Propagation of the sonorous vibrations in a cylindrical and unlimited gaseous column 179 131. Curve representing a sound wave 179 132. Propagation of a sonorous wave through an unlimited medium . . . 181 133. Experiment proving the co-existence of waves. Propagation and reflec- tion of liquid waves on the surface of a. bath of mercury .... 183 134. A tuning-fork mounted on a sounding-box 194 135. Optical study of vibratory movements 196 136. Optical curves representing the rectangular vibrations of two tuning- forks in unison 197 137. Optical curves. The octave, fourth and fifth . 197 138. Open tube with manometric flames 199 139. Manometric flames. Fundamental note, and the octave above the fundamental note 200 140. Apparatus for the comparison of the vibratory movements of two sonorous tubes 201 141. Manometric flames simultaneously given by two tubes at the octave . 202 142. Manometric flames of two tubes of a third 202 143. M. Helinholtz'a resonance globe 205 144. M. Koenig's apparatus for analysing clang-tints 206 145. The human ear ; section of the interior tympanum ; chain of small bones. Internal ear ; labyrinth 210 146. Details of the auditory ossicles 211 147. Section of the cochlea 211 148. Auditory apparatus of fishes ; ear of the Ray 212 149. The human voice ; interior view of the larynx. Glottis ; vocal chords 213 150. Propagation of light in a right line 224 151. Rectilinear propagation of light 224 152. Cone of shadow of an opaque body. Completed shadow 225 153. Cones of umbra and penumbra 226 154. Silhouettes of perforated cards ; ei^ect of the umbra and penumbra . 227 155. Inverted image of a candle 228 156. Images of* the sun through openings in foliage . 229 157. Dark chamber. Reversed image of a landscape 230 158. Measure of the velocity of light by the eclipses of Jupiter's satellites . 232 159. M. Fizeau's instrument for the direct measure of the velocity of light . 235 160. Measure of the velocity of light by M. Fizeau 236 161. Law of the square of distances 241 162. Rumford's photometer 1 243 163. Bouguer's photometer , , , 244 LIST OF ILLUSTRATIONS. FIQ. 164. Phenomena of reflection 249 165. Experimental study of the laws of the reflection of light 251 166. Reflection from a plane mirror. Form and position of the images . . 252 167. Reflection from a plane mirror. Field of the mirror 253 168. Reflections from two plane parallel mirrors. Multiple images ... 254 169. Images on two mirrors inclined at right angles to each other .... 255 170. Images, in mirrors at right angles (90) 255 171. Images in mirrors at 60 255 172. Images in mirrors at 45 256 173. Symmetrical images formed in the kaleidoscope 256 174. Polemoscope 257 175. Magic telescope 258 176. Concave mirror. Inverted image, smaller than the object 259 177. Concave mirror. Inverted images, larger than the object 260 178. Concave mirror. Virtual images, erect and larger than the object . . 261 1 79. Concave mirror. Path and reflection of rays parallel to the axis. Prin- cipal focus 262 180. Concave mirror. Conjugate foci 263 181. Concave mirror. Virtual focus 263 182. Concave mirror. Real and inverted image of objects 264 183. Concave mirror. Erect and virtual image of objects 264 184. Upright virtual image in convex spherical mirror 265 185. Convex mirror. Erect and virtual image 266 186. Caustic by reflection 266 187. Caustic by reflection * 267 188. Cylindrical mirror. Anamorphosis 267 189. Reflection on conical mirrors. Anamorphosis 268 190. Light reflected very obliquely 269 191. Irregular reflection or scattering of light on the surface of an unpolished body 270 192. The Ghost (produced by reflection) 271 193. Arrangement of the unsilvered glass- and the position of the Ghost . . 273 194. Phenomena of refraction of light. The bent stick 275 195. Refraction of light. Apparent elevation of the bottoms of vessels . . 276 196. Experimental demonstration of the laws of refraction 278 197. Law of sines 279 198. Explanation of the bent stick 280 199. Apparent elevation of the bottoms of vessels ; explanation .... 280 200. Total reflection. Limiting angle 281 201. Phenomenon of total reflection 282 202. Phenomenon of total reflection, in the shutter of a camera obscura . . 283 203. Atmospheric refraction. The effect on the rising and setting of stars . 284 204. Normal view. ) Deviation due to refraction through plates with ) 205. Oblique view. ) parallel faces ) 206. Path of a luminous pencil 287 207. Multiple images produced by refraction in plates with parallel faces . 288 208. Path of the rays which give place to the multiple images of plates with parallel faces . 288 xxviii LIST OF ILLUSTKATIONS. Fia. PAGE 209. Geometrical form of the prism 288 210. Prism mounted on a stand 288 211. Deviation of luminous rays by prisms 289 212. Images of objects seen through prisms 290 213. Magnifying glass or lens with convex surfaces, side and front view . . 291 214. Converging lenses. Bi-convex lens ; plano-convex lens ; converging meniscus 292 215. Diverging lenses. Bi-concave lens , plano-concave lens ; diverging meniscus 292 216. Secondary axes of lenses. Optical centre . . :.-,,.. ...... 293 217. Path of rays parallel to the axis. Principal focus 294 218. The lens may be considered as an assemblage of prisms 295 219. Path of rays emanating from a luminous point on the axis. Conjugate foci 296 220. Path of rays emanating from a point situated between the principal focus and the lenses. Virtual focus 296 221. Eeal image, inverted and smaller than the object 297 222. Eeal image, inverted and larger than the object 298 223. Image of an object situated at a distance from the lens greater than the principal focal distance, and less than double that distance . . . 298 224. Erect and virtual images of an object placed between the principal focus and the lens 299 225. Principal virtual focus of diverging lenses 299 226. Erect virtual images, smaller than the object in a bi-concave lens . . 300 227. Camera obscura 301 228. Lens-prism of the camera obscura 302 229. Megascope 302 230. Magic lantern 303 231. Phantascope 304 232. Solar microscope, complete 304 233. Section of the solar microscope 305 234. Decomposition of light by the prism. Unequal refrangibility of the colours of the spectrum 307 235. Recomposition of light by a lens 309 236. Recomposition of light by prisms 310 237. Recomposition of white light by a revolving disc 311 238. Unequal refrangibility of various colours 312 239. Unequal refrangibilities of simple colours. Newton's experiment . . 313 240. A fragment of the solar spectrum 325 241. Spectroscope 327 242. M. Ed. Becquerel's phosphoroscope 345 243. Disc of the phosphoroscope 346 244. Grimaldi's experiment. Dark and bright fringes produced by a system of two small circular holes ,* . .-. . . 358 245. Interference of luminous waves 358 246. Fresnel's experiment of two mirrors ; experimental demonstration of the principles of interference ,.*,%. . 360 247. Effects of diffraction in telescopes. (Sir J. Herschel) 363 LIST OF ILLUSTRATIONS. xxix FIG. PAG 8 248. Strise of mother-of-pearl seen with a magnifying power of 20,000 diameters 365 249. Thin plate of air comprised between two glasses, one plane, the other convex. (Newton's experiment of coloured rings) 369 250. Newton's coloured rings 369 251. Colours of thin plates in the soap-bubble 373 252. Specimen of Iceland spar 377 253. Double images of objects seen through a crystal of Iceland spar . . . 378 254. Positions of the extraordinary image in relation to the plane of incidence. Principal section 380 255. Principal sections and optic axis of Iceland spar 380 256. Artificial section perpendicular to the optic axis 381 257. Crossing of the rays which produce the ordinary and extraordinary image 381 258. Eock crystal 383 259. Propagation of ordinary and extraordinary images of a double refracting crystal. Equal intensity 386 260. Equal intensity of ordinary and extraordinary images 386 261. Huyghens' experiment. Variations in intensity of the images seen when one prism of Iceland spar is rotated over another 387 262. Polarization of the ordinary ray by double refraction 388 263. Division of the ordinary ray. Variable intensities of the images of the polarized rays 389 264. Division of the extraordinary ray. Intensities of the images of the polarized rays 389 265. Specimen of Siberian tourmaline 391 266. The polariscope of Malus perfected by JVL Biot 394 267. Eelation between the polarized ray and the angle of polarization of a substance and the refracted ray 395 268. Colours of polarized light in compressed glass 399 269. Colours of polarized light in unannealed glass 400 270. Pincette of tourmaline 401 271. Horizontal section of the eyeball 407 27 la. Diagrammatic views of the nervous and the connective elements of the retina, supposed to be separated from one another 409 272. Formation of images in the normal eye 410 273. Formation of the image in the eye of a long-sighted person .... 411 274. Formation of the image in the eye of a short-sighted person .... 411 275. S'Gravesande's ring. Expansion of solids by heat 417 276. Expansion of solids 417 277. Linear expansion of a solid rod 418 278. Expansion of liquids by heat 419 279. Expansion of gases by heat 419 280. Expansion of gases 420 281. Eeservoir and tube of the mercurial thermometer 421 282. Determination of the zero in the mercurial thermometer ; temperature of fusion of ice 422 283. Determination of the point 100, the temperature of boiling water under a pressure of 760 millimetres , , 423 LIST OF ILLUSTRATIONS. FIG. PAGE 284. Centigrade thermometers with their graduated scales 424 285. Thermometrical scales 425 286. Air thermometers of Galileo and Cornelius Drebbel 427 287. Differential thermometers of Leslie and Rumford . 428 288. Unequal expansion of two different metals for the same elevation of temperature 429 289. Metallic dial thermometer 430 290. Breguet's metallic thermometer 430 291. Room of the Conservatoire des Arts et Metiers. Walls rectified by force of contraction 434 292. Dutch tears 435 293. Measure of the linear expansion of a solid, by the method of Lavoisier and Laplace 436 294. Laplace and Lavoisier's instrument for the measure of linear expansion 437 295. Experiment proving the contraction of water from to 4 .... 441 296. Effects of expansion produced by the freezing of water 447 297. Ebullition in open air 449 298. Papin's digester 450 299. Ebullition of water at a temperature lower than 100 451 300. Spontaneous evaporation of a liquid in the barometric vacuum. First law of Dalton 452 301. Invariability of the maximum tension of the same vapour at the same temperature. Dalton's second law 453 302. Inequalities of the maximum tensions of different vapours at the same temperature. Dalton's third law 454 303. Radiation of obscure heat in vacua 459 304. Reflection of heat ; experiments with parabolic conjugate mirrors . . 460 305. Burning mirror 462 306. Refraction of heat . 463 307. Echelon lens . . . 464 308. Measure of the emissive powers of bodies. Experiment with Leslie's cube 466 309. Elements of the thermo-electric pile 468 310. Thermo-electric pile for the study of the phenomena of heat .... 469 311. Apparatus used by Melloni to measure the reflecting powers of bodies 470 312. Melloni's apparatus for measuring the diathermanous power of bodies . 474 313. Cube of boiling water 474 314. Plate of blackened copper heated to 400 474 315. Incandescent spiral of platinum 474 316. Intensity of radiant heat. Law of the squares of the distances . . . 476 317. Unequal conductivities of copper and iron 478 318. Ingenhouz' apparatus for measuring conducting powers 478 319. Experiment on the conductivity of iron compared with that of bismuth 480 320. Unequal conductivity of quartz in different directions 480 321. Property of metallic gauze ; obstacle which it opposes to the propagation of heat 482 322. Measure of the specific heat of bodies . Simple ice calorimeter . . . 490 323. Measure of the specific heat of bodies by the ice calorimeter of Laplace and Lavoisier . .... 490 LIST OF ILLUSTRATIONS. xxxi FIO. PAOE 324. M. Pouillet's Pyrhelioraeter . 494 325. Combustion of iron in oxygen 497 326. Flame of a candle 498 327. Oxyhydrogen blowpipe 499 328. Joule's experiment. Determination of the mechanical equivalent of heat 506 329. Attraction of iron filings by a natural or artificial magnet 512 330. Magnetic pendulum 513 331. Attraction of a magnetic bar by iron 514 332. Magnetic figures. Distribution of iron filings on a surface . . . . 515 333. Consequent points, or secondary poles of magnets 515 334. Attraction and repulsion of the poles of magnets 516 335. Magnetization by the influence of magnetism 517 336. Magnetization by influence at a distance 518 337. Rupture of a magnet ; disposition of the poles in the pieces . . . . 518 338. Magnetic needle 519 339. Magnetic declination at Paris, October 1864 520 340. Inclination of the needle at Paris, October 1864 520 341. Magnetic needle, showing both the inclination and declination . . . 521 342. Coulomb's magnetic balance 522 343. Processes of magnetization. Method of single touch 523 344. Magnetism by separate double touch. Duhamel's process 524 345. Magnetization by the method of ^pinus 525 346. Compound magnet, formed of twelve magnetic bars 526 347. Iron horse-shoe magnet, with its armature and keeper 527 348. Magnet formed of two compound bar magnets 527 349. Natural magnet furnished with its armature 528 350. Attraction of light bodies 533 351. Electrical pendulum. Phenomena of attraction and repulsion . . . 535 352. Distribution of electricity on the surface of conducting bodies . . . 539 353. Distribution of electricity on the surface of bodies 540 354. Faraday's experiment to prove that electricity is located on the outer surface of electrified bodies 541 355. Tension of electricity at the different points of a sphere and of an ellipsoid 542 356. Tension of electricity on a flat disc, and on a cylinder terminated by hemispheres . 542 357. Power of points. Electric wind 544 358. Electric fly 544 359. Electricity developed by influence or induction 545 360. Distribution of electricity on an insulated conductor electrified by induction 546 361. Electrical induction through a series of conductors 548 362. Cause of attraction of light bodies 549 363. Quadrant electroscope 551 364. Gold-leaf electroscope 551 365. Otto von Guericke's electric machine 553 366. Plate electric machine . 555 xxxii LIST OF ILLUSTRATIONS. FIG. PAGE 367. Nairne's machine, furnishing the two electricities 558 368. Armstrong's hydro-electric machine 560 369. Electrophorus with resin cake 561 370. Electrical bells . . . . 562 371. Electrical hail 563 372. Luminous tube ; 564 373. Luminous globe . 565 374. Luminous square 565 375. Kinnersley's thermometer 566 376. Electrical mortar ,- . ' < . . . 566 377. Cuneus' experiment (the Leydea jar) 268 378. Charging the Leyden jar 569 379. The condenser of ^Epinus 570 380. Charging the condenser of .^pinus 571 381. Leyden jar with moveable coatings 572 382. Instantaneous discharge of a Leyden jar by means of the discharger . 573 383. Successive discharges of a Leyden jar. Chimes 574 384. Sparkling Leyden jar 574 385. Leichtenberg's figures. Distribution of the two kinds of electricity . 575 386. Leichtenberg's figures. Distribution of the positive electricity . . . 576 387. Leichtenberg's figures. Distribution of the negative electricity . . . 577 388. Battery of electrical jars 578 389. Universal discharger 579 390. Experiment of perforating a card 580 391. Experiment of perforating glass 581 392. Franklin's portrait experiment . 582 393. Press used in Franklin's portrait experiment 582 394. Volta's pistol. Interior view 583 395. Explosion of Volta's pistol 583 396. Fulminating pane 584 397. Contraction of the muscles of a frog. Repetition of Galvani's experiment 586 398. Volta's condenser 588 399. Voltaic or column pile 589 400. Electricity developed by chemical action 591 401. Crown, or cup pile 593 402. Wollaston's pile 594 403. Spiral pile 595 404. Couple of Daniell's battery 596 405. Couple of Bunsen's battery 597 406. Pile formed by five Bunsen's elements 598 407. Decomposition of water by the voltaic pile 601 408. Action of an electrical current on the magnetic needle 605 409. Deviation of the southern pole towards the left, under the influence of the upper current 606 410. Deviation to the left of the current. Lower current 606 411. Deviation to the left of the current. Vertical current 607 41 2. Schweigger's multiplier 607 413. Concurrent actions of the different portions of the wire in the multiplier 608 LIST OF ILLUSTRATIONS. xxxiii FIO. PAGE 414. System of two astatic needles . 609 415. Galvanometer . . 609 416. Action of a magnet on a current 611 417. Law of the attraction and repulsion of a current by a current . . . 611 418. Direction of a solenoid in the meridian, under the action of the earth . 613 419. Particular currents of magnets 614 420. Resulting currents at the surface of a magnet 614 421. Magnetization of a steel needle by a solenoid : right handed and left handed spirals 615 422. Magnetization by a spiral : production of consequent points .... 616 423. Horse-shoe electro-magnet 617 424. Electro-magnet .* 617 425. Electro-magnet with its charge 617 426. Magnetic chain 618 427. Induction by a current 621 428. Induction by the approach of a current 622 429. Induction by a magnet 623 430. Induction by the approach or removal of a magnetic pole 624 431. Clarke's magneto-electric machine 625 432. RuhmkorfFs induction coil 627 433. Commutator of RuhmkorfFs machine. Plan and elevation .... 629 434. Sparks obtained by the discharge of static electricity 632 435. Forms of electric discharges (Van Marum) 633 436. Electrical brush, according to Van Marum 635 437. Positive and negative brushes 636 438. Light in the barometric vacuum 636 439. The electric egg 637 440. Electric light in rarefied air. Purple bands 637 441. Carbon points of the electric light, and the Voltaic arc between them . 639 442. Luminous sheaf in rarefied air. Discharge of induction currents . . 641 443. Stratified light in rarefied gas 641 444. The mirage in the African desert 647 445. Explanation of a mirage 649 446. Paths of the effective rays through a drop of rain after a single internal reflection 651 447. Path of the effective rays after two interior reflections 651 448. Theory of the rainbow ; formation of the principal and secondary arc . 653 449. De Saussure's hair hygrometer 656 450. Forms of snow crystals (Scoresby) 657 451. Dissection of a block of ice by the solar rays. Crystalline structure of ice 660 452. Ice-flowers (Tyndall) 661 453. Rutherford's maximum and minimum thermometers 662 454. Maximum and minimum thermometers of M. Walferdin 663 455. The Gramme machine 679 456. Brayton's petroleum motor . 680 ,c INTEODUCTOEY CHAPTER FRENCH AND ENGLISH SCIENTIFIC UNITS. IN the varied examinations into the qualities and properties of matter with which Physical Science is especially concerned, certain units of measurement are essential. And it is unfortunate that in different countries these units are not the same. The Metric or French system, however, is now so universally acknowledged to be the best for scientific purposes, that the Editor by the advice of eminent scientific friends has retained it in this work. Its retention renders necessary a few words by way of introduction. One great advantage of the Metric System over our own is that it is a decimal system : thus, by the simplest decimal system of multi- plication and division, we are enabled to perform with speed and ease any calculations connected with it which may be necessary; another is that the same prefixes are used for measures of length, surface, capacity, and weight ; and, finally, these various measures are related to each other in the simplest manner. Unit of Length. The English unit of length is the yard, the length of which has been determined by means of a pendulum, vibrating seconds in the latitude of London, in a vacuum, and at the level of the sea. The length of such a pendulum* is to be divided into 3,913,929 parts, and 3,600,000 of these parts are to constitute a yard- The yard is divided into 36 inches, so that the length of the seconds pendulum in London is 39*13929 inches. The French unit of length, called the mbtre (from fierpea), I measure), has been taken as being the ten-millionth part of the quadrant of a xxxvi INTRODUCTORY CHAPTER. meridian passing through Paris ; that is to say, the ten-millionth part of the distance between the equator and the pole, measured through Paris. It is equal to 393707898 inches. The metre is divided into one thousand millimetres, one hundred centimetres, and ten dddmktres ; while a decametre is ten metres, a hectometre one hundred metres, a kilometre one thousand metres, and a myriometre, ten thousand metres. The following table gives the value of these measurements in English inches and yards : In English Inches. In Englifch yards. Millimetre 0-03937 0-0010936 Centimetre Decimetre . .... 0-39371 3-93708 0-0109363 0-1093633 METRE 39-37079 1-0936331 Decametre 393-70790 10-9363310 Hectometre Kilometre ....... 3937-07900 39370-79000 109-3633100 1093-6331000 Mvriometre 393707*90000 10936-3310 00 One English yard is equal to O91438 metre ; while one mile is equal to 1-60931 kilometre. In the annexed woodcut a decimetre, with its divisions into centimetres and millimetres, is shown, and compared with four inches divided into eighths and tenths. Unit of Surface. For the unit of surface, the square inch, foot, and yard adopted in this country are replaced in the metric system by the square millimetre, centimetre, decimetre, and metre. 1 square metre 1 square inch 1 square foot 1 square yard 1-1960333 square yards. 6-4513669 square centimetres. 9-2899683 square decimetres. 0-83609715 square metre. INTRODUCTORY CHAPTER. xxxvii In the annexed woodcut a square inch and a square centimetre are shown, in order to give an idea of measures of surface which will often be referred to in the following pages. Unit of Capacity. The cubic inch, foot, and yard- furnish measures of capacity ; but irregular measures, such as the pint and gallon, are also used in this country. The gallon contains ten pounds avoirdupois weight of distilled water at 62 F. ; the pint is one-eighth part of a gallon. The French unit of capacity is the cubic decimetre or litre (\irpa, the name of a Greek standard of quantity), equal to 1/7607 English pints, or O2200 English gallon ; and we have cubic inches, decimetres, centimetres, and millimetres. 1 litre 61-027052 cubic inches. 1 cubic foot 28-315311 litres. 1 cubic inch 16'386175 cubic centimetres. 1 gallon 4-543457 litres. Unit of Mass or Weight. The English unit of weight the pound is derived from the standard gallon, which contains 277'274 cubic inches ; the weight of one-tenth of this is the pound avoirdu- pois, which is divided into 7,000 grains. The French measures of weight are derived at once from the measures of capacity, by taking the weight of cubic millimetres, centimetres, decimetres, or metres of water at its maximum density, that is at 4 C. A cubic metre of water is a tonne, a cubic decimetre a kilogramme, a cubic centimetre a gramme, and a cubic millimetre a milligramme. .' ' In English grains. In Ib. Avoirdupois. , 1 lb.=700 grammes. Milligramme ( T y^th part of a 'gramme) Centigramme ( T J ff th ) Decigramme ( ^th ) GRAMME 0-015432 0-154323 1-543235 15-432349 0-0000022 0-0000220 0-0002205 0-0022046 Decagramme ( 10 grammes) . . . Hectogramme ( 100 ) . . . : Kilogramme ( 1000 ,, ) . . . Myriogramme (10000 ) . . . 154-323488 1543-234880 15432-348800 154323-488000 0-0220462 0-2204621 2-2046213 22-0462126 xxxviii INTRODUCTORY CHAPTER. Besides these units, there are others on which a few words may be said, as the units before referred to are implicated. The Unit of Time or Duration is the same for all civilised coun- tries. The twenty-fourth part of a mean solar day is called an hour, and this contains sixty minutes, each of which is divided into sixty seconds. The second is universally used as the unit of duration. Having now units of space and time, we are in a position to fix upon a Unit of Velocity. The units of velocity adopted by different scientific writers vary somewhat ; the most usual, perhaps, in regard to sound, falling bodies, projectiles, &c., is the velocity of feet or metres per second. In the case of light and electricity, miles or kilo- metres per second are employed. We have next the Unit of Mechanical Work. In this country the unit of mechanical work is usually the foot-pound, viz. the force necessary to raise one pound weight one foot above the earth in opposition to the force of gravity. A horse-power is equal to 33,000 Ib. raised to a height of one foot in one minute of time. In France the kilogrammetre is the unit of work, and is the force necessary to raise one kilogramme to a height of one metre against the force of gravity. One kilogrammetre 7'233 foot-pounds. The cheval vapeur is nearly equal to the English horse-power, and is equivalent to 32,500 Ib. raised to a height of one foot in one minute of time. The force competent to produce a velocity of one metre in one second, in a mass of one gramme, is sometimes adopted as a unit of force. Unit of Heat. These units vary : the French unit of heat, called a calorie, is the amount of heat necessary to raise one kilogramme (2-2046215 Ib.) of water one degree Centigrade in temperature ; strictly from C. to 1 C. In this country we sometimes take one pound of water and 1 Fahrenheit as the units ; sometimes one pound of water and 1 C. Thermometric degrees. The value of different thermometric INTRODUCTORY CHAPTER. XXXIX degrees is discussed in the work itself (vide Heat, Book IV., Chapter i.). The following facts may be found useful : 1 Fahrenheit 1 Centigrade 1 Reaumur = 0-55 C. = 0-44 R. = 0-80 R. = 1-81T F. = 1-25 C = 2-25 F. Centigrade degrees -T- 5 X 9 + 32 Reaumur ,, -f- 4 X 9 + 32 Fahrenheit - 32 ~^- 9 X 5 )> 1? - 32 -f- 9 X 4 Centigrade -4- 5 X 4 Reaumur 4 X 5 Fahrenheit degrees. > Centigrade Reaumur >i jj Centigrade r BOOK I. GEAVITY. OF THE UNIVERSITY PHYSICAL PHENOMENA. BOOK I. GRA VI TY. CHAPTER I. PHENOMENA OF GRAVITY ON THE SURFACE OF THE EARTH. Manifestation of weight by motion : fall of bodies, flowing of liquids, ascent of gas Pressure of bodies in equilibrium ; stability of the various solid, liquid, and gaseous strata which constitute the terrestrial globe Crumbling away of mountains ; fall of avalanches and of blocks of ice in the polar regions Air and sea currents. A STONE left to itself in the air falls, and its movement is arrested only on touching the ground ; a round body, or a solid ball, rolls along a plane inclined , to the horizon ; a liquid mass, such as a brook or large river, flows on the sloping sur- face which forms its bed; smoke and steam rise into the air. All these phenomena, and many others that we shall review, are the varied manifestations of one ever-active force, universally distributed throughout all nature, which is called Weight. All bodies, without exception, which are found on the surface of our planet in the depths of its crust, or in the gaseous strata of which its atmosphere is formed have weight. This is a fact so obvious that in the case of solid and liquid bodies it hardly requires to be stated. We shall soon have occasion to show that it holds good also with regard to gases and vapours. B 2 PHYSICAL PHENOMENA. [BOOK Nor is it only moving phenomena which familiarize us with the action of weight: it exercises itself also incessantly on bodies which appear to us to be at rest, and which in reality are only in equilibrium. The stone which has touched the ground, the fall of which our eyes have followed, continues thenceforth to weigh on the surface which upholds it, and this pressure, which is rendered evident by the constant tension of a spring (Fig. 1), is rendered sensitive to our organs by the effort which the hand is obliged to use to support the stone. A book placed on the table remains at rest but presses on its support, which itself rests on the ground. A mass of metal suspended at the lower end of the thread or flexible cord stretches the thread or cord ; this tension, which continues as long as the suspending thread is not cut, proves the continuous action of the force on the suspended body. IP ct We must therefore clearly understand that rest is not synonymous with inaction, and we may be assured that, on the earth, no material particle, whether solid, liquid, or gaseous, is ever for one moment free from the action of this force. Let us now endeavour to give a general picture of the terrestrial phenomena phenomena of equilibrium and of motion which are produced by this force. Astronomy teaches us that the earth is of the form of a nearly spherical ball, and has two movements movements in which all the parts of its mass participate at the same time : one of uniform rotation round one of its diameters, the other of translation, which draws it with varying velocity along an elliptic orbit, the sun being in a focus of that orbit. But neither the one nor the other of these movements directly affects the equilibrium of its various parts. The solid masses which form its crust ; the nucleus, probably in a state of incandescent fusion, which forms the interior ; the liquid part of its surface, the oceans; and lastly, the gaseous envelope which surrounds every portion of the spheroid, are in a FIG. 1. Action of weight shown by the tension of a spring. CHAP, i.] PHENOMENA OF GRAVITY. 5 state of relative stability, resulting from mutual pressure, due to the force which is now in question. It appears certain that the entire earth was once fluid, and that the different strata of which its interior is formed have ranged themselves in the order of their densities that is to say, the heaviest at the centre, the lightest at the surface, according to the same conditions which experience has proved to be necessary to the stability of liquids and to their equilibrium under the action of weight. And to speak only of the parts accessible to observation it is seen that such is precisely the order of their succession. Below we have the solid crust the solid surface of the earth : afterwards comes, spread over three quarters of this surface, the liquid part or sea ; then above both, the gaseous strata which form the atmosphere. Of these different constituents, the air presses on the water, and both press on the solid ground. Let us examine the surface of the continents and islands. We find everywhere that the relief of the ground is such that all its parts mutually support each other. In the mountains, as in the plains, weight acting on each particle has arranged the masses in such a way that equilibrium is never or very rarely destroyed. Suppose the action of weight suppressed ; the other physical forces, no longer finding resistance, would overturn the fields, rocks, and mountains, and would everywhere substitute disorder and confusion in place of the order which results from their present stability. It is again the pressure due to weight which man utilizes when he builds his most durable constructions in imitation of nature. The mass of the materials, their vertical disposition, or, better still, their slope, as in the case of the Pyramids of Egypt, have enabled some of the monuments constructed by man to defy the action of the elements and of centuries. We shall have occasion to notice in the second part of this work other applications of the action of weight to the arts and various industries. Let us here only remark, as an instance of this, that we look to it to produce adherence of the smooth wheels of locomotives to the rails : it is the enormous weight of the engines which prevents their driving-wheels from continually revolving without making any progress ; and it is not a little curious that, in the infancy of the locomotive, the result of the pressure on the rail due to the weight of the engine was so PHYSICAL PHENOMENA. [BOOK r. little understood, that it was thought that cogged wheels instead of smooth ones would be necessary. It is their weight also which keeps the waters of rivers in their natural beds, and lakes and seas in their basins, where these masses would remain at rest if exterior forces did not perpetually arise to agitate them. It happens sometimes that, under the influence of causes of irregular and terrestrial origin, such as earthquakes and winds, to which may be added the periodical oscillations of the tides, the sea is upheaved to great heights, and breaks beyond its usual limits. But it is soon drawn back to its more common state of equilibrium, either by its own weight or by friction another cause of stability, the origin of which is also weight. Laplace, as the result of an inquiry into what were the conditions necessary to the absolute stability of the equilibrium of seas, proved that it is sufficient that the density of the ocean be less than that of the earth a condition which is precisely realized in nature. Thus, if they were lighter, the waters of the sea would be in a perpetual state of mobility; if they were heavier, the variations from a state of equilibrium owing to accidental causes would be considerable, and would occasion frightful catastrophes both on continents and islands. But the persistence of the action of weight is not observable only in the land and water masses: the air is also subject to it. Without this pressure, which keeps them to the earth's surface, the elasticity, or the force of expansion, which is, as we shall soon see, a distinctive property of gases, joined to the centrifugal force due to the rotation of the earth, would soon dissipate the atmo- sphere into space. Such are, as a whole, the phenomena due to the continuous and latent action, so to speak, of weight on our globe. It is this action which everywhere maintains equilibrium, and which re-establishes it when it is disturbed by the action of physical forces. The phenomena of motion, due to the same force, form an equally interesting and magnificent picture. The infiltration of the waters through the earth's surface to different depths is due to this irresistible tendency of all bodies towards the centre of the earth. It is this tendency which by degrees undermines the land and rocks, CHAP. I.] PHENOMENA OF GRAVITY. and, disturbing their equilibrium, gives rise to the falling away of the sides of mountains and hills, and in time fills up the valleys. These movements have not the action of weight only for their origin, and we shall see further on how this action combines itself with those of other physical or chemical forces, and particularly with that of heat, to cause most of the motion -of which the surface of our globe and its atmosphere are the constant scene. Often the work of disorganization remains unperceived until the instant when the catastrophe occurs. Masses of high rocks being undermined, all at once lose their equilibrium, and slide or are dashed down, destroying everything in their path. Entire mountains have thus covered towns and villages with their debris, and history has recorded numerous examples of these terrible events. In the thirteenth century, Mount Grenier, the summit of which still towers above the mountains which border the Valley of Chambery on the south, partly crumbled away, and buried the little town of Saint- Andre' and many villages: the " dbimes de Myans" are still shown, where lie the debris and the victims. In 1806 a no less terrible landslip took place, and precipitated from the sides of Mount Euffi, into the Valley of Goldau, an enormous mass of rock, which completely buried many villages, and partly filled up a little neighbouring lake. It would be superfluous to calculate what is the destructive energy of similar masses precipitated by the action of weight from a height often prodigious, and the velocity of which increases with the height of the fall. Avalanches are phenomena of the same order, and are more frequent than the fall of mountain-sides and rocks. Masses of snow, collected on the inclined side of a mountain, or on the edge of a precipice, slide by their own weight, then detach themselves, and fall, crushing everything in their path. Often a slight shock a pistol-shot, or a shout even is sufficient to destroy the equilibrium, and occasion the phenomenon. In the icebergs, or mountains of ice in the polar regions, the pressure of the blocks one upon the other gives rise to similar effects, in which the irre- sistible action of weight again shows its power. Glaciers, too those rivers of hardened snow pressed into compact ice descend the slopes of the mountains under the pressure of the weight of the upper strata. This movement of slow progression is so irresistible, that 8 PHYSICAL PHENOMENA. [BOOK i. the lateral and underlying rocks are striated and polished by the crystalline mass, and by the debris of boulders and pebbles which it draws along. In volcanic eruptions, the explosive force of the interior gases often sends forth into the air cinders, fragments of stone, and rocks. But if these masses thus seem to escape for a moment from the action of gravity, the strife of the two forces is not of long duration, and the projectiles obey the invincible law of all terrestrial bodies. It is the same law which determines the fall of hail, rain, snow that is to say, the particles of aqueous vapour which have been condensed, and thus rendered heavier than the stratum of the air to which they rose, under the combined influence of heat and even paradoxical as it may seem of weight itself. Thus much, then, concerning the fall, properly so called, of bodies of which the equilibrium, from some cause or other, has been disturbed. But there is, on the surface of our planet, quite another series of movements, in which weight plays the most im- portant part, and the continuity of which produces an admirable circulation on our planet, without which life itself would soon be extinct. The incessant evaporation of liquid masses gives rise to the formation of clouds, and it is the difference between the weight of the air, and of the particles of vapour of which clouds are formed, which causes their ascending movement. Eain, due to the fall of these same particles when liquefied, falls through the action of terrestrial gravity, to the lowest levels forms brooks and rivers, and these fluvial masses following the natural slope of the ground, reach the sea, sometimes flowing with majestic slowness, at other times rushing noisily over a rugged bed. Sometimes stopped by natural obstacles, the waters spread themselves in the form of lakes : or else, arriving at the edge of a wall of rocks, flow over in cascades. Such are the falls of the Rhine at Schaffhausen, of Niagara, and the Zambesi cataracts in Central Africa. Currents are not peculiar to the solid portion of the surface of the earth. The ocean is furrowed with real rivers, the regular movements of which are determined by the action of weight, although their origin is due to another physical agent heat. It is also weight which regulates all the movements of the atmospheric CHAP, i.] PHENOMENA OF GRAVITY. gaseous mass, which unites its restless power to the action of the other natural forces. In conclusion, there is no action on our planet in which weight does not intervene sometimes to establish equilibrium, at others to give rise to motion. Even when it appears to be destroyed or counterbalanced, it is still at work, and is ever present wherever a particle is found, apparently invariable, and, according to the ideas experiment has given us of matter, as indestructible and eternal as matter itself. 10 PHYSICAL PHENOMENA. [BOOK i. CHAPTER IT. WEIGHT AND UNIVERSAL GRAVITATION. Common tendency of heavy bodies to fall towards the centre of the earth Weight is a particular case of the force of universal gravitation All the particles of the globe act on a falling stone as if they were all situated in the centre of the earth The force of gravity acts beyond the atmosphere even in the celestial spaces : the sun, planets, stars all bodies, gravitate towards each other. ALL the varied and numerous phenomena to which we referred in the previous chapter have the same origin a fact which will become more evident as experimental proofs are given. All are due to the action of a similar cause, or force, since this term is now given to every cause capable of producing or of modifying motion in a body as of bringing it back to a state of rest. What the essence or primordial cause of this force is, is a problem which science does not seek to solve : it confines itself to studying the effects of the force by means of observation, and thence to discover the law which regulates them ; and in this we shall soon see it has completely succeeded. The direction of the action . of weight, that is to say, the line in which the heavy body tends to move or is moved when it meets with no resistance ; the point at which the force is applied ; and, lastly, its intensity or the energy with which it attracts or pulls each material particle, are facts exactly determined. We shall recur in detail to them in the following chapters. We know by experiment that a force resides somewhere, that it has its centre of action in a given place. We may say more : we cannot conceive it acting without a material body to act upon. Where, then, is the centre of action of terrestrial gravity ? It is not in the heavy body itself. Indeed, according to a principle of CHAP. IF.] WEIGHT AND UNIVERSAL GEAVITATION. 11 paramount importance in the science of motion, or dynamics the principle of inertia a body cannot put itself in motion when it is at rest, nor of itself modify its movement when in motion. It is, then, outside a falling body that we must look for the cause of its fall. We are so accustomed, from our infancy, to see all bodies which surround us falling under the action of weight, or in other words to see the force of gravity at work, that the question seems to be an idle one. But, as D'Alembert has said, " It is not without reason that philosophers are astonished to see a stone fall, and those who laugh at their astonishment would soon share it themselves, if they would reflect on the question." It is from above downwards, in the vertical of any place that is to say, in a line upright or perpendicular with regard to the surface that all bodies fall, and it is in the same direction that they press on their supports. Weight, then, we see, acts as it were from the interior of the earth ; and since for points at short distances apart, the verticals, or upright lines, at these points seem parallel, it may be supposed that, instead of a single force, there exists an infinity of forces, all acting in the same manner and in the same direction. But it is easily seen that this last conclusion is not exact. Weight, or gravity, everywhere acts in the same manner. In all places, in all latitudes, at the equator, at the poles, in the temperate regions of the world, its influence is felt always in a direction perpendicular to the horizon. To know at what point of our globe this multiple action is concentrated, we must find out if all the verticals have a single common meeting-place. Let us take any one of the meridians of our planet. Each part of the circle which forms the meridian indicates an horizon. FIG. 2.- Convergence of the verticals towards the centre of the earth. and the line perpendicular to this, or the vertical of the place, is no other than one of the radii of the circumference ; that is to say, a line running to the centre of the 12 PHYSICAL PHENOMENA. [BOOK i. sphere. Thus all verticals, such as A z, Fig. 2, though apparently parallel when adjacent ones only are considered, are in reality con- vergent ; they are directed towards the centre, c, of the earth. This is only a first approximation : the earth not being exactly spherical, but flattened at the poles and swelled out all round its equatorial circumference, the verticals of the different latitudes do not pre- cisely tend to the same point. We shall observe also that besides this cause of deviation there exist local irregularities which render the determination of the real centre of the action of gravity very complex. But from our present point of view these different deviations have no importance. Let us now register this first fundamental result : All bodies have a tendency to fall towards the centre of the earth. Gravity acts on them, as a single force concentrated in this point. This law has no exception. It applies to bodies placed on the surface or at any height whatever in the atmosphere ; on the earth's crust, or in the deepest mines, observation always confirms its truth. This convergence of all falling bodies which tend towards one point, is in contradiction with a popular prejudice still prevalent. Many persons when they are told that the earth is round, and that it is inhabited on every part of its surface, cannot conceive how at their antipodes the inhabitants of the planet can walk, as it were, feet uppermost, and how material bodies, solid or liquid, can remain in equilibrium. By reflecting a little they would soon see that the idea of above and below is quite relative; that on a sphere in space each part of the surface is equally horizontal, and the tendency of all bodies towards the centre of the sphere well explains the state of equi- librium which exists on whatever part of the surface they are placed. But whence comes this central force ? Is it a secret property independent of matter ? Does the earth alone enjoy this mysterious power ? These important questions remained unanswered two centuries ago, since which time Galileo's experiments on falling bodies, and the profound speculations of Huyghens on the principles of mechanics, enabled the genius of Newton to reach the general cause which produces all the phenomena of gravity on the surface of the earth as well as throughout the entire universe. Weight is, in fact, a particular case of a force at work in all parts of the CHAP, ii.] WEIGHT AND UNIVERSAL GRAVITATION. 13 universe the force of universal gravitation. In virtue of this force any two particles of matter gravitate or fall towards each other, that is to say, they have a mutual tendency to re-unite, which depends on their respective masses and on their distance apart. Here is the law of this dependence : If we take for unity the force which draws two equal masses, situated at a unit of distance apart, towards each other, if one of the masses be doubled, the force itself will be doubled : if the other mass be replaced by one three times greater, the force will be now tripled, and, in consequence, will be six times greater than at the beginning. If now, the masses remaining the same, we make the distance twice, three times, four times less, the force of gravitation will be four, nine, sixteen times greater. Thus, attraction, or gravitation we shall use this latter term in preference (discarding altogether in future the term weight, which by this time should have served its purpose), because it supposes nothing as to the unknown essence of the force itself is propor- tional to the product of the masses, and varies inversely as the square l of their distances. Such is the fundamendal principle of which the phenomena of weight are so many particular manifestations. It was not an easy thing to deduce from it all the consequences, to calculate the re- ciprocal actions of all the small masses composing the entire bulk of the earth, and the effect resulting from all these combined actions. Newton, and after him the great geometers who have developed his discovery, D'Alembert, Euler, Maclaurin, Lagrange and Laplace, have devoted themselves to this task. They have shown that a spherical mass of homogeneous matter acts on an exterior point in the same way as if all the matter were concentrated at its centre. The same thing is true of a homogeneous spherical layer, and consequently of a series of strata of this same form, the density of which continues to increase according to a definite law. Such is precisely the case with the earth: and Newton thus explains how the direction of gravity is everywhere vertical to the 1 The square of a number is the product of the multiplication of the number by itself: thus 9 is the square of 3 ; 100, the square of 10; 1,000,000 the square of 1,000, and so on. H PHYSICAL PHENOMENA. [BOOK i. surface, or the straight line between the heavy body and the centre of the globe. A body situated in the interior of the earth is attracted by the mass which lies beneath it, but the action of the particles of the exterior layer destroy each other, so that the intensity of gravita- tion goes on diminishing from the surface to the centre. 1 In like manner, this intensity diminishes in the case of bodies exterior to the earth, in proportion as their distance from the earth increases. Thus, then, the source of gravity at the surface of our globe lies in the entire mass of which it is composed. There is not a single particle, however small it may be, which does not take part in the general action. Nay, more : when a stone falls, at the same time that it feels the influence of the mass of the globe it reacts on this globe by its own bulk : the two bodies come together by gravitating one towards the other. The motion of the stone, however, is alone perceptible, as its mass is almost nothing compared to that of the earth. But more of this presently. It has been stated that gravitation is universal. Not only, indeed, does it govern all the phenomena of terrestrial gravity, but it extends its power to the most remote parts of the heavens. The moon and the ea-rth gravitate reciprocally towards each other, arid they both gravitate towards the sun. All the planets of our solar system continually act on one another, and on the immense sphere which shines at their common focus. By its enormous mass, the sun keeps all of them in their orbits, so that the movements of all the celestial bodies which compose the system are mutually balanced and varied under the influence of the same force perpetually acting in each of them. We have endeavoured to give elsewhere 2 an idea of these grand problems, the solution of which is the triumph of science. Let us 1 In fact, the intensity of gravity first increases from the surface to a distance from the centre which is estimated at nearly seven-tenths of the radius ; it after- wards lessens to the centre. These variations are due to this fact, that the con- centric layers of which our globe is formed are not homogeneous ; their density increases from the surface to the centre, and the density of the superficial strata is less than two-thirds of the mean density. These results have been deduced from pendulum observations. 2 " The Heavens : an Illustrated Handbook of Popular Astronomy." By A. Guillemin. Translated by Mrs. Lockyer. CHAP, n.] WEIGHT AND UNIVERSAL GRAVITATION. 15 recall only two proofs of the existence of the force of universal gravitation in the celestial spaces. The tides those periodical oscillations of the sea are produced by the action of the masses of the moon and sun : and aerolites, celestial bodies in miniature, which sometimes fall on our planet, show that the action of terrestrial gravity is capable of diverting exterior masses from their orbits. The most recent researches in stellar astronomy prove, moreover, that the same force regulates the movements of the most distant stars. The double stars are systems of suns, situated at immense distances from our globe, and revolving round each other: here, again, it is certain that their motions are effected according to the same laws which regulate those of the planets laws which are a direct consequence of gravitation, that is, of their weight. 16 PHYSICAL PHENOMENA. [BOOK i. CHAPTEK III. LAWS OF ATTRACTION. FALLING BODIES. First experiments of Galileo on falling bodies E^ual velocity of bodies falling in vacua Vertical direction of gravity Deviation from the vertical due. to the rotation of the earth Galileo's inclined plane ; Attwood's machine ; Morin's machine ; kvvs of falling bodies Influence of the resistance of the air on the velocity of bodies falling through the atmosphere ; experiments of De"saguliers. IT is recorded of Galileo that in his youth, when he was Professor of Mathematics at the University of Pisa, making his first experiments on the fall of heavy bodies, he wished to see if it were true, as had been said and believed from the time of Aristotle, that the unequal velocity noticed in different bodies falling from a given height was due to their unequal weight, or if it depended on the nature of their material. It was from the top of the famous Leaning Tower of Pisa that he made these experiments : balls of different metals gold, copper, lead having the same dimensions, but different weights, reached the ground at nearly the same instant: a ball of wax, however was much more retarded. But the differences in the times of falling were not decided enough to be attributed to the inequality of weight, so that it did not appear probable that, as held by many, a thing twice as heavy as another would fall twice as fast. Having let the same thing fall through the air and through water, he proved that the differences between the times of their respective falls depended upon the density of the medium through which they fell, and not on the weights of the falling bodies themselves. Galileo hence concluded that it is to the resistance of the air we must attribute the differences in the time of fall observed. Fm. 8. The Leaning Tower of Pisa. CHAP. III.] LAWS OF ATTRACTION. 19 When a body falls through air, or any other medium, it must constantly displace the molecules of which the medium is composed, and this is only possible by communicating to them a part of its own movement. Suppose, then, we let fall at the same instant a ball of lead and a ball of cork of equal weight : the latter loses more of its own movement than the first does in displacing the same quantity of air, because being of a lighter substance it is larger, so that its speed is naturally more diminished. The difference would be still more perceptible if the fall, instead of being effected through the air, were to take place in a dense gas. Galileo's discovery has since been exactly con- firmed by experiment, and the honour of this confirmation belongs to Newton. Take a long glass tube furnished at both ends with two frames of copper, one hermetically closed, the other terminated by a stopcock, which allows the tube to be adjusted on the table of an air-pump, an instrument by which we can carry off, or exhaust, the air which it contains. We now introduce into one end of the tube bodies of different densities, such as small pieces of wood, metal, feathers, paper, cork, &c. After exhausting the air by means of the air-pump, and turning the stopcock to prevent its re- entrance, we turn the tube quickly, and place it in a vertical position. All the little bodies at once quit the top and fall together in the direction of the axis of the cylinder (Fig. 4). If the tube be inverted before the air is extracted, the unequal rate of fall is clearly shown. If the experiment be repeated several times, gradually letting the air into the tube, it will be observed that this in- equality decreases with the rarefaction of the air in the tube. When the vacuum is as complete as possible, all the bodies, although of different den- sities, reach the lower part of the instrument at the same time. It is then the resistance of the medium which is the cause of the c 2 IG. 4. Experiment showing the equal ve- locity of bodies falling iTi vacuo. 20 PHYSICAL PHENOMENA. [BOOK T. unequal rate of fall of bodies more or less heavy or more or less dense. This resistance not only retards the motion, but also produces devia- tions in the direction of the fall of the lighter bodies. A sheet of paper, for instance, thrown into the air, takes a curved and often very irregular flight to the ground. If we take a piece of money, a penny for instance, and a disc of paper of the same size, and let them fall separately from the same height, the money will touch the ground before the paper. If we afterwards place the disc on the penny, and let them fall together, both will touch the ground at the same instant. The metal, in the latter case, prevents the resistance of the air at the lower face of the paper. What has just been said of solid bodies applies equally to liquids and gases. A mass of water is divided, in its fall, into a number of very small drops, the formation of which is due to the resistance of the air and the mobility of the liquid particles. This division is very perceptible in jets and in cascades or natural sheets of water which fall from great heights. If, in order to experiment on the fall of liquid bodies, we use a tube in which a vacuum has been made, the water will be found to fall en Hoc to the lower part, keeping the cylindrical form of the vessel, and its fall produces a dry noise a " click," as would that of a solid body. Such a tube forms what is called a " water hammer." Smoke inclosed in a similar vacuous tube also falls : it is thus seen that gaseous and vaporous bodies have a certain weight. We may state, in passing, that the resistance of the air to the fall of bodies is a fortunate thing for agriculture, which already suffers too much from the ravages produced by hail. Without this resistance the smallest rain would strike the surface of the ground with ever-increasing force, and would cause great damage. Here, then, is one point gained, and the first law of falling bodies proved : All bodies situated on the surface of the earth, whatever may be- their volume and their mass, fall in vacuo with equal velocity. An important inference may be at once drawn from this, namely, that the force of gravity acts with equal energy on each particle of matter, absolutely as if each of the particles which compose a body were separate and independent. Experiment has proved to us that gravity acts in the same way on all bodies, whatever be CHAP. III.] LAWS OF ATTRACTION. 21 their volumes and densities, whilst the weight of the body is the sum of the action of gravity on all the particles, and in consequence it varies, either with the volume, for homogeneous bodies of the same kind of matter, or, if the volume changes, it varies with the density. Let us inquire further into the phenomena of the fall of bodies on the earth's surface. The direction of gravity and this is a fact that every one can Fin. 5. The direction of gravity is perpendicular to the surface of liquids at rest. prove for himself is, in every part of the earth, vertical ; that is, in a straight line perpendicular to the plane of the horizon. This plane may be determined by the surface of still water. A very simple practical way to assure oneself of this fact is to observe the position that a flexible thread stretched by a heavy weight takes when the thread comes to rest, after many oscillations. Such a 22 PHYSICAL PHENOMENA. [BOOK i. thread is called a plumb-lime or plummet, and is used by work- men who wish to construct an upright building. Placing the plumb-line above a liquid mass at rest, for example a mercury bath, it is easily seen that the direction of the string and that of its image are in the same straight line (Fig. 5), and consequently, in virtue of the laws of the reflection of light, which we shall discuss in the sequel, both are perpendicular to the horizontal surface of the liquid. The different verticals, we have already said, are not parallel ; but at very slight distances the angle which they form is so small that it is impossible to measure it. This is not the case if we take two places on the earth somewhat distant from each other : in this case their respective verticals can be measured by means of astronomical observations. If the two places are on the same meridian, and have the same geographical longitude, the angle of the verticals is measured by the difference of latitude. The difference between the directions of gravity between Paris and Dunkirk is thus found to be about 2 12', between London and Edinburgh about 4 25' ; the vertical which passes through the top of the cross of St. Paul's and that which passes through the flagstaff on Victoria Tower make but a very small angle with each other. 1 Hence it follows that the waters of a lake or of a sea are bounded by a surface which is not plane, but spherical, or rather spheroidal, although at every part or point of the earth's surface it is confounded with the plane of the horizon of the place. We must therefore understand that when it is said that heavy bodies fall in a constant direction, which is that of the vertical of the place, this constancy implies only a parallelism of fall at places very near together. Lastly, let us add that the rotatory movement of the earth produces a deviation in the fall of bodies. A body at a (Fig. 6), 1 If the experiment is made in the neighbourhood of a very high mountain, the plumb-line is deflected from the vertical, under the influence of the attraction of the mass of the mountain. This deviation, always very slight, was first measured by Bouguer and Lacondamine, on the side of the Chimborazo. In 1774 Dr. Maskelyne measured the attractive influence of Mount Schihallion, which he found equal to about 12" ; that is. two plumb-lines, situated on either side of the mountain, instead of forming between them the angle indicated by the difference of latitude of the stations, formed one larger by 12 seconds. CHAP. IIL] LAWS OF ATTRACTION. 23 situated at a certain height in the air, would fall at the foot of the vertical at A, if the earth was immovable. But during the time of its fall, the rotatory movement makes it describe an arc a of, larger than the arc A A" described by the base of the vertical. Left to itself, it retains its velocity of primitive impulsion, and ought to fall at A" to the east of the lower point. Such is the deviation which the theory indicates, and which being nothing at the poles, goes on increasing towards the equator. Experiment confirms the reasoning : in the atmosphere, however, it is difficult to succeed in the experi- ment, on account of the disturbances in the air ; but it can be proved FIG. 6. Eastern deviation in the fall of bodies. that a metallic ball A dropped at the mouth of a very deep mine, falls at B', a little to the east of the foot B of the plumb-line which marks the vertical. The deviation depends of course on the depth of the mine : at the equator it is 33 millimetres for a well 100 metres deep. For a mine at Freiburg, in Saxony, M. Reich proved an eastern deviation of 28 millimetres at a depth of 158*5 metres, theory indicating 26'6 millimetres. It is evident, then, that we have here an experimental proof of the earth's rotation. Galileo, in his experiments on the fall of heavy bodies, did not confine himself to destroying the popular fallacy, which was still prevalent in his time, regarding the inequality of the velocity of fall being attributable to the difference of weight or to the density of the substances. He observed that the velocity acquired increased with the heights of the fall ; that the spaces traversed were not simply pro- portional to the times employed to traverse them, in fact, that the fall of heavy bodies, instead of being a uniform, is an accelerated movement. Such an assertion doubtless had been made before him, 24 PHYSICAL PHENOMENA. [COOK i. but he had the glory of discovering the precise law of variation of the velocity acquired and the space described. Supposing that gravity, whatever its essence might be, acted always with the same force, he concluded that the velocity acquired ought to be proportional to the time, and ke proved his hypothesis by a celebrated experiment to which his name has remained attached. This was the inclined plane of Galileo. The rapidity with which heavy bodies, metallic balls for instance, travel in their fall does not easily allow of direct observation. But Galileo knew that a heavy body left to itself on a plane inclined to the horizon, and subjected only to the action of gravity, follows in its move- ments the same laws as if it fell vertically ; the friction of the Fia. 7. -Movement of heavy bodies on an body On the plane and the re- inclined plane. sistance of the air during the fall, in the two cases being disregarded. The force which draws the body down the inclined plane is no other than gravity, diminished in the ratio of the two lines A c and A B, which measure its height and its length. In the case represented in the figure the force of gravity is reduced to little more than a quarter of its natural value. The movement being considerably retarded by this arrangement, Galileo could easily measure the spaces traversed during each successive second. But as the experiments of the inclined plane do not give results of great precision, the laws of falling bodies are determined at the present day by various instruments which are found in all physical laboratories, and which will be here described. Already in the seventeenth century, Eiccioli and Grimaldi assured themselves of the exactness of Galileo's experiments, but they confined them- selves to dropping a weight from the tops of towers of unequal heights, and measuring the times of the fall by the oscillations of the pendulum. In 1699 Father Sebastian invented a machine for the same purpose. Lastly, an English physicist, Attwood^ constructed one which still bears his name: and in our time General Morin has invented another, which registers directly the results of the experiment. CHAP. III.] LAWS OF ATTRACTION. 25 The plan invented by Attwood to retard the movement of falling bodies is this: a very fine silken thread is passed round a wheel (Fig. 8), moving easily on friction rollers, the thread having at its two extremities metallic cylinders of exactly the same weight. In this state, the pulley, the line, and the weights remain at rest, because the two equal weights produce equilibrium. If an additional weight is placed on one of them, the system will be put into motion: the two portions of the line will be moved FIG 8 Pulley of Attwood's machine. in an opposite direction, each still, however, keeping its vertical direction. But it will be at once seen that the speed of the fall will be the more retarded as the additional weight is small com- pared with the sum of the two equal weights. Let us suppose that each of these weighs 12 grammes, and the additional one weighs 1 gramme only. The total weight of 25 grammes being put into motion by a force which is only a twenty-fifth part, it is 26 PHYSICAL PHENOMENA. [BOOK i. clear that the speed will be that which Km. 9. Experimental study of the laws of falling bodies. Attwood's machine. a falling body would possess if the inten- sity of gravity were twenty-five times less. Observation is thus rendered easy, with- out disturbing laws of motion. 9 shows the Fig. arrangement of the the machine. At the top of a column a pulley is seen, the axle of which rests on two systems of parallel wheels (friction roll- ers see Fig. 8) ; then the line which passes round the pulley is stretched by equal weights on either side. A vertical scale, care- fully divided, is placed behind one of the weights, on which scale the distance from the base of the weight to the zero of the scale, that is, the point of departure of the weight, may be read in each of its positions. This scale has two movable plates, which can be fixed by screws at any of its divisions. The lower plate simply arrests the movement of the system at will. CHAP, in.] LAWS OF ATTRACTION. 27 The other plate is in the form of a ring, and the opening is large enough to allow the weight suspended to the line p to pass through, but on the other hand stops the additional weight p on account of its O 1 elongated form. A pendulum beating seconds is added : each movement of the second- hand makes a clear sharp noise, by means of which the passing seconds can be counted without looking at -the dial. A contrivance at- tached to the clock enables each experiment to begin at the precise instant when the seconds' hand is at the zero of the dial, at the upper part of the latter. The additional weight, first placed above the weight which occupies the division of the ver- tical scale, is suddenly let go by the action of the mechanism, and motion begins. The experiments are per- formed in this way : Place the lower plate in such a place on the column that the cylindri- cal weight surmounted with the weight p will touch it precisely at the commence- ment of the second second, which is determined by the coincidence of the second beat of the pendulum with the click of the weight on the plate. Suppose this point be at the twelfth FIG. 10. Experimental study of falling bodies. Law of spaces described. 28 PHYSICAL PHENOMENA. [BOOK i. division at the scale (Fig. 10). It is then observed, in conducting this operation successively during two, three, four seconds, &c., that the lower plate must be at the following divisions, in order that the click of the weight coincides each time with the successive beats of the clock. These divisions are marked by the numbers 48, 108, 192, &c. Thus the spaces described are : After 1 second 12 centimetres. 2 seconds 48 = 12 X 4 3 v 108 =1-2X9 4 ..... 192 = 12 X 16 5 300 = 12 X 25 The space, then, through which a falling body travels, must be multiplied by the numbers 4, 9, 16, 25 .... to obtain the space described during 2, 3, 4, 5 .... seconds of fall. If the additional weight be changed, the numbers which measure the spaces traversed in each second would change : their ratio, however, would still remain the same. Here, then, is the first law, the one discovered by Galileo : The .space described ly bodies falling freely under the action of gravity is proportional to the square of the time elapsed from the beginning of the fall. It remains for us now to determine the law of velocity that is, to learn what is the speed acquired after 1, 2, 3 .... seconds of fall. Whilst the body which falls remains subject to the action of gravity, this velocity goes on increasing at each instant during the fall, and cannot in consequence be directly observed. To render this determination possible, the continuous action of gravity must be suppressed at the moment the following second begins, so that the body may continue to move uniformly, and in virtue of the acquired velocity alone. It is important to understand what is meant by the velocity of a body which falls, or, to speak generally, which is endowed with an accelerated motion. This velocity of motion at a given moment is measured by the space through which the body would travel uniformly in each of the following seconds if the force ceased to act, and the motion ceased to be accelerated. The ring of Attwood's CHAP. III.] LAWS OF ATTRACTION. machine realises this hypothesis. It is sufficient to fix it successively at the divisions that were shown in the first experiment, then to find by trial at which part of the scale the lower plate must be in order that the weight, relieved of its overweight, may strike it at the beginning of the following second. The experiment, supposing that p has the same mass as p', will give the following numbers : 36, 96, 180, &c. (see Fig. 11). Hence it follows that the uniform velocity of falling bodies, acquired after 1, 2, 3 . . . . seconds of fall, is : After 1 second . 2 seconds. 3 24 centimetres per second. 48 72 The velocity goes on increasing in proportion to the time; the second law which governs the fall of heavy bodies may then be thus enun- ciated : When a heavy body falls freely under the action of gravity, its spaed is accelerated : its velocity, at any moment of the fall, is proportional to the time elapsed since the commence- ment of motion. It follows also from the same ex- periments that the velocity acquired after one second of fall carries the body through double the space passed through during the first second ; and it is easily seen that this is indepen- dent of the unit of time chosen. The same laws are proved experimentally by means of the machine invented by M. Morin, of which Fig. 12 gives a general view. A weight of a cylindro-conical form descends freely along FIG. 11. Experimental study of fulling bodies. Law of velocity. PHYSICAL PHENOMENA. [BOOK i. two vertical rods: it is furnished with a pencil, which marks a continuous line on a cylinder covered with a sheet of paper. If the cylinder were immovable, the line marked by the weight during its fall would be a straight vertical Line, which would indi- FIQ. 12. M. Morin's machine. cate nothing as to the spaces traversed during successive seconds. But the cylindrical column is made to turn uniformly on its axis, by the aid of a system of toothed wheels moved by the descent of a weight, and uniformity of rotation is produced by a fan -regulator, the spindle of which is connected with the train. Owing to this motion of the cylinder under the pencil in its descent, the pencil traces a curve, and an examination of this curve shows us the law CHAP. III.] LAWS OF ATTRACTION. 31 which governs the spaces described by the body during each second at different parts of its fall. The curve is what is called in geometry a parabola, the funda- mental property of which is as follows : The distances of the successive points of the curve from a line drawn perpendicular to the axis of the parabola from its vertex, are proportional to the squares of the distances of these points from the axis itself. The line perpendicular to the axis being divided into five equal parts, the five distances from the vertex to the points of division, 0, 1, 2, 3, 4, 5, will be in the ratio of Q 1, 2, 3, 4, 5, but the five vertical lines let fall from the divisions will be in the ratio of 1, 4, 9, 16, and 25, that is, propor- tional to the squares of the first numbers. Now the cylinder having turned uni- formly on its axis, the equal portions of the circumference which separate the points of division of the horizontal line mark the successive seconds of fall of the weight, and the vertical lines are the spaces traversed. As to the law of velocities, it is a direct consequence of that of spaces. It must not be imagined that the machines described give results of mathematical exactness. There are many hindrances, such as the friction of the parts, and the resistance of the air, which are opposed to such results ; but the differences which arise from them are very slight. 25 FIG. 13. Parabola described by the weight in its fall. The experiments made by means of Attwood's machine show moreover that gravity acts on the falling body in a continuous and constant manner. For the spaces traversed during successive seconds may be represented by the odd numbers 1, 3, 5, 7, 9, &c. ; and as the velocities acquired at the commencement of the second and following seconds are 2, 4, 6, 8, 10, &c., so that if no force acted during each of these seconds, the spaces described would be represented by 2, 4, 6, 8, 10, &c., there is a constant difference, due to the continued action of the force of gravity during each second, precisely equal to 32 PHYSICAL PHENOMENA. [BOOK i. the space traversed during the first second. This difference therefore marks the continuous action of gravity. Again, it is seen that if a body is thrown up vertically, the height to which it rises depends on the amount of force exerted, moreover, its velocity decreases, and when it descends under the action of gravity, its increasing speed at each point along its path is precisely equal to that which it possessed at the same point during its ascent. The experiments made by the aid of Galileo's inclined plane and Attwood's machine are founded on an artificial diminution of the intensity of gravity, which, without changing the laws which govern their fall, retards the motion of falling bodies. But precisely on this account they do not enable us to measure the actual space traversed during one second of fall ; and, moreover, the experiments must be made in vaciw. M. Morin's machine would give this space approximately, but the result would require corrections for friction and the resistance of the air. We shall see further on that the exact space has been determined by a more precise method. The intensity of the force of gravity, moreover, as we shall soon see, is not rigorously constant : it varies with the place, according to latitude, and even with the local features of the terrestrial erust. Lastly, in the same place, the intensity varies with the height above the ground, or with the depth beneath it. It must be borne in mind that the following figures refer to the fall of bodies in vacua, in the latitude of London, and at a little distance from the sea-level. Under these conditions, a body travels during the first second of its fall, 16^ feet. The velocity acquired after one second is then 32J feet, and it is this latter number which is taken as a measure of the force of gravity. Fall in 1 second = 1 X 16,V - 16 T \ 2 seconds = 4 X 16 ^ = 64^ 3. = 9 X 16& = 144ft 4 = 16 X 16& = 257^- 5 = 25 X 16,1 = 402^ The time that a body takes to fall from a certain height, and CHAP, in.] LAWS OF ATTRACTION. 33 the velocity acquired at the moment it touches the ground, may also be found in like manner. In the case of a i ailing body the velocity is uniformly in- creased by gravity ; in the case of an ascending one it is uniformly decreased. To throw a body to a vertical height of 400 feet we must give ft a velocity of 161 feet per second. This body, then, takes 5 seconds to ascend, and it would descend in the same time. Let us repeat, in order that the reader may not imagine that the above numbers are found to be rigorously true in practice, that the resistance of the air is an element which much influences the movements of rising or falling bodies, and that the ratio of their weight to the surface which they offer to this resistance makes the result vary. The experiment made by a physicist of the eighteenth century, Desaguliers, before Newton, Halley, Derham, and many others, may here be referred to. Having dropped from the lantern above the dome of St. Paul's different bodies, such as leaden balls 2 inches in diameter, and bladders filled with air, of 5 inches in diameter, he found that the lead took 4J seconds to fall through 272 feet, the height of the lantern above the ground ; and that the bladders took 18 J seconds. Now, in vacua, the space would have been passed through by both bodies in 4J seconds. As the resistance of the air increases with the velocity of the fall, it is clear that bodies which fall from a great height, after having acquired a certain speed, finish their descent with a uni- form movement. It has been calculated that a drop of water, the volume of which would be about the T 000>0 l 00 ; 000 th of a cubic inch, would fall through perfectly calm air with a constant velocity of 5 inches a second, so that it would not travel more than 25 feet in a minute. This explains the relatively small velocity of rain- drops, in spite of the considerable height of the clouds from which ML 34 PHYSICAL PHENOMENA. [BOOK i. CHAPTER IV. LAWS OF GRAVITY. THE PENDULUM. The Pendulum Galileo's observations Definition of the simple pendulum Iso- chronism of oscillations of small amplitude Relation between the time of the oscillations and the length of the pendulum Variations of the force of gravity in different latitudes Borda's pendulum Lengths of the pendulums which beat seconds in London, at the equator, and at the poles Calculation of the oblateness of the earth Experiments proving that the density of the earth increases from the surface to the centre. "VTEWTON, seated one day in his garden at Woolsthorpe, saw an *' apple break off from the branch of a tree, and fall at his feet. It was this simple circumstance which suggested to him his pro- found researches on the nature of the force of gravity, and which made him ask whether this mysterious action, to which all terres- trial bodies are subjected, whatever their height in the atmosphere, whether at the bottom of valleys or at the top of the highest mountains, did not extend even to the moon. Thanks to the meditations of this great genius, we had not long to wait for the solution of this grand problem : but it was not till twenty years later tha,t the edifice of which Kepler, Galileo, and Huyghens had prepared the foundation, which the successors of Newton finished, and which bears this triumphant superscription " Universal Gravi- tation," was at last constructed in its majestic beauty. Is this anecdote, repeated by all biographers of the great man, really true ? It matters little : the essential point is that it is probable. But we should be mistaken if we imagined that it was of a nature to diminish the glory of the philosopher. Such things had happened millions of times before, to his ancestors and to his contemporaries. Such a fact as the fall of an apple could only CHAP, iv.] LAWS OF GRAVITY. 35 excite such thoughts in a mind capable of the highest specula- tions, and moved by a will powerful enough to be always thinking them out. It was a similar occurrence which caused Galileo to undertake his researches on the motion of the pendulum. He was then pro- fessor at Pisa, and, as we have before stated, was studying the laws of falling bodies. " One day," we read, " while present at a religious ceremony in the cathedral paying, however, it would seem, very little attention to it he was struck by a bronze lamp a chef- d'oeuvre of Benvenuto Cellini which, suspended by a long cord, was slowly swinging before the altar. Perhaps, with his eyes fixed on this improvised metronome, he joined in the singing. The lamp by degrees slackened its vibration, and, being attentive to its last movements, he noticed that it always beat in the same time." l It was this last observation which struck Galileo. The lamp, when the motion had nearly ended, described smaller and smaller arcs through the air, the period of swing, however, remaining the same. The able Italian philosopher repeated the experiment, and discovered the connection which exists between the period of oscillation and the length of the cord supporting the oscillating weight. Huyghens completed this beautiful discovery, and gave the mathematical law of the motion of the pendulum. Let us try to give an idea of this law, and show how it is connected with the theory of gravity. Imagine a material and heavy point M' (Fig. 14) suspended to one of the extremities of an inextensible line without weight. These are conditions which cannot be realised in practice, but they are accessible in theory. The line being fixed by its upper end, the action of gravity on the material point M' stretches the line in the vertical direction, and the system will remain at rest. Let us now suppose that the string is moved out of the vertical, still being kept tight and straight, and is then abandoned to itself in a vacuum. What will happen ? The action of gravity in the new position in M continues on the material point: but as this force always acts in a vertical 1 J Bertrand, " Galileo and his Works." D 2 36 PHYSICAL PHENOMENA. [BOOK i. direction, and as the string is no longer in that line, the resistance of the latter cannot completely annul the force of gravity. The material point, being attracted, will then fall, but as the string is inextensible, the fall can only be effected along an arc of the circle having its centre at the point of suspension A, and its radius the length of the string A M. It is as if the point were on an inclined plane, with its summit at M, and with an inclination gradually becoming smaller and smaller. Calculation shows that the movement will be effected with increasing velocity, until the time when the string will have returned to its FIG. 14. Oscillatory movement of a simple penduhim. vertical position ; then, by virtue of its acquired speed, it will describe an arc equal to the first, but with decreasing velocity. Arrived at M", at the same height as the point M, its motion will cease. It will be easily understood that the material point- will recommence a movement similar, and perfectly equal to, the first, as the circumstances are the same, but in the contrary direction. This would be perpetual motion, if the supposed conditions could be fulfilled. The ideal instrument we have just described is called the pendulum the Simple pendulum, in contradistinction to the real but compound pendulums, which may be actually constructed and observed. The whole movement from M to M" is called a swing or an oscillation, and its duration or period is obviously the time that the object takes to make the entire oscillation. It is scarcely necessary to state that the perpetuity of the oscillations or of the movement of the pendulum is purely theoretical. In reality, many causes exist which by degrees destroy the motion, and end by stopping it. The suspended body is not only a material point, but generally a metallic lens-shaped disc or ball. The rod is itself often large, and the resistance of the air destroys part of the motion of the pendulum at each oscillation. Let us add to these causes of retardation the friction of the knife-edge on the plane of suspension. Nevertheless, the laws of the simple pendulum have CHAP, iv.] LAWS OF GRAVITY. 37 been successfully applied to the oscillations of compound pendu- lums, and the resistances which necessarily proceed from the relative imperfection of the pendulums have been taken into account with every possible precision. These laws, which it is so important to understand, and which have made the pendulum the best instrument for the measurement of time, the most precise indicator of the irregularities which the terrestrial spheroid presents, and a scale by the aid of which the density of our planet and of all the bodies of our solar system can be weighed, may now be stated. The first law is that discovered by Galileo from observation : it is as follows : " The time of very small oscillations of one and the same pendulum is independent of their amplitude ; the oscillations are isochronous that is to say, they are all performed in the same time" By small oscillations must be understood those the angle of which is less than four degrees. Within this limit the oscillations of greater amplitude are made in a very little longer time than the others, but the difference is very slight, and it is not until after a great number of oscillations that all the little differences of which we speak become perceptible. It is theory, then, which demonstrates the isochronism of pen- dulum oscillations. But the law is easily 'verified by experiment. If we carefully count a considerable number of oscillations, and by a good chronometer measure the number of seconds elapsed, these two numbers obtained give, by simple division, the time of one oscillation, which will be found to be the same either at the beginning or at the end of the experiment. This equality in the time required for passing through unequal distances under the influence of a constant force appears singular at first sight; but on reflecting a little it will be understood, without further demonstration, that in the case of greater amplitude the pendulum commences its swing in a direction more out of the vertical ; the force of gravity, therefore, gives it greater velocity, by the help of which it soon makes up for the lead which a similar pendulum would have in describing an arc of less amplitude. The second law which governs the motion of the pendulum establishes a relation between the time of the oscillations and the length of the pendulum. 38 PHYSICAL PHENOMENA. [BOOK i. Let us imagine a series of pendulums, the smallest of which beats seconds, the others performing their oscillations in 2, 3, 4 . . . seconds respectively. The length of these last would be 4, 9, 16 . . . times greater than the length of the first: the times following the series of the simple numbers, the lengths following the series of the squares of these numbers. This is expressed in a more general manner by saying: The periods of oscillation of pendulums are in the direct ratio of the square roots of their lengths. Theory and observation agree in demonstrating this important law : but since we speak of experimental verifications, and since we know that it is impossible to realize a simple pendulum, it is time to state how the laws of this ideal pendulum are applied to the real or compound pendulums. Pendulums of this kind are ordinarily formed of a "bob," or spherical ball of metal, with a rod adjusted in the direction of the centre of figure of the sphere or of the bob. This rod is fixed at its upper part into a sharp metal knife-edge, which rests on a hard and polished plane (Fig. 15). Such are the pendulums the oscillations of which control the motion of clocks. In such a system, what is understood by the length of the pendulum is not the distance from the point of suspension to the lower ex- tremity of the heavy body, but the approximate distance between this point and the centre of figure of the ball, when the rod of the pen- dulum is thin and the ball is made of very dense metal platinum, for example. This last point then takes the name of centre of oscillation. We will show the reason for this fundamental distinction. In a simple pendulum there is only con- sidered to be one material point; in the com- pound pendulum their number, whether in the rod or in the ball, is infinite. It is as if there were a series of simple pendulums of different lengths compelled to execute their movements together. Their most distant particles find their FIG. 15. Compound pendulum. CHAP, iv.] THE PENDULUM. 39 movement accelerated; contrariwise, it is retarded in the case of those nearest the point of suspension. Between these extremes there is one particle, the duration of whose oscillations is precisely equal to those of a simple pendulum of equal length. Calcula- tion makes us acquainted with the position of this particle in the bar that is to say, the point which we have just termed the centre of oscillation. Let us now try to understand how it is possible, by means of pendulum observations, to solve several important questions which deal with the form of our planet and its physical constitution. The periods of the small oscillations of a pendulum depend upon its length, according to the law we have just stated. But these two elements also depend on the intensity of the force of gravity in the locality where the oscillations are performed. Hence it follows that, if we observe with great precision the number of oscillations that a pendulum the length of which is known with rigorous exactness executes in a sidereal day, we shall be able to calcu- late the precise duration of a single oscillation, and thence deduce the intensity of the force of gravity that is to say, twice the space in which a heavy body falling in vacua passes through in a second This intensity is, in fact, connected with the length of the pendulum and the period of its oscillation. It is by this method that the value was found which has been already given for the latitude of Paris 9-8094 metres. This determination once obtained, it is possible to obtain by calculation the length of the pendulum which beats seconds. This length is at Paris 0'994 metre, at London 3'2616 feet. Now let us imagine that an observer travels from the equator to either pole. As the earth is not spherical, the distance of the observer from the centre of the earth will vary. Greatest at the equator, it will pro- gressively diminish, will pass through a mean value, and will be the smallest possible at the poles themselves. Now, for this reason alone, the energy of the action of gravity in these different places must decrease from the poles to the equator. Another influence will also contribute to diminish the intensity of this force that is, the rotation of the earth, the velocity of which, being nil at the two poles, progressively increases with the latitude, developing 40 PHYSICAL PHENOMENA. [BOOK i. at each point a greater centrifugal force, which partly counter- balances the action of terrestrial gravity. 1 For these two reasons, the intensity of the force of gravity will vary in different latitudes. How will our observer perceive it ? By observing the oscillations of the pendulum, which furnishes us with two different but equally conclusive methods. The first method consists in employing a pendulum of invariable length ; the rod and the bob, soldered together, are fixed to the knife-edge in a permanent manner. Such a pendulum, having a constant length, or at least only varying with changes of temperature, will oscillate more rapidly as the force of gravity is increased; so that, in going from the poles to the equator, the number of oscillations in a mean FIG. 16. Effect of centrifugal force. day will be smaller and smaller. Thus, a pendulum a metre in length, which at Paris makes in vacuo 86,137 oscillations in twenty- four hours, if carried to the poles would make 86,242, and at the equator would only make in the same time 86,017 vibrations. The other method is to set a pendulum in motion, to measure with the greatest care the number of its vibrations, and also its length at the time of the experiment ; then to deduce the length of a simple pendulum beating seconds at the same station. The 1 The centrifugal force is rendered manifest in physical lectures by the aid of an apparatus shown in Fig. 16. Circles of steel rapidly turning on an axis take the forms of ellipses flattened at the extremity of the axis, the flattening being more considerable as the velocity of rotation is greater. CHAP. IV.] THE PENDULUM. 41 lengths of the pendulums beating seconds in different places, compared with each other, enable us to calculate the ratios which exist between the intensity of the force of gravity at those places. We possess a great number of observations, made by one or other of the two methods in various regions of the two hemispheres, from the seven- teenth century to the present time. The most illustrious men have asso- ciated their names with these investi- gations, which are of such importance to the physics of the globe. We give here (Figs. 17 and 18) a sketch of the pendulum employed by Borda, so well known for the accuracy of his researches. This is the pendulum which was used in the observations made at Paris, Bordeaux, and Dunkirk, by Messrs. Biot and Mathieu. Borda's pendulum was formed of a ball of platinum, suspended by simple adherence, and by the aid of a metal cap lightly covered with grease, to a fine metallic wire, which was attached at its upper extremity to a knife-edge similar to that which supports the pendulum-rods of clocks. The knife-edge rested on two well-polished fixed planes of hard stone, the position of which was perfectly hori- zontal. These planes were themselves fixed to a large bar of iron attached to supports fixed in a solid wall, in such a manner as to obtain perfect immobility. The oscillations were counted by comparing them with those of the pendulum of a clock placed against the wall, the movement of the clock being regulated by the stars. By the help of a telescope placed at a distance of ten metres, the successive coincidences of the two pendulums were observed, and from the number of the 17.' Borda's pendulum. Platinum sphere and knife- edge. 42 PHYSICAL PHENOMENA. [BOOK i. coincidences and the number of seconds elapsed the number of oscillations was deduced. This number having been thus ascertained, the length of the pendulum was measured by operations of the greatest delicacy, the Fio. 18. Borda's pendulum. Measurement of the time of an oscillation by the method of coincidences. details of which cannot, be given here. They will, however, be found in Vol. II. of Blot's "Physical Astronomy." CHAP, iv.] THE PENDULUM. 43 Having stated the length of the pendulum's beating seconds at Paris and London, we shall now give the length which calculation and observation have determined for similar pendulums located at the poles, equator, and at a mean latitude of forty-five degrees. The intensity of the force of gravity in these different places that is to say, the number of metres indicating the velocity acquired in a second by heavy bodies falling in vacua is also shown. Length of the Intensity of the seconds pendulum. force of gravity. At the equator ...... 90i1>3 978103 At the latitude of 45 degrees . 993'52 9'80606 At the poles V 1'V .... 996' 1 9 9'83109 It must hot be forgotten that the variation of the force of gravity in different parts of the earth depends, as we have before said, both on the form of the globe which is not spherical, but ellipsoidal and on the centrifugal tendency engendered by the velocity of rotation. .The force diminishes therefore from the poles to the equator more than it would do without this rotation. But we know what proportion must be attributed to each of these causes in the phenomena observed. By the aid of pendulum observations it has been found pdssible to calculate the flattening of the earth, and to predict in this manner the results of geodetic operations, as well, as to support Clairaut's hypothesis on the increasing densities of the interior strata from the surface to the centre. By careful comparisons of pendulum oscillations, executed in different regions of the globe, it has been found that they sometimes indicate a force of attraction much greater than that given by calcu- lation ; while in other regions the intensity is, on the contrary, more feeble than the elliptical form of the earth would require. As the excess of the action of gravity has been observed especially in islands situated in the open sea, whilst the opposite is found to be the case on the coast, or in the interior, of continents, it has been concluded that the water-level is somewhat depressed in the middle of the ocean, and that it rises in the vicinity of large extents of land. 1 Here, then, we find the pendulum indicating inequalities in the curvature of the terrestrial spheroid. 1 Saigcy, " Physique du Globe." E 2 44 PHYSICAL PHENOMENA. [BOOK r. By observing the difference of length of the pendulum which beats seconds at the top of a very high mountain and at the level of the sea in the same latitude, the density of the globe may be inferred. Another method to arrive at the density consists in observing the oscillations of the pendulum at the sea-level and at a great depth in the interior, or at the sea-level and at the top of a high mountain. The present Astronomer-Royal, Sir G. B. Airy, made some experiments in the Harton mines, on the vibra- tions of two pendulums placed, one at the surface, the other at the bottom of the mine, at a depth of 420 yards. The latter moved more quickly than the upper pendulum, and its advance of two seconds and a quarter in twenty-four hours showed that the intensity of the force of gravity was increased from the surface of the earth to the bottom of the mine by about -^^th part of its value. This result proves that the density of the terrestrial strata increases from the surface towards the centre ; since, if it were otherwise, the attraction due to the interior nucleus would diminish with depth, and the oscillations of the pendulum would be more and more slow, which is contrary to the fact. The density of the strata comprised between the surface and the bottom of the mine being known, and the connection between this density and that of the nucleus being deduced from the acceleration observed, the mean density of the terrestrial globe may be calculated. The same research has been pursued by other methods, and has given slightly different results a fact not at all astonishing in a problem of such delicacy. To sum up : the terrestrial globe is acknowledged to weigh nearly five and a half times more than an equal volume of water. It is also proved that the density of the concentric strata of which the earth is formed continues to increase from the surface towards the centre. Physicists agree in accepting as an inference from considerations which cannot find place here for the density of the central strata, a value double of the mean density, which in its turn is nearly double of the superficial strata. CHAP. V.] WEIGHT OF BODIES. 45 CHAPTER V. WEIGHT OF BODIES EQUfLIBRTUM OF HEAVY BODIES CENTRE OF GRAVITY THE BALANCE. Distinction between the weight of a body and its mass Loss of weight which a body undergoes when it is taken from the poles to the equator Centre of gravity, (1), in bodies of geometric form ; (2), in bodies of irregular form The Balance ; conditions of accuracy and sensibility Balance of precision Method of double weighing Specific gravity and density of bodies. " On precision in measures and weights depends the progress of chemistry, physics, and physiology. Measures and weights are the inflexible judges placed above all opinions wliich are only supported by imperfect observations." J. MOLESCHOTT, La Circulation de la Vie : Indestrnctibilite de la Matibre. EAVITY acts in the same manner on all bodies, whatever their VT form or size, or whatever the nature of their substance. This follows from the equal velocity which all bodies acquire in falling from the same height and in the same place. A heavy body, then, may be considered as the aggregation of a multitude of material particles, each of which is acted on individually by gravity (Fig. 19). All these equal forces are parallel, and thus produce the same effect as a single force equal to their sum applied at a certain point. This resultant of all the actions of gravity is the weight of the body. The point where it is applied, and which is called its centre of gravity, is that which must be supported, in any position of the body, in order that the latter may remain in i i I 1- FIG. 19. Weight of a body of gravity. 46 PHYSICAL PHENOMENA. [BOOK i. equilibrium. The centre of gravity is not always situated iii the interior of the body: in some cases it falls outside it. Although for simplicity's sake we used the word weight in the first chapter as a synonym for gravity, the force of gravity must not be confounded with weight : and it is also important to distinguish weight from mass. Mass, sometimes, is described as the quantity of matter which a body contains : but this definition is vague, and does not express the difference which exists between the two terms. An example will explain the precise sense which is given to this word in physical inquiries. Let us take a heavy body a piece of iron, for example. To determine its weight, let us suspend it to a spring, or dynamometer (see Fig. 1), such that its degree of tension will show the intensity of the action of gravity on the body. Let us notice the divided scale the exact point where the upper branch of the instrument stops ; and let us suppose that this first observation is made, for instance, in the latitude of Paris. Now transport the piece of iron and the dynamometer either to the equator or towards the poles. The intensity of the force of gravity is no longer the same: the spring will be less extended in one case, and more so in the other. The weight, as we ought to expect, after what we know of the variations of the force of gravity, has changed. And nevertheless we are dealing with the same quantity of matter : it is the same mass which, in the three cases, has been used for the experiment. Thus, then, the quantity of matter the mass remaining the same, the weight varies, and in the same ratio as the intensity of the action of gravity varies ; so that that which remains constant is the ratio, which should, for this reason, serve as a definition for the mass. This variation in the weight of bodies when they are transported from one place to another in a different latitude would equally take place if the bodies were to change their altitude : that is, if their height above or below the sea-level were to be changed, their masses remaining always constant. But this change we shall not be able to piove by the aid of balances, because in these instruments equilibrium is produced by bodies of equal weight, and the variation in question will take place both in the weight to be measured and in the weight which is used as a measure. CHAP. V.] WEIGHT OF BODIES. 47 Calculation shows that a mass weighing one kilogramme, or 1,000 grammes, at Paris, would not, when taken to the equator, pull the dynamometer farther than 997108 gr. The same weight taken to either pole would pull it as far as a weight of 1000'221 gr. at Paris. Let us now return to the centre of gravity. It may be interest- ing, and moreover it is often useful, to know the position of the point, which, being fixed or supported, the body remains in equilibrium when it is subjected to the action of gravity only. When the matter of which the body is composed is perfectly homogeneous, and when its form is symmetrical or regular, the determination of the centre of gravity is simply a question of geometry. Let us take the most ordinary cftses. FIG. 20. Centres of gravity of parallelograms, a triangle, a circle, a circular ring, and an ellipse. A heavy straight bar has its centre of gravity at its point of bisection. In reality, the material bar is prismatic or cylindrical, but in the case where the thickness is very small in comparison with the length we may neglect it without inconvenience. The same remark is applicable to very thin surfaces, and they are considered as plane or curved figures without thickness. The square, rectangle, and parallelogram have their centres of gravity at the intersections of their diagonals (Fig. 20). The triangle has it at the point of inter- section of the lines which fall from the summit of each angle on to the middle of the opposite side, that is to say, at one-third the distance of the vertex from the base, measured along any of these lines. If these surfaces were reduced to their exterior contours, the position of the centre of gravity would not be changed 48 PHYSICAL PHENOMENA. [BOOK i. The centre of figure of a circle, a circular ring, or of an ellipse, is also its centre of gravity. Eight or oblique cylinders, regular prisms, and parallelepipeds (Fig. 21) have their centres of gravity FIG. 21. Centres of gravity of a prism pyramid, cylinder mm cone. at the middle points of their axes. That of the sphere, and the ellipsoid of revolution, is at its centre of figure (Fig. 22). To find that of a pyramid, or of a right or oblique cone, a line must be drawn FJG. 22. Centres of gravity of an ellipsoid and a sphere of revolution. from the vertex to the centre of gravity of the polygonal base, and the centre lies along this line at one-fourth of the distance of the vertex from the base. These statements are true for homogeneous bodies of geometrical CHAP. V.] EQUILIBRIUM OF HEAVY BODIES. form. But, in nature, the form is often irregular, or the material of the body is not equally dense in all its parts. In such cases, the determination of the centre of gravity is made by experiment. A simple way of finding it is by the suspension of the body by a string. When it is in equilibrium, the centre of gravity will lie along the prolongation of the string, the direction of which is then vertical. A second determination must be made by suspending the body by another of its points; this furnishes a new line, in which the centre of gravity lies. The intersection of these two lines, then, gives the centre of gravity (Fig. 23), which may be sometimes inside, sometimes outside the heavy body. The definition of the centre of gravity indicates that, when this point is supported or fixed, provided that all the material points of which the body is composed are rigidly united, equilibrium is secured. But this condi- tion is difficult to fulfil, as very often the centre of gravity is an interior point, by which the body cannot be directly fixed or supported. If the suspension is made by a string or flexible cord, equilibrium will estab- lish itself; the centre of gravity will then be on the vertical line passing through the point of suspension. If, when this position is obtained, the body is disturbed, it will form a compound pendulum, will execute a certain number of oscillations, and will again come to a rest. This is what is called stable equilibrium, and it is an essential condition of this kind of equilibrium that the position of the centre of gravity be lower than the point of suspension, so that when the body is disturbed the centre of gravity rises. In general, in order that a heavy body be in equilibrium under the action of gravity, it is necessary and sufficient that its centre of gravity be in the vertical line passing through the point of support when it is suspended from a point above it, or within the area of the plane of support if it rests on fixed points. Figs. 24 'and 25 give ( t*'w. 23. Experimental determination of the centre of gravity of a body of irregular form or non-homogeneous structure. 50 PHYSICAL PHENOMENA. [BOOK i. examples of the latter. The Leaning Towers of Bologna and Pisa (Fig. 3 represents the second of these structures) are singular cases in which the equilibrium is preserved, owing to the circumstance that the Fio. 24. Equilibrium of a body supported on a plane by one or more points. centre of gravity of the edifice is in the vertical line falling within the base. But it is to be understood that the materials of which these towers are built must be cemented together in such a manner, FIG. 2o. Equilibrium of a body resting on a plane by three support*. that each of them cannot separately obey the force which would cause its fall. The water-carrier and porter, represented in Fig. 26, take posi- tions inclined either to the side or the front, so that the centre of gravity of their bodies and the load which they sustain, taken together, is in a vertical. line falling within the base formed by their CHAP. V.J CENTRE OF GRAVITY. feet. The same condition is fulfilled by the cart (Fig. 27), which travels transversely along an inclined road : it remains in equilibrium so long as the centre of gravity is vertically above the base com- prised between the points where the wheels touch the ground. It Fu;. M. I'ojsitions uf equilibrium of persons currying loads. would upset if this were not so, either from too great au inclination of the road, or from a too rapid movement impressed on the vehicle and its centre of gravity, flinging the line outside the wheel. Fio. 27. Equilibrium on an inclined plane. When a body is supported by a horizontal axis, around which it can turn freely, its equilibrium may be either stable, neutral, or unstable. It is stable, if the centre of gravity is below the axis; 52 PHYSICAL PHENOMENA. [BOOK i. neutral, if this centre is on the axis itself ; and unstable, if the centre of gravity is above the axis. Fig. 28 furnishes an example of each of these cases. The determination of the centre of gravity of one or more heavy bodies is a problem which frequently finds numerous applications in various industrial arts. But another question, no less interesting and FIG. 28. Stable, neutral, and unstable equilibrium. useful, is to determine that resultant of which the centre of gravity is the point of application, or, to use the common expression, to weigh bodies. The instruments destined to this use have received the name of Balances, or Scales. The Balances used are very varied in their forms and in their mode of constructions, and we shall describe them in detail when we treat of the Applications of Physics. Here we shall confine ourselves to the description of the delicate balances used in scientific researches. The principle on which their construction is based is this : A lever, a rigid, inflexible bar, resting at its centre on a fixed point, on which it can freely oscillate, is in equilibrium when two equal forces are applied to each of its two extremities. To make a lever of this kind serve as a balance, it is indis- pensable that certain conditions be attended to in its construction. It is necessary, first, that the two arms of the lever or beam A o, OB, be of equal length and of the same density, in order to CHAP. V.] CENTRE OF GRAVITY. 53 PlG. 29. Scales. produce equilibrium by themselves. The two scales, in one of which is placed the standard weight, in the other the body to be weighed, ought also to be of exactly the same weight. In the second place, the centre of gravity of the system ought to be below the point or axis of suspension, and very near to this axis. It follows from this second condition, that the equilibrium will be stable, and that the oscil- lations of the beam will always tend to bring it back to a hori- zontal position, which is the in- dication of the equality of weight between the bodies placed in the two scales. These two conditions are neces- sary, in order that the balance be exact ; but they are not suf- ficient to make it sensitive or delicate that is, to cause it to indicate the slightest inequality in the weights by an unmistakable inclination of the beam. In order that a balance be very exact and delicate, it is further necessary : 1st. That the point, or axis of suspension, of the beam and of the two scales should be in the same right line. In this case, the sensibility is independent of the weights on the scales. 2nd. That the beam be of a great length, and as light as possible ; which makes the amplitude of the oscillations greater for a given in- equality of the weights. This is the reason which necessitates the centre of gravity of the balance being very near the axis of suspension of the beam, without, however, absolutely coinciding with it. Let us now show how these conditions are realized in the delicate balances used by physicists and chemists. The beam is made of a lozenge shape, formed out of a metal plate of steel or bronze, cut away in such a way as to diminish its weight without increasing its flexibility. Through its centre passes a steel knife-edge, the horizontal edge of which forms the fulcrum of the beam. This edge rests on a hard and polished plane of agate, for example. The two extremities of the beam carry two other very 54 PHYSICAL PHENOMENA. [BOOK i. small knife-edges, which, being horizontal and parallel to those of the principal one, support movable steel plates, to which are attached the rods which hold the cups or scales. The three edges which we have described must be placed exactly in the same plane, and their distances from each other must be perfectly equal. In the middle and above the beam, two buttons are fixed, one above the other, one of which is made like a nut, so that it can be screwed up or down at will. It is used to raise or lower the centre of gravity of the balance in such a way as to bring it nearer to or further away from the axis of FK;. 30. Chemical hfdancc : the beam. suspension, and thus give to the balance the degree of sensibility required. Above and in front of the middle knife-edge, the beam carries a long metallic rod or needle, which oscillates with it, and its position is exactly vertical when the plane, formed by the three axes of sus- pension, is horizontal. The lower extremity of this needle moves over an ivory arc, the zero division of which corresponds to this last position, and determines it. On either side of zero, equal divisions indicate the amplitudes of the oscillations of the needle : if these amplitudes be equal on each side, we are assured of the horizontality of the bf/am and of the equality of the weights in the scales. CHAP. V.] THE BALANCE. 55 A balance thus constructed should be placed on a firm plane ; and by the use of the elevating screws placed at the foot of the instrument, and by observing the needle, its position must be made exactly horizontal before beginning work. To avoid the influence of currents of air and the deterioration proceeding from dampness or other atmospheric agents, the balance is also inclosed in a glass case, which is shut daring the weighing, and is only opened to insert or FIG. 31. Chemical balance. remove the weights and the suostances to be weighed. Chloride of calcium is also placed in the case to absorb the moisture. Moreover, when the apparatus is not in use, a metallic fork is made to raise the beam by means of rackwork inclosed in the column, so that the knife-edges may keep their sharp edges, which, without this precaution, the pressure would in time render dull. 56 PHYSICAL PHENOMENA. [BOOK i. We now see with what precision the conditions of exactitude of a balance destined to scientific uses, such as the instrument just described, are realized. This precision is indispensable in the delicate determinations required in physical researches and modern chemistry. But they do not suffice : the operator must also add the ability which experience produces, and precautions on which we cannot enter. It is unnecessary to state that the precision of the balance would be completely useless if the weights were not themselves rigorously exact. Sometimes, besides the series of mean weights, the operator possesses another series of small weights, which he has carefully constructed himself, of very fine platinum wire, which he uses for weights lower than a gramme, as decigrammes, centigrammes, and milligrammes. At the present time, balances are made delicate enough to detect a milligramme ('0154 grain) when each scale is charged with five kilogrammes (13*39 lb.). In the balances used in chemical analysis, tenths of milligrammes ('00154 grain) even are weighed; but then the total charge must be very small, two grammes for example. Physicists frequently employ the method of double weighing, to remedy any inequality in the arms of the beam. They place the body to be weighed in one of the scales, and then establish equi- librium by putting in the other scale an ordinary tare formed of leaden shot. In this state, if the arms be not exactly the same length, the apparent equilibrium does not prove the equality of the weights. But if, on removing the body, it is replaced by weights graduated until equilibrium be again established, it is easily under- stood that these weights exactly represent the weight sought for, since they produce the same effect as the body itself does under the same conditions. It will be seen further on, that the weight of a body is modified by the medium in which it is weighed, so that it is lessened by the weight of the fluid which it displaces. On the other hand, its volume varies with the temperature, and consequently the same body does not always displace the same quantity of fluid. Hence the neces- sity of taking account of these elements of variation, unless the precaution is taken of weighing in a space void of air that is to say, in vacuo. CHAP, v.] WEIGHT OF BODIES. 57 The unit of weight generally adopted by scientific men of all countries is that of the metric system of weights and measures the kilogramme. A cubic decimetre of distilled water, weighed in vacua at the temperature of four degrees centigrade above its freezing-point, in the latitude of forty-five degrees, and at the level of the sea, weighs one kilogramme. Such is the exact definition of the unit of weight. It must not be forgotten that, if the weight varies with the latitude and with the height above the level of the sea, the variation does not manifest itself in a balance, because it affects in the same manner the weights placed in both scales. These causes of error may, therefore, be neglected when the balance is employed. We may state also, in bringing this chapter to a close, what is understood by specific gravity and density : further on, we shall see how the values in question are experimentally determined. Equal volumes of different substances have not the same weight; a block of stone weighs more than a piece of wood, and less than a piece of iron, of the same dimensions ; this is a fact easily proved, and known by every one. Let us suppose that we take, as the unit of volume of each, the cubic decimetre, for instance, and weigh them all at a constant temperature, the values obtained will be what are called the absolute weights of these substances. The absolute weights would vary, if the unit of weight were changed, but their relations would remain invariable. It is then usual to take one of them for unity: the weight of water is thus chosen, because water is a substance spread all over the earth, and it is easily procured in a state of purity. The weight of a cubic decimetre of any other substance, expressed in units each of which is the weight of a cubic decimetre of water (a gramme) is called relative or specific weight, or specific gravity. In making similar comparisons between the masses of different substances taken in unit volumes of each, we determine also what is called the relative density of substances. The numbers thus obtained are precisely the same as the specific gravities, they ought not to be confounded one with the other, under the common denomination of density. 58 PHYSICAL PHENOMENA. [BOOK i. CHAPTER VI. WEIGHT OF LIQUIDS. PHENOMENA AND LAWS OF EQUILIBRIUM : HYDROSTATICS. Difference of constitution of solids and liquids ; molecular cohesion Flowing of sand and powders Mobility of the molecules of liquid bodies Experiments of the Florentine Academicians ; experiments of modern philosophers Pascal's law of equal pressures Horizontality of the surface of a liquid in equilibria Pressure on the bottom of vessels ; pressures normal to the sides ; hydraulic screw Hydrostatic paradox ; Pascal's bursting-cask Equilibrium of super- posed liquids ; communicating vessels. T)HENOMENA the most curious and the most worthy of attracting -L our attention are daily passing before our eyes without our taking any notice of them, much less considering the causes which give rise to them. Such are, for example, the different appearances under which we see bodies, sometimes solid, sometimes liquid, sometimes gaseous, and sometimes passing successively through the three states. In what does ice differ from water, and how does the latter transform itself into vapour ? What difference is there between the arrangements of the molecules which constitute these three forms of one substance ? These are questions very difficult of solution, on which science possesses few data, which we will review in the several chapters of this work. We shall confine ourselves here to those which are indispensable to the understanding of the phenomena we are about to describe. That which distinguishes a solid body when it is not submitted to mechanical or physical forces capable of breaking it, or of making it pass into a new state, is its constant form. Let us con- sider a stone or a piece of metal. Its particles are so solid that they keep their mutual distances, separating from each other only under an exterior force, more or less strong. It follows that the position of CHAP. VI.] WEIGHT OF LIQUIDS. 59 the centre of gravity of the body remains invariable, and that what- ever movement a stone receives, whether it is thrown into the air or falls under the action of gravity, all its particles will participate in the motion at the same time and in the same manner. Cohesion is the force which thus unites the different molecules of a body one to the other. It happens, when a solid body is reduced to very fine particles to small dust that this cohesion appears to be, if not annulled, at least considerably diminished. Hence it is that it n is difficult to maintain a heap of sand in the form of a high cone : the grains slip one over the other, and their movement along the slope of the mass is somewhat analogous to the flow- ing of a liquid on an incline. This analogy appears still more striking when we fill a vessel with fine powder, and make a hole in the bottom. The flow resembles that of a liquid (Fig. 32), but in appearance only, for each grain, however small it be, is a mass which has all the properties of a solid body, and, indeed, does not differ from one. What then, from a physical point of view,, is the special characteristic which distinguishes liquids from solids ? It is that, whilst in the latter molecular cohesion is strong enough to prevent the movement of its different particles, in liquids, on the contrary, this force is nothing, or nearly nothing. Hence the extreme mobility of their particles, which slide and roll one over the other under the action of the slightest force. In consequence of this mobility, a liquid mass has in itself no definite form ; it takes, when in equilibrium, the form of the vessel or natural basin which contains it, the walls of which prevent it from moving under the action of gravity. It must not be imagined from this that there is no cohesion in liquids. When a liquid mass is in motion, its particles do indeed change place, but they are not isolated or separated, as happens in the case of sandy matters : the distance between the particles does not change, and, if the form is modified, the volume remains F 2 FIG. 3-2. Flowing of sand. 60 PHYSICAL PHENOMENA. [BOOK r. FIG. 3S. Cohesion of liquid molecules. invariable. When a solid disc is applied to the surface of a liquid which moistens it (Fig. 33), it requires a certain effort to separate it from the liquid, and the liquid stratum which the disc takes with it is a proof that this effort was necessitated by the force which united the liquid molecules to each other. It would be the same if a rod were dipped in a liquid susceptible of moistening the substance of which the rod is formed. On drawing it out, a drop of liquid would be seen suspended at the end. Lastly, the spherical form which dew-drops, when deposited on leaves, or small drops of mercury lying on a solid surface (Figs. 34 and 35), present, is explained by the preponderance of the molecular cohesion over the action of gravity, which other- wise would tend to spread out the small liquid masses in question over the surfaces which sustain them. Nevertheless, this cohesion is very slight, as may be shown by the mobility of the particles and the facility with which the cohesion is overcome : a mass of water pro- jected from a certain height falls to tiie ground in a shower of spray, due,- as we have already seen, to the resistance of the air. Moreover, there is a great difference in this respect between various liquids. Some are viscous, and their molecules are but slowly displaced, requiring time to take the form of the vessels which contain them; such are resins, and sulphur at certain temperatures. Soft bodies are in a kind of transition state between solids and liquids. 1 Other bodies, such as the ethers and alcohols, possess 1 The cohesion of the particles which form solid bodies can be overcome by sufficient pressure. Some experiments of great interest made by M. Tresca have proved the fact in appearance paradoxical that the hardest solids can, without changing their state, flow like liquids under great pressure. FIG. 34. Spherical form ot dew drops. CHAP, vi.] WEIGHT OF LIQUIDS. 61 a great degree of liquidity, and pass with the greatest facility into a state of vapour. Lastly, there is a certain number of liquids like water, in a degree of liquidity which is a mean between these two extremes. We shall see further on that heat and pressure have a very important influence on these different states. Whatever these differences may be, the phenomena which we are about to pass under review are manifested by all liquid bodies, to Fio. S5. Cohesion of liquid molecules ; drops of mercury. degrees which vary only according to their more or less perfect liquidity. Most people have heard of the celebrated experiments made at the end of the eighteenth century by the physicists of the Academy del Cimento, of Florence, on the compressibility of liquids. Does water, or more generally speaking, does any liquid change its volume, when submitted to a considerable mechanical pressure ? Such was the question which these men asked themselves, and which they believed they solved negatively. They caused a hollow silver sphere to be made, filled it with water, and immediately hermetically sealed it. Having then strongly compressed it, they saw the water oozing through its walls. They made other experiments with the same result, and they concluded that liquids do not diminish in volume under the action of the greatest mechanical forces, or, in otl-ier words, that they are incompressible. But more recent experiments . have invalidated those of the Florentine Academicians. The compressibility of water and many other liquids has been demonstrated. Canton in 1761, Perkins in 1819, Oersted in 1823, and, more recently, Despretz, Colladon and Sturm, Wertheim and Kegnault, have measured with continually increasing accuracy the diminution of volume brought about in sundry liquids subjected to a determinate pressure. We shall see later that this diminution is extremely slight, so slight that 62 PHYSICAL PHENOMENA. . [BOOK i. it need not be taken into account in the study of hydrostatic phen- omena. We will now give a description of the more important of these phenomena. Imagine two cylinders of unequal diameter communicating at their bases by a tube (Fig. 36). Two perfectly fitting pistons move freely in the interior of each of them, and the tube and the cylinders below the pistons are filled with water. We find by this experiment that, in order to obtain 16JC equilibrium in the instrument, if the charge of the piston of the small cylinder, added to its own weight, is, for example, one kilogramme, or one pound, the largest piston must be charged, its own weight included, by as many times one kilogramme or one pound as the sur- face of the large cylinder contains that of the small one. In the example represented in Fig. 36 FIG. 36. Principle of tlie hydraulic press. one kilogramme balances sixteen. It seems as if the pressure exercised by the surface of the small piston were transmitted, without any modifi- cation of its energy, through the liquid to each equal portion of the surface of the large one. Such is, in fact, the principle on which rests the construction of a machine of the greatest utility, which will be described in the Applications of Physics, and which is known under the name of the hydraulic press or ram. The discovery of this principle is due to Pascal : it is a consequence of the mobility and elasticity of liquid particles. It may be formulated as follows : Pressure, exercised on a liquid contained in a closed vessel, is transmitted with the same energy in all directions. By this it must be understood that if we take on the liquid or on the interior walls of the vessel a surface equal to that on which the pressure is exercised, this surface will undergo a pressure exactly equal to the first ; if the surface which receives the pressure is double, triple, quadruple, &c., of that which transmits it, it will support a double, triple, and quadruple pressure. So that, if we open in the sides of the vessel orifices of any dimensions, it is necessary, to maintain equilibrium, to exercise on the pistons CHAP. VI.] WEIGHT OF LIQUIDS. 63 FIG. 37. The pressure exercised on one point of a liquid is transmitted equally in every direction. which shut these orifices pressures proportional to their surfaces (Fig. 37). In order to prove this by experiment, it is necessary, in measuring the pressures exercised or transmitted, to take into account the pressures which proceed from the force of gravity, or that which the liquid ex- ercises on itself or on the walls -of the vessel by its own weight. The experiment shown in Fig. 36, and actually realized in the hydraulic press, is an evident cfon- sequence of Pascal's principle. We have seen and it is a fact which every one can prove by observation that the direction of the plumb-line is perpen- dicular to the surface of a liquid at rest. It can be easily understood that it could not be otherwise. In fact, when the surface of a liquid is not plane and horizontal, a particle such as M (Fig. 38) finds itself on an inclined plane, and, in virtue of the mobility proper to liquids, it glides along the plane under the influence of its own weight. Equilibrium will be impossible until the cause of the agitation of the liquid having ceased, the surface becomes by degrees level, and is exactly plane or horizontal. The large liquid surfaces of the seas, lakes, and even of pools, are rarely in repose. The agitations of the air, high winds, or light breezes, are sufficient to produce the multitudes of moving prominences, which are called waves, or simple ripples. But if, instead of taking into con- sideration a small portion only, we embrace with the sight or in thought an extent of sufficient radius. or if we contemplate this extent from a considerable distance, the inequalities are effaced over the whole ; the liquid appears to be at rest ; and its surface is clearly a horizontal plane. We must always bear in mind that the earth is spheroidal ; that the verticals of the different places are not parallel ; that the real surfaces of the seas and great lakes participate in its curvature, as is proved by various optical phenomena described in one of our FIG I. Tlie surface of liquids in repose is horizontal. 64 PHYSICAL PHENOMENA. [ROOK i. preceding works. 1 But this only serves to confirm the essential condition of the equilibrium of a liquid contained in a vessel and submitted to the action of the force of gravity only. The exterior surface of a liquid in equilibrium is always level, or plane and horizontal. This is on the exterior. Let us now see what happens in the interior. Each liquid particle possessing weight, it originates a pressure which is exercised vertically, and ought to transmit itself in every direction to the other portions of the liquid, and to the walls of the vessel which contains it. FIG. 39. Pressure of a liquid on the bottom of the vessel which contains it. What is the result produced by the pressure of all the particles ? The following experiment will answer this question. Let us take a cylindrical vessel, without a bottom, supported by a tripod of a certain height (Fig. 39). A flat disc, in the form of a plate, suspended by a wire attached to one of the arms of a balance, is applied exactly to the lower edges of the cylinder, so 1 See " The Heavens." CHAP, vi.] WEIGHT OF LIQUIDS. 65 as to form a bottom to it. In the other scale, a counterpoise is placed equal to the difference between the weight of the cylinder and that of the disc. Lastly, standard weights are added, which cause the disc to press against the bottom edge of the cylinder. Water is then poured into the latter. By degrees the pressure of the liquid on the movable bottom increases ; when it has become equal to the added weights, the least excess of liquid detaches the disc, and the water flows out. But the pressure diminishes by this outflow, and the disc again adheres closely to the cylinder. A pointer which touches the surface of the water marks its level at the moment of equilibrium. It is seen from this first experiment, that, as we should expect, the pressure exercised oil the bottom of the vessel is precisely equal to the weight of the liquid. If now we repeat the experiment with a vessel with the same sized orifice at bottom as the cylinder, but wider at the top, and consequently of much greater content, we find identically the same result that is to say, the same weight counterpoises a column of liquid of the same height. The result is the same if a vessel nar- rowed at the top is employed, provided that the surface of the base remains the same. Thus, the pressure exercised by the weight of a liquid on the bottom of the vessel which contains it is independent of the form of the vessel, but proportional to the height of the liquid, and lastly, equal to the weight of a liquid column of the same height, having the bottom of the vessel for a base. The experimental demonstration of the first part of this law may also be shown by the aid of Haldat's apparatus; but the measure of the pressure is not directly given, as in the first method. It is shown by the elevation of a column of mercury in a tube, as shown in Fig. 40. If, instead of inquiring the degree of pressure on the bottom of the vessel, we wished to find that exercised on the surface of a liquid stratum, or the sides of the vessel, this pressure would be found to be the same, with equal surfaces and the same depth ; for it is also measured by the weight of a vertical liquid column, having the pressed surface for its base, and for its height the distance of the stratum from the surface of the liquid. 66 PHYSICAL PHENOMENA. [BOOK i. The following experiment demonstrates this law in the case of a surface taken on an interior horizontal stratum : A cylinder, open at the two ends, and furnished with a disc or movable covering, which serves it as a bottom, is plunged ver- tically into a vessel full of water (Fig. 41). The hand is obliged to exert an effort in introducing the cylinder, which proves that the liquid exercises an upward pressure which holds the disc against FIG. 40. Pressure of a liquid on the bottom of a vessel : Hal;lat'>- the edges of the cylinder and prevents the water from getting in. If, now, water is poured into the tube, equilibrium continues as long as the interior level is lower than the exterior one. At the moment when equality is attained in the levels, and even a little before, on account of the weight of the disc, the latter gives way, and equilibrium is destroyed. The same result is always produced to whatever depth the cylinder is immersed. Hence this law : CHAP. VI.] WEIGHT OF LIQUIDS. G7 In a liquid in equilibrium under the sole action of the force of gravity, the pressure on a definite point of the same horizontal stratum is constant ; it is measured by the iveight of a liquid column having for base the area of the surface under pressure, and for height the vertical depth of the stratum. The lateral pressures on the walls are measured in the same way. It must be added that their pressure is always exerted normally, that is to say, perpendicularly to the surface of the walls, so that it is exerted in a direction contrary to the action of gravity, if the wall is horizontal above the liquid. FIG. 41. Pressure of a liquid on a horizontal stratum. FIG. 42. The pressures of liquids re normal to the walls of the containing vessel. We will give some experiments which prove the existence and the directions of these pressures. A cylinder (Fig. 42) is terminated by a very thin metallic ball pierced with holes in all directions. If it be filled with water, it will be seen to spout out through all the orifices, and the direction of the jet is always normal to the portion of surface whence it escapes. In the rose of a watering-can the water escapes in virtue of this property of liquids to press laterally against the walls of the vessels which contain them. The hydraulic tourniquet shows the lateral pressure exerting itself G8 PHYSICAL PHENOMENA. [BOCK T. in two opposite directions at the two extremities of a doubly curved horizontal tube (Fig. 43). If this tube were not open, the lateral pressure on the end would be counterbalanced by an equal and contrary pressure at the elbow, and the instrument would remain at Fio. 43. Hydraulic, tourniquet. rest ; but the orifices at each extremity permit two liquid jets to escape, and as the pressure on each elbow is no longer counterbalanced, a backward movement follows and a rotation of the tube is set up. The pressures, lateral or. otherwise, exerted normally on the walls explain all that is peculiar in the equality of pressure on the bottom of vessels of different forms. In a wide-mouthed conical vessel, the lateral walls support the ex- cess of the total weight of the liquid over that of the column FIG. 44. Hydrostatic paradox. which measures the pressure on the bottom. In a narrow-topped vessel, the walls are subjected to pressures in a direction opposed to that of the force of gravity, and CHAP. VI.] WEIGHT OF LIQUIDS. the amount of this pressure is precisely equal to that which is wanting to form the liquid cylinder, the weight of which is equivalent to the pressure on the horizontal bottom of the vessel (Fig. 44). Thus is explained the phenomenon, which at first appears so singular, of liquid columns very different in weight when they are measured in the scale of a ba- lance, nevertheless exerting the same pressure on a unit of surface in the bottom of a vessel, if the weight of the liquids be equal. Pascal proved this fact, which is called the hydro- static paradox. He burst the staves of a solidly construc- ted barrel, filled with water, the 1) u n g - h o 1 e o f which was sur- mounted by a very narrow, high tube, and he did this by simply tilling this tube with water ; that is to sa y> by adding to the whole weight an insignificant FIG. 45. Hydrostatic paradox. Pascal 1 : addition (Fig. 45). The walls of the barrel had to support the same pressure as if they had been surmounted by a mass of water having a base equal to the bottom of the barrel and the same height 70 PHYSICAL PHENOMENA. [BOOK i. as the length of the column of water in the tube. One kilogramme of water can produce, in this manner, the same effect as thousands of kilogrammes. If, in the same vessel, we introduce liquids of various densities, not susceptible of mixing for example, mercury, water, and oil these liquids will range themselves in the order of density. Moreover, when equilibrium is established (Fig. 46), the separating surfaces are plane and horizontal. This experimental fact might be fore- seen, for the equilibrium of a single liquid requiring, as we have before seen, a horizontally of surface, this equilibrium is not broken, when this surface also supports at every point a pressure due to a superposed liquid. It is possible, with great precautions, to obtain equilibrium with two liquids of nearly equal densities, by placing the heavier one uppermost, but the equili- brium is unstable, and the least agitation again establishes the order of densities. This is the reason of the existence, in the fiords or gulfs on the Norwegian coasts, of the sheets of fresh water brought by the rivers, which have been observed ; these maintain themselves on the surface of the salt water without mixing with it, although sea-water is heavier than fresh water. Vogt records that in one fiord one of these sheets was I 1 50m. deep. This phenomenon is only possible in calm localities, as the agitation caused by winds would soon mix the fresh water with the salt. The same fact has been noticed in the Thames, the tides bringing the sea- water to a great distance in the bed of the river. The equilibrium of a liquid contained in a vessel and submitted to the action of gravity alone is independent of the form of the vessel. Hence this very natural consequence, that a liquid rises to the same height in two or more vessels which communicate one with the other. Experiment shows that the level is always the same in different tubes or vessels connected together by a tube of any form CHAP. Vf.] WEIGHT OF LIQUIDS. 71 whatever, provided always that the diameter of each be not too small (Fig. 47). It is this principle which serves as a basis to the theory of arte- sian wells, the construction of the fountains which play in public or private gardens, and the distribution of water in our towns. We shall return to these interesting applications in another volume. It is the principle only which interests us here. The water which arrives at the orifice of an artesian well often proceeds from very distant reservoirs, forming as it were subterranean rivers, the level of which, at the source, is higher than at the point of outflow. The pressure is thus transmitted to a distance, and the FIG. 47. Equality of height of the same liquid in communicating vessels. jet which follows would rise precisely to the same height as the original source, were it not for the resistance of the air and the friction to which the ascending column is subject in its passage. The same thing happens with the jets of water fed by a reservoir higher than the basin and communicating with it by subterranean pipes. If two communicating vessels contain liquids of different den- sities, the heights are no longer equal (Fig. 48). Let us first try mercury. The level will be established in the two tubes at the same height. In the left-hand tube, let us now PHYSICAL PHENOMENA. [BOOK i. pour water. The mercury will rise in the right-hand tube, under the influence of the pressure of the new liquid. Equilibrium having been established, it is easily proved that the heights of the level of the water and of the mercury, measured from their common FIG. 48. Coiinmuiicating vessels. Heights of two liquids of different densities. plane of separation, are in the inverse ratio of their densities. For example, if the mercury rises three millimetres, the column of water will have a length of 40 - 8 millimetres ; that is to say, a length DV6 times greater. Now, a volume of water weighs 13 - 6 times less than an equal volume of mercury. CJAP. vii.] EQUILIBRIUM OF BODIES IN LIQUIDS. 73 CHAPTER VII. EQUILIBRIUM OF BODIES IMMERSED IN LIQUIDS. PRINCIPLE OF ARCHIMEDES. Pressure or loss of weight of immersed bodies Principle of Archimedes Experi- mental demonstration of this principle Equilibrium of immersed and floating bodies Densities of solid and liquid bodies ; Areometers. ~T7\ VERY BODY knows that when we immerse in water a sub- -i-^ stance lighter than itself, a piece of wood, or cork, for instance, it requires a certain effort to keep it there. If left to itself, it rises vertically and comes to the surface, where it floats, partly in and partly out of the water. What is the cause of this well-known phenomenon ? The force of gravity. In the air, the same body left in the air falls vertically ; in water, the lateral pressures, the downward pressures, and those in the contrary direction, are partly destroyed, and are reduced to a pressure which is exerted in a direction contrary to the force of gravity. We have proved the existence of this pressure in an ex- periment before described (Fig. 41). It is stated, and experiment confirms the theory, that this pressure is precisely equal to the weight of the liquid displaced. The point of application of this force, which is called the centre of pressure, is the centre of gravity of the volume of liquid, the place of which is occupied by the body. The loss of weight of which we speak being greater, for bodies lighter than water, than the weight of the body itself, it is evident that it must cause the body to move in a direction opposite to that which gravity would impose on it; hence the rising of the piece of wood or cork to the surface of the liquid. But this kss occurs also in the case of bodies heavier than water, and in any kind of liquid. Every one knows that it was Archi- G 74 PHYSICAL PHENOMENA. [BOOK r. medes, one of the greatest geometers and physicists of antiquity, who had the glory of discovering this principle, which is known by his name : All bodies immersed in a liquid suffer a loss of weight precisely equal to the weight of the displaced liquid. The experimental demonstration of the principle of Archimedes is made by means of the hydrostatic balance. Take a hollow cylinder, the capacity of which is exactly equal to the volume of a solid cylinder, so that the latter can exactly fill the FIG. 49. Experimental demonstration of the principle of Archimedes former. Both are furnished with hooks, so that the solid cylinder can be placed, with the hollow one above it, below one of the pans of the hydrostatic balance (Fig. 49). This done, the beam is raised by means of rackwork fitted to the column of the balance, high enough to permit a vessel filled with water to be placed beneath the two cylinders, when the beam is horizontal. In this state, equilibrium is established by the aid of a counter- poise in the other scale. If then the beam of the balance is lowered, CHAP. VH.] EQCJILIBRIUM OF BODIES IN LIQUIDS. 75 the solid cylinder is immersed in the water, and equilibrium is dis- turbed; This alone would suffice to demonstrate the vertical pressure, or the loss of weight of the immersed body. To measure this weight, the solid cylinder itself is placed entirely in the water, and equili- brium is re-established by pouring water slowly into the hollow cylindrical vessel. It will then be seen that the beam will again become horizontal, as soon as the hollow cylinder is quite filled. Thus the loss of weight is exactly equal to the weight of the water poured in, that is to say, the water displaced by the immersed body. The preceding experiment then fully proves the principle of Archimedes. How is it then that equi- librium is not disturbed, when, after having exactly balanced a vessel contain- ing liquid and a solid body placed side by side on the plate of a balance, the solid body is immersed in the water ? The solid body loses weight, as has been proved. Nevertheless the equilibrium remains. It must be that the vessel and its contents have been increased by an equivalent weight, or that, to put it another way, the water undergoes from above FIG. 50. Principle of Archimedes. Reaction of one immersed body on the liquid which contains it. downwards a pressure equal to that at work upwards. That this explanation is correct is proved by the aid of the apparatus above described. A vessel partly filled with water is weighed. Then the solid cylinder is immersed, supported separately, as is shown in Fig. 50. Equili- brium is disturbed : the beam leans to -the side of the vessel. By how much is the weight of the water augmented by the immersion ? <; 2 76 PHYSICAL PHENOMENA. [BOOK i. Precisely by the weight of the displaced water : as is proved by the fact that, in order to again establish equilibrium, it is sufficient to take from the vessel a volume of water exactly sufficient to fill the hollow cylinder of the same interior capacity as the body immersed. The principle of Afchimedes is of great importance. It enables us to determine the conditions of equilibrium with immersed or floating bodies, to explain numerous hydrostatic phenomena, and to solve a host of problems of great practical interest. For example, it enables us to determine beforehand what must be the forni 3 weight, and distribution of the cargo of ships, in order that stable equilibrium be properly combined with the other qualities of the vessel, such as rapidity, &c. At every point we have> in the phenomena which take place in liquids, proofs of the existence of pressure. When we take a bath, if we compare the effort which is necessary to raise one of our limbs to the top of the water with that which it requires in air, we are struck with the difference. Very heavy stones, that we should have great trouble to lift out of Water, are moved and lifted with facility when they are immersed in it. Lastly, when we walk into a river 1 which imperceptibly gets deeper, we feel the pressure of our feet on the bottom diminish by degreeSj until at last we no longer have any power to walk forward. The weight of our body is nearly Counter- balanced by the pressure of the liquid, and we tend to take a horizontal position in consequence of the unstable equilibrium in which we find ourselves. This brings us to say a few words on the conditions of equilibrium of bodies immersed in liquids or capable of floating on their surface. It is at once evident that an immersed body cannot be in equili- brium if its weight exceeds that of an equal volume of the liquid. In this case it falls, under the action of the excess of weight over pressure. Neither will it remain in equilibrium if its weight is less than the displaced liquid: in this case it will rise to the surface, urged by the excess of pressure over its weight or over the force of gravity. It is thus that cork, wood at least certain kinds of wood wax, and ice, swim on the surface of water, whilst stones, most of the metals, and numerous other substances fall to the bottom. Since mercury is a liquid of great density, most of the metals float on its surface. A leaden ball, a piece of iron, or copper, will not sink in it ; gold and platinum will." CHAP. vil.J EQUILIBRIUM OF BODIES IN LIQUIDS. 77 We shall now examine the case of a body the specific gravity of which is precisely equal to that of the liquid. If its substance is perfectly homogeneous, the body will remain in equilibrium, in whatever position it is placed, in the middle of the liquid. In this case, the weight and the pressure not only are equal and opposite, but are both applied at the same point ; that is to say, the centre of gravity and the centre of pressure coincide. Fish rise and fall, at will, in water. These different movements are rendered possible by the faculty these creatures have of com- pressing or expanding a sort of elastic bag filled With air, situated in the abdomen. According to the volume of the swimming-bladder the name of the organ in question the body of the fish is sometimes lighter and sometimes heavier than the volume of Water which it displaces : in the first case it rises, in the second it descends. M. Delaunay quotes, in his Course of Physics, a very curious phe- nomenon which is very easily explained by the principle of Archi- medes. " When," he says, " a grape is introduced into a glass full of champagne, it immediately falls to the bottom. But the carbonic acid, which continually escapes from the liquid, soon forms many little bubbles rolind it. These bubbles of gas add, so to speak, to the bulk of the grape, increase its volume, without its weight being sensibly augmented : the pressure of the liquid which was at first less than the weight of the grape, soon becomes greater than this weight, and the grape rises to the surface of the liquid. If, then, We give a little jerk to the grape, and detach from it the bubbles of Carbonic acid which adhere to its surface, it again de- scends to the bottom of the glass, after a short time to remount. The experiment may thus be continued as long as any carbonic acid escapes." If the immersed body is not homogeneous, if, for example, it is made of cork and lead, the substances having been combined in such a manner as to weigh together as much as the displaced water (Fig. 51), without having a common centre of gravity, the centre of gravity of the whole and the centre of presswe no longer coincide. To establish equilibrium these two points must be in the same vertical plane, as in the positions 1 and 2, or otherwise equilibrium will be unstable, if, as in 2, the centre of gravity is uppermost. In position 3, this condition not being realized, equili- 78 PHYSICAL PHENOMENA. [BOOK i. brium will only take place when the oscillations of the body bring it to the first position. When a body displaces a volume of liquid, the weight of which is greater than its own, either in consequence of its real volume or of its form, it floats on the surface. In this case, the weight of the water which the portion immersed displaces is precisely that of the body and the load which it supports : thus a ship with its cargo of men, materials, and mer- chandise, weighs altogether just as much as the volume of the sea^water displaced. Moreover, the second condition of equilibrium is still the same ; that is to say, the centre of gravity of the body and the centre. of pressure must be on the same vertical line. But it is no longer indispensable to stability that the first point be below the other. Besides, according FIG. 51. Equilibrium of a body immersed in a liquid of the same density as its own. to the position and the form of the floating body, the form of the displaced volume itself changes, and the centre of pressure changes with it, so that at each instant the conditions of equilibrium vary. In ships, perfect equilibrium never exactly exists, even when the sea is smooth and calm. Oscillations of greater or lesser amplitude are always taking place ; the principal point to attain is that, under the most unfavourable circumstances, the movements of the vessel shall not be decided enough to upset it. The principle of Archimedes is of the greatest use in science, in determining the specific gravity of liquid or solid bodies. Let us briefly indicate the methods adopted for this purpose. CHAP. VII.] EQUILIBRIUM OF BODIES IN LIQUIDS. 79 Let us remember that the specific gravity of a body is the rela- tion which exists between its weight and that of an equal volume of pure water taken at a temperature of 4 degrees centigrade. How can we find the number which expresses the specific gravity of a body ? First, we must obtain its weight : for this the balance is used. Secondly, we must know the weight of an equal volume of water: the opera- tions necessary for this determination will be described in the sequel. These two numbers obtained, the quotient, the first divided by the second, gives the specific gravity. The only difficulty is then to find the weight of a volume of water equal to that of the body. We shall explain the three methods employed. Let us take the case of a piece of iron weighing in the air 246 '5 gr. It is sus- pended by a very fine cord to one of the plates of the hydro- static balance, and to establish equilibrium a counterpoise is placed in the other plate. Then the balance is lowered until the piece of iron is immersed in the water (Fig. 52). At this moment the beam falls on the side of the tare, and it is necessary to put weights equal to 31*65 gr. in the plate which holds the body, to re-establish equilibrium. These weights re- present the displaced water. On dividing 246'5 by 31-65, 7'788 is found to be the specific gravity of the iron, which shows that for equal volumes the iron weighs 7 and 788 thousandths times as much as water. We now come to the second method. Fig. 53 represents an instrument called an areometer, 1 which was Fia. 52. Dcusii> of solid bodies. Mettiod of the hydrostatic balance. 1 From the Greek apaios, right, and pfrpov, measure. Areometers were first used to determine the densities of liquids. SO- PHYSICAL PHENOMENA. [BOOK i. invented by the physicist Charles, although it is generally attributed to Nicholson ; it is constructed so that when placed in water the liquid is precisely level with a standard point on its upper rod, when the pan which surmounts this rod is charged with a known weight, let us say 100 grammes. We place the body whose specific gravity is sought for in the little pan at the top, and standard weights are added to obtain the level If, for instance, 35'8 gr. have been added, the difference, 64'2 gr., of this last weight and the 100 grammes evidently gives the weight of the body in air. From what has been said it will be seen that the areometer is a true balance. Fio 53. Densit. of solid holies. Arooir.cter of Charles or Nicholecu. The body is next taken out of the upper pan, and is placed in the little vessel suspended under the instrument : it loses some of its weight, so that the areometer rises, and more standard weights must be added to bring it again to the level : let us suppose 31 grammes added this is the weight of a volume of water equal to that of the body. Dividing 64'2 by 31, we find 2'07 the ratio sought (the specific gravity of sulphur). CHAP. VII.] EQUILIBRIUM OF BODIES IN LIQUIDS. 81 In the case where the body is lighter than water, the small basket is reversed over it, and the body, which pressure causes to rise^ meeting with an obstacle, still remains immersed. A third method to determine the specific gravities of bodies is that of the "specific gravity bottle." Placed in the pan of a balance is the fragment of a body the weight of which is known, but of which the specific gravity is sought, and, by its side, a flask exactly filled with water and well stopped by means of a ground stopper (Fig. 54). Equilibrium is obtained by standard weights. The body is then Fio. 54. Density nf solid bodies. Method of the specific gravity bottle. FIG. 55. Density of liquids. Hydrostatic balance. introduced into the flask, which is again stopped, care having been taken to push the stopper to the same level. A certain quantity of water has come out, the volume of which is precisely equal to that of the body which takes its place. After having well dried the flask, it is replaced in the pan of the balance, and the weights required to restore equilibrium give the weight of the water expelled. Having the weights of equal volumes of the substance and of water H 82 PHYSICAL PHENOMENA. [BOOK i. its specific gravity is easily determined. This process is not an application of the principle of Archimedes, like the first two. These three methods require some precautions ; the body im- mersed in the water retains, adhering to its surface, air-bubbles which must be removed. If the body easily absorbs water, or even dis- solves in it, another liquid is used oil, for example in which case we must determine the density of the body relatively to the oil, that of the oil being known, or determined as below. The specific gravity of liquids is determined by processes analogous to those we have just described. A hollow glass ball, ballasted so that it is heavier than the liquids to be weighed, is hooked under the pan of the hydrostatic balance (Fig. 55). FIG. 56 Specific gravity of liquids. Fahrenheit's Areometer. FIG. 57. Specific gravity of liquids. Method of the specific gravity bottle. Weigh it in air and then in water, the difference of the weights gives the weight of a volume of water equal to its own. Dry it well, and weigh it in the liquid of which the specific gravity is wanted, the difference between this weight and that in air gives the weight of an equal volume of the liquid. Dividing the latter weight by the former, the quotient is the specific gravity sought. Fahrenheit's areo- meter (Fig. 56), immersed in water, requires a given weight to be CHAP. VII.] EQUILIBRIUM OF BODIES IN LIQUIDS. 83 placed on it, so that a fixed standard point on its rod is level with the surface of the liquid. It is clear that this additional weight, together with that of the instrument, marks the weight of the volume of water displaced. Immersed in another liquid, in oil for example, we obtain in the same way the weight of a volume of oil equal to the volume of the body. The division of the second weight by the first gives the specific gravity of the oil. Lastly, with a flask terminated by a straight tube (Fig. 57), which is successively filled with water and some other liquid as far as the standard mark on the stem, the weights of the two equal volumes of water and of the liquid are found, and thence the specific gravity. To terminate this chapter, we give a table of the specific gravities of some of the most common solids and liquids. As we shall soon see, the volumes of the bodies vary according to the degree of temperature at which they are determined. These variations do not affect their weight, but precisely on that account the specific gravity of the body is variable. It has therefore been necessary to reduce them to a constant temperature. For water only, this tem- perature is 4 C. ; for all the other solid and liquid substances, it is convenient to take that of melting ice, or C. SPECIFIC GRAVITIES OF DIFFERENT BODIES AT C. SOLIDS. Metals. Rolled platinum . 22'06 Cast gold . . . 19-26 Cast lead . . .11-35 Cast silver . . . 10 '47 Minerals, Diamond Marble . Granite . Sandstone Rocks, &c. . . . 3-53 . 2-65 to 2'84 . . . 2-75 . . . 2'60 Vegetables, &c. Boxwood . . . Heart of oak . . Black ebony . . Oak 1-32 1-17 1-19 0'91 Drawn copper wire '8'95 Cast ditto . . . 8'85 Iron 7-79 Tin 7 "29 Quartz . Glass . Porcelain Sulphur . . . 2 ; 65 . . . 2-50 . . . 2-24 . 2 08 Beech .... Willow .... Poplar .... Cork 0-75 0-49 0-39 0-24 Aluminium . . 2'67 Ice at 0. . . . 0'93 Elder pith . . . 0-08 LIQUIDS. Mercury . . . 13-596 Bromine . . . 2'966 Concentrated sul- phuric acid . 1*841 Nitric acid . . 1'520 Water at 4 . I'OOO Water at . . 0-9998 Olive oil . . . 0-915 Sea-water . . 1-026 Essence of turpen- Milk . . . . 1-03 tine .... 0*865 Bordeaux. . . 0-994 Alcohol. . . . 0-792 Burgundy . . 0-921 Sulphuric ether . 0'736 H 2 84 PHYSICAL PHENOMENA. [BOOK i. CHAPTER VIII. WEIGHT OF THE AIK AND OF GASES. THE BAROMETER. The air a heavy body Elasticity and compressibility of air and other gases Pneumatic or fire syringe Discovery made by Florentine workmen Nature abhors a vacuum Experiments of Torricelli and Pascal Invention of the barometer Description of the principal barometers. WE live at the bottom of a fluid ocean, which envelopes all portions of the terrestrial spheroid, and of which the mean depth is at least a hundred times greater than that of the seas. The substance of which this ocean is formed is the air, a mixture of various other gases, the two principal being oxygen and nitrogen. Carbonic acid gas, aqueous vapour, sometimes ammonia, are also found, but in variable proportions, whilst the two gases first named are everywhere found in the same proportion a proportion such that, by volume in 100 parts, 21 are oxygen and 79 nitrogen. Air is, as is well-known, the indispensable aliment to the respira- tion of animals. Those even which habitually live in water cannot do without it. It is not less necessary to the vegetable world, which, under the influence of light, decomposes the carbonic acid in the air, fixes the carbon and liberates the oxygen, which, in its turn, is absorbed in animal respiration. The transparency of the air itself is so great that we cannot see it, at least when we are dealing with a stratum of small thickness. In the case of great distances the effect of the interposition of gaseous strata is very perceptible ; it gives to distant bodies, such for example as mountains bounding the horizon, a bluish tint, and this tint, very brilliant and pure, forms the colour of the sky CHAP, vni.] WEIGHT OF THE AIR AND OF GASES. 85 when the .atmosphere is cloudless. Were it not for the blue colour of the atmosphere, the sky would be colourless, that is, entirely black; and the stars would then stand out brightly in broad day. During the night, the aerial envelope, being no longer lighted up by the rays of the sun, but only by the feeble light of the moon and stars, appears of a dark blue ; and, if in the day we observe it from a very high mountain, the same appearance is produced the thinner stratum of the air above us, which moreover is less dense in the higher regions, absorbing but a slight portion of the blue rays of the solar light. The existence of air is revealed to us by other phenomena, which act upon us through the medium of the organs of hear- ing and touch. When the air is still, it is only necessary for us to move in order to feel its presence. The mass of air resists the dis- placement which we cause in it, and the resistance is sensible to our hands or our face. But the material nature of the air is manifested still more perceptibly by the movements with which it is itself animated ; from the lightest breeze to the most violent winds, hurricanes, and tempests, all atmospheric agitations are continual proofs of its existence. Lastly, it is in consequence of the vibrations communicated to the air by sonorous bodies that sound is propagated to our ear. The air itself, when it is put in vibration under favourable conditions, becomes a producer of sound, as we shall see further on. Most of the properties of air have been utilized, and we shall, in the sequel, describe numerous and very interesting applications. The object of this chapter, meanwhile, is the study of the properties of air con- sidered as a body which has weight, and of those phenomena due to the weight of air or other gaseous substances. That air has weight is easily proved by a very simple experiment. We shall shortly describe the instrument which is used to ex- haust the air which it contains from a vessel or receiver to make a vacuum, as physicists say. This is called an air-pump. If we take a hollow glass tube fitted with a metallic neck furnished with a stopcock, and weigh it after having made a vacuum (Fig. 58), we have only to open the cock and allow the air to enter, to see that the beam of the balance leans towards the side of the ball. To re- establish the interrupted equilibrium, weight must be added about 1*29 grammes for each litre that the globe holds. PHYSICAL PHENOMENA. [BOOK i. Thus then is the weight of the air directly demonstrated. The same experiment, made with other gases, proves in the same manner that bodies in a gaseous state, like liquids and solids, obey the action of gravity. Galileo first sus- pected and enunciated the import- ant truth that air is heavy; but the experiment we have just indi- cated is due to Otto de Guericke, the inventor of the air-pump. If the air contained in a vessel is heavy, that is, if its weight is susceptible of being valued by means of a balance, the immense volume of air which rests on the surface of the earth must press on it in proportion to its mass, and this pressure, which is doubtless enormous, must be manifested in some way. This is indeed what happens ; but before studying these phenomena, let us say a few words on the properties of gases, both those which they possess in common with liquids, and those which characterize them in a special manner. Like liquids, gases are formed of particles molecules which glide one over the other with extreme facility. Thus we see gaseoiis masses give way to the least force dividing themselves, and allow- ing all the movements of solid and liquid bodies to continue in their midst, and not opposing them with sensible resistance, until the velocity and displacement of their molecules become considerable. ;" : Gases are eminently elastic and expansible. Let us take a flattened and compressed bladder, only inclosing a small volume of air in comparison with the quantity which the same bladder when filled out would hold (Fig. 59). In this state, the interior air does not increase in volume, because the elastic force with which its molecules fire endowed, and which we are about to demonstrate, is balanced by FIG. 58. Experimental demonstration of the weight of air and other gases. CHAP; vin.] WEIGHT OF THE AIR AND OF GASES. 87 the pressure of the exterior air. Let us place this bladder under the receiver of an air-pump. In proportion as the vacuum point is approached, we shall see the bladder increase in volume ; it swells out, and may burst under the interior pressure which distends its walls. Let the air again into the receiver it immediately returns to its primitive volume; which at once proves that air and any other gas would conduct itself in the same manner is elastic and compressible. FIG. 59. Elasticity and compressibility of gases. These two properties are also proved by the aid of the fire-syringe. In forcing a well-fitted and greased piston into a glass tube filled with air (Fig. 60), we experience a slight but increasing resistance, and the volume of the air diminishes one-half, two-thirds, &c. This first operation proves the great compressibility of gases. When the piston has arrived at the end of its course and is abandoned to itself, it returns spontaneously to its original position a proof no less evident of the elasticity of the air. As compression produces heat, this apparatus may be used to light a piece of tinder placed under the piston ; but in this case the compression* must be very rapid. Hence the name given to the in- strument. Gases then, like liquids, are elastic and compressible ; but whilst this latter property is very slight in liquids, it is, on the contrary, very marked in the case of gases. We may also notice that if liquid molecules have a cohesion nearly nil, in gases the 88 PHYSICAL PHENOMENA. [BOOK T. molecules have a tendency to repel each other, which is only counter- balanced by pressure from without. Hence it follows that when this pressure diminishes, the volume of the gas increases ; in liquids the volume remains constant, at least as long as the body retains the same state. One last property which distinguishes liquids from gases, is the very feeble comparative density of the latter. Whilst the weight of a litre of liquid may be as high as 13596 grammes (the weight of a litre of mercury), and is never lower than 715 grammes (ether), the weight of a litre of gas or vapour never exceeds 20 grammes and may be as low as 9 centigrammes. Moreover, in gases as in liquids, the principles of equality of pressure and of equality of transmission of pressure in every direction, are indi- cated by theory and verified by experi- ment ; we shall have occasion soon to give some examples of this. Let us now return to the phenomena due to the FIG. 60. Pneumatic syringe. weight of the air. We have seen that Galileo was the first who suspected that the air has weight. The history of the discovery is well known. It was made in 1640. Some Florentine workmen, ordered to construct a pump in the palace of the Grand Duke, were greatly astonished that, in spite of the good condition into which they had put the mechanism, the water would not rise to the upper extremity of the pipe of the body of the pump, that is to say, beyond 32 Roman feet (about 10'3m.). The learned men engineers and Florentine academicians who were consulted on this anomaly, did not know what to answer. They addressed themselves to Galileo, then aged seventy-six 'years, whose immense reputation had not been shaken by persecutions. Galileo at first gave an evasive answer, but the question made hjm reflect. He saw at last that the pressure of the air must be the cause which made the water rise to this precise height, and that " Nature's abhorrence of CHAP, viir.] WEIGHT OF THE AIR AND OF GASES. 89 a vacuum "was an idle explanation, as it required us to suppose that this abhorrence would not manifest itself beyond a given height. He proved the weight of the air by weighing a bottle, before and after the air had been expelled by the vapour caused by the ebullition of a certain quantity of water. But he left to his disciple Torricelli the care of extending the verification of his conjectures. A year after the death of Galileo, it occurred to Torricelli to examine how mercury, a liquid denser than water, would act in vacuo. He took a long tube closed at one end, which he filled with this liquid; then, covering the open end of the tube with his finger, in such a way as to prevent the liquid from falling out and the air from getting in, he plunged this extremity into a vessel full of mercury. Leaving the liquid to itself, he then held the tube in a vertical position (Figs. 61 and 62). Torricelli saw the liquid descend from the top, and after a few oscillations, settle itself at a level which remained nearly invariable at 28 Eoman inches (29'92 English inches or 76 centimetres) above the level of the mercury in the vessel. If Galileo's idea was right, if the column of water of 32 feet was really maintained by the pressure of the atmosphere, the same pressure would raise the mercury, being thirteen times and a half heavier than water, to a height thirteen times and a half less. Now, 28 inches are thirteen and a half times less than 32 feet ! Such, in its simplicity, is this grand discovery. Such is Torricelli 's tube, or, as it is now called, the barometer, an instrument used to measure the pressure of the atmosphere. It was not without oppo- sition that the explanation of Torricelli on the elevation of water and mercury was accepted by the scientific men of his day. But addi- tional experiments suggested by Pascal left no doubt. Pascal remarked that if the weight of the air were really the cause of the observed phenomena, the pressure ought to be less in proportion as the barometer was observed at a greater height in the atmosphere, since the gaseous column superposed above the exterior liquid would be less. The height of the mercury in Torricelli's tube ought then to be smaller at the top of a mountain than in the plain. Hence the famous experiments which he made with Perier, his brother-in-law, on the Puy-de-D6me, and those which he executed himself at the base and at the top of the tower of Jacques la Boucherie. The 90 PHYSICAL PHENOMENA. [BOOK i. results were in every point conformable to the inferences drawn from the new theory. 1 The height of the mercury in Torricelli's tube is independent of its diameter, provided always that this diameter be not too small : m FIG. 61. Torricelli's experiment. PIG. 62. Tonicelli's experiment. Effect of the weight of the atmosphere. for then other forces which we shall study subsequently have a great influence on the level of the liquid. This fact is a very natural 1 " I have thought," wrote Pascal to Pe"rier, " of an experiment which will remove all doubt, if it be executed with exactness. The experiment should be made in vacuo several times, in one day, with the same quicksilver, at the bottom and at the top of the mountain of Puy, which is near our town of Clermont. If, as I anticipate, the height of the quicksilver be less at top than at the base, it will follow that the weight or pressure of the air is the cause of this ; there certainly is more air to press at the foot of the mountain than at its summit, while one cannot say that Nature abhors a vacuum in one place more than in another." CHAP, viii.] WEIGHT OF THE AIR AND OF GASES. 91 consequence of the equal transmission of pressure in liquids: the column of mercury acts by its weight on all the mercury in the trough, so that each element of surface equal to the section of the tube is pressed equally by this weight. And as there is equili- brium, it follows that the pressure of air on this same unit of surface is precisely equal to the pressure of the mercury. What must we conclude from this ? That the mass of the atmosphere presses on the earth's surface, as if this surface were everywhere covered with a stratum of mercury about 76 centimetres thick. Let us add, that the pressure in the air being transmitted equally and in every direction, the weight of the atmosphere makes itself felt wherever the air penetrates and by whatever remains in communication with it, as in the interior of houses, in cavities and on the surface of bodies. This explains why all bodies situated on the earth's surface are not crushed by this enormous pressure, which is not less than 10,333 kilogrammes (about 10 tons) on the average on each square metre of surface. The surface of the human body being nearly a square metre and a half for a person of average height and size, each of us always supports a load which is about equal to 15,500 kilogrammes (nearly 1 5 tons). We have just given the reason why this load does not crush us : all the pressures exercised on every part of our body and from within produce equilibrium. At first sight it seems incomprehensible that we should not be ground to dust under the effect of these contrary pressures. The reason is very simple. All the fluids contained in our organism act against the pressure of the atmosphere, and it is this constant reaction which explains our insensibility to pressure, and the absence of the pheno- mena which the pressure of the air seems, at first, certain to cause. This reaction is not a simple hypothesis, as the process of " cupping " proves. " Cups " are small vessels of metal or glass, which are applied to the skin: a vacuum being made inside them, the skin swells up, the small veins burst, and the blood flows out, because it is no longer maintained in the veins by atmospheric pressure. In ordinary courses of physics, some interesting experiments are introduced to show the energy of atmospheric pressure. These we will rapidly describe. One of the first known is that of the Magdeburg hemispheres : it is attributed to Otto de Guericke. 92 PHYSICAL PHENOMENA. [BOOK i. Two copper hemispheres fitting one on to the other, in such a way as to form a hollow sphere, are fixed by a stopcock to the pipe of the air-pump (Fig. 63). While they are full of air, the slightest effort is sufficient to separate them. But when a vacuum is made in the interior of the sphere, it requires a considerable effort to effect the separation. This is easy to account for, since the pressure on two hemispheres of only 2 decimetres (about 8 inches) in diameter, is 324 kilogrammes (about 6 cwts.) on each of them. In one of his experiments, the illustrious burgomaster of Magde- burg caused each hemisphere to be pulled by four strong horses without being able to separate them ; the diameter of the hemispheres being 65 centimetres (26 inches), the pressure was 3,428 kilogrammes (about 3J tons). The total pressure on the hemispheres is even greater ; but we speak only of what is exerted in the direction of FIG. 63. Magdeburg hemispheres. FIG. 64. Bursting a bladder by exhausting the air beneath it. resistance, which equals on either side the pressure on a circle of the same diameter as the sphere. Another experiment consists in making a vacuum in a vessel, over the mouth of which a bladder has been stretched, which prevents the air from getting in. As the vacuum point is approached, the membrane is depressed under the weight of the exterior air, and at last it bursts (Fig. 64), a loud detonation similar to that of a pistol-shot accompanying the rupture. This detonation is evidently owing to the sudden entrance of the air into the cavity of the CUAP. VII1.J WEIGHT OF THE AIR AND OF GASES. 93 vessel. If an apple is applied to the end of a thin metallic tube, in the exterior of which a vacuum is made, being pressed by the weight of the atmosphere, it is cut by the edges of the tube, and a part penetrates into the interior. Lastly, there is a curious experiment which demonstrates the pressure of the air on the surface of liquids. A cylindrical glass bell jar, mounted on a metallic stand, is furnished with a tube and stop- cock, which allows of its being screwed on the air-pump, and a FIG. (55. Jet of water in vucuo. vacuum being made in its interior. When the vacuum is made, the lower end of the tube is immersed in a basin filled with water, and the tap is turned, which opens the communication between the interior of the vessel and the liquid. The atmospheric pressure which is exerted on the water in the basin causes a jet which strikes the top of the bell jar (Fig. 65). In what has preceded, we have supposed that the weight of the column of air was the only cause of the atmospheric pressure ; that this pressure was constant ; and that it was equivalent, on a given 94 PHYSICAL PHENOMENA. [BOOK i. surface, to the weight of a column of water of 32 feet, or 10*33 metres, or to that of a column of mercury of 29*92 inches, or 76 centi- metres, having the same sectional area. But experiment proves that this pressure is subject to variations, even in the same place. Further on, we shall study these variations in their relation to meteorological phenomena ; but for this purpose we must possess an instrument which indicates them. This instrument, which in prin- ciple is no other than Torricelli's tube, and which is called a barometer, deserves a detailed description. It has been differently arranged according to the use to which it is destined, and with the object of rendering its indications precise. The most simple and at the same time the most exact barometer is nothing more than a tube of glass, which is chosen straight, regularly cylindrical and perfectly homogeneous, of a diameter about three-quarters of an inch, or 2 or 3 centimetres. It is immersed, after having been filled with mercury, in a trough filled with the same liquid. The trough and the tube are fixed against a vertical support, and remain in the place where the observations are to be made. It is nothing more, as is seen, than a Torricelli's tube. But properly to arrange it, various precautions must be taken, the importance of which is very obvious, and which are equally necessary for the construction of other barometers. Thus, it is essential that the mercury used be of great purity. This is arrived at by acting upon oxide of mercury with nitric acid ; and great care must especially be taken that it does not contain air-bubbles, as their lightness would cause them to rise along the sides of the tube into the vacuum, which is called the Torricellian vacuum. Aqueous vapour and air, being elastic gases, would press the upper level of the mercury, so that its height would not indicate truly the pressure of the atmosphere. To effect this, the tube must be dried and perfectly cleaned before filling it. Once the tube is filled with mercury, the liquid is boiled in it over burning charcoal, until all the air-bubbles it contains are expelled. At this moment the aspect of the mercury should resemble a bright mirror; the bright and metallic lustre with which it shines indicating the perfect purity which is indispensable for our purpose. The large diameter of the tube which forms the standard or CHAP. VIII.] WEIGHT OF THE AIR AND OF GASES. .95 normal barometer possesses this advantage over smaller ones, that it gives a level to the mercurial column which is not altered by the molecular force called capillarity. In this instrument, in order to obtain the height of the barometer, it is sufficient to measure the vertical distance which separates the upper level from that of the mercury in the trough. This is done with a special instrument called a cathetometer, which is com- posed essentially of a divided vertical scale on which a glass vernier moves. There may be seen on Fig. 66, which represents a standard barometer, a double screw fixed to the trough. The lower end should be on a level with the mercury, which is easily accomplished by means of the screw, and it is the distance from the upper point of this screw which the draughtsman has forgotten to figure to the upper level of the mercury in the tube which the cathetometer gives. By adding to it the constant length of the screw, we have the height, or the atmospheric pressure sought for. The cistern barometer is dis- tinguished from the preceding one by having a glass cistern into which the tube is inserted (Fig. 67) ; possessing a large surface, the level of the mercury in it may be considered as constant. The stand on which the instrument is fixed is furnished with a graduated scale, on which slides a movable index placed in such FIG. 66. Normal or standard barometer. Fir,, 67. An ordinary cistern barometer. 96 PHYSICAL PHENOMENA. [BOOK i. a way that its lower edge is on a level with the surface of the mercury. The zero of the scale being by hypothesis the level of the mercury in the cistern, the reading of the height is made at once on the scale. Lastly, the scale is furnished with a vernier, which gives the fractious of millimetres or inches. The arrangement which renders this instrument less perfect than the preceding, is that the level of the cistern or the zero of the scale is supposed to be constant ; whereas under the influence of the variations of temperature the glass and the mercury expand, and this produces variations in the position of the zero point. Frequently, after a time, these accidental variations produce a permanent altera- tion, and the scale has to be slightly rectified. The barometers suggested by Fortin, Gay-Lussac, and Bunten are not liable to these inconveniences. But as they are principally constructed with the object of being easily transported, the diameter of the tube is smaller than in a standard baro- meter, so that capillarity depresses the upper level of the mercury. The observations made with these instruments require therefore a cor- rection to free the readings from this error. But in Gay-Lussac's barometers arid those of Bunten, as in the standard barometer, the height is measured by two corresponding scales at the two levels of the liquid, so that the difference, with all corrections made, gives the real atmospheric pressure. In that of Fortin, the zero point is maintained constant by an ingenious contrivance which will be easily com- prehended from Fig. 68. We have a section of the cylindrical cistern which incloses the mercury in which the slender part of the tube is immersed. The upper part of the cylinder is of glass, and shows the level of the- liquid. A metallic point in the interior indicates the position of the zero of the scale and the level the mercury ought to attain every time an observation has to be made. As the mercury rests Fie. 68.-- Cistern of Fortiu's barometer. CHAP. VIII.] WEIGHT OF THE AIR AND OF GASES. 97 on a bag of impermeable leather connected with the lower walls of the cistern, and as the metallic base is traversed by a screw, the end of which presses against the elastic bag, it follows that we can at will raise or depress the bottom of the liquid, or, what is the FIG. 69. Fortiii's barometer, as arranged for travelling. same thing, raise or depress its surface, and thus obtain the level required. For travelling, in order that the movements of the heavy fluid may not break the tube the screw is raised, until the cistern T 98 PHYSICAL PHENOMENA. [BOOK i. is entirely full in its upper part. As all the apparatus is inclosed in a brass cylinder, which preserves it from shocks, the level of the mercury of the tube is observed through two longitudinal apertures on opposite sides, which enables us to view the glass tube ; on the edges of these apertures the divisions, in inches or millimetres, of the scale, which has its zero at the constant level determined by the position of the cistern, are engraved. An index, furnished with a vernier and a milled head, which enables it to be moved by the aid of a rack and pinion, gives the precise position of the level on the scale, and the height in hundredths of millimetres or inches. The apparatus is supported by a tripod resting on the ground, and care must always be taken to place the tube in a vertical position, which is rendered easy by its mode of suspension. Fortin's barometer is convenient for scientific explora- tions, because the air cannot enter, and the movements and joltings inseparable from travelling cannot break it. The readings require to be corrected for the effect of capillarity. Moreover, as temperature causes the density of liquids to vary, a correction must also be made to eliminate this source of error. Fig. 70 shows the arrangement of Gay-Lussac's baro- meter as modified by Bunten. Two portions of the same tube are united by a very narrow or capillary one. A small opening allows the air to penetrate above the lower Fio.70. Gay- barometer, level. The barometric height is measured on a scale Sunten d by divided in millimetres or inches, the height of the upper level being taken, and the height of the lower level being subtracted from it ; the difference evidently giving the pressure. As the tubes have the same diameter, Gay-Lussac thought it would be unnecessary to correct for the influence of capillarity ; unfortunately, however, it has been found that this influence is not the same in the barometric vacuum and in the lower tube. This is unfortunate, as the instrument is easy to transport, it is not large, and the air can only with difficulty penetrate the barometric chamber, on account of the slight diameter of the intermediate tube. In travelling it is inverted. The modification designed by Bunten renders the CHAP. VIII.] WEIGHT OF THE AIR AND OF GASES. introduction of air still more difficult, since if the bubbles penetrate along the walls of the tube, they lodge themselves in the narrow space in the widest part of the capillary tube, and have no action on the level of the mercury. Some of our readers will perhaps be anxious to know by what means the variations of the atmospheric pressure can be indicated FIG. 71. Dial or wheel barometer. by a movable needle on a graduated dial. The dial or wheel barometers, to which we allude, are not of great scientific value, because they are rarely constructed with sufficient precision ; they are used in rooms as ornamental objects. The dial-barometer is composed of a siphon tube, the open branch of which (Fig. 71) supports an ivory float. This float rises and falls, and by its motion turns, by means of a silken thread, a pulley, on the axle of which I 2 100 PHYSICAL PHENOMENA. [BOOK i. the needle is fixed. The needle turns in either direction, according as the surface of the liquid rises or falls ; the dial is divided by comparing it with a fixed barometer. We shall see, further on, what is signified by the weather indications which we are accustomed to see written against the different divisions of the dial. For many years metallic or aneroid barometers have been substituted with advantage for these instruments, the indications of which are only of inferior precision. These are based on the elasticity and the flexion of metals formed into thin plates. A flattened brass tube, the section of which is elliptical, is exhausted of air and carefully closed (Fig. 72). It is curved in the form I 1 10. 7'2. Bourdon's aneroid barometer of an arc of a circle, and fixed at its middle point, so that the disengaged extremities of the two halves of the tube can oscillate on either side this fixed point. When the barometric pressure increases, the pressure flatteos the tube, which effect causes the curvature of the two arcs to augment, and their free extremities approach each other; the opposite takes place if the pressure diminishes. The disengaged extremities of the tube are con- nected with levers which move the axis of a cogged sector. The needle of the dial, which is connected by a pinion to this sector, moves either in one direction or the other, and in this manner traverses the divisions on the dial, which are engraved by comparison with a standard barometer. CHAP. VIII.] WEIGHT OF THE AIR AND OF GASES. 101 In the aneroid represented in Fig. 73, the pressure of the air is exerted on the corrugated top of a metallic drum, the interior of which has been exhausted of air. When the pressure aufments, this top sinks down ; it rises, on the contrary, if the pressure diminishes, and its movements are transmitted to a needle by a pecular mecha- nism, the detailed description of which would here be superfluous. Fiu. 73. Vidi's aneroid barometer The invention of this barometer is due to M. Vidi. It has been recently perfected by an English optician, Mr. Cooke. This kind of barometer is preferable to the dial-barometers, although from time to time it is necessary to modify the graduation or to apply corrections on account of the variations to which the molecular state of the tube in the Bourdon barometer, or that of the metallic box and of the antagonistic spring in Vidi's instrument, is subject. 102 PHYSICAL PHENOMENA. [BOOK L CHAPTER IX. WEIGHT OF THE AIR AND OF GASES (continued}. PUMPS MARIOTTE'S LAW THE AIR-PUMP. Principle of the ascent of liquids in pumps Suction and force pumps The siphon Air-pump ; principle of its construction Double and single barrel air-pumps Condensing pumps Mariotte's law. THE discoveries of the weight of the air and of atmospheric pressure only took place a little more than two centuries ago. But long before Torricelli and Galileo, the application of the principle had taken precedence of the theory, as is proved in the account we have given, as history has handed it down to us. It is, in fact, the pressure of the air which is the cause of the ascending movement of water in pumps. Now, the invention of these useful instru- ments is generally attributed to Ctesibius, a celebrated geometer and mechanician, who lived at Alexandria 130 B.C., or about a century after Archimedes. We shall now briefly describe the different instruments known under the name of pumps, the object of which is the movement of liquids and gases, keeping here particularly in view the explanation of the action of these instruments. We return, in the volume which treats of the applications of physics, to the detailed description of those which have a special use in the industrial arts. Let us take a hollow cylinder, in which a piston furnished with a rod may be moved up and down, and in the bottom of which an orifice is made (Fig. 74). The piston having been lowered to the bottom of the cylinder, the instrument is immersed in a vessel or reservoir full of water ; then the piston is raised by its rod. What happens ? The space void of air, which the piston leaves under it CHAP. IX.] WEIGHT OF THE AIR AND OF GASES. 103 in its ascending movement, will be filled with water, first until the level of the water is the same in the cylinder as in the reservoir. This takes place in virtue of the principle of the equilibrium of liquids in communicating vessels, so that it would happen even if there was air under the piston. But the water still rises above this level, keeping in contact with the piston the lower surface of which it constantly touches ; and it is easy to understand that its movement is due to the pressure which the outer air exerts on the liquid surface of the reservoir. Let us suppose that the cylinder has an elevation of more than 32 feet : the liquid column will rise until it attains about this height. At this moment its weight is in equilibrium with the pres- sure of the atmosphere ; if the piston con- tinues to rise, the water will not follow it. This is precisely the obstacle which the Florentine workmen encountered, and which caused the physicists belonging to the Court of the Grand Duke to believe that Nature ceased to abhor a vacuum beyond 32 feet. Such is the principle of the pump to which is given the name of Suction-pump, because the piston appears to suck up the liquid as it rises. We shall now show how the instrument is generally arranged when it fulfils the object for which it is intended ; that is, to give us a supply of water which has been raised to a certain height above the level of the reservoir. The cylinder, or body of the pump, is furnished with a cylin- drical tube of small diameter, the lower extremity of which is placed in the reservoir. At the junction of the cylinder and tube a valve is fitted, which opens upwards. The piston itself has one or more open- ings, furnished with valves, the action of which is in the contrary direction to the first (Fig. 75). It is easy to see what will happen when we give an alternating movement to the piston in the body of the pump. At its first ascent a vacuum is made under it. The air in FIG. 74. Principle of the suction- pump. 104 PHYSICAL PHENOMENA. [BOOK i. the suction-tube lifts the valve by its pressure, and the water rises to a certain height. When the piston again descends, the air which is introduced into the body of the pump is compressed : on the one hand, its pressure closes the lower valve, and, on the other, the compressed air lifts the valves of the piston and escapes upwards. At each stroke the water rises higher and higher, till it comes in contact with the lower wall of the piston, and passes through the valves to^its upper surface. It will be easily seen how the water is forced to flow out by a lateral orifice at the upper part of the pump. Moreover, once the pump is in action, when the piston rises a vacuum is made beneath it, and tiie water continues to press against its lower side. The valve of the suction-tube remains constantly open, and the ascent of the water is determined by the move- ment of the piston. The effort necessary to raise and lower the piston, when the punip is in action, is easily measured. If the piston descends, its own valves are open; the pressures transmitted to its opposite sides by the liquid are equal the one to the other, and consequently are counterbalanced, and the only resistances felt proceed from the friction of the liquid and the piston. But if the piston is raised, the atmospheric pressure is alone annulled, as it is exerted on the reservoir on the one hand, and on the upper level of the liquid on the other. The effort required is measured by the weight of a column of water, having for its base the surface of the piston, and for its height the vertical distance between the two levels of the liquid. If, for example, this distance is 2 metres, and the base of the piston is 1 square decimetre, it will require a force of 20 kilogrammes to raise the piston, without taking into account the resistance due to friction. Experiment shows that it is not possible to give to the suction- FIG. 75. Suction-pump. CHAP. IX. ] WEIGHT OF THE AIR AND OF GASES. 105 pump a depth of more than about 20 feet, instead of 32 feet as indicated by theory. The reason of this lies in the escape of air and water which always takes place between the pump itself and the piston ; besides, the water of the reservoir nearly always contains air in solution, and this frees itself from the ]iquid whenever it is brought up to a region of less pressure. In the Force-pump (Fig. 76) the body of the pump is immersed in water, so that the liquid is introduced into it by simple communi- cation. Moreover, the piston is solid, and the tube used to raise the FIG. 76. Force-pump. FIG. 77. Combined suction and force-pump. water, starting from the lower part of the pump, is furnished at the point of junction with a valve which opens towards the outside. The piston in its descending course presses the water ; this pressure shuts the valve of the pump and opens that of the conducting pipe, and forces the liquid out. The Suction and Force-pump (Fig. 77) combines the arrangements of both the pumps we have just described. The ascent of the water is caused by suction ; and the piston, which is solid (i.e. is not fur- nished with valves), in coming down presses the liquid into the lateral tube. 106 PHYSICAL PHENOMENA. [BOOK i. We will now describe an instrument known to most people the siphon which is of great use in transferring liquids from one vessel to another : it is the pressure of the air which causes the action in this case also. A tube formed of two curved branches, of unequal length, is filled with part of the liquid which is to be transferred, and its shortest branch is immersed in the vessel which contains this liquid (Fig. 78). As soon as this is done, the liquid is seen to flow from the openiug at the end of the longest branch as long as the shortest remains immersed. What is the cause of this continual flowing ? Nothing is more easy to explain. At the surface of the liquid in the vessel, and at the Fio. 78. The siphon. lower and free extremity of the tube, the atmospheric pressure is exerted with almost equal intensity and in contrary directions. At the point where the tube is in the vessel, this pressure serves to sustain the liquid in the left-hand branch, and it would be maintained there in equilibrium if the length of the two branches were the same and both the ends were immersed in vessels at the same level. All the portion of the liquid contained in the tube above the level of the CHAP, ix.] WEIGHT OF THE AIR AND OF GASES. 107 vessel, remains in equilibrium under the influence of these opposite pressures. There remains then in the large branch of the siphon a column of water the gravity of which disturbs the equilibrium and determines the direction of its flow. Ifc might be imagined that when once the liquid in the tube had escaped, the action would stop; but it must be remarked that for this the two branches of the liquid would, need to be separated by a vacuum, which the pressure exerted on the liquid in the vessel by the atmosphere tends continually to fill, so that in reality this separation never takes place, and the flowing continues. The forms of siphons differ, according to the use to which they are destined, and also according to the nature of the liquid to be transferred. We describe some of them in the volume on the Applications of Physics, when we explain their applications in great hydraulic works. It remains for us to terminate the study of the phenomena of gravity, by describing the instruments which are used to exhaust the air from a receiver, or any vessel, or, on the other hand, to com- press it there; and by stating how the pressures of gases are determined, and according to what laws these pressures vary when the volume which they occupy is made to vary. Torricelli's experiment on the tube gave a very simple means of making a vacuum, and a vacuum as perfect as possible ; for the space situated above the column of mercury, which has received the name of the barometric chamber, is almost a perfect vacuum. But if the process is simple, it is far from being practical, since it would necessitate the use of an enormous quantity of mercury, if the space which we wished to rarefy were considerable, and moreover the pre- cautions required to be taken at each operation would be irksome. Thus long ago other means were sought. It was in 1654 that the first air-pump was thought of and constructed. Otto de Guericke was the inventor, and we have quoted many curious experiments due to this able physicist. It soon received important improvements from Boyle, Papin, Muschenbroek, and Gravesande. At first it was only formed of one cylinder; but the necessity of having two, to get rid of the great resistance which is felt while working the one-cylinder instrument was soon obvious. We cannot give the history in detail of the progress of any mechanical instrument, 108 PHYSICAL PHENOMENA. [BOOK i. and content ourselves with describing the air-pump as it is now used by all physicists. And first let us deal with the principal arrangements. Let us imagine two cylinders, each furnished at the bottom with a valve which opens upwards, and with a piston having an orifice closed by a valve which opens in the same direction. The two orifices in the base of the cylinder communicate by a common pipe with a well- ground glass plate, on which the receiver is placed, and at the centre of which is the opening of the pipe. Fig. 79 shows in section one of the cylinders, its twa valves, and the communicating canal. The action of this half of the instrument being well understood, it will be easy to comprehend the whole. Let us begin at the moment when the piston touches the lower part of the cylinder. The receiver is filled with air at the atmospheric pressure. At the moment when we raise the piston, a vacuum is made in the lower part of the cylinder. The air of the receiver which filled the communi- cating canal lifts up the lower valve by its elastic force and spreads itself in the vacuum, the valve of the piston being kept shut by the pressure of the air which is exerted externally FIG. 79. Action of the piston and valves in the air-pump. Qn ft -Q ^ e gur f ace Q f ^he piston. This passage of air from the receiver into the cylinder takes place until the piston has reached its highest position. It is clear that at this moment the quantity of air contained in the receiver has diminished, and that it has diminished one-half, if the volume of the cylinder is precisely equal to the volume of the receiver and canal. Let us now send the piston in a contrary direction. At the moment when it begins to descend, the capacity of the cylinder diminishes, the pressure of the air which it contains increases, exceeds that of the air of the receiver, and the lower valve is closed. Then, in propor- tion as the descent of the piston lessens the capacity, the confined CHAP. IX.] WEIGHT OF THE AIR AND OF GASES. 109 air increases in density : on our assumption of its capacity, this density will again become equal to that of the atmospheric air, as soon as the piston attains half of its course. Beyond this point the interior pressure increases, lifts up the valve of the piston, and the air escapes altogether, until the piston again rests on the lower part of the cylinder. This single up-and-down movement, analysed in its effects, explains the whole of the operation, as it has sufficed to rarefy the air in the bell-jar one-half: that which remains will be again rarefied at a Fio. 80. Detail of the piston and its valves. Fits. 81. Air-pump with two cylinders. Transverse section. second, then at a third trial, and so on. The pressure will become the quarter, eighth, and then the sixteenth of the first pressure, as we shall soon see in explaining Mariotte's law. This proportion would of course change, if the ratio of the capacity of the cylinder to that of the receiver were changed. Figs. 80, 81, 82, and 83 will now explain the real arrangement of the air-pump, and show the utility of the second cylinder. The first shows how the two valves are placed, that in the piston and that at no PHYSICAL PHENOMENA. [BOOK i. the bottom of the cylinder. The valve of the piston is a small plate, a, with a light spring pressure on the opening, but which gives way to a very slight pressure in the contrary direction. The valve of the cylinder, 6, is conical ; a rod, T, which moves by friction in the piston, raises or lowers it, but only for a very short distance. Fig. 81 shows that the rods of the pistons are formed with rackwork which works into a pinion, so that, with the help of a handle with two arms, it is possible to lower one piston and raise the other. Thanks to this arrangement, the work done is doubled ; but and this is the end for which it was proposed the resistance is reduced to its minimum; for, in proportion as the vacuum is made, each piston when rising must overcome the atmo- spheric pressure which acts on its base ; but, on the other hand, this pressure helps the other piston to descend. In this way, then, there is a compensation or equilibrium between these two forces which act indeed in the same direc- tion, but all the force is done away with by the resistance of the pump, without fatiguing the operator. Figs. 82 and 83 give the plan and the exterior view of the air-pump with two cylinders. It will be seen how the pipe, which unites the two cylinders by a tube, com- municates at the centre with the plate, which is of ground glass, perfectly plane, on which is fixed the well-greased edge of the receiver in which the vacuum is to be made. If the receivers have the form of tubes or balls, &c., they are screwed into the aperture in the centre of the plate. A stopcock in the middle of the tube of communication is pierced with holes, which enable us either to establish or close the communi- cation between the pump and the receiver, or to permit the exterior air to penetrate into the cylinders or into the receiver only. In the same pipe, a bell glass (H, Fig. 83) is seen, containing a barometric tube, or manometer, which is used to indicate to what degree the exhaustion has proceeded in the receiver ; that is to say, FIG. 82. Plan of the air-pump with two cylinders. CHAP. IX.] WEIGHT OF THE AIR AND OF GASES 111 what is the pressure of the quantity of air which this latter still contains. Lastly, the best air-pumps are furnished with an arrangement, the invention of which is due to M. Babinet. This is a stopcock by the aid of which, and a special pipe, the receiver is allowed to com- municate with one cylinder only. The air which it still contains is forced through another pipe under the piston of the second cylinder. FIG. 88. Exterior view of the air-pump. and there, thanks to the increase of pressure which follows, it ends by raising the valve. The degree of vacuum is thus extended to a limit, such that the pressure of the air which still remains in the receiver is scarcely appreciated by the manometer. it Bianchi's air-pump has only one cylinder. But the piston divides into two compartments, which alternately receive and expel the air: it is, properly speaking, a double-action pump. Fig. 84 112 PHYSICAL PHENOMENA. [BOOK T. explains the manner in which this pump acts. A rod supports the two movable conical valves, which shut and open alternately under the action of the piston, thus opening and closing the com- munication of each compartment with the receiver. The air of the lower compartment, compressed when the piston descends, raises a valve held by a spring, over the orifice of the pipe formed in the piston-rod ; it escapes to the outside by this pipe. The air of the upper compartment escapes by a valve of the same kind fitted to the lid of the cylinder. A system of toothed wheels is put into motion by a handle ; and as the cylinder can oscillate in a vertical plane, the alternate move- ment of the piston is accomplished by a continuous movement of rotation, the velocity of which is regulated by a very heavy fly-wheel (Fig. 85). With this machine a vacuum can be rapidly pro- duced in receivers, the capacity of which may increase with the dimensions of the cylinder. 1 We have had already several times occasion to describe some curious experi- ments made by the aid of the air-purnp: we shall in the sequel refer to others connected with the phenomena of heat, sound, and electricity. We shall content ourselves here by indicating some which concern the phenomena of weight. For example, it is proved that water ordinarily contains, in solution, air retained in it by the atmospheric pressure. In the receiver, we see the bubbles of air attached to the sides increase as the pressure diminishes, and mount to the surface of the water. Smoke, which in the atmosphere rises above the lower strata, falls in vacuo like a heavy FIG. 84. Bianchi's nir-]>uni]> ; interior view of the cylinder. 1 M. Deleuil has constructed an air-pump specially intended for industrial uses, the piston of which does not touch the walls of the cylinder. The thin stratum of air which remains in the space serves as a fitting to the piston, so that the resist- ance due to the friction of the piston in the ordinary cylinder is done away with. M. Deleuil obtains in a receiver of 14 litres in capacity a degree of rarefaction measured by 3 millimetres of pressure only. CHAP, ix.] WEIGHT OF THE AIR AND OF GASES. 115 mass. This phenomenon shows that the principle of Archimedes is true for gases as for liquids, as may be shown by another experiment with a little instrument called a baroscope, the inventor being Otto de Guericke. A balance supports at each end of its beam two metallic balls, the one hollow and thin, the other solid and of small volume : weighed in air, these two balls exactly establish equilibrium (Fig. 86). When the apparatus is brought beneath the receiver of the air-pump, we see the equilibrium dis- turbed when the air is exhausted, and the beam is inclined towards the largest sphere. This sphere lost then in the air a certain portion of its weight, which is precisely equal to the weight of the displaced air. This proves to us that to determine the exact FIG. 86. -The baroscope. Fio. R7. Condensing machine. Interior view of the piston. weight of bodies, it is necessary to weigh them in vacuo, or at least to correct the error due to the pressure of the air. For delicate weighing in chemistry, or for the precise determination of densities, this correction is indispensable. The application of the principle of Archimedes to balloons or aerostats forms the subject of a future description. 1 Instead of making a vacuum in a vessel or receiver, it is possible, on the contrary, to accumulate and to compress the air or other gases within it. This operation is accomplished by means of con- densing machines or pumps. 1 Applications of Physics. 116 PHYSICAL PHENOMENA. [BOOK r. Condensing machines are constructed exactly like air-pumps, with one modification all the valves open in a contrary direction. On examining Fig. 87, which represents a section of the con- densing machine, it will be immediately seen what is the action , Fia. 88. Silbermann's condensing pump* Exterior view. FIG. 89. Silbermann's condensing pump. Section. of the mechanism, and how, instead of rarefying or expelling the air, the oscillatory movement of the piston must on the contrary accumulate and compress it. 1 1 The condensing pump of this kind, of which we give the section and the exterior view, is due to a physicist whose merit equals his modesty, M. J. Silber- niann. The stopcock, the position of which is shown below the valves, enables us to condense in the one. air or any other gas contained in the other ; to reverse CHAP. IX.] WEIGHT OF THE AIR AND OF GASES. 117 At the present day, condensing pumps formed with one cylinder, with a solid piston, and with two valves placed at the bottom of the cylinder, one communicating with the outer air, the other with FIG. iK>. Connected condensing pumps. the receiver (Figs. 88 and 89), are used in preference. If a more rapid compression is required, a pair of pumps are used. Fig. 90 shows the general arrangement of instruments of this kind. M. Regnault the order of communication of the receivers; or, again, to re-establish between them equilibrium of pressure ; lastly, to make a communication between them and the atmosphere. It is both an air-pump and a condensing pump. 118 PHYSICAL PHENOMENA. [BOOK i. used it to obtain air or vapour, the pressure of which was equivalent to thirty times the atmospheric pressure, or capable of supporting a column of mercury thirty times 76 centimetres ; that is, 22'80 metres. Let us now state on what principle we rely to estimate the pressures of gases, and what law the variations of these pressures, under the influence of the change of volume only, follow. This law, the discovery of which is due to the physicist Mariotte, is given thus : If a gaseous mass is submitted to a series of different pressures, the volumes which it successively occupies vary inversely as the pressures which it undergoes. Here is an experimental demonstration of this law: We take a long bent tube, the smaller arm of which is closed, and the large one open (Fig. 91). If it is perfectly cylindrical, the scale, divided into equal parts, the divisions of which are seen on the stand to which it is fixed, indicates in the tube equal capacities. If it is not cylindrical, it is divided into unequal portions of equal capacity. Let us introduce a certain quantity of mercury, and, by shaking, make the liquid extend in two columns of the same height, the levels of which correspond to the zeros of the two scales. At this moment, equilibrium exists between the outer air which presses the mercury in the large open arm. and the interior air confined in the closed arm. The pressure of the latter is then equal to that of the atmosphere. Let us pour mercury into the large arm. Equilibrium will be disturbed, and the mercury will rise in the closed arm. Let us stop when the level attains division 12; that is to say, when the volume of gas has been reduced one-half. We shall prove that the difference of the levels of the mercury is precisely equal to the barometric height at the moment of the experiment. Now, it is clear that at this moment it is this difference of level which measures the increase of pressure of the confined gas; the total pressure is then two atmospheres. Fio, 91. Experimental prouf of Mariotte'a law. CHAP, ix.] WEIGHT OF THE AIR AND OF GASES. 119 On again pouring mercury into the large arm, we shall see the level rise in the smaller branch as far as the divisions 16, 18, 19.2 for example, which supposes the volume of gas reduced to a third, quarter, and fifth of its original volume. Now, it is found that the pressures are successively three, four, five atmospheres. Generally, the volume occupied by the air or by any other gas varies precisely in inverse ratio to the pressures which this gas supports ; which proves the law. The law is proved with the same facility when we submit the gaseous mass to decreasing pressures : lower than the atmosphere the volume increases as the pressures diminish. It is seen by this law, the importance of which is extreme, how gases are compressible, and how they differ in this respect from liquids the compressibility of which is confined within very narrow limits. In the preceding experiments, the temperature is supposed constant. If Mariotte's law were exactly true, it would follow that all gases are endowed with equal compressibility, and that it increases how- ever great the pressures to which they are submitted. Dulong and Arago have proved the exactitude of the law, for air, to 27 atmo- spheres ; but M. Despretz and M. Eegnault (later) have arrived at the conclusion that this compressibility is not precisely the same for all gases, and, moreover, that it is slightly variable for the same gas. Air, nitrogen, and carbonic acid are really condensed more than Mariotte's law would allow ; hydrogen acts in a contrary direction. As to the gases susceptible of passing into a liquid state, the variation has been found much more considerable, according as the experiments have been made at a temperature nearer that at which they are liquefied. Doubtless, at this temperature the gases undergo mole- cular modifications the nature of which is not yet known, but which differ from the effects due to the variations of pressure. The measure of the pressure of the air which remains under the receiver of the air-pump when a vacuum is made, a measure effected with the help of a manometer or short barometer, is a direct application of Mariotte's law. BOOK II. SOUND. BOOK II. SOUND. CHAPTEE I. THE PHENOMENA OF SOUND. THE absence of all sound, of all noise, in a word absolute silence, is to us synonymous with, immobility and death. We are so accustomed to hear, if it is only the noise we ourselves make, that we can scarcely conceive the idea of a world completely silent and dumb, as the moon appears to be, if we are to believe astronomers. Phenomena of sound are perpetually manifested on the earth, although of course there is in this respect a vast difference between our great cities, the thousand noises of which are perpetually deafening us, and the low and confused murmur which is heard in the solitude of the fields, on the mountains, or in the plains. We cannot fail to be struck by the contrast between the calm of the Alpine and the Polar regions, in which all life disappears, and the resounding shores of the ocean ! There the silence is broken only by the dull rolling of avalanches, the cracking of ice, or the roaring of violent gusts of wind. The rumbling of thunder, so prolonged in the plains or in valleys, does not exist on the highest mountains : instead of the terrible report which generally characterizes thunderclaps, the reper- cussion of which multiplies their duration, we have there a harsh sound, similar to the discharge of fire-arms. On the sea- shore, on the contrary, the ear is deafened by the continuous sound of the waves which break in foam on the rocks, and by the dull, uniform roaring L 2 124 PHYSICAL PHENOMENA. [BOOK ir. which like a solemn bass accompanies the sharper notes which the waves produce when they strike the sand and pebbles. In the midst of fields arid forests the sensation is quite different. We hear a low moaning formed by the union of a thousand varied sounds: the grass which bends under the wind, the insects which fly or creep about, the birds whose voices are lost in the air, the sound of the branches of the trees which rustle under the impulse of the light breeze, or which are bent and broken by violent winds. From all this comes a harmony, sometimes gay and sometimes grave, but always different from the discordant clatter which fills the populous streets of great towns. Watercourses, rivers, brooks, and torrents join their notes to this concert ; in mountainous countries there is the noise of cascades which dash upon the rocks, and sometimes the terrible roaring of falling rocks which destroy and bury everything in their passage. But of all natural sounds, the most continuous and violent are those which arise and are propagated through the atmosphere: masses of air dragged along by an irresistible movement, sometimes shrieking, sometimes roaring with fury, strike against all obstacles which oppose them, such as the unevenness of the ground, mountains, rocks, forests, or -solitary trees. When electricity is associated with these actions they become more terrible, and the frightful reports of thunder drown all other sounds. Volcanic explosions and earthquakes alone rival in power this great voice of nature. An immense detonation was heard under the towns of Quito and Ibarra, arising from the catastrophe which destroyed Eiobamba in February 1797 ; but, curiously, it was not heard at the place of the disaster. The upheaval of Jorullo, in 1759, according to Humboldt, was preceded by subterranean roarings which lasted two entire months. To complete this list of sounds naturally produced in the earth and the atmosphere, there remains for us to mention the detonations which accompany the fall of cosmical meteors, aerolites, and bolides. These explosions usually occur at great heights, and persons who have heard them compare them either to the discharge of artillery or to the prolonged rolling of thunder. The phenomena of sound which are most interesting to us are those which men and animals produce by the aid of special organs : the human voice, that indispensable interpreter of our thoughts and CHAP, i.] THE PHENOMENA OF SOUND. 125 sentiments ; and the cries of animals, which express in a ruder mariner their various impressions, their wants, joys, and their griefs. The most powerful of all arts music was created by man to express that which articulated language could not express ; and to add still more to the gifts of nature, he has discovered how to multiply the resources of his voice by the aid of various instruments. The necessities of labour and of human industry have caused man to produce many other sounds and noises which do not commend themselves either for melody or harmony, but most of which are inseparable from the works in which they originate, and share, so to speak, in their character of utility. In manufactories, work- shops, and forges, the noise of hammers and saws, of all sorts of tools, and of steam-engines, often continues uninterruptedly night and day. But how can it be helped ? To our thinking, it is a music which is infinitely preferable to that of musketry and cannon on the field of battle ; just as far as the contest of work and of science is higher than the action of brute force. However varied the several phenomena we have passed in review may appear, they all relate in reality to one mode of movement, of which we must study the nature and formulate the laws. We will commence by enumerating the different ways in which sound can be produced and propagated, in solids, liquids, and gases. 126 PHYSICAL PHENOMENA. [BOOK n. CHAPTEE II. PKODUCT10N AND PKOPAGATION OE SOUND. REFLECTION OF SOUND. VELOCITY OF SOUND IN DIFFERENT MEDIA. Production of sound by a blow or percussion, and by friction, in solids, liquids, and gases Production of sound by the contact of two bodies at different tem- peratures ; Trevelyan's instrument Chemical harmonicon The air a vehicle of sound ; transmission of sound by other gases, by solids and liquids Pro- pagation of sound at great distances through the intervention of the ground Velocity of sound through air ; influence of temperature ; experiments of Villejuif and Montlhery Velocity of sound in water ; experiments made on the Lake of Geneva, by Colladon and Sturm Velocity of sound through different solid, liquid, and gaseous bodies. PEKCUSSION, or the shock of two bodies against each other, is one of the most usual methods by which sound is produced. The hammer which strikes the anvil, the clapper which causes bells to sound, drumsticks, the rattle, and a hundred other instances which the reader will easily call to mind, are examples of the production of sound by the percussion of solid bodies. The most varied noises can thus be obtained, but we shall find that this variety depends both on the form and the nature of the sonorous body and on the way in which the sound is conveyed to our ears. In the water-hammer experiment, the noise proceeds from the shock of a liquid mass against a solid body. Friction is another cause of the production of sound or noise: thus it is that by the aid of a bow, the horsehairs of which have been rubbed with a resinous substance called colophane, the expended cords of certain stringed instruments are made to resound; so also in the case of bells of glass or metal. Sounds are also obtained by longitudinal friction applied to cords or metallic rods. When certain substances, such as wood, stone, &c., are drawn along the ground, they CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 127 produce a noise which is due to friction : carriage-wheels which roll along the roadway also produce a sound which is due in great part to friction, but also to some extent to percussion. The act of drawing aside a tense cord, as is usual in playing instruments like the guitar, harp, or mandoline, produces a sound which is due both to percussion and to friction. When liquid and solid bodies are brought into contact by means of percussion or friction, sounds and noises are produced; but the same movements in liquids, without the intervention of solid bodies, also produce sound : such is the agitation which is produced by the Ml of raindrops on the surface of a pond or river. In gases, sound, as we shall presently see, is caused by a series of condensations alternating with dilatations ; but it may also be induced by percussion or friction. Thus, the air hisses when it re- ceives a violent stroke from a cane or whip : arid the wind produces loud sounds when it strikes against trees, or houses, or other solid bodies. The roaring sound which is sometimes heard in chimneys is due to a movement of the air which we shall study when we consider the nature of the sounds produced by the movement of gases in tubes. Of the same kind is the sound produced by those musical instruments which are known as wind instruments. The human voice and the cries of animals belong also to this class. Explosions of gases, the noise which accompanies the electric spark and the reports of gunpowder, are sounds caused by rapid changes of volume, and by successive dilatations and contractions of gaseous masses. Among the most remarkable modes of producing sound, we may mention the contact of two solid bodies at different temperatures. This singular phenomenon was described for the first time in 1805, by Schwartz, the inspector of a Saxon foundiy. Having placed a silver ingot at a high temperature on a cold anvil, he was astonished to hear musical sounds during the cooling of the mass. In 1829, Arthur Trevelyan accidentally placed a warm soldering iron on a block of lead ; almost immediately a sharp sound was heard. He was thus induced to study the phenomenon under different con- ditions, and he invented various instruments to illustrate the cause of the production of this sound. These will be described when we speak of sonorous vibrations. The passage of an electric current produces sound in a bar of 128 PHYSICAL PHENOMENA. [BOCK ir. iron suspended at its centre, arid one extremity of which is in the centre of an induction coil. Lastly, the combustion of gases in tubes gives rise to the production of musical sounds. If we light a jet of hydrogen generated by the small apparatus called by chemists the philosophical lamp, and intro- duce it into the interior of a tube of greater diameter than itself and open at both ends, we hear a sharp or dull sound, which varies with the length, diameter, thickness, and nature of the substance of the tube. If several of these tubes are arranged together, a series of musical sounds may be ob- tained, and tunes may be pro- duced. Hence the name of " chemical harmonicon " by which this musical instrument is known. This fact was the starting-point of the curious experiments of Schaffgotsch and Tyndall on singing flames. Hitherto we have considered the production of sound or noise in sonorous bodies which may be either solid, liquid, or gaseous ; let us now inquire how sound, that of a clock which is striking, for instance, reaches our ears. We can answer this question by means of observations and very simple understand the real nature of the FIG. 92. Philosophical lamp or chemical harmonicon. experiments, even before we phenomenon of sound. It is a well-known fact that sound takes an appreciable time to travel from a sonorous body to the ear. When we see a person at some distance from us who is striking blows with a hammer, we see the hammer fall before we hear the noise of the percussion. In the same way the report of a gun or cannon reaches the ear after the flash produced by the explosion has been visible to the eye. In all these cases, the interval included between seeing the flash and hearing CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 129 the sound, indicates a difference between tho velocity of light and that of sound ; but as the velocity of light, compared with that of sound, may be considered as infinite, this interval gives without any perceptible error the time which sound takes to be propagated from one point to another. We learn by daily observation that this interval increases with the distance. I remember having admired on the coast of the Mediterranean the curious spectacle of a man-of-war practising with cannon. I saw the smoke of the guns, then the ricochet of the cannon-balls on the crests of the waves, long before I heard the thunder of the report. Sound is propagated by a succession of impulses : we shall soon learn with what velocity. But what is the medium which serves as a vehicle to this movement ? Is it the ground ? Is it communicated by the intervention of solids, liquids, or the air, or by these several media at once ? The following experiment will answer these questions. Let us place under the receiver of an air-pump a clockwork arrangement fur- nished with a bell, the hammer of which is temporarily fixed, but is capable of being moved at will by a rod (Fig. 93). Before exhausting the receiver, the bell is dis- tinctly heard when struck by the hammer. But in proportion as the air is rarefied the sound diminishes in intensity; and as soon as the vacuum is approximately perfect, it is completely lost if the precau- tion has been taken to place the appa- ratus on a cushion of cork, or wadding, or any substance which is soft and more or less elastic. The hammer is then seen to strike the bell, but no sound can be heard. If we now introduce into the receiver any other gas, such as hydrogen, carbonic acid, oxygen, ether-vapour, &c., the sound is again heard. Thus air and all gases are vehicles of sound. But they do not all possess this property to the same extent. Thus, according to Tyridall's experiments, the conduc- tivity of hydrogen gas for sound is much less than that of air, at an FIG. 93. Sound is not piopagated in a vacuum. 130 PHYSICAL PHENOMENA. [BOOK IT. equal pressure, while the velocity of propagation is nearly four times greater in hydrogen than in air. Solid bodies also transmit sound, but in very varied degrees depending on their elasticity. Thus in the preceding experiments, even when the vacuum is nearly perfect, if we place the ear close to the receiver, we hear a very feeble sound transmitted to the sur- rounding air by the cushion and the plate of the air-pump. The transmission of sound through solids is proved even better by the fact that the sound of the bell is simply enfeebled if we place the clockwork apparatus on the glass plate of the air-pump without the intervention of a soft cushion. Water, and liquids in general, are also vehicles of sound, and as regards intensity and velocity they are better conductors than air. A diver when under water hears the least noise ; for example, that made by flints rolling and knocking against each other. We must not confound the sounds which we perceive through the medium of the air with those which solids such as the ground or elastic bodies transmit to us. If the ear be placed at the extremity of a rather long piece of wood, we can clearly distinguish the noise produced by the friction of a pin or the tip of a feather at the oppo- site extremity, while a person standing near the middle, but with his ear not close to the wood, hears nothing. The ticking of a watch hung at the end of a long tube of metal is distinctly heard at the other end, while those near the watch do not perceive any sound. Hassenfratz, "having descended one of the quarries under Paris, instructed some one to strike the walls of one of the subterranean galleries with a hammer : he gradually went further away from the point where the blows were given, and on placing his ear against the wall he distinguished two sounds, one being transmitted by the stone and the other by the air. The first arrived at the ear much sooner than the other, but it also died away much more rapidly in pro- portion as the observer removed further from the source, so that it ceased to be heard at the distance of a hundred and thirty -four paces, while the sound transmitted by the air only ceased to be heard at a distance of four hundred paces." (Haiiy.) Similar experiments, when tried with long wooden or iron bars, give the same result, both as to the higher velocity and reduced intensity. CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 131 Humboldt, in describing the dull noises which nearly always accompany earthquakes, quotes a fact which shows the facility with which solid bodies transmit sound to great distances. " At Caracas," he says, " in the plains of Calabozo and on the borders of Eio-Apure, one of the affluents of the Orinoco, that is to say over an extent of 130,000 square kilometres, one hears a frightful report, without experiencing any shock, at the moment when a torrent of lava flows from the volcano Saint- Vincent, situated in the Antilles at a distance of 1,200 kilometres. This is, as regards distance, as if an eruption of Vesuvius was heard in the North of France. At the time of the great eruption of Cotopaxi in 1744, the subterranean reports were heard at Honda, on the borders of Magdalena : yet the distance between these two points is 810 kilometres, their difference of level is 5,500 metres, and they are separated by the colossal mountainous masses of Quito, Pasto, and Popayan, and by numberless ravines and valleys. The sound was evidently not transmitted by the air, but by the earth, and at a great depth. At the time of the earthquake of New Granada, in February 1835, the same phe- nomena were reproduced in Popayan, at Bogota, at Santa Maria, and in the Caracas, where the noise continued for seven hours without shocks ; also at Haiti, in Jamaica, and on the borders of Nicaragua." To resume : the transmission of sound from a sonorous body to the ear can be effected through the medium of solids, liquids, or gases, but the atmosphere is the most usual medium. Hence it follows that there is no sound beyond the limits of the atmosphere. The noise of volcanic explosions, for example, cannot reach the moon ; and in like manner the inhabitants of the earth do not hear sounds which may be produced in interstellar spaces. The detonations of aerolites therefore prove that these bodies at the moment of explosion are within our atmosphere, the limits of which have not been pre- cisely determined. On high mountains the rarefaction of the air produces a great diminution in the intensity of sounds. Accord- ing to Saussure and others, a pistol fired at the top of Mont Blanc makes less noise than a small cracker. Ch. Martins, in describing a storm which he witnessed in these high regions, says, "The thunder did not roll; it sounded like the report of fire- arms." Gay-Lussac, during his celebrated balloon ascent, remarked 132 PHYSICAL PHENOMENA. [BOOK ii. that the sound of hid voice was considerably weakened at a height of 20,000 feet. Let us now inquire with what velocity sound is propagated through the different media we are about to describe ; and first of the velocity of sound through air. Many scientific men of the last centuries, among whom were Newton, Boyle, Mersenne, and Flamsteed, endeavoured to determine FIG. 94. Measure of the velocity of sound through air, between Villejuif and Montlht-ry, in 1SL' this velocity, either theoretically or by experiment, but the numbers at which they arrived were either too low or too high. We owe the first precise experiments to the commission of the Academic des Sciences in 1738. Again, in 1822, several physicists made deter- minations in the same manner, and the following was their method of proceeding. They were divided into two groups, which were placed respectively at Montlhery and at Villejuif, these two stations being chosen because there was no obstacle to interfere with sight. CHAP, ii.] PRODUCTION AND PROPAGATION OF SOUND. 133 Gay-Lussac, Humboldt, and Bouvard were at Montlhery ; Prony, Arago, and Mathieu at Villejuif. They were each provided with a good chronometer; and two pieces of cannon of equal bore, charged with cartridges of the same weight, were placed at each of the stations. The experiments began at eleven o'clock in the evening, with a serene sky and a nearly calm atmosphere. Twelve alternate shots at intervals of ten minutes were fired from each station, starting from a given signal, and each group of observers noted the number of seconds which elapsed between the appearance of the light and the arrival of the sound. The mean of the diffeient numbers was 54 seconds 6 tenths ; and as the distance of the two pieces of artillery, carefully measured, was 18,612 metres 5 decimetres, they concluded that sound travels 340 metres 9 decimetres a second (1118'152 feet) in nir at a temperature of 16 C. The reciprocity of the determi- nations was in order to compensate for the influence of the wind. The temperature of the air exercises an influence which theory and experiment have equally confirmed. If the temperature in- creases, sound is propagated with much greater rapidity ; and the velocity diminishes with the fall of temperature. 1 But because the velocity of sound varies with the temperature, and also as we shall presently see with the humidity or hygroinetric state of the air, the results obtained are probably more or less inexact. The strata of air in which sound is propagated are far from being homogeneous, and it is now known that their temperature during the night increases with the height. To avoid these different causes of error, M. le Roiix measured in a direct manner the velocity of sound through a mass of air contained in a cylindrical tube of 72 metres in length. The air was dried, and its temperature kept at by surrounding the tube with ice. The sonorous impulse was produced by the single blow of a wooden hammer, which was caused to strike a membrane of caoutchouc stretched over one of the extremities of the tube. This impulse, after having travelled 1 In addition to the preceding experiments, we must quote those of Benzenberg in 1811 ; Goldingham in 1821 ; Moll and Van Beeck, Stampfer and Myrbach in 1822 ; lastly, of Bravais and Martins in 1844. If we reduce the various deter- mined velocities to zero,, and calculate tliem as having been made in dry air, we obtain as a result a mean of 332 metres, or 1088'96 feet a second. 134 PHYSICAL PHENOMENA. [BOOK n. along the tube, set in motion a second membrane stretched at the other extremity of the tube. Lastly, the beginning and the end of the propagation were registered automatically by electricity, and its duration measured by a particular kind of chronoscope. Numerous experiments gave M. le Eoux a velocity of 330*66 m. a second : a number almost identical with the velocity, at the same temperature, 0, indicated by the experiments of the Bureau des Longitudes in 1822. If we adopt this last number, we deduce for the velocity of sound at different temperatures, from 15 C. to 50 C., the following numbers : VELOCITY OF SOUND IN AIR. Number of metres Number of yards Temperature (C.) per second. per second. 15 321-46 350-92 - 10 326-23 356-10 5 327-62 357-60 ...... 330-66 360-90 + 5 3,33-67 ...... 364-18 -f 10 . ... . . . 333-66 364-17 + 15 339-62 370-73 + 20 342-55 373-89 + 25 345-46 377'05 + 30 348-34 380-22 -f 35 .- 351-20 383-39 + 40 354-04 386-40 -f 45 ...... 356-85 389-50 4-50 359-65 392-56 The experiments of 1738 and 1822 not only resulted in the deter- mination of the velocity of sound ; they also proved that this velocity is not modified by variations of atmospheric pressure : that the wind increases or diminishes it according as it blows in the same or in a contrary direction, whilst it does not effect any change if it blows in a direction perpendicular to that of the transmission of the sound. Furthermore, this velocity is uniform at every portion of the distance traversed, and it is the same with sharp or dull sounds, feeble sounds, or those whose intensity is considerable. We are all aware that neither the time nor the precision of a piece of music executed by an orchestra is altered, whatever may be its distance from the listener. When the distance increases, all the sounds are lessened in the same degree, but this is the only alteration CHAP, n.] PRODUCTION AND PROPAGATION OF SOUND. 135 which they suffer, which could not happen if tones or sounds of different intensity were propagated with different velocities. Lastly, the velocity of sound through air appears to be the same in a horizontal, vertical, or oblique direction. This fact results from the observations made in 1S44 by Martins and Bravais, between the summit and the base of the Faulhorn, and by Sta'mpfer and Myrbach at two stations situated at different heights above the level of the sea, FIG. 95. Experimental determination of the velocity of sound through water Very singular consequences follow from the difference which exists between the velocities of light, sound, and projectiles. Thus the soldier struck by a cannon-ball can see the fire which comes from the mouth of the cannon, but he does not hear the noise because the velocity of sound is less than that of the bullet ; but if he is struck at a great distance, as the resistance of the air diminishes more and more the velocity of the projectile, it may happen that he both sees the light and hears the shot before he is struck. 136 PHYSICAL PHENOMENA. [BOOK IT. Sound is propagated through water with about four-and-a- quarter times its velocity through air. This was shown by some experiments made on the Lake of Geneva by two scientific men, Golladon and Sturm. Their mode of experimentation was as follows. The observers were seated in boats, one moored at Thonon, the other on the opposite shore of the lake. The sound was produced by the stroke of a hammer on a bell immersed in the water, and at the other station, a speaking- FIG. 96. Experiments made on the Lake of Geneva, V>y Collation ami Sturm. trumpet, having a mouth of large aperture, also under the water, received the sound propagated by the liquid mass by means of a sheet of metal placed over the opening. The observer, whose ear was placed at the mouth of the trumpet, was furnished with a chronometer or chronograph, which indicated seconds and fractions of a second; and he was made aware of the precise instant when the bell was struck by the flash produced by the ignition of some powder, which was ignited by the lowering of a lighted match fastened to the hammer in the ^ CHAP, ii." 1 PRODUCTION AND PROPAGATION OF SOUND. 137 form of a lever. Figs. 95 and 96 indicate the arrangement, which will be easily understood without a more detailed explanation. The distance of the stations 13,487 metres was traversed by the sound in nine seconds and a quarter, which gives 1,435 metres for the velocity of sound in water at a temperature of 8 0. Lastly, the velocity of sound in solid bodies has also been ex- perimentally determined. M. Biot, having operated on a cast-iron pipe 951 metres in length, found that sound is propagated through this metal with a mean velocity of 3,250 metres a second, which is more than, nine-and-a-half times the velocity through air at the same temperature. The velocities of sound per second in different media, solid, liquid, and gaseous, are as follows : Velocity of sound through gases at . Velocity of sound through liquids Velocity of sound through solids l Air 362 yards or 331 r J Oxygen 317 Hydrogen 1270 Carbonic acid 262 Water of the Seine at 15 . . 1437 r Sea-water at 20 1453 at 23 1160 Ether at 1159 Tin 2498' 1 Silver 2684 Platinum 2701 Oak, walnut 3440 Copper 3716 Steel, iron 5030 Glass 5438 Fir-wood 5994 138 PHYSICAL PHENOMENA. [BOOK n. CHAPTER III. PROPAGATION OF SOUND. PHENOMENA OF THE REFLECTION AND EEFEACTION OF SOUND. Echoes and resonances Simple and multiple echoes ; explanation of these phenomena Laws of the reflection of sound ; experimental verification Phenomena of reflection at the surface of elliptical vaults Experiments which prove the refraction of sonorous impulses. WE shall learn hereafter that light and heat are propagated directly by radiation and indirectly by reflection. Moreover, when this propagation takes place through media whose nature and density differ, the direction of the luminous and calorific waves undergoes a particular deviation known to physicists as refraction. The same phenomena of reflection and refraction occur in the case of sound as in that of heat and light, and they follow nearly the same laws. That sound is reflected, when in being propagated by the air or any other medium it strikes against an obstacle, is a fact with which every one can make himself familiar by observation. Echoes and resonances are phenomena due to the reflection of sound. When we stand in a large room, the walls of which are not covered with objects, such as curtains, which stifle sound, we notice that our voices are strengthened, and the sound of steps or of sonorous bodies is heard with great distinctness. In a still larger room words appear doubled, which often renders them difficult to be understood. This strengthening of sound, due to reflection from walls, &c., is what is called resonance. If the distance from the observer to the reflecting surface ex- ceeds 65J feet (20 metres), he distinctly hears each word which he CHAP. III.] PROPAGATION OF SOUND. 139 pronounces a second time : this is the simple echo. If each word is repeated two or three times, it is a multiple echo. Let us understand the cause of these various phenomena. However short the duration of a sound may be, the sensation which it induces in the ear of the listener remains a certain per- ceptible time, which is about -^ of a second. During this time sound travels nearly 34 metres, so that if the distance A o from the observer to the reflecting surface (Fig. 97) is less than 17 metres, the sound of the word which he has pronounced has time to reach the wall and return to his ear before the sensation is entirely exhausted. The reflected sound will then be blended with that which he hears in a direct manner ; and as a number of partial reflec- tions are produced in dif- ferent parts of the room, a confused murmuring will follow, which is called a resonance. The same ex- planation applies to the case of two or more per- sons occupying the same room and speaking either separately or together, and the resulting confusion of sound would become greater as the rapidity of utterance increased. If now the distance o A exceeds 17 metres, when the sound of the syllable is reflected to the ear the sensation is ended, and we hear a repetition more or less feeble of the direct sound. This is an echo. The greater the distance, the greater will be the number of syllables or distinct sounds. For example, let us suppose this distance to be 180 metres, and that in one second the observer pronounces three syllables, the words being Answer me. To go to the reflecting surface and to return, the sound takes a little over a second ; the direct sensation is ended, and the ear hears for the second time, distinctly, Answer me. This is a simple echo. A multiple echo occurs between distant parallel reflecting surfaces. M 2 Fio. 97. Reflection of sound. Phenomena of resonance. 140 PHYSICAL PHENOMENA. [BOOK IT. In this instance the sound reflected by one of them is reflected a second time from another, and so on; but obviously, by these successive reflections, the sounds are weakened more and more. Edifices, rocks, masses of trees, even clouds, produce the phenomenon of echo. Among the most curious is the echo of the chateau of Simonetta, in Italy, which repeats the words spoken as many as forty times between the parallel wings of the edifice. We find in the Cours de Physique, of M. Boutet de Monvel a curious fact, which visitors to the Pantheon can verify. In one of the vaults of this building, "it is sufficient for the guide who shows them to strike a sharp blow on the front of his coat to awaken in these resounding vaults a noise nearly equal to that of a cannon." This is a phe- nomenon of echo, and of concentration of sound. In ancient and modern works a number of instances of multiple echoes are mentioned, the more or less surprising effects of which may be questioned, but they are all easily explained by the suc- cessive reflections of sound. Such an one existed, it is said, at the tomb of Metella, the wife of Crassus, which repeated a whole verse of the ^Jneid as many as eight times. Addison speaks of an echo which repeated the noise of a pistol-shot fifty-six times. It was noticed, like that of Simonetta, in Italy. The echo of Verdun, formed by two large towers about 52 metres apart, repeats the same word twelve or thirteen times. The great pyramid of Egypt contains subterranean chambers con- nected by long passages, in which words are repeated ten times. Again, Barthius speaks of an echo situated near Coblentz, on the borders of the Rhine, which repeats the same syllable seventeen times. This had a very peculiar effect, because the person who spoke was scarcely heard, whilst the repetitions produced by the echo were very distinct sounds. Among echoes in England we may note one in Woodstock Park, which repeats seventeen syllables by day and twenty by night; while in the Whispering Gallery of St. Paul's the slightest sound is answered from one side of the dome to the other. While living, for some years, on the sea-coast of Hyeres, I heard a most magnificent echo : for a whole morning, reports of artillery fired from a vessel anchored in the roads were reflected from the sides of the mountains on the coast in prolonged echoes, which made me at CHAP, in.] PROPAGATION OF "SOUND. 141 first imagine the presence of a whole lleet ; the effect was like that of thunderclaps. A single discharge seemed to last a minute. The reflection of sound is subject to very simple laws, of which we shall now give an outline. As we shall presently see, they result from the nature of the vibratory movement which constitutes sound, and they are also experimentally proved. To explain this, let us imagine for the present a sound-ray, like a ray of light, to start from a centre of disturbance and follow a right line. When this ray comes in contact with a reflecting surface, let us call it an incident ray; then the reflected ray is the line along which the sound rebounds from this surface into the medium whence it came. The angles which the incident and reflected rays form with a line perpendicular to the surface at the point of inci- dence are called respectively the angles of incidence and reflection. These definitions being clearly understood, the following are the laws of the reflection of sound : First law. The incident sound-ray and the reflected sound-ray are in the same plane with the line perpendicular to the surface at the point of incidence. Second law. The angle of incidence is equal to the angle of reflection. The experimental proof of these laws is very simple. Let us place two metallic mirrors of a para- bolic form that is, obtained by the revolution of the curve called a parabola about its axis (Fig. 98) face to face in such a manner that their axes coincide. The parabolic curve is necessary be- cause it possesses, near its sum- X7 " mit A, a focus F, to which all \v lines such as MZ, parallel to the N^ axis AF, impinging Upon differ- F t o. 98. -Property of the parabola, ent points of the parabola, are reflected. The rays proceeding from the focus and those parallel to the axis, form equal angles with the normals to the parabola, at every point, such as the point M. All rays parallel to the axis coming in contact with the parabola will be reflected to the focus at F. 142 PHYSICAL PHENOMENA. [BOOK n. Now, if a watch is placed in the focus of one of these parabolic mirrors, the sound-rays or sonorous waves produced by the ticking movement will be received on the mirror and reflected parallel to the axis ; they then will strike the concave surface of the second mirror and be concentrated at its focus. The observer, who must employ a tube in order not to intercept the waves, will easily hear the sound of 'the watch if he places the extremity of the tube at the focus of the second mirror (Fig. 99). The sound is heard nowhere else, even by persons who place themselves near the space between the two mirrors, and at a short distance from the watch. Fia. 99 Experimental study of the laws of the reflection of sound. The curve called an ellipse has two foci, and the rays sent from one are reflected to the other. A room with an elliptic roof should therefore produce the same phenomenon as the two parabolic mirrors ; and this is confirmed by experiment. The Museum of Antiquities at the Louvre possesses a room of this kind, in which two persons placed at the opposite extremities of the room in the two foci, are able to converse in a whisper, utterly regardless of the presence of persons who are in other positions. CHAP. III.] PROPAGATION OF SOUND. 143 Eefiection of sound is made use of in many instruments, which we shall have occasion to describe when speaking of the applications of physics to the sciences and arts. Sound is propagated, as we have before seen, by all elastic media, but with varying velocities, which depend in a certain degree on the density of the medium. When sound passes from one medium to another, its velocity changes ; and if it enters the second medium obliquely, a deviation of the sonorous wave results, which deviation brings the ray nearer the normal to the surface of separation of the FIG. 100. Reflection of sound from the surface of an elliptical roof. two media, if the velocity is less in the second than in the first. When a ray enters a prism in which it is retarded, light undergoes a similar deviation, which was proved by experiment long before the true theoretical explanation was discovered ; and as the phenomenon has been long known as refraction, the name of refraction of sound has been given to the similar deviation of the sound-waves. M. Sondhauss has placed the existence of this deviation beyond doubt by the following experiment. He made a lens of collodion, and filled it with carbonic acid gas. In this gas, the velocity of sound is 144 PHYSICAL PHENOMENA. [BOOK ii. less than in air. The sonorous waves which impinged upon the convex surface of the lens were refracted on passing through the gas, and, issuing on the opposite side, were brought to a focus. If a watch is placed in the axis of the lens on one side, there is on the FIG. J01. Sonorous refraction. M. Sondhauss's instrument. axis at the other side a point where the ticking of the watch is heard distinctly, and better than in any other place. There is there- fore an evident convergence of the sonorous waves towards the conjugate focus of the lens ; and in this we have a proof of the refraction of sound. The following are the laws which it obeys : First law. The incident sound-ray and the refracted sound-ray are in the same plane with the line perpendicular to the surface at the point of incidence. Second law. If any points "be taken, one on the incident and one on the refracted ray, at equal distances from the point of incidence, and perpendiculars le drawn from them on the line perpendicular to the surface at the point of incidence, the ratio between these perpendiculars is constant. CHAP, iv.] SONOROUS VIBRATIONS. 145 CHAPTEE IV. SONOROUS VIBRATIONS. Experiments which prove that sound is produced by the vibratory movement of the particles of solid, liquid, and gaseous bodies Vibrations of a cord, rod, or bell Trevelyan's instrument Vibrations of water and of a column of air- Nature of sound : pitch, intensity, and clang-tint The pitch depends on the number of vibrations of the sounding body ; Savart's toothed wheel ; Cagniard- Latour's and Seebeck's syrens Graphic method Variable intensity of sound during the day and night Limit of perceptible sounds. SOUND is a vibratory movement. Sonorous bodies are elastic bodies, the molecules of which, under the action of percussion, friction, or other modes of disturbance, execute a series of alternating movements across their position of rest. These vibrations are communicated to surrounding gaseous, liquid, and solid media in every direction, and at last reach the organs of hearing. The vibratory movement then acts through the drum of the ear upon the special nerves of that organ, and produces in the brain the sensation of sound. The existence of these sonorous vibrations may be proved by very simple experiments. If we take a violin string and stretch it at its two extremities upon a surface of a darkish colour this condition is realized in stringed instruments and if sound is then produced by the aid of a trans- verse bow, or by plucking the string from its position of rest, the string will appear to expand from its two extremities to the middle, and will here present an apparent enlargement, due to a rapid alternating movement across its normal position. The string is seen at the same time, so to speak, in its extreme and in its mean positions, in consequence of the persistence of luminous impressions on the eye. (Fig. 102.) 146 PHYSICAL PHENOMENA. [BOOK n. Instead of a string, let us imagine a cane or a flexible metallic rod fixed at one of its ends. On moving it from the position of rest, it undergoes a series of oscillations, the amplitude of which continues to decrease until at last the motion ceases. During the vibrations of the rod, a sound is heard which decreases and ends with the movement. (Fig. 103.) The rim of a glass or metal bell, rubbed with a bow, emits sounds which are frequently very loud. FIG. 102. Vibrations 01 stretched string. The existence of the vibrations which induce these sounds is easily proved. If we take a rod of metal the point of which grazes the rim of a glass bell without touching it, when the bell vibrates the rod strikes the glass with sharp and repeated strokes, and the noise thus produced is quickly distinguished from the sound produced by the bell. (Fig. 104.) The ball of a pendulum is also sent back with force, and oscillates during the time that the sound continues. In the same way a metallic ball placed in the interior of a bell moves about when this latter is caused to resound, as in Fig. 105, and thus proves the existence of the vibrations with which the molecules of the sounding body are animated. CHAP. IV.] SONOROUS VIBRATIONS. 147 Trevelyan's instrument, of which we have spoken before, and by the aid of which sounds are obtained by the contact of two solid bodies at unequal temperatures, also proves the existence of the vibrations which produce sounds. If we place a bar terminated by two knobs on the heated metal, the weight of this bar renders its vibrations slower, and we can watch the alternating motion of the rod and knobs. (Fig. 106.) Tyndall has devised an ingenious FIG. 103. Vibrations of a metal rod. way of showing these vibrations. He fixes at the centre of the vibrating metal a small disc of polished silver, on which a beam of the electric light is cast. The light is reflected from the mirror to a screen, and as soon as the warm metal comes in contact with the cold lead, the motion of the spot of light is apparent on the screen. When we study the effects of heat, we shall observe that the cause of the oscillations of the metal, in Trevelyan's instrument, is the alternate dilatation of the lead at the points of contact of the warm metal ; this 148 PHYSICAL PHENOMENA. [BOOK IT. dilatation produces small nipples/ which, by their rising, throw the heated rocker from side to side, and this alternating motion takes place with sufficient quickness to produce vibrations in the air, which reach our ears as sound. (Fig. 107.) We shall presently see other proofs of the existence of these mole- cular movements, when we describe the processes used to measure the number of vibrations produced by sounding bodies. When a solid FIG. 104. Proof of the vibration of a glass bell. body produces a sound, the vibratory movement is readily rendered perceptible by the trembling communicated to the hand on touch- ing it. The vibrations of liquids and gases, when they produce or transmit sound, can also be rendered visible. A glass goblet, half filled with water, vibrates like the glass bell of which we have spoken, when the edges are rubbed either with the 'wet finger or with a bow. (Fig. 108.) We observe also on the surface of the liquid a multitude of waves, which are divided into four and CHAP. IV.] SONOROUS VIBRATIONS. 143 sometimes into six principal groups, and these waves become more serrated as the sound becomes more sharp. If the sound is greatly FIG. 105. Vibrations of a metal clock bell. intensified, the amplitude of the vibrations becomes so great that the water is jerked from each section in the form of fine rain. Lastly, if FIG. 106. Treveiyan's instrument. we connect a sonorous tube with a pair of bellows, we can prove the vibration of the interior column of air in the following manner. A 150 PHYSICAL PHENOMENA. [BOOK ii. frame covered with a membrane is suspended by a string in the interior of the tube ; when the tube is caused to emit a sound, we perceive the grains of sand which previously were at rest on the membrane to be jerked up ; thus proving that the vibrations of the gaseous column have been transmitted to the membrane itself and to the light grains which rested upon it. (Fig. 109.) Vibrations transmitted by the air sometimes possess great power. Window-panes shake and are sometimes even broken in the neigh- bourhood of a very loud report, such as that of a cannon. FIG. 107. Trevelyan's instrument. Cause of vibratory movements. FIG. 108. Vibrations of liquid molecules. We have thus demonstrated by experiment the fundamental fact that sound results from a vibratory motion produced by the molecules of solid, liquid, or gaseous elastic bodies, which vibrations are trans- mitted to the organ of hearing by the intervention of different media CHAP. IV.] SONOROUS VIBRATIONS. 151 which extend between the sonorous body and the ear. We now understand why sound is not propagated in a vacuum. The bell struck under the receiver of the air-pump vibrates freely, but its vibrations are no longer transmitted, or at least are very imperfectly transmitted, by the cushion which supports the instrument, and by the small quantity of air which always remains in the most com- plete vacuum which it is possible to produce by an air-pump. We shall endeavour shortly to give some idea of the nature of sonorous vibrations, and of the successive condensations and dilatations which result from their propagation through elastic media, in order to explain how the laws of acoustics, which all our observations and experiments confirm, have been proved by theory. For the present we shall con- tinue to describe phenomena. Sounds are distinguished from each other by several characteristics, which we shall next describe. The most important of these, not so much from a physical as from a musical point of view, is the " pitch," that is to say, the degree of acuteness or of graveness of sound. Every one can distinguish acute from grave sounds, whatever may be the sonorous body which produces them. Two sounds of the same pitch are said to be in unison. The intensity of a sound is quite different from the pitch ; Flo m _ vibrations of a gaseous the same sound can be loud or feeble, with- out ceasing to have the same degree of acuteness or of graveness. Lastly, different sounds are distinguished from each other by their quality, or " clang-tint," as Tyndall proposes to call it (timbre, French; klangfarbe, German). When a flute and a violin, for example, emit the same musical sound with equal force, the ear will not fail to distinguish a difference between the two sounds, such that it will be impossible to confound them. It is this peculiar quality by which we recognise the sound of a voice which is familiar to us. The pitch of a sound depends on the greater or smaller number of 152 PHYSICAL PHENOMENA. [BOOK ii. vibrations which are produced by the sonorous body and propagated through the media by the help of which sound is conveyed. This number increases as the sound becomes more shrill, and we shall now see by what means philosophers have proved this important fact, and how they have counted the movements, which the eye or our other senses could only have observed in a confused and uncertain way. The toothed wheel invented by Savart enables the number of vibrations which produce a given note to be determined. The sound which to give us a musical note must fall with regular pulsations FIG. 110. Savart's toothed wheel. Study cf the number of vibrations producing sounds of given pitch. on our ears, irregular pulsations only producing noise is produced in this instrument by the teeth of a rapidly revolving wheel striking against a piece of card. When the velocity of the wheel is small, we only hear a series of separate strokes, the whole of which, properly speaking, do not produce a musical note, and the pitch is conse- quently absent. But in proportion as the velocity of the wheel increases, the multiplied vibrations of the card transmitted to the air produce a continuous and regular note, the acuteness of which is greater as the velocity of the wheel increases. An indicator is fixed to the toothed wheel, which gives the number of revolutions which it CHAP. IV.] SONOROUS VIBRATIONS. 153 makes in a secoud : this number, multiplied by that of the teeth, gives the half of the total number of vibrations ; for it is clear that the card, at first bent from its position of rest, afterwards returns on itself, and produces two vibrations for each tooth which strikes it. Savart obtained with a whe^l furnished with 600 teeth as many as forty revolutions a second, and subsequently 48,000 vibrations in the same time; which corresponds, as we shall see further on, to a sound of extreme elevation or acuteness. The Syren, invented by Cagniard-Latour, is also used to measure (even with greater precision than the toothed wheel of Savart) the vibrations of a given sound. FIG. 111. Cagniard-Latour's Syren. FKJ. 112. Interior view of the Syren. In this ingenious instrument the sound is produced by a current of air from a pair of bellows, which air passes through a series of holes placed at equal distances round two metallic plates, one being fixed and the other movable. When the holes correspond, the current of air passes, and its force of expulsion acting on the oblique channels which form the holes, gives movement to the upper plate. This act causes the coincidence to cease, then establishes it again, then stops it, and so on, the result being the production of a series of puffs which produce vibrations, increasing in rapidity, in the air. N 154 PHYSICAL PHENOMENA. [BOOK if. If there are twenty holes, there are forty vibrations for each turn of the plate : so that in counting the number of revolutions which are effected for a given sound in a second, the total number of vibrations can be easily calculated. The axis of the movable plate works, by means of an endless screw, in a toothed wheel, the number of teeth being equal to that of the divisions of a dial outside. When the wheel advances a tooth, the needle marks one division ; so that the number of divisions passed over by the needle gives that of the turns, and then, by simple multiplication, that of the Fio. 11.!. Seebeck's Syren. sonorous vibrations. At the end of each revolution, a catch turns a second wheel one division ; so that if the first wheel has a hundred teeth, the needle of the second dial indicates hundreds of turns. The indicator is disposed so that it only moves at will ; that is to say. when the attained velocity has produced the note which we desire to examine as regards the number of vibrations which consti- tute it. The chief difficulty is to maintain a constant velocity, so as to have a note of invariable pitch for as long a time as possible. CHAP. IV.] SONOROUS VIBRATIONS. 155 The syren also acts in water ; in this case the liquid rushes through the holes under the pressure of a lofty column of water, and thus produces vibrations. The sound which follows proves that liquids enter into direct vibration, like gases, without sound being communicated to them by the vibrations of a solid. The name syren comes from the circumstance that the instrument sings under water like the enchantresses of the fable. Seebeck's syren, represented by Fig. 113, is constructed in quite a different manner, but the principle is the same, viz. that the note Fu;. 114. Graphic, study of the sonorous vibrations. I'honautography. is produced by the regular passage of air in puffs through the holes of a disc. The disc is caused to rotate by clockwork, and the velocity of its rotation is measured by an indicator. Around it is a wind- chest communicating with a pair of bellows: and it acts as distributor of the current which is transmitted by caoutchouc tubing to any series of holes in the disc which the experimenter may wish to use. A great number of experiments can be -made with this syren by varying the number and distribution of the holes in different discs 156 PHYSICAL PHENOMENA. [BOOK ir. Lastly, certain graphic methods, recently invented, but the first idea of which is due to Savart, allow us to determine with exacti- tude the number of sonorous vibrations. A tuning-fork, or metallic rod, furnished with very fine points, may be caused to trace undulating lines on the surface of a turning Fro 115. Cora hinnt'on of two parallel vibratory movements. cylinder covered with lamp-black. The number of sinuosities thus marked is that of the vibrations. This method is specially employed when we wish to compare together two sounds with respect to their pitch. For example, we fix on a tuning-fork the point which trace? the sinuous lines, and on a second tuning-fork the plate covered with lamp-black where these lines are traced. Then causing the two CHAP. IV. SONOROUS VIBRATIONS. 157 tuning-forks to vibrate simultaneously, the sinuous line obtained will be evidently the result of the combination of two vibratory move- ments, parallel if the two tuning-forks vibrate in the same direction, rectangular if they vibrate at right angles. Figs. 115 and 116 are facsimiles of proofs obtained by these two combinations for various musical intervals. The various experiments which we have just described tend t prove that the pitch of a sound depends only on the i vibrations executed by the sonorous body in a given time. Fio. 116. Combination of two rectangular vibratory movements. intensity of the sound, whether strong or feeble, undergoes no change ; the nature of the sonorous body and the particular quality, which is called the clang-tint, has likewise no influence on the number of vibrations. The amplitude of the vibrations gives to sound greater or less in- tensity, as may be proved by many familiar experiments. When a bow is drawn across the string of a violin, or of any other similar instru- ment, the sound decreases in proportion as the vibration of the cord is less considerable. The more vigorous the friction of the bow. the more marked are the oscillations, and the greater the intensity nf the sound. Since, then, its pitch is not modified, we must conclude 158 PHYSICAL PHENOMENA. [BOOK it. that the number of vibrations is not altered, although the motions of the cord are made with greater rapidity, the path traversed in an equal time being greater when the amplitude is itself greater. When an elastic body produces a sound, the molecules of which it is composed are not equally moved from their positions of rest : there are some even, as we shall soon see, which remain in a state of repose. A bell, for example, when struck by a hammer, is caused to become elliptic, first in one direction, then in another at right angles to the first. The zones of metal at its base execute slower vibrations and of greater amplitude than the zones near the top. But the solidity of the zones or rings produces a compensation between these amplitudes and the different velocities, and there results for the sound produced a mean pitch and intensity which depends on the dimensions and nature of the metal of which the bell is formed. This indicates an evident analogy between these vibrations and the oscillations of the compound pendulum, the length of whjch we have seen is a mean between the lengths of the oscillations of a series of simple pendulums of different lengths. The above remarks relate only to the intrinsic intensity of sound, which depends on the amplitude of the vibrations executed by the moving molecules. But as sound is transmitted to our ear through the medium of the air, the intensity will be greater as the volume of air displaced at the same time is more considerable, and conse- quently the dimensions of the sonorous body will themselves be greater. A string stretched on a straight piece of wood gives a weaker sound than if it were stretched on a sounding-board, as in musical instruments, the violin, piano, &c. Most people know that if a tuning-fork is caused to vibrate first in the air, and then placed on a table or on any other elastic body, the sound acquires, by this increase of volume of the vibrating body, a much stronger intensity. The intensity of a sound received by the ear at different distances decreases in the inverse ratio of the square of the distance. Thus, at 10 yards the intensity is four times greater than at 20 yards, nine times more than at 30 yards, &c. provided that the circumstances of the propagation remain the same, and that reflecting bodies are not present to strengthen the sound. Hence it follows that if two sounds, one being four times louder than the other, are produced at two different stations, the observer who is placed at a distance from the CHAP, iv.] SONOROUS VIBRATIONS. 159 weakest of them, one-third of the whole distance which separates them, will believe that he hears two sounds of the same intensity. The reason is as follows : Sonorous waves are propagated spheri- cally around the centre of disturbance, hence the vibrations put into movement successive spherical shells, the volume of which is in pro- portion to the surface, and therefore increases as the squares of their distances from the centre. Since the masses of the dispersed layers are greater and greater, the movement which is communicated to them by the same force must diminish. In columns, or cylindrical tubes, the successive impulses are equal : the intensity of the propagated sounds must therefore remain nearly the same, whatever the distance may be. This is also confirmed by observation. M. Biot, in the experiments by which he determined the velocity of sound in solid bodies, proved the fact, that the sound transmitted by the air in the pipes of the aqueducts of Paris was not sensibly enfeebled at a distance of nearly a kilometre. Two persons speaking in whispers could easily hold a conversation through these pipes. "There is only one means not to be heard," says M. Biot, "not to speak at all." Speaking-trumpets and acoustic tubes are applications of this property which we have just described. We shall speak of some of these hereafter. This property of cylindrical sound channels explains certain acoustic effects shown in rooms or vaults of different monuments. The mouldings of the vaults or walls form channels where the sound is propagated with great facility and without losing its first intensity. In Paris, there are two rooms of this kind ; one square and vaulted, situated at the Conservatoire des Arts et Metiers; the other, of a hexagonal form, in the Observatory of Paris : in both, the angles, being joined by an arch, form deep furrows, which eminently conduce to the conduction of sound without enfeebling it. Two persons also can converse in whispers, from one corner to the other, without the auditors placed between them being able to hear any of their conver- sation. In St. Paul's cathedral the gallery of the dome affords a similar instance: the gallery of Gloucester is another example, the cathedral of Girgenti in Sicily, and the famous grotto of Syracuse, at t he present day known as the " Grotta della Favella," and in olden times as that of the Ear of Dionysius. It was in the ancient Latomiae, 160 PHYSICAL PHENOMENA. [BOOK n. or quarries of Syracuse, that the Tyrant had contrived a secret com- munication between his palace and the caverns where he kept his victims, taking advantage of the peculiar arrangement of the grotto to listen to their conversation. The intensity of the sound perceived varies according to the density of the medium which propagates it. We have seen this already, in the experiment made under the receiver of the air-pump . the sound of the bell is enfeebled in proportion as the vacuum is increased. The contrary would take place, as Hauksbee has proved, if the air were compressed in the receiver wherein the sonorous body is placed. Persons who ascend into the high regions of the air, either on mountains or in balloons, all notice the gradual decrease of sound due to the diminution of the density of the atmospheric air. In water, the sonorous waves are transmitted with greater intensity than in air, if the sonorous body vibrates with the same energy in both media. In solid bodies of cylindrical or prismatic form, sound is propagated without being enfeebled as much as in the air or other gases. We most of us know the experiment of placing the ear at the end of a long wooden beam, when we can hear very distinctly the slightest noise for example, that pro- duced by the friction of a pin. Savages place the ear near the ground to hear distant sounds which could not be transmitted by the air through the same distance. It is a fact generally known and of easy observation, that sound is heard further during the night than during the day. This increase of intensity is attributed to the homogeneity of the strata of air and their relatively calm condition, which allows the sonorous waves to be propagated without losing their energy by reflection. It must also be remembered that during the day various noises conduce at the same time to make an impression on the ear, each of which must be less easily distinguished. According to the observations of Bravais and Martins, the distance to which a sound reaches depends also on the temperature of the air : this distance is greater during the cold of winter, in snowy regions of the pole, or high mountains. Here it is to the homogeneity of the air rather than to its density that we must attribute this result, for on the summit of mountains the density of the air is less than in the plains. The intensity of transmitted sound certainly depends on the state of repose or CHAP, iv.] SONOROUS VIBRATIONS. 161 agitation of the air. In calm weather it is distinctly heard at great distances : wind enfeebles sound even when it comes from the point where the body gives out the sounds. The direction of the vibrations, that is to say, the manner in which the auditor is turned relatively to the point whence the sound starts, has also a great influence on its intensity. When we hear the flourish of a hunting horn, if the performer turns the mouth of his instrument in different directions the intensity varies, so that it seems sometimes to get nearer to and sometimes further away from the hearer. The circumstances which tend to modify the intensity of sound are thus very varied. It is therefore difficult to determine the greatest distance to which it can reach. In the remarkable examples which are quoted, of sounds heard at considerable distances, it is probable that it is the ground rather than the air which serves as a vehicle to the sonorous vibrations. We have already quoted Humboldt on the subject of the reports produced by earthquakes and volcanic eruptions, which are propagated to distances of 500 to 800 miles. Chladni relates many facts which prove that the noise of cannon is often heard at very great distances ; at the siege of Genoa it was heard at ninety miles from Italy ; at the siege of Mannheim in 1795, at the other side of Swabia, at Nordlingen and Wallerstein ; at the battle of Jena, between Wittenberg and Treuenbrietzen. " I have myself heard," he says, " cannon-shots at Wittenberg at seventy- five miles, not so much by the air as by the disturbance of solid bodies, by placing the head against a wall." Nevertheless, sound, such as the rolling of thunder and the detona- tions of meteors, which sometimes burst at enormous heights, is often propagated to a great distance by the air. Chladni mentions certain meteors the explosion of which was not heard until ten minutes after the luminous globe was seen : this supposes a height of not less than 120 miles. The bolide observed in the middle of France on the 14th of May, 1864, presented the same peculiarity, and the observers calculated four minutes between its appearance and their perception of the noise of its report. " Since the explosion," says M. Daubre*e, writing on this subject, " is produced in strata of air highly rarefied, the fact that it gives rise on the surface of the earth to a noise of such intensity, and over a horizontal extent so considerable, demonstrates that its violence in high regions exceeds all that we know." Unless, 162 PHYSICAL PHENOMENA. [BOOK n. indeed, this should be an effect of repercussion of the sound on strata of air of unequal density, analogous to the rolling of thunder in storms. We know hut little at present of the production of the indefinite varieties of tones. We shall speak hereafter of recent researches on this subject ; the phenomena which we must first notice are necessary for the right understanding of the proposed explanations. Experimenters have tried to determine the limit of perceptible sounds ; but it is clear that this limit depends partly on the sensibility of our organs. The gravest sound appears to be that which is pro- duced by a sonorous body executing thirty-two simple vibrations in a second. Savart found for the most acute, 48,000 vibrations. But M. Despretz made a series of tuning-forks the sounds of which were strengthened by resonant boxes, and he at last distinguished the sound of greatest sharpness which a tuning-fork can produce to be caused by 73,700 vibrations per second. Such shrill sounds produce in the organ of hearing a sensation almost painful. CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 163 CHAPTER V. LAWS OF SONOROUS VIBRATIONS, IN STRINGS, RODS, PIPES, AND PLATES. Experimental study of the laws which govern the vibration of strings Monochord or Sonometer Nodes and ventral segments ; harmonics Laws of the vibra- tions of sonorous pipes Vibrations in rods and plates Nodal lines of square, round, and polygonal plates. IN the present day, the art of music is so generally understood that those of our readers who have knowledge of it, or who have seen it produced, know the mechanism of stringed instruments, such as the violin. Four strings of unequal diameter and of different textures are stretched between two fixed points by the aid of pegs, and when caused to vibrate, either by the hand or by drawing a bow across them, they produce sounds of different pitch. The sounds produced by the fully opened out strings (that is to say, when they vibrate in the whole of their length) must have a certain connection of tone between them. When this connection is destroyed, the instrument is not in tune. What does the musician then do ? By screwing and unscrewing the pegs he stretches or slackens those of the strings which do not give out the desired sounds : as he tightens them the sound becomes more acute; on the other hand, if he loosens them it becomes more grave. But four sounds would not be sufficient to provide all the varied notes of a piece of music. The performer multiplies the number at will, by placing the fingers of his left hand on certain points of each of the strings. In doing this he reduces to different lengths the portions of these strings which the bow causes to vibrate. These facts show that certain relationships exist between the pitch of the different sounds given out by the instrument and o 2 104 PHYSICAL PHENOMENA. [BOOK n. the length, diameter, tension, and substance of the strings; as the pitch itself depends on the number of the vibrations executed, it necessarily follows that this number is connected by certain laws with the elements already mentioned. Some of the most im- portant were noticed by the ancient philosophers, and particularly by the Pythagoreans. But it is to the geometers of the last century, amongst whom are the illustrious names of Taylor, Bernouilli, D'Alembert, Euler, and Lagrange, that we owe the complete demon- stration deduced from purely theoretical reasons. The exactness of the calculations has been confirmed by experiments. We shall now endeavour to explain these laws. In the present day they are readily proved by means of a peculiar instrument, called a monochord or sonometer, to which is attached an apparatus which FIG. 117. Sonometer. enables us to ascertain the numbers of vibrations produced. The sonometer, or monochord (Fig. 117) is formed of a box of fir-wood to strengthen the sound ; above this box one or several strings are fixed at their extremities by iron pins, and stretched by weights which serve to determine the tensions of each of them. A divided scale beneath the strings shows the lengths of the vibrating parts which can be altered at will by the aid of a movable bridge which moves along the scale under the strings. Let us take a string of catgut or metal, and stretch it by a weight sufficient to cause it to produce a perfectly pure sound, of a pitch appreciable to the ear; and let us suppose that its total length measured by the scale is 1-20 metre, and that the sound which it gives out corresponds (as verified by the Syren) to 440 vibrations CHAP, v.] LAWS OF SONOROUS VIBRATIONS. 165 a second. Let us place the movable bridge first at the half, then at J, \, and T V of the total length; and in each of these successive positions let us cause the shortest portion of the string to vibrate. Measuring the different sounds obtained, we shall find the following number of vibrations a second: 880, 1,320, 1,760, and 5,280. It only remains for us to compare the numbers which indi- cate the different lengths of the string, and those which indicate the number of vibrations, to discover the law. T ., ,. , ( 120 60 40 30 10 Length of string . . . ] , , L T z 3 4 TiJ t -- :->(':>, ; V }V: : -./^XN ''* l\^'\!/\. ; ,- K / r/! bir-'/Sv^XN^] - 1 \ x -~^, / Vv - ^q ! . -~y\ i AH 1 l/V i ! .-1 /Xj [/" ( -^--^'-- ~^\ \ ' '' ' ' : &3U U"';^-'"^--' ^ L-'--./;'- - "'.- -\ / .,\x..,v.-: >:^ FIG. 127. Nodal lines of vibrating square plates, according to Savart. a sounding bell. The vibrations are communicated by the air to the membrane, and the sand with which this is covered indicates the position of the nodal lines. It is well known that when two plates of the same substance and similar figure, but of different thicknesses, give the same nodal lines, the sounds produced vary as the thickness, if the surface is CHAP. V.] LAWS OF SONOROUS VIBRATIONS. 177 the same ; that is to say, that the number of vibrations is proportional to the thickness. If the thickness remains constant, the numbers of the vibrations are in the inverse ratio of the surfaces. We do not yet know the law according to which the sounds produced by the same plate succeed eacli other when the figures FIG. 128. Nodal lines of vibrating circular or polygonal plates, according to Chladni and Savart. formed by the nodal lines change. We only know that the lowest note produced by a square plate fixed in the centre is obtained when the nodal lines are two in number, parallel to the sides, and pass FIG. 129. Nodes and segments of a vibrating bell. through the centre as shown in the first plate (Fig. 127). When the two nodal lines form the diagonals of the square (as in the first plate of the second line, Fig. 127), the sound is the fifth of the first one, which may be called the fundamental note. 178 PHYSICAL PHENOMENA. [BOOK IT. CHAPTER VI. PROPAGATION OF SOUND IN AIR. SOUND WAVES. Nature of sound waves ; their propagation in a tube The wave of condensation and the wave of rarefaction Length of sonorous undulations Propagation through an unlimited medium ; spherical waves ; diminution of their amplitude with, the distance Direction of sound waves Co-existence of undulations Perception of simultaneous sounds ; Weber's experiments. 4 WE have just seen how the vibrations of sonorous bodies can be rendered sensible, and how their number can be counted, and we have proved by experiment the laws of their vibrations in solids of different forms, and in gaseous, cylindrical, or prismatic columns. But when a body sounds, the vibrations which its molecules exe- cute, reach our ear, so as to impress us with the sensation of sound by a gradual disturbance of the mass of air intervening between the centre of disturbance and our organs. Tn the absence of this vehicle, sound is no longer perceived, or at least only in a very weakened form, after having been propagated through more or less elastic solid bodies, which establish an indirect communication between the sonorous body and the ear. Thus the air itself enters into vibration under the impulse of the movements of the particles of the sonorous bodies, and it undergoes successive condensations and dilatations, which are propagated with a constant velocity, when the density and temperature remain the same, and when the homo- geneity of the gaseous mixture is perfect. We shall now explain by what means sonorous waves succeed each other in the air or any other gas, and how their length can be measured. Let us suppose that one prong of a tuning-fork is placed in front of a tube and is caused to vibrate. The vibrations are propa- gated along the column of air in the tube. We will observe what CHAP. VI.] PROPAGATION OF SOUND IN AIR. 179 takes place in the column of air when the prong executes a whole vibration ; that is to say, leaves its position a" to go to of, and afterwards to return to a", passing each time by its mean position a (Fig. 130). This alternating movement is similar to that of the pendulum, so that the velocity of the prong is alternately increasing and decreasing according as it gets nearer to or more distant from the position a. During the movement from a" to a', the air in the tube, receiving the impulse from the prong, will undergo successive and unequal condensations, which will be transmitted from one to the other, and these waves will be carried along the column of air FIQ. 130. Propagation of the sonorous vibrations in a cylindrical and unlimited gaseous column. FFG. 131. Curve representing a sound wave. like the waves along the surface of water. On this point we shall have more to say presently. These condensations at first increasing will attain a maximum ; they will then diminish until the vibrating prong has reached the position a'. At its return from a to a" the same gaseous layers, returned to their normal density, will dilate by virtue of their elasticity to fill the space left in the column of air by the second movement of the fork. To each complete vibration of the prong, a series of condensations therefore corresponds : a condensed half- wave ; then a series of dilata- tions ; a dilated half- wave. Their whole forms a complete sonorous wave, which passes along the tube. To represent to the eye the condition of the column of air in the whole length of a sonorous wave, it has been found convenient to represent the different degrees of condensation by perpendiculars p 2 ISO PHYSICAL PHENOMENA. [F.OOK ir. placed above and at right angles to the direction of the wave, and the dilatations which follow (Fig. 131), by perpendiculars traced below this direction : these two lines have a minimum length when the density is the normal density : their maximum lengths correspond to the maximum condensations and dilatations. The curve AA" lf A' I} A l then represents the state of the successive strata of the tube at the moment when the prong of the tuning-fork has executed an entire vibration ; AA X is the path traversed during this time, that is to say, the length of the sonorous wave. The space traversed by this wave will be double, triple, &c. after the 2, 3, . . . . first vibrations. It is now easy to understand how the wave-length of a sound of a given pitch can be calculated. Let us suppose a sound produced by 450 vibrations a second. At the temperature of 15 C. if such is the temperature of the air at the time of the experiment as the velocity of propagation is 340 metres during the same interval, it is clear that at the moment when the wave reaches this distance, there are in the air as many successive sound waves as there are complete vibrations from the centre of emission ; that is, 450. Each of them has then a length of the four hundred and fiftieth part of the space traversed, that is, of 340 metres ; hence the length of wave in this case is 755 millimetres. If we pass now from the case in which the sound is propagated in a column of air to that in which the propagation is made in all directions emanating from a point, the successive conden- sations and dilatations of the strata of air will be distributed at equal distances from the centre of emanation. The waves will be spherical, without either their velocity of propagation or their length changing. Only the amplitude will diminish, and consequently the intensity of sound. Figure 132 will give the reader an idea of the manner in which sonorous waves are distributed round a centre of emission. We see the series of condensed and dilated half-waves, and the un- dulating lines starting from the centre show how the condensations and dilatations lose their amplitude in proportion as the distance increases. To account for the fact that waves are propagated without the parti- cles of air moving with them, sound waves may generally be compared to the movement of a cord which is sharply jerked by the hand. The undulations traverse the cord from one end to the other ; and if it is CHAP, vi.] PROPAGATION OF SOUND IN AIR. 181 fastened by one of its extremities, the wave returns on itself. In either case, the movement is transmitted without any real change in the distance of the molecules from the point whence the impulse is derived, The same effect is observed when we throw a stone into water ; the disturbance produced in the liquid mass is propagated in a series of concentric waves which disappear as the distance increases, but the molecules of water are not transported, as it is easy to prove FIG. 132. Propagation of a sonorous wave through an unlimited medium. to oneself by observing the fixed position of light substances floating on the surface. But in these examples, which are otherwise useful in giving us some idea of the mode of propagation of sound waves, there is an essential difference which must not be forgotten. The condensations and dilatations of the air caused by trhe vibrations of sonorous bodies are effected in the same direction as the movement of propagation ; they take place parallel to the direction of each 182 PHYSICAL PHENOMENA. [BOOK n. sonorous wave, whilst the undulations of the cord, or those of the surface of the water, are effected in a direction perpendicular to the movement of propagation. We shall soon see that something like this takes place with the waves which traverse the medium called the ether, which have their origin in vibrations from luminous sources. All this perfectly accounts for the transmission of a single sound which the air carries, so to speak, to our ear. But if the air is thus the vehicle of sonorous vibrations, how does it happen that it pro- pagates, without alteration, the vibrations of many simultaneous sounds ? We are at a concert ; numerous instruments are simulta- neously emitting sounds which differ in intensity, pitch, and quality. The centres of emission are distributed over the room ; how is it that the mass of air inclosed by the walls is able at the same time to transmit so many vibrations without the production of complete chaos of sound ? Or again, it is morning. A fine thick rain falls, and the drops on striking the ground produce a multitude of little noises which arrive in a distinct form to our ear ; the songs of birds, which the corning of spring awakens everywhere, rise in the air, and seem to pierce the light mist which the rain sheds on the horizon. Above this warbling, cock-crowing, barking of dogs, jolting of heavy carts on the paved road, rise the sound of bells, and here and there human voices, all of which sing, cry, speak, and sound altogether without the ear finding any confusion. These multiple sounds, the simultaneity of which arid their resonances would make them discordant if they were all produced in a narrow space, are drowned in the vast extent of the stratum of air which covers the plain, and mingle into pleasing har- mony. Here, the same question presents itself: How can the air transmit distinctly and at the same time so many undulations emanating from different centres, so many vibrations which are not isochronous ? How can the intensity, pitch, and quality of each sound co-exist, in this elastic and movable medium, without alteration ? This is a problem the data of which appear so complex, that it is beyond analysis. Nevertheless, theory accounts for these phenomena, the explanation of which appears so difficult at first sight, and simple experiments justify the theoretical conclusions. Two distinguished geo- meters of the last century, Daniel Bernouilli and Euler, demonstrated the principle of the co-existence of small movements and oscillations in CHAP. VI.] PROPAGATION OF SOUND IN AIR. 183 the same medium. The following is their theory. If we throw into water two or more stones near to each other, we perceive concentric circles produced by each of them, which cross without destroying one another, especially if their amplitude is not too great. Fig. 133, which we borrow from the work of M. Weber, uber die Wellenlehre, shows how waves cross each other on the surface of a liquid, and how they are reflected from the sides of the containing vessel. The form of the FIG. 133. Experiment proving the co-existence of waves. Propagation and reflection of liquid waves on the surface of a bath of mercury. latter is elliptical, it is filled with mercury, and the waves which are seen on its surface are those produced by the fall of a drop of the liquid in one of the foci of the ellipse. Concentric circular waves are produced at this focus, then reflected waves which all tend to collect at the second focus of the curve. The same results are evi- dently produced as if a drop had fallen at the same time at the other focus. 184 PHYSICAL PHENOMENA. [BOOK ir. This ingenious experiment proves, then, on the one hand, the possible co-existence of waves, and, on the other, the law of their reflection. After the reservation of which we have spoken above as to the direction of sound waves, we thus obtain a very good idea of the reflection of sounds and their simultaneous propagation through the air. CHAP. VIT.] MUSICAL SOUNDS. 18' CHAPTER VIT. MUSICAL SOUNDS. THE GAMUT, OR MUSICAL SCALE. Distinction between noises and musical sounds Definition of the gamut; intervals which compose it The scale of the musical gamut is unlimited ; convention which limits it in practice Names and values of the intervals of the natural major scale Modulations ; constitution of the major gamuts proceeding by sharps and flats Minor scale. THE human ear, as we have remarked in the preceding chapter, is limited as regards its perception of sound. It has been proved by experiment that 32 simple vibrations per second is the limit of grave sounds, while that of acute sounds is 73,000 vibrations. Between these extreme limits the scale of sounds is evidently continuous, so that there is an infinity of sounds having a different pitch appre- ciable to the ear, and passing from the grave to the acute, or from the acute to the grave, by imperceptible degrees. All the sounds comprised in this scale, and susceptible conse- quently of being compared among themselves as regards pitch, are what are called musical sounds; by combining them by means of succession or simultaneity, according to determined rules of time, pitch, intensity, or quality, the musician is able to produce the effects which constitute a musical composition. Are all the sounds and noises perceptible to the ear, musical sounds ? Undoubtedly not, if we mean by musical sound that which a composer or artist thinks right to introduce into his work to add to the desired effect. Not only must these sounds be closely connected by bonds which are determined by the pitch, but they must also unite certain particular qualities the examination of which belongs to the domain of art rather than of science. The question becomes altered if the term musical sound is applied exclusively to those whose pitch is appreciable, and which the ear can compare to other 186 PHYSICAL PHENOMENA. [BOOK n. higher or graver sounds, the vibrations of which may be measured according to a constant and regular law. In this case, physicists dis- tinguish noises properly so called from musical sounds. Noise fre- quently proceeds from a confused mixture of different sounds which the ear can scarcely distinguish from each other, but the separation of which is possible. At other times, noise is nothing but a sound the vibrations of which do not last long enough to enable the hearer to appreciate the relative pitch. The cracking of a whip, the collision of two stones or two pieces of wood against each other, and generally of any two bodies which are but weakly sonorous, the report of fire-arms, are noises of this last kind ; whilst the dull surging of a stormy sea and the rustling of leaves in a forest proceed from the mixture of a multitude of sounds or confused noises. The attempts which have been made to compare the pitch of simple noises with musical sounds prove that the distinction of which we speak is more apparent than real. Physicists have succeeded, by varying the dimensions of a series of wooden balls and causing them to come together in collision, in making them emit the tones of the musical gamut ; but, in order that the ear should easily seize their relationship, it is necessary that the sounds succeed each other at very short intervals. On the other hand, we can separate the noises formed of sounds mixed together, and can distinguish some of the elementary sounds of which these noises are composed. The sensibility of the ear, joined to the habit of comparisons of this kind, contributes greatly to render these distinctions possible. Let us now endeavour to form some idea of the succession and con- nection of sounds which constitute musical scales known under the name of gamuts and which form the physical basis of modern music. The name of " gamut " is given to a series of seven sounds which succeed each other, proceeding from the grave to the acute, or from the acute to the grave, and which are comprised between two extreme notes having the following character, viz. that the highest sound is produced by double the number of vibrations of the lowest. The most acute note being the eighth of the series, the two extreme notes are the octaves of each other : one being the lower octave, the other the higher one. If we now start from the eighth note, considered as the starting-point of a series similar to the first, and if we take care to strike a new series of notes having between them the same CHAP, vii.] MUSICAL SOUNDS. 187 degrees of pitch as the first, it will be noticed that the impression left on the ear by their succession has the greatest analogy with that which results from hearing the notes of the first scale. A melody formed of a succession of notes taken from the first series, preserves the same character if it is sung or played with the help of notes of the same order taken in the second series. It would be the same if we formed in a similar manner one or more gamuts higher or lower. A musical scale of this kind, formed of consecutive gamuts, is unlimited, or at least has no other limits than those of our power of perceiving sounds. Before giving the intervals which separate the successive notes of the gamut, or in other words the ratio of the number of vibra- tions which correspond to each of them, we may remark that the note from which we start to form a gamut, or to study music, is arbitrary, as there are an infinite number of similar musical scales placed by nature at the disposal of musicians. But, for the practice of music, the want has been felt of taking conventionally a fixed point of departure. Hence in modern music we find certain definite notes (the vibrations of which are determined by the vibrations necessary to produce one of them) called by certain definite names : the names being the letters of the alphabet, A, B, C, T), E, F, G, repeated for each octave. So long as it is merely a question of singing or of music executed by the human voice, a convention of this kind is not necessary, as the voice is an organ sufficiently flexible to emit at will notes of any degree of acuteness or gravity within its natural limits. Hence for such purposes we may consider the gamut as a thing independent of any particular pitch, and it is convenient to call the notes of such a gamut by some other names. Those used are derived from the first syllable of each line of a Latin hymn written by Faulus Diaconus : Ut quam laxis 7?esonare fibris M ira gestorum .Famuli tuorum Solvi polluti iabii reatum SanctQ Johannes. The Italians- substituted Do for Ut for the first note of the gamut, in the seventeenth century. 188 PHYSICAL PHENOMENA. TBOOK TT. Our arbitrary names for the seven notes of this gamut, which may be independent of pitch, in passing from the gravest to the highest note, are as follows : 1st note. 2d. 3d. 4th. ftlh. 6th. 7th. Do, Re, Mi, Fa, Sol, La, Si. After what we have said of the manner in which the preceding gamut is formed, and of the analogy, if not the identity, which exists between the notes in different octaves, we can understand why the same names have been given to the notes of the successive gamuts. Musicians distinguish them by placing numerical signs after the names of the notes, to mark the order of succession of the gamut. The two scales we now give one lower, the other higher than the former may for our purposes be written thus : Gamut above Do Ee Mi Fa Sol La Si -i i i i i i i Gamut below Do Re Mi Fa Sol La Si 2222222 It also results from the constitution of the successive scales that the notes of the same name are an octave from each other, like the extreme notes of each scale. Thus, Do t , Ee v Mi t , are the acute octaves of Do. 2 , Ee 2 , Mi 2 . Before proceeding further, let us recall the laws of the vibrations of strings and tubes, and we shall understand that if we stretch a series of seven strings, so as to make them give out the seven notes of the scale, we shall obtain the seven notes of the acute scale, the octave of the first, by dividing the strings into two equal parts. If instead of strings we had taken seven open or closed tubes, giving the scales by their fundamental notes, we must take seven tubes of half the length to obtain the more acute scale, and seven tubes of double the length to obtain the notes of the lower scale. If we compare, with reference to their pitch, each of the seven notes of a scale to the lowest note to that which forms what is called the tonic, or key-note, there are many different intervals, of which the names are as follows : From Do to Do Unison. Re to Do Second. Mi to Do Third. Fa to Do Fourth. Sol to Do Fifth. La to Do Sixth. Si to Do Seventh. And lastly, Do to Du Octave. i The musical interval is defined in physics as the relationship of the numbers of vibrations of the notes of which it is formed. Unison CHAP, vii.] MUSICAL SOUNDS. 180 and the octave are the only ones of which we have given the value : 1 or y measures the interval of unison ; 2 or f measures the octave. It remains for us to speak of the numbers which measure the other intervals. The following are those which are now adopted by the majority of physicists : Do Do Unison = 1 Re Second = | Mi - Third = Fa Fourth = | Sol,, Fifth = f La Sixth = | Si Seventh = ^ 5 Do Octave = 2 i As these only express the relationship, they can be written in the form of whole numbers, and the seven notes of the scale will then be found to be represented in one or the other of the following ways : Do Re Mi Fa Sol La Si Do i I I i f f V 2 24 27 30 32 36 40 45 48 In other words, if the tonic or key-note, Do, be produced by 24 vibrations in a given time, the following notes will be produced by 27, 30, .... 48, &c. It is easy to calculate by the aid of this table the consecutive interval of the notes of the scale. Do Re 'Mi Fa Sol La Si Do _ 101 .9. l_0 I) 1 2. Rumford's photometer. sented in Fig. 162. It is based on the fact, that if shadows thrown on the same screen by an opaque body illuminated by two different lights have the same intensity, the illuminating powers of the two lights are equal, if they are at the same distance from the 1 It is now proved that the central parts of the solar disc are the most luminous, contrary to what would be the case if there were an equal emission of light over the whole surface. Astronomers, however, have shown that this appearance is due to an absorbing atmosphere of small height, so that more light is absorbed at the borders than at the centre. U 2 244 PHYSICAL PHENOMENA. [BOOK in. screen, or are in the inverse ratio of the squares of these distances, if they are at unequal distances. Let us suppose that we wish to compare the illuminating powers of a jet of gas and an ordinary candle. A black cylindrical rod is placed vertically in front of a screen of white paper, and the two lights are arranged so that the shadows of the rod will both be projected on the paper, nearly in contact. Then we gradually move the light which gives the most intense shadow, until the eye can no longer distinguish any difference between the intensities of the shadows. To judge better of the equality of the shadows, we look at the screen on the side which is not directly illuminated by the candle and the flame of the gas. At this moment, the luminous parts of the screen receive the rays of both lights at once, whilst each shadow is only lighted by one of them : the equality of their tints then indicates the equality of the illuminating powers of each separate source. The illuminating powers of the two lights are then, according to the first principle, in the inverse ratio of the squares of their distances from the screen. Fio. 163. Bouguer's photometer. Bouguer's photometer (represented in Fig. 163) is based on the equality of brightness of two portions of a surface separately illumi- nated by each of the light sources. An opaque screen prevents the light of each source from reaching that part of the surface which is illustrated by the other. This surface formerly consisted of a piece of oiled paper, or ground glass. CHAP, in.] PHOTOMETRY. 245 M. Leon Foucault uses in preference a plate of very homogeneous porcelain, sufficiently thin to be translucent. The two illuminated portions are separated by a narrow' line of shadow projected through the screen, and the eye placed behind judges easily of the moment when the illumination is equal. This equality once obtained, the intensities, of the lights are deduced from their respective distances from the plate of porcelain. We will confine ourselves to the description of these two kinds of photometers, both of which serve to prove the law of the square of distances. Tho verification is very simple : it is sufficient to put on the one side one candle : it will then be found that there must be placed four at double the distance, nine at triple the distance, to obtain either equally dark shadows on the screen, or equal illumination in both portions of the sheet of porcelain. The following are some of the results obtained by the instruments : If we use two equal lights, two candles, for instance, and if we place one of them at a distance eight times further from the screen than the other, it will be found that the shadow of the first dis- appears. At this distance the intensity of its light is sixty-four times less than the other. Bouguer, to whom we owe this experi- ment, concluded that one light, of whatever intensity, is not per- ceptible to our eyes in presence of a light sixty-four times brighter. This explains to us how it is that, in broad daylight and in a clear sky, the stars are no longer visible ; why from the interior of a well- lighted room we see nothing but darkness out of the windows, and again, why we can scarcely distinguish, when in full sunlight, what passes in the interior of an apartment. Bouguer and Wollaston both tried to compare the light of the sun with that of the full moon, taking as comparison the light of a candle. They both found that the sun's light was equal to the united light of about 5,600 candles placed at a distance of 30 centimetres. As to the light of the full moon, Wollaston found it equal to the 144th part of that of a candle placed at the distance of 3 in> 65. Whence he concluded, by easy calculation, that the light of the sun was equal to about 800,000 times that of the full moon. Bouguer only found the number 300,000. Quoting the number obtained by Wollaston, a number which differs much from that of the French philosopher, Arago adds : " I cannot tell in what consists 246 PHYSICAL PHENOMENA. [BOOK in. the enormity of this number compared with Bouguer's determination, for the method employed was exact, and the observer of incontestable ability." It will be seen from this how difficult photometrical determina- tions are, especially when they refer to lights, the intensity of which is as prodigiously different as those of the sun and moon. Much has yet to be done in devising new experimental methods. CHAP, iv.] REFLECTION OF LIGHT. 247 CHAPTEE IV. REFLECTION OF LIGHT. Phenomena of reflection of light Light reflected by mirrors ; diffused light ; why we see things Path of incident and reflected rays ; laws of reflection Images in plane mirrors Multiple images between two parallel or inclined surfaces ; kaleidoscope Polemoscope ; magic lantern Spherical curved mirrors ; foci and images in concave and convex mirrors Caustics by reflection Conical and cylindrical mirrors Luminous spectres. LONG before human industry, stimulated by the requirements of luxury and frivolity, had dreamed of polishing metals and glass in order to make their surfaces brilliant for mirrors and looking- glasses, nature presented many examples of the phenomena which physicists call the reflection of light: for the surface of limpid and tranquil water, as of a pool or lake, reflects a faithful image of the country which surrounds it, the azure vault of the sky, clouds, sun> stars, trees, rocks, and the living beings who walk on the banks and sail over the liquid surface. This is on a large scale the model which industrial art has to copy, and which would enable us to study, not only conveniently but accurately, the path which light takes when, coming from luminous sources or illuminated objects, it is reflected from the surface of bodies. The necessity of comprehending never precedes that of admiring and enjoying, and the discovery of the laws which govern the reflection of light was doubtless made long after the imitation of the phenomena we have just described. Light is not always reflected in the same manner from the surface of bodies. The reflection varies according to many circumstances, among which we shall first consider the nature of the reflecting substance and the condition of its surface. If we consider bodies whose surface is naturally smooth and polished, like liquids in a state of rest, mercury, &c., or susceptible of 248 PHYSICAL PHENOMENA. [BOOK in. acquiring this quality by mechanical processes, as glass and most of the metals, &c., the reflection of light from their surface will not show these bodies themselves, but the illuminated or luminous objects which are situated in front of them. Light reflected in this manner produces the images of these objects, the dimensions and form of which depend on those of the reflecting surface ; but in pro- portion as the degree of polish is more perfect, the light and colour will be better preserved. These are reflectors or mirrors. Physicists then say that light is reflected regularly or specularly. 1 When light is reflected by bodies possessing a tarnished, dull, or rough surface, it does not produce images, but it shows the bodies from which it emanates, so that each point of their illuminated surface serves for other objects the part of a luminous point. The light which a polished surface receives is never entirely reflected. If the body is transparent or translucent, a portion of the received light penetrates into the interior and traverses the substance, and is usually partly extinguished or absorbed. It is often a very small amount of the luminous rays which are reflected from the surface. If the body is opaque, the reverse takes place ; the light received is in great part reflected, bat a certain quantity is absorbed by the thin strata at the surface of the body. Let us next consider the path which light follows in the pheno- menon of reflection, always supposing the medium homogeneous. Very simple experiments, which every one can verify more or less rigorously, will indicate to us the laws which govern this propagation. Let us employ a bath of mercury for a reflecting surface, and for a luminous object a star, the rays of which, coming to the surface of the earth from a distance which is practically infinite, may be considered exactly parallel. The direction of the rays coming from the star and falling on a certain point of the mirror formed by the mercury is easily determined by means of a theodolite, the axis of which is fixed in an exactly vertical position (Fig. 165). If we look directly at the star, the line i' s' of the telescope indicates the direction of the incident luminous rays, and the angle s' i' N', equal to the angle s I N, is the angle of incidence; that is to say, that formed by a luminous ray with the perpendicular to the surface at the point of incidence. 1 From speculum, a mirror. Fio 164. -Phenomena of reflection. CHAP. IV.] REFLECTION OF LIGHT. 251 In order to find the direction of the reflected luminous rays, we must turn the telescope on its axis until we see the image of the star on the surface of the mercury bath. When the image is brought to the centre of the telescope, it is certain that the angle R' i' N' is equal to the angle of reflection NIK. Thus, in reading the measure on the graduated circle of the instrument, the angle of reflection can be com- pared with the angle of incidence. Now, whatever may be the star FIG. 165. Experimental study of the laws of the reflection of light. observed, and whatever its height above the horizon, it is always found that there is perfect equality between these angles. Moreover, that position of the circle of the theodolite which enables the star and its image to be seen evidently proves that the ray which arrives directly from the luminous point, and that which is reflected at the surface of the mercury, are in the same vertical plane. 252 PHYSICAL PHENOMENA. [BOOK in. These two laws have been expressed by physicists in the follow- ing form : The angle of incidence is equal to the angle of reflection. The incident and the reflected ray are loth in the same plane, which is perpendicular to the reflecting surface. These are two very simple laws, but they suffice to afford an expla- nation of the most complex phenomena, and of the action of the most varied optical instruments, whenever these phenomena and instru- ments have reference to the reflection of light from the surface of bodies. We shall soon be able to judge for ourselves. In the first place we will speak of the images which appear on the surface of mirrors, that is to say, of all bodies sufficiently polished to allow the light which falls on their surfaces to be reflected in a FIG. 166. Reflection from the plane mirror. Form and position of the images. regular manner. These images vary in dimensions and form with the form and dimensions of the reflecting surface ; but it will be sufficient for us to give some idea of the luminous effects produced by plane, spherical, cylindrical, and conical mirrors. We all know that mirrors with a plane surface such as looking- glasses and liquid surfaces in a state of rest show images which faithfully represent the objects which they reflect. The dimensions, form, and colour are reproduced with exactitude ; the image alone is always symmetrical with the object, so that the right side of one is the left of the other, and vice versd. Again, the apparent distance of the image behind the mirror is precisely equal to the real distance of the object in front of the mirror. Fig. 166 perfectly explains these conditions. CHAP, iv.] REFLECTION OF LIGHT. 253 All the luminous rays which the extremity of the flame of a candle throws upon a plane mirror, diverge in every direction after their reflection from the surface of the mirror ; but the equality of the angles of incidence and reflection causes these rays to con- verge behind the mirror at a point symmetrically situated in rela- tion to the luminous rays. The eye which receives one of these rays will then be affected as if the luminous object were situated at the point of convergence, and it will there see the image. What- ever may be the position of the observer in front of the mirror, the position of the image will be the same, although it appears to occupy different points on the same mirror. The lower end of the candle will form its image in the same manner, and so with all the intermediate points. From this it is seen that the image of any lumi- nous object will be formed, point by point, of all the partial images symmetrically situated behind the mirror, at distances from its surface equal to the distances of each of the points of the object. Fig. 167 shows how the image of an object can be Seen in a plane mirror, With- , . -, t , t 1 T out the object being directly in front of it; it suffices that the eye be placed so as to receive the reflected rays, that is to say rays in the divergent space Q M M' P. This is called the field of the mirror. In mirrors, or ordinary looking-glasses, the form and colour of the reflected objects are generally slightly altered, because it is difficult to obtain a perfect polish and an exactly plane surface. The diffused light is then mixed with the light reflected from the mirror, and communicates to it the colour which the substance of the mirror possesses. We also observe in tinned mirrors that the objects frequently form a double image : one, the more feeble of the FIG. 17. -Reflection from a plane mirror. Field of the mirror. 254 PHYSICAL PHENOMENA. [BOOK in. two, is formed on the exterior surface of the mirror; the other, the more brilliant, is that which is given by. the mirror properly so called, that is to say, by the internal tinned surface. Metallic mirrors have not this inconvenience, but they possess others which are much greater : the quantity of light that they reflect is not so great, and their surface tarnishes rapidly in contact with the air. If we place two or more plane mirrors in various ways, we obtain singular effects from the multiple reflections which are cast back from one mirror to another. FIG. 168. Reflections from two plane parallel mirrors. Multiple images. The most simple of these effects is that which is produced by two plane parallel mirrors (Fig. ll)8). A luminous object interposed between the two mirrors shows on each of them one image, a v o ly which becoming a luminous object to both mirrors, gives rise to two new images more distant than the first, a 2 , o 2 . These form new ones, and so indefinitely ; so that with the eye conveniently placed, we shall see an infinity of images which become more arid more feeble on account of the loss which the light undergoes by each successive reflection. These effects are easily observed in a room containing two parallel and opposite looking-glasses. The two series of images soon become confused when they are influenced by a luminous point? CHAP, iv.] REFLECTION OF LIGHT. 255 but if we wish to distinguish them it is sufficient to look at an object the surfaces of which are of different colours and forms. Two plane mirrors forming an angle produce images the number of which is limited and dependent on the angle. But they are all Fio. Itj9. Images on two mirrors inclined at right angles to each other. observed to be placed in a circle, having for its centre the point of intersection of the mirrors, and for its radius the distance from the FIG. 170. Images in mirrors at right angles (DO"). FIG. 171. Images in mirrors at 60. luminous point. Figures 170 to 172 represent the images formed by mirrors inclined at 90, 60, and 45. The first system gives three images, the second five, and the third seven. These multiple 256 PHYSICAL PHENOMENA. [BOOK in. reflections have suggested the construction of various instruments, among which may be mentioned the kaleidoscope, invented by Brewster. In a pasteboard tube are fixed three plates of glass forming an equilateral prism, the bases of which are closed respectively by two parallel plates, one of transparent, the other of ground glass, between which are placed little objects, such as pieces of coloured glass. The eye, on looking through the smaller end of this kind of telescope, sees these pieces of glass, the multiple images of which are formed by reflection on the three mirrors ; hence result regularly disposed figures, which can be varied at FIG. i72.-ima g es in mirrors at 45 will by turning the instrument round (Fig. 173). In Brewster's kaleidoscope there are only two mirrors, and the FIG. 173. Symmetrical images formed in the kaleidoscope. name of catoptric chamber is ordinarily given to instruments which contain three or more. CHAP, re.] REFLECTION OF LIGHT. 257 The magic mirror is nothing more than a combination of two plane mirrors inclined so as to reflect the images of objects separated from the spectator by certain obstacles. It is used, under the name of the polemoscope, during sieges, to observe the exterior movements of the enemy, while the soldiers remain in shelter behind a parapet (Fig. 174). Some years ago a poor man was seen on the quay of the Louvre, who showed to the amazed spectators the fa9ade of the Institute through an enormous paving-stone. This magic-glass which enablea .-J ft ^ v< ^- m . IT? FIG. 174. Poleuioscope. people to see through opaque bodies, was composed of a tube broken in the middle, in which was placed a stone ; but the two pieces were really united by tubes (in the supports) twice bent at a right angle, and containing four plane mirrors inclined at 45, as snown in Fig. 175. The luminous rays could then, by following the bent line, pass round the stone .and reach the eye. Other instruments of much greater scientific importance than those just mentioned are also based on the laws of reflection of light from the surface of plane mirrors. But their description 258 PHYSICAL PHENOMENA. [BOOK in. would draw us beyond the limits to which we are restricted in this first volume, and we shall confine ourselves to a simple men- tion of them. They are the sextant, the goniometer, and the heliostat. The sextant is used on board ship to measure the angular distances of two distant objects ; for instance, a star and the moon's edge. Goniometers are instruments employed to measure the angles made by the sides of crystals ; and the name of heliostat is given to an apparatus used to reflect the sun's rays in an invariable direction, in spite of the daily movement of the earth, which causes that body to pass over the heavens from east to west. When light, instead of being reflected from a plane surface, falls on a polished curved one, the laws of reflection remain the same for each point of the mirror ; that is to say, the angles of reflection and of incidence are always equal at each point, on either side the perpen- FJQ. 175. Magic telescope. dicular to the plane tangent in the point, or from the normal to the surface at the point of incidence : moreover, the incident ray, reflected ray, and the normal, are in the same plane. But the curvature of the surface modifies the convergence and divergence of the luminous rays which, after reflection, fall on the eye : from this result particular phe- nomena, and, in the case of luminous objects, the formation of images, whose distance and position vary with the form of the mirrors, as also with their dimensions and distances from the objects themselves. Let us now study the phenomena of the reflection of light from the surface of spherical, cylindrical, and conical mirrors. CHAP. IV.] REFLECTION OF LIGHT. 259 A section through a hollow metallic sphere gives us a spherical concave mirror, if the concave surface is polished, and a spherical convex mirror, if the convex surface is polished. If the spherical portion is a tinned piece of glass, the stratum of tin is outside for a concave and inside for a convex mirror. But we have already stated why it is preferable to use mirrors of polished metal for the observa- tion of physical phenomena. We shall speak here of these alone. Let us observe what happens when a luminous object, for instance, the flame of a candle, is placed at various distances from a concave mirror in a dark room. We shall in these experiments FIG. 176. Concave mirror. Inverted image, smaller than the object. place the luminous point in the axis of figure of the mirror, that is, in the line which joins the centre of the sphere to which it belongs to the middle or the top of the spherical segment. Let us first place the light at a distance from the mirror greater than the radius of its curvature. It will be easy, by the aid of a x 2 200 PHYSICAL PHENOMENA. [BOOK in. screen, to receive the reflected rays, and see that they form a smaller and inverted image of the object at a point in the axis comprised be- tween the centre of the sphere and the centre of the light-source (Fig. 176). On moving the luminous source further from the mirror, we must, in order to receive the image, approach nearer and nearer to the screen from the point of the axis called the principal focus of the mirror (we shall soon see why), and the inverted image will by degrees diminish. If the candle is brought forward from its actual position towards the centre, we observe that the image, still inverted and smaller than the object, will gradually get larger as it approaches FIG. 177. Concave minor. Inverted images, larger than the object. the centre. If the candle comes to the centre, the image will arrive there at the same time, and will be blended with it in position and size. If we now continue to bring the candle nearer to the mirror, we cause the image to pass beyond the centre ; it becomes larger and larger, always retaining its reversed position. In proportion as the object approaches the principal focus the image increases in size and becomes more and more diffused, until it is too large to be received on the screen. When the source of light reaches the focus, the image is situated at an infinite distance and has therefore practically vanished. Thus far, the image of the luminous object has been real, that is, it has actually existed in the air, at the point where it is formed, CHAP, iv.] REFLECTION OF LIGHT. 261 and the reunion of the luminous rays has materially reproduced, so to speak, the form and colour of the object. We have also been able to receive this image on the screen. This is no longer the case, however, if we place the luminous object at a less distance than the principal focus of the mirror. The real image then exists no longer ; but the eye still perceives behind the mirror, as in plane mirrors, an image of the candle : this is called a virtual image. It is upright and larger than the object, as shown in Fig. 178, and its apparent dimen- sions go on diminishing, in proportion as the light is brought nearer FIG. 178. Concave mirror. Virtual images, erect and larger than the object. to the mirror. It would have the dimensions of the object itself, if it touched the reflecting surface. These various phenomena can be easily observed by the concave mirrors used for the toilet, the curva- ture of which is calculated in such a way that, at a short distance from the mirror, the observer, who is at the same time the object, finds himself in the position described in the preceding experiment : in this case, he sees his figure increase or diminish. On going further and further away from it, he will see reproduced, in inverted order, the phenomena above mentioned. 262 PHYSICAL PHENOMENA. [BOOK in. Let us now return to these phenomena, and see how the laws of the reflection of light account for the various conditions which characterize them. For this purpose we must determine the path which a ray or luminous pencil follows, when it is reflected from the surface of the concave mirror. Fig. 179 shows a cylinder of parallel, luminous rays, that is, rays which have emanated from a point situated on the axis of the mirror at a distance which may be considered as infinite. It is thus with the light which comes from the sun, stars, or even, on the surface of the earth, from an object at a distance, compared with the radius of curvature of the mirror. Both geometry and observation agree in proving that all such rays when reflected cut the principal axis at a point situated at an equal distance between the centre c and the apex A of the mirror. Their reunion produces in F, the principal focus, an image of the point, which the eye will per- ceive there, since the FIG 179.-Concave minor. Path an d reflection of rays divergent ray 8 which parallel to the axis. Principal focus. penetrate our organ of vision will produce the same effect as if they issued from a real luminous object, situated at the focus. The phenomenon is the more exact as the surface of the mirror is smaller, that is, as the angle of the cone, having its highest point at the centre c of the mirror while its base is the mirror, is smaller. This angle must not exceed 8 or 10 degrees. If the mirror is spherical, the curvature is the same at each of its points; and the reflected rays will then follow a similar path in relation to the secondary axis, that is to say, to the right lines which join each point of the mirror to the centre. There are endless secondary foci on these axes, situated like the principal focus, at equal distances between the centre and the mirror. Figs. 180 and 181 show the path of the luminous rays, when the object is situated at a distance which is not infinite, and which lies near the mirror CHAP, iv.] REFLECTION OF LIGHT. 263 The equality of the angles of reflection and incidence indicates in these various instances how the points of convergence of the rays, either on the principal or on the secondary axes, are situated at the very points where experiments has shown us that the images are formed. Indeed, if the luminous point is at s (Fig. 180), beyond the centre of the mirror, a ray s I is reflected in I s and cuts the axis between the centre (c) and the focus. Bring- ing the luminous point now to the centre itself, the rays fall normally, and follow, after reflec- tion, the course which they at first took from the light : the luminOUS FlG - 180.-Concave mirror. Conjugate foct point and its focus then coincide. If the point still approaches the mirror, but to a less distance than the principal focus, the reflection takes place on the axis beyond the centre. It is evident, and experiment also confirms the fact, that if the path of a luminous ray is s I s (Fig. 180) from the object s to the focus s, the path will be exactly the reverse when the ray starts from the point s, so that the points s and s are alternately foci one of the other. These are called conjugate fod. F IQ - 181. Concave mirror. Virtual focus. The conjugate focus of the principal focus is infinite; in other words, the rays which emanate from this point are sent back parallel to the axis of the mirror. At the points situated between the princi- pal focus and the mirror, the focus is virtual, because the reflected luminous rays are divergent (Fig. 181) : we can no longer therefore consider them as conjugate foci. Lastly, the two figures 182 and 183 show how, in the one case, the images are real, inverted, and smaller than the object, and in the other, upright, virtual, and larger than the luminous object. To 264 PHYSICAL PHENOMENA. [BOOK in. construct the images geometrically, and to account for their positions and dimensions compared with those of the object, the images are sought at each extreme point A, B. To this end we join A c, B c (these are the secondary axes); then, the rays parallel to the FIG. 182. - Concave mirror. Real and inverted image of objects. principal axis are reflected to the focus F. The points of contact of the reflected rays with the corresponding secondary axis give a and b, images of the extremities of the object. This construction is easily followed by means of the figures. FIG. 183. Concave mirror. Erect and virtual image of objects. In convex mirrors, the foci and images are always virtual ; and this fact is accounted for, if we follow the path of the rays and lumi- nous pencils for each different point of a luminous object. We also .see why, in these mirrors (Fig. 185), the image is upright and always CHAP. IV.] REFLECTION OF LIGHT. 265 smaller than the object. The dimensions, moreover, become smaller as the distance from the object to the mirror augments. If the surface of the mirror is very large, a disfigurement is observed, which is more apparent as the surface is increased in extent. Any one may see this by looking into the polished balls which are placed in gardens, and in which the surrounding distant country is reflected. FIG. 184. Upright virtual image in convex spherical mirror. When we examine, in a spherical mirror, the path of the reflected rays proceeding from a luminous point, situated on the axis at any distance, we see that these rays successively cross each other, first on the axis at its different points, then beyond the axis, in such a man- ner that the points of intersection form a surface which geometers call a caustic. At all the points of this surface the light is more concentrated than elsewhere, and its maximum concentration is at 266 PHYSICAL PHENOMENA. [BOOK in. the focus of the given point. The caustic varies in form with the position and distance of the luminous point ; but the existence of it can be proved by experiment. Place a screen of white cardboard, cut so as to take the form of the mirror. When this is exposed to the light of the sun, or to that of a lamp, we perceive on some por- tions of the screen a brighter light, the outlines of which in- dicate the form of the caustic, which is evidently the same FIG. 185. -Convex mirror Erect and virtual image. whatever may be the position of the screen as regards the centre. A circular metallic plate, polished inside, and placed on a plane, would in the same manner indicate the form of this curve for a cylindrical mirror (Fig. 186). This experiment is due to Brews ter. When a glass full of milk is exposed to the rays of the sun, or still better, as Sir J. Herschel states, a glass full of ink, we perceive on the surface of the liquid a bright curved line ; it is the intersection of the caustic of the cylindrical con- cave mirror, which the glass forms with the limiting plane of the liquid at the upper surface (Fig. 187). In optics parabolic concave mirrors are largly employed. These possess the property of concentrating rays parallel to the axis of the parabola to the focus of this curve, whatever may be the angle of the mirror, and they also send back in parallel lines all the light from FIG. 186. Caustic by reflection. CHAP. IV.] REFLECTION OF LIGHT. 267 a luminous object situated at the focus. Spherical mirrors only produce this result when the surface is very small. Concave or convex cylindrical mirrors produce images in which the dimensions of the objects are not altered in the direction of the length of the cylinder; but which, on the contrary, are varied along in a direction per- pendicular to the first, that is to say, along the circumference of a section. The rays reflected along a line parallel to the axis follow the path which they would take in a plane mirror ; those which are reflected on a circumference follow the path which their reflection from a spherical mirror would produce. If the cylinder is convex, the FIG. isz.-caustic by reflection. images will always be narrower in the direction of its width ; if con- cave, they will sometimes be narrower and sometimes wider according to the distance of the object. Fio. 188. Cylindrical mirror. Anamorphosis. 2C8 PHYSICAL PHENOMENA. [BOOK in. In convex conical mirrors the reflected images are disfigured in the direction of the circumferences, and as the degree of curvature changes from the base to the apex, a narrowing in the dimensions ^ produced, which is more considerable as they approach the apex. If the conical surface were concave, the form of the image would be pyramidal, but for certain positions of the object it would be enlarged. FIG. 189. Reflection on conical mirrors. Anamorphosis. In both these mirrors the reflection of luminous rays always takes place rigorously according to the laws which we have stated ; so that we can take odd and deformed drawings, in which the eye cannot distinguish any figure, which nevertheless, when reflected in cylin- CHAP, iv.] REFLECTION OF LIGHT. 269 drical and conical mirrors, present a faithful representation of known objects. The name of anamorphosis is given to this changing of forms, and opticians have pictures which they sell with conical or cylindrical mirrors, in which the lines and colours have been com- bined to produce regular images of landscapes, persons, animals, &c. (Figs. 188 and 189). We have, in what has gone before, solely considered light reflected regularly from the surface of polished bodies ; and the phenomena produced by this reflection show sufficiently, as we have stated above, that if the degree of polish were perfect, the reflecting body would be invisible to us. We should see the more or less disfigured image of the luminous objects which surround it, but we should not see the mirror itself. And if, with the exception of the sources of light, all bodies were in the same condition, we should only see an indefinite multitude of images of luminous bodies, of the sun, for example, without seeing anything else. In a dark room, if the solar rays fall on a mirror, the surface of this latter gives a dazzling image of the sun ; but the other points of the reflecting body are only slightly visible by the irregularly reflected or scattered light. It is this light which enables the mirrors to be seen from all parts of a dark room. Fio. 190. Light reflected very obliquely. The proportion of specular and scattered light reflected by a body varies with the polish of its surface, and also with the nature of the body, its colour, and, lastly, with the angle of the incident rays. A piece of white paper reflects light in every direction ; but its white- ness is brighter the more perpendicularly it is exposed to the 270 PHYSICAL PHENOMENA. [BOOK m. source of light. Moreover, if the observer is placed so that he can examine the surface of the paper in directions more and more oblique, the brightness of the scattered light diminishes, but by way of com- pensation the eye receives an increasing number of rays regularly reflected. It is for this reason that on placing the flame of a candle very near the surface of a sheet of paper, and looking at it obliquely towards the candle, a very distinct image will be seen of the reflected flame as in a mirror. When we say that scattered or diffused light is light reflected irregularly, we do not mean that the rays of which it is composed follow other laws, during reflection, than light reflected by mirrors. The irregularity which it undergoes proceeds from the roughness of the surface of the dull rough bodies, which receive the light under varied angles of incidence and disperse it in every direction. When such a surface is looked at very obliquely, the roughnesses hide each other, and the rays emanating from parallel sources in the general direction of the surface become more and more numerous, which explains the *" 1 ^S^^tS'S^SSt^^ li8 '" increasing proportion of light regularly reflected. That the quantity of light reflected by means of mirrors varies with the condition of their surface is not to be doubted. A piece of polished glass becomes a mirror ; unpolished, it would scarcely scatter the diffused light. Wood, marble, horn, and numerous other substances are the same. But the reflecting power, if we give this name to the property to reflect light to a greater or less extent, varies, with equal degree of polish, according to the nature of the substances and the angle of incidence. Of a hundred rays of light received by water, glass, polished black marble, mercury, or speculum metal, with an incidence of 50, water reflects 72, glass 54, marble 60, and mercury and speculum metal 70. If the incidence augments, the number of reflected rays per cent, diminishes for the first three bodies in rapid proportion, and at the most is no more than 2 or 3, at from 60 to 90 ; whilst, under this latter incidence, mercury reflects 69 rays out Fia. 192. The Ghost (produced by reflection). CHAP. iv.J REFLECTION OF LIGHT. 273 of 100. Dark-coloured substances reflect only a little light. Lamp- black does not scatter light, arid reflects but a small amount. When light is reflected from a polished but transparent surface, images are produced, but they are very feeble, as a great part of the incident light passes through the substance. This is the reason why mirrors and ordinary looking-glasses are tinned at the back, and the images are thus formed on an opaque body of good polish. But untinned glasses could be used, and they give good coloured and very bright images when the objects which they reflect are well lighted, and when the space which surrounds them is at the same time in relative darkness and receives little or no diffused light. Such is the principle of the fantastic apparitions known at theatres as ' Ghosts ' (Fig. 192), and which have been recently used with success in the drama. The room in which the spectators are seated is in darkness, and the stage, separated from the room by a sheet of plate glass, FIG. 103. Airangenunt of the uusilvercd glass and the position of .the Ghost. is so slightly lighted up, that the glass is quite invisible. By giving to this an inclined position (Fig. 193), it reflects the image of a person who is strongly illuminated and stands under the front part of the stage, called the first sub-stage. The actor is seen apparently on the stage by the spectator as a virtual image, animated, and y 274 PHYSICAL PHENOMENA. [BOCK in. the actions of the performer can thus be seen in a way to delude the spectators and make them believe in the appearance of a real intangible phantom. The necessity of giving to the glass an inclined position, in order to make it retiect, causes the ghost to appear inclined towards the spectators, and this defect is especially per- ceptible to the spectators sitting at the sides. CHAP. V.] REFRACTION OF LIGHT. 275 CHAPTEE V. REFRACTION OF LIGHT. Bent stick iu water ; elevation of the bottoms of vessels Laws of the refraction of light; experimental verification Index of refraction Total reflection Atmospheric refraction ; distortion of the sun at the horizon. WHEN a straight stick is thrust into clear water, that part of it which is beneath the liquid does not appear to be continued in a straight line. The stick seems to be bent from the surface of the water, and the end which is immersed rises as if it had FIG. 194. Phenomena of refraction of light. The bent stick. diminished in length. If the stick is placed vertically, or if the eye receives the visual rays in a direction which causes it to be seen as if it were vertical, the stick no longer appears bent, but I 2 276 PHYSICAL PHENOMENA. [BOOK m. simply shortened. This phenomenon is easily shown by putting the end of a pencil into a tumbler full of water. If before filling a vessel with transparent liquid we look at the bottom of the vessel over the edge from a fixed position, and if, without removing the eye from its place, water is poured gently in, the bottom of the vessel appears to rise gradually, and at last seems much higher than before. To make this experiment more striking, put a piece of money on the bottom of the vessel in such a position that the edge of the vessel entirely hides it. As the level of the water rises the object becomes visible and appears to rise with it, and takes the apparent position indicated in Fig. 195. FIG. 195. Refraction of light. Apparent elevation of the bottoms of vessels We have all, moreover, noticed that objects seen through a flask of clear water appear enlarged, distorted, and removed from their real position. If we follow the movements of fishes as they swim about in glass globes, it is surprising to see these animals, sometimes disappearing, sometimes becoming considerably larger, and sometimes gradually diminishing, until we see them in their actual dimensions. All these phenomena are due to what physicists call the refrac- tion of light that is to say, to the deviation which luminous rays undergo when they pass obliquely from one medium into another, for example, from air into water. When light leaves a luminous or illuminated object it moves in a right line as we have just seen provided that the medium through which it passes is homogeneous. Thus the rays which enable us to see the end of the stick in the water are rectilinear so long as their passage is through the water, which is a homogeneous medium. The path followed by the same rays in leaving the liquid surface and passing to our eye is likewise rectilinear, because it CHAP, v.] REFRACTION OF LIGHT. 277 takes place through another homogeneous medium. But the second direction is not a continuation of the first, and the complete course followed by the luminous rays forms a broken line, the angle of which will be found at the point of incidence, at the separating surface of the two media. Similar phenomena are seen in all kinds of liquids, in trans- parent solids like glass, and also in gases ; only, as we shall presently see, the deviation varies with the nature of the medium. The principal phenomena connected with the refraction of light were examined long ago, and the appearance of objects when seen through clear water was doubtless observed in very remote ages. The ancient astronomers, Ptolemy for example, noticed the effects of atmospheric refraction, that is, the deviation .which the luminous rays from the stars undergo in passing from the vacuum of planetary space through the denser medium of our atmosphere. But it was not until the commencement of the seventeenth century that a young Dutch geometer, Willebrod Snell, discovered the cause of this devia- tion, and the laws which govern the passage of a luminous ray when it passes obliquely from one homogeneous medium to another. These laws sometimes bear the name of Descartes, because this great man discovered them in his turn, or at any rate explained them under a form which is still retained in science. Let us examine the nature of these laws. In order to prove them experimentally, a ray, or a bundle of rays, is caused to fall obliquely on the surface of a liquid contained in a semi- cylindrical glass vessel placed within a graduated circle, and the angle which the path of the ray makes with the vertical is then measured : this is the angle of incidence. The ray enters the liquid, is then broken or refracted, and is seen to approach the vertical line. The angle of refraction is smaller than the angle of incidence. If we vary the angle of incidence, the angle of refraction varies also ; and we do not at once perceive the relation which exists between these variations. But because the refracted ray is always in the plane of the graduated circle as well as the incident ray, and it is the same with the vertical, it follows that the first law is as follows: When a luminous ray passes obliquely from one medium into another, it is bent aside, and both the incident and the refracted ray 278 PHYSICAL PHENOMENA. [BOOK ITT. remain in the same perpendicular plane, normal to the surface of sepa- ration of the medium. We may also add, that if the ray of light enters perpendicularly to the surface, it continues its path in the same direction. There is no refraction for the normal incidence. Fig. 196 represents the instrument as arranged for proving the second law. The incident ray coming from the sun, for instance, falls at I on a mirror inclined in such a manner as to reflect it in the direction FIG. 196. Experimental demonstration of the laws of refraction. of the centre through a little hole in a diaphragm. An index, furnished with a point at its extremity, indicates the direction of the incident ray, and the line o' a can be measured on the horizontal divided scale, which can he moved up or down. This line, or, better, its relation to the length of the ray o' a, is what geometers call the sine of the angle of incidence. Another index, also furnished with a diaphragm pierced with a hole, receives the refracted luminous ray after its passage through the water, and o' b is measured on the scale, which gives the sine of the angle of refraction. Let us observe that CHAP, v.] REFRACTION OF LIGHT. 279 the luminous ray, on emerging from the water into the air, does not undergo a new refraction, as it passes out by an incidence normal to the surface of the cylindrical vessel. Let us suppose that the first observation gives us two sines, such that, by dividing that of the angle of incidence by that of the angle of refraction, the quotient is 1/335. If we repeat the experiment several times, changing the direction of the incident ray, we find that in each fresh experiment the quotient of the sine of incidence by that of re- fraction will continue to be 1/335 ; and it will be the same as long as the two media are air and water. But this number, which is called the index of refraction, varies when one of the media is changed or when both change ; thus, from air to glass the index of refraction is no longer equal to that from air to water. It has also been found convenient to calculate the indices of all transparent bodies, on the supposition that the light passes from a vacuum into each of them. By this means absolute indices are obtained. Generally speaking, the refraction increases with the density of the second medium, although there are many exceptions. Thus, the refractive power of a medium very usually increases with its density. The second law of refraction of light may be thus stated : For the same two media, the quotient of the sines of the angles of incidence and refraction is a constant number, whatever the incidence may be. The laws we have just studied indicate the path which light follows when luminous rays pass from one medium to another. But this path, as both reasoning and experiment prove, remains the same if the light passes from the second medium into the first. Then the incident ray becomes the refracted ray, and vice versa. For example, if the luminous point is in the water at s, the ray which falls at the point I of the surface will be deviated from the perpendicular, following Fl - the direction I R ; the path SIR will be the same, only reversed, as if the incident ray had been at R I ; so that the angles of incidence 280 PHYSICAL PHENOMENA [BOOK in. and refraction will have inverse sines, the quotient of which, how- ever, will be always constant. These laws account for the phenomena described at the commence- ment of the chapter. The eye which examines the end of a stick in water, sees it by means of the luminous rays which this extremity sends to the sur- face ; which rays are refracted the more as their incidence is more oblique. Tlie phenome- non is therefore the same as if the luminous point were situ- ated at the point of conver- gence 01 these rays, and the the stick in this point. The FIG. 198. Explanation of the bent stick. eye in reality sees the end of FIG. 199. Apparent elevation of the bottoms of vessels ; explanation. same effect is produced for all intermediate points, and the stick appears bent The same explanation accounts for the elevation of CHAP, v.] REFRACTION OF LIGHT. 281 the bottoms of vessels filled with liquid. Even when we look at the bottom in a perpendicular direction, the effect is produced, because the eye does not receive a single ray, but a bundle of rays, which diverge more on passing through the air, on account of re- fraction, than through the liquid. The point then appears to rise towards the surface from o to o' (Fig. 199). A singular phenomenon called total reflection results from the laws of refraction, which may be proved by experiment. Let us imagine a luminous point placed in water, at the bottom of a vessel. This point sends out rays of light in every possible direction at the surface of separation of the air and water. Now, do all these rays emerge ? We shall see that this is impossible, and that there is a certain angle, variable with the nature of the medium, beyond which the luminous FIG. 200. Total reflection. Limiting angle. ray cannot penetrate into a less refractive medium. Indeed, since the angle of refraction is greater than the angle of incidence, a moment will arrive when the first angle having become a right angle, the angle of incidence I N' is still less than a right angle. The refracted ray no longer emerges ; it grazes the horizontal surface of the liquid. Beyond this, the angle of incidence always increasing, the angle of refrac- tion would become greater than a right angle. In this case the ray returns into the liquid, and is reflected, according to known laws, to the inner surface of separation. As in the least incidences the emer- gence is not complete, and there is a partial reflection of the rays, so when the emergence is nil, there is said to be a total reflection. All the luminous rays which, coming from 0, cut the surface of separation 282 PHYSICAL PHENOMENA. [BOOK in. of the two media, are thus divided into two portions : the first, containing those which emerge, forms the cone of refracted rays ; the second is composed of all the rays which cannot emerge, and which are therefore reflected back into the interior of the more refractive medium. Fitt. 201. Phenomenon of total reflection. We name the limiting angle that beyond which the total reflection commences. This angle is about 48 for rays which are refracted from water into air, while it is only 41 from glass to air. A very simple experiment proves the phenomenon of total CHAP. V.] REFRACTION OF LIGHT. 283 reflection, and, at the same time, shows that reflection thus obtained exceeds in brightness all those which are obtained directly; for example, at the surface of mercury or polished metals. A glass of water is held in such a position that the surface of the liquid is above the eye (Fig. 201). If we look obliquely from below at this surface, it appears brighter than polished silver, and seems to possess a metallic brilliancy. The upper part of an object plunged in the water is seen reflected as in a mirror. A diver immersed in perfectly still water, and having his eyes directed towards the surface of the liquid, would witness singular phenomena. Kefraction will cause him to see, in a circle of about 97 degrees in diameter, all the objects situated above the horizon, more distorted and narrowed, especially in height, as they approach the sensible horizon. " Beyond this limit, the bottom of the water and the submerged objects would be reflected, and would be pictured to the sight as distinctly as by direct vision. Moreover, the circular space of which we have spoken would appear to be surrounded by a perpetual rainbow, coloured slightly, but with much delicacy." (Sir J. Herschel.) The phenomenon of total reflection also explains how it happens that an isosceles and rectangular glass prism, fitted to the opening of the shutter of a camera obscura, intercepts all the light coming from the outside, and leaves the room in the most complete obscurity. The rays which enter the prism by its perpendicular side do not suffer refraction, but when they have arrived at the oblique surface, the angle of incidence is 45 degrees; that is to say, greater than the limiting angle. The total reflection takes place, and there is no emergence. The rays which alone could enter would be due to oblique incidences which are prevented by the tube containing the prism. z 2 FIG. 202. Phenomenon of total reflection, in the shutter of a camera obscura. 284 PHYSICAL PHENOMENA. [BOOK in. The phenomenon of refraction occurs whenever a ray passes obliquely from one medium into another, provided that they differ in nature and density. It is evident, then, that the luminous rays emanating from planets, the sun, the moon, and fixed stars, which, after having travelled through the celestial space, have to traverse the strata of our atmosphere before reaching the eye, are subjected to refraction. Hence then we do not see these bodies in the direction of the right lines which really join each of them to the position which we occupy on the surface of the earth. There is no exception except for those situated at the zenith of each horizon. Atmospheric refraction depends on the angular height of the body observed above the horizon ; it depends, likewise, on the law which regulates the decrease FIG. 203. Atmospheric refraction. The effect on the rising and setting of stars. of density of the strata of air constituting the atmosphere. As we have at present very uncertain data concerning this law, it would be very difficult to measure directly the deviations which correspond to the various heights of bodies. Happily, astronomy has come to the help of physics. As the angular distance of a star from the celestial pole remains invariable, it follows that, whatever may be the height to which the diurnal movement brings it above the horizon, the differ- ences, which observation indicates between the distances obtained from the greatest elevation and at the horizon, can only proceed from atmospheric refraction. Hence it is possible to construct a table of astronomical refractions from the horizon to the zenith. CHAP, v.] REFRACTION OF LIGHT. 285 At the horizon the refraction is nearly 34'. As the diameters of the sun and moon have a less value, it follows that at sea, when no object hides the horizon, the disc of the sun at sunrise will appear entirely above the liquid surface before the top of that* luminary has emerged above the real horizon. The day is thus found lengthened in the morning by refraction, and the same thing happens in the evening with the setting of the sun. The same phenomenon accounts for the peculiarity observed in many eclipses of the moon, that the latter body is seen eclipsed, while the sun, whose light the earth, interposed between it and the moon, is cutting off, is still visible above the western horizon. Lastly, it is atmospheric refraction which, in total eclipses of the moon, allows a certain number of solar rays to reach our satellite, preventing its disc from being completely invisible. This disc, then, presents a very marked reddish colour, similar to the tint of the atmosphere at sunset. 286 PHYSICAL PHENOMENA. [BOOK in. CHAPTER VI. REFRACTION OF LIGHT. PRISMS AND LENSES. Transparent plates with parallel faces ; deviation of luminous rays Multiple images in a silvered mirror Prisms Phenomena of refraction in prisms Converging and diverging lenses Real and virtual foci of converging lenses ; real and virtual images Foci and images of diverging lenses Dark chamber Megascope Magic lantern and phantascope Solar microscope. WHEN a luminous point is examined through a plate of trans- parent substance, glass for instance, the two plane faces of which are parallel, if the eye and the luminous point are on the same perpendicular in regard to the plate, the luminous point is seen in the direction where it would be seen without the inter-, position of a refractive medium. This is the case because there is no refraction for normal rays, that is for rays falling perpendicularly on a surface. Ho 204. Normal View. FIG. 205. Oblique View. Deviation due to refraction through plates with parallel faces. But the same result does not take place in the case of an oblique incidence, for then the position of the luminous point is altered, and the deviation may be rendered evident by a very CHAP. vi. J REFRACTION OF LIGHT. 287 simple experiment. Take a sheet of glass, place it upon a piece of paper, upon which straight and curved lines have been drawn in such a manner that the glass only covers one part of the lines. If we look at it perpendicularly, we shall observe that the lines seen through the glass are a continuation of the lines seen by direct vision. If we look at it obliquely, we shall notice a deviation, a solution of continuity, the more marked as the incidence of the luminous rays is more oblique. This deviation is due to refraction, and it increases with the thickness of the plates. It evidently follows from this that transparent plates, such as window-panes, and the glass used to cover engravings, distort the images ; but this defect is scarcely perceptible, and is rarely remarked. When we speak of deviation, we mean lateral displacement, for the luminous ray which traverses one or more plates with parallel faces, preserves after its emer- gence a direction parallel to that of the incident ray, as shown in Fig. 206. This property is a con- sequence of the parallelism of the normals to the points of incidence and emergence as well as of the law of refraction for two media, the refractive power of which FlG 206 _ Path of a luminoug pencil- is known. Experiment proves that the rays are always parallel when they emerge, after having traversed any number of plates, even when these plates are not formed of the same substances and when they are not all parallel to each other ; and theory foresaw this result. Again the same result is produced when plates of different substances are so arranged. The lateral displacement depends, in every case, on the refractive power of the substances and the thickness of the plates. If we place a candle in front of a silvered mirror, and hold it obliquely so as to examine the image, we shall perceive, before the bright image formed on the inner silvered face, a more feeble image proceeding from the outer face of the glass, and also a series of images still less brilliant behind the first. These latter images are due to the rays which, after being refracted the first 288 PHYSICAL PHENOMENA. [BOOK in. time in the thickness of the plate, are partially reflected by the silvered surface and by the interior surface of the external plane FIG. 207. Multiple images produced by FIG. 208. Path of the rays which giye place to the refraction in plates with parallel faces. multiple images of plates with parallel faces. FIG. 209. Geometrical form of the prism. FIG. 210. Prism mounted on a stand. of the mirror. Fig. 208, which gives the successive path of these rays, accounts for the phenomenon we have just described. CHAP. VI.] REFRACTION OF LIGHT. 289 We will now examine the phenomena which depend on the refraction of light when it traverses a refractive medium, the plane faces of which are not parallel, that is to say, in prisms. Fig. 209 shows both in perspective and in section the geometrical form of a prism as used in optics. For the convenience of experi- ment the prism is mounted on a stand, in such a manner that it can be turned round or in- clined at will (Fig. 210). The effect of a prism on a luminous ray, which enters ob- liquely at one of its faces, tra- verses the prism, and emerges from the other face, is to de- viate the ray towards the side which constitutes the base. It is sufficient for us to examine Fig. 211, which shows the path of the incident and refracted rays, to prove this : the inci- dent ray s I after the first re- fraction takes the path I E in the prism, is again refracted on emerging from the prism, and finally issues in the direc- tion E R. This is confirmed by observation, for if we examine an object through a prism, by placing its edge in a horizontal position, the image appears raised up, if the base is be- low ; and it is lowered, if the base occupies the reverse position. In fact, the eye sees the luminous points in the direction of the rays which leave the prism. If, as we have just seen, the bundle of rays diverges and approaches the base of the prism, their convergence will take place towards the summit, and the eye will see the point raised or lowered according as the base is above or below the opposite angle. FIG. 211. Deviation of luminous rays? by prisms. 290 PHYSICAL PHENOMENA. [BOOK in. The deviation of the rays increases with the angle of the prism, when the angle of incidence of the rays remains the same. For the same prism, in proportion as the incident ray approaches the normal the angle of emergence increases, and there is a direction in which the rays attain the limiting angle of total reflection, when there is no more emergence. This depends, of course, on the substance of which the prism is composed. PIG. 212. Images of objects seen through prisms. In the case of a glass prism of 45, all rays which fall below the normal towards the base cannot emerge ; but those which fall towards the summit become emergent rays. If the angle of the prism is double, that is to say, a right angle, no luminous ray, whatever may be its incidence, can emerge out of the prism; so that such a prism, with a blackened base, if placed at the opening CHAP, vi.] KEFRACTION OF LIGHT. 291 of a shutter in a dark room in a transverse position, and so as to close the opening, would allow no luminous ray to enter. We shall presently describe other phenomena of great interest, obtained by the aid of prisms, through which rays from different light-sources pass ; phenomena which show that white light is formed of a multitude of rays of different colours, each being refracted in a different degree. This is called the decomposition or dispersion of light. But having now dealt with deviation, we must first consider the path of a ray when it traverses transparent media with curved surfaces. LENSES. If we construct of glass, or of other transparent substance, a disc with two convex faces, that is to say, two segments of a sphere with their bases in conjunction, we have what is called a FIG. '213. Magnifying glass or lens with convex surfaces, side and front view. lens. The name is taken from the resemblance which exists between the form of such a mass and that of the well-known vegetable the lentil. There are various kinds of lenses; that which we are about to describe, which forms the instrument called the magnifying glass, is used by almost every one, as for instance naturalists, engravers, watchmakers, &c., who wish to enlarge the smallest parts of objects so as to be able to see them in detail. There can be no doubt that glass lenses and their magnifying 202 PHYSICAL PHENOMENA. [BOOK in. effects have been known for ages. Analogous objects have been found in the ruins of Nineveh, Pompeii, and Herculaneum. Spec- tacles have been used in Europe since the beginning of the fourteenth century. But it is only for the last three hundred years that the knowledge of the laws of refraction has enabled opticians to construct and to combine lenses so as to obtain various desired effects with accuracy. Physicists have extended the name of lenses to all transparent masses, terminated, at least on one side, by curved, spherical, or cylindrical surfaces, even when these surfaces are concave instead of convex, as in the magnifying-glass. More often, and indeed when- ever the contrary is not stated, the surfaces of lenses are both spherical ; or one may be plane, and the other spherical. "We shall thus regard a lens throughout this work. All lenses may be con- veniently grouped in two classes, according to the path which the light which traverses them follows. Some, as in the magnifying-glass, Fio. 214. Converging lenses. Bi-convex lens ; plano-convex lens ; converging meniscus. Fio. 215. Diverging lenses. Bi-concave lens; plano-concave lens ; diverging meniscus. are converging, that is to say, the luminous rays after their passage through the lens are drawn together ; others are diverging, because, on the other hand, the rays become more distant from each other, or diverge either on entering, or issuing from, the refractive medium of which they are formed. These can be very simply distinguished at first sight, for converging lenses are always thicker at the centre than at the circumference, while diverging lenses are thinner at the centre than at the circumference. CHAP. VI.] REFRACTION OF LIGHT. 293 The type of converging lenses is the magnify ing-glass or bi-convex lens, the two surfaces of which, generally of the same curve, are convex. Next we have the plano-convex lens, one surface of which is plane, the other convex. Lastly, the third converging lens is the converging meniscus, one surface being concave and the other, a more decided curve, rounded or convex. Fig. 211 gives the form of each of these lenses seen edgewise, supposing the section to be made in the direction of the diameter. The type of diverging lenses is the bi-concave, formed of two concave surfaces. Next, the plano-concave lens, one surface being concave, the other plane ; and the diverging meniscus, the two sur- faces of which are, one convex, the other concave, this latter having a sharp curve. We may also state that the principal axis of a lens is the right line which passes through the centres of the spheres to which their surfaces belong, or, if one of these is plane, the line which, from the centre of the curved surface, falls perpendicularly on the plane surface. In converging lenses, the axis passes through the lens at its greatest thickness; while with divergent lenses it passes where the lens is thinnest. Without the aid of experiment, the known laws of refraction indicate to us that a ray of light which is propagated in the direction of the axis will traverse the lens without deviat'on, and will continue its path in the line of the axis, exactly as if it normally traversed a plate with parallel faces. There are other lines which have an analogous property, and which are called secondary axes. They are those lines which cut the principal axis at the middle of the maximum or mini- mum thickness : I i' (Fig. 216) is a secondary axis in each of the lenses represented. When a luminous ray N I on entering follows the direction of one of these lines, it emerges in a direction N' i' parallel to that of the incident ray; and as the thicknesses of lenses are generally very small, it may be said that the incident ray and the FIG. 216. Secondary axes of lenses. Optical centre. 294 PHYSICAL PHENOMENA. [BOOK in. emergent ray pass in the direction of the secondary axis. The optical centre of a lens is the point where the principal axis and the secondary axes meet. The optical centre is still in the interior, if the two surfaces have not the same curvature, but it is no longer situated at an equal distance from the two surfaces. For plano-convex and plano-concave lenses, the optical centre is on the curved surface ; in the converging and diverging meniscus lenses it is outside the lens. These definitions being understood, let us now examine the path of light through a bi-convex lens. If we place it facing the sun, so that its principal axis is parallel to the rays of light issuing from that luminary, and then receive the light which emerges from the lens on a screen \ laced a short distance on the other side of it, we shall FIG. 217. Path of rays parallel to the axis. Principal focus perceive on the screen a luminous circle, the clearness and dimen- sions of which depend on the distance of the screen from the lens. When we move it further away or nearer to the screen, we find a position when this brightness will be at its maximum, and the clearness of the circular image will be greatest and its magnitude the least. This would be a mathematical point, if the source of light were itself a point. This point, to which the parallel rays converge after their refraction to the principal axis, is called the principal focus of the lens. The distance F A from the focus to the lens, which is called the principal focal distance, depends both on the substance of which the lens is made and on the curvature of its surfaces. The greater the curvature, the less is the focal distance, which is expressed by saying, that the lens is of short focus. CHAP. VI.] REFRACTION OF LIGHT. 295 If a lens is placed in the opening of a dark room, the con- vergent path of the sunlight can be traced in the air, because the luminous cone renders evident the particles of dust which fly about in the room. The convergence of luminous rays produced by bi-convex lenses readily explains the path of refracted light through a prism. The effect produced by this latter medium is to cause the luminous ray to approach the base of the prism. Now, a bi-convex lens may be considered as an assemblage of superposed prisms, the angle being more acute as it approaches the principal axis, while the de- viation is greater as the angle is more obtuse. Fig. 218 shows this convergence, and experiment agrees with theory in showing that the point of meeting is on the principal axis, provided that the rays are very near the axis. Let us examine the different circumstances which result, when the luminous point s (Fig. 219) is near the lens, and in the principal axis. The ex- planation is the same, when the luminous rays, instead of start- ing from a point situated at an infinite distance, proceed from a light situated on the axis at a finite distance. Only, in this case, the focus does not coincide with the principal focus. As long as this point is on one side of the lens, beyond its focal distance, its focus s is formed on the axis beyond the principal focus, and the more it approaches, the more distant is the focus. If it should happen to be at the distance from the lens of double the focal distance, the corresponding focus is precisely at the same distance. If it again approaches the lens, the focus continues to recede, until the luminous point, attaining the focal distance itself, its focus Fio. 218. The lens may be considered as an assemblage of prisms. 296 PHYSICAL PHENOMENA. [BOOK in. disappears, or in other words it is situated at an infinite distance, the rays leaving the lens parallel. Hitherto the convergence of luminous rays has been really effected after their departure from the lens; the focus is real; which it is easy to prove by receiving the luminous cone on a screen where the concentrated rays will produce an image of the object, a luminous point, for instance, if the object itself is a luminous point. Again, the two points of the axis where we find the object in one part, and the focus in another, are reciprocal Fia. 219. Path of rays emanating from a luminous point on the axis. Conjugate foci. one to the other, that is to say, if the focus becomes the luminous point, the first position of the luminous point marks the new focus (Fig. 219). This is the reason why physicists give to these points, the focal distance of which can be found by calculation, the name of conjugate foci. The same fact has been proved in the case of mirrors. The luminous point s approaches from the principal focus towards the lens, till its dis- tance is less than the focal distance (Fig. 220) Then, the luminous rays, after emergence, recede from the axis or diverge, so that there is no longer a real focus. It is now no longer possible to collect the divergent beam on a screen ; but the eye sees the luminous rays FIG. 220. Path of rays emanated from a point situated between the principal focus and the lenses. Virtual focus. CHAP, vi.] REFRACTION OF LIGHT. 297 as if they emanated from this focus, and the impression they receive is that of the image of the luminous point. The nearer the object approaches the lens, the more does the image itself approach it ; and when the object comes into contact with the transparent surface, the image arrives there at the same time. These results can be proved both by calculation and experiment. Let us examine, experimentally, images both real and virtual, which are formed at the focus of a bi-convex lens or, in general, of a convergent lens, when it is placed opposite a luminous object. We have already seen how the image of an object whose distance may be considered as infinite, and which sends to the lens a beam of parallel rays, is formed : it is thus that the sun produces an image in the principal focus of the lens. FIG. 221. Real image, inverted, and smaller than the object. If the object A B is at a finite distance, more than double of the principal focal distance, it will be real, inverted, and smaller than the object. This may be proved by receiving the image of a lighted candle on a screen which we can move nearer or further away from a lens, until we obtain a perfectly clear image. As the distance of the candle diminishes, the image, which is always real, will recede and become larger, until it is of precisely the same size as the object itself. If the distances are measured which separate the lens from the screen and from the candle, they are found to be equal, and each is doiible that of the principal focal distance. As the candle continues to approach the lens, the real image enlarges and recedes; and it is then larger than the object (see Figs. 222 and 223). We must increase the distance of the A A 298 PHYSICAL PHENOMENA. [BOOK in. screen if we wish for clearness, but it will be seen that the brightness diminishes, which is explained by the dispersion of the luminous rays proceeding from the lens on a surface which increases quicker than the quantity of light received. FIG. 222. Heal image, inverted, and larger than the object. When the candle has arrived at the focal distance, the image disappears; and this is easily explained, for as the rays issue parallel to the axis, there can no longer be convergence. Thus far, the FIG. 223. Image of an object situated at a distance from the lens greater than the principal focal distance, and less than double that distance. image has always been real; mother words, it has always been possible to receive it on a screen ; its existence has been independent of the observer. This will no longer be the case if we continue to CHAP. VI.] REFRACTION OF LIGHT. 299 advance the candle or other luminous object towards the lens ; for then the screen placed at any distance will only give diffused light. If, however, instead and in place of the screen, we substitute our eyes> we shall see through the lens an image of the candle, no longer inverted, but erect and magnified. How then does it happen that the eye receives the sensation of an image which is not then real ? FIG. 224. Erect and virtual images of an object placed between the principal focus and the lens. The luminous rays which each of the points of the object sends to the lens issue from the refractive medium in a divergent form. The eye which receives them undergoes the same sensation as if it were acted upon by rays emanating directly from luminous points situated on the other side of the lens, but at a much .greater FIG. 225. Principal virtual. focus of diverging lenses. - distance than the object to which they belong. Hence; the increase of apparent dimensions ; and also, the direction of the image, which, becoming virtual, ceases to be inverted (Fig. 224). In this instance, in proportion as the object approaches the lens the image diminishes, until it touches one of the surfaces of the lens, when the image becomes sensibly equal to the object itself. These are the images produced by converging lenses. A A 2 300 PHYSICAL PHENOMENA. [BOOK in. Diverging lenses have no real focus. For example, in the case of a bundle of rays parallel to the axis which occurs when the luminous point is situated on the axis at an infinite distance in issuing from the lens the rays diverge ; their point of intersection is situated on the axis in front of the lens, and is called the principal focus, a focus which is no longer real but virtual. The eye which receives the divergent beam emerging from the lens experiences the same sensation as if there was actually a luminous point at the focus. Diverging lenses do not produce a real image, because the luminous rays, on emerging from a refractive medium, are separated from each other, and have no effective point of union. But if we apply to them the treatment before adopted in the case of the erect and virtual image given by a converging lens, we perceive that the images of diverging lenses are likewise vir- tual and erect. But there is this differ- ence, viz., that their FIG. 226,-Erect virtual images smaller than the object apparent dimensions are always less than those of the objects which they represent. Fig. 226 indicates the cause of this, and enables us to understand why images which become smaller as the object is more distant, attain the size of the object itself when this latter touches the lens. Both converging and diverging lenses are used in the construction of numerous optical instruments, in astronomical telescopes, micro- scopes, lighthouses, &c. We have described the most important of these in the volume which treats of the "Application of Physics," and shall see how wonderfully science is concerned in these operations. We shall here confine ourselves to the construction of the most simple instruments, in which real images are caused to produce various optical effects; these are principally the camera obscura, the megascope, the magic lantern, the solar microscope, and the phantascope. CHAP. VI.] REFRACTION OF LIGHT. 301 In considering the propagation of light in right lines, we have seen that if a small hole is made in the shutter of a perfectly dark room the image of exterior objects is thrown on the screen. This inverted image is only distinct in the case of distant objects. To obviate this inconvenience and to give brightness to the images, Porta conceived the idea of receiving the light on Fio. 227. Camera obscura. a spherical concave mirror, which reflects both the rays and the image on the screen. But he also obtained effects much more remarkable, by placing a converging lens in the hole of a shutter, when the images of outer objects were found to be given with distinctness on a screen, the distance of which from the opening of the shutter varied with the distance of the objects themselves. It is easy to determine this distance by moving the screen back- wards and forwards. Designers employ this dark chamber, in order to trace on paper the outlines of a landscape they may wish to produce. They make use of it in the form indicated in Fig. 227. Instead of a lens, they use a prism (Fig. 228), the side of 302 PHYSICAL PHENOMENA. [BOOK in. which, turned towards the object, is convex, and, by total reflection from its plane surface, which is inclined at 45, it projects the beam of light upon the table, on which is placed white paper. The image thus formed is perfectly clear, and the draughtsman has nothing to do but follow the outlines in pencil. This modification of the camera obscura is due to M. C. Chevalier, the optician. The megascope is a dark chamber used for the purpose of reproducing an object on a large scale, such as a statuette, or picture. Fig. 229 will save us a more detailed descrip- tion. We may remark that, as the bright- ness of the object is enfeebled by the dis- persion due to enlargement, a mirror is used FlG ' camTra^cui-r f ^ t0 P r J ect tne SUn ' S ra y s n tne Object, and to obtain a sufficiently intense light. The magic lantern is a megascope in which the object is illuminated by means of a reflecting lamp. By the use of this FIG. 229. Megascope. apparatus, the Enlarged images of pictures painted on glass with transparent colours are projected on a screen. The tube through CHAP, vi.] REFRACTION OF LIGHT. 303 which the inverted drawings are placed incloses a system of two lenses, one plano-convex, the other bi-convex, which produce an erect image on a screen in front of the instrument. By using Drummond's light to illuminate the objects, far more brilliant images are obtained ; and, by moving the screen further away and bringing the lenses nearer together, the images can be greatly enlarged. Towards the end of the last century, a Belgian physicist, Eobertson, obtained an extraordinary success by exhibiting, in public, apparitions of phantoms, which, in the profound darkness surrounding the spectators, appeared gradually to advance into the middle of the room, and to increase in size. This was done by means of an apparatus called a phantascope, analogous to the magic lantern, that is to say, consisting of a box, containing a reflecting lamp, and furnished with a tube having the same system of two lenses to project the image of a drawing on a screen placed in front of the in- strument. But in this case the lantern is supported by a moving table, one of the feet of which FIG m _ Magic lautern> has a pulley com- municating its movement to the lenses through the intervention of an eccentric and lever. When the table moves further from the screen, the plano-convex lens approaches the convex lens, the image increases, and the illusion is produced in a much more com- plete manner than by the aid of a movable diaphragm ; the light which the image receives varying in proportion to its size. Eobertson, who owed the secret of this invention to an artist named Waldech, was careful to exclude all extraneous light ; and, to avoid any noise produced by the apparatus, the wheels were covered with wool. He further augmented the illusion by imitating the noise of thunder, rain, the cries of animals, &c. In Fig. 231, a double lantern is shown, from which, beside' the image of the spectre or any other fantastic personage, that 304 PHYSICAL PHENOMENA. [BOOK in. of a landscape in harmony with the scene produced, can be projected on the screen. The same double apparatus also gives polyoramic views ; that is, effects of varied landscapes, a succession of day and night, calm sea and tempest, &c. Each lan- tern is disposed in such a manner as to project each double view at the same place on the screen. One of them is at first closed, and a landscape illuminated by the sun is seen ; by degrees the light diminishes, twilight comes, then night, and imperceptibly the second view is substituted for the first. Children and even grown persons, often admire these ^pictures and effects of light : the principle interests us here, rather than the details of the mechanism. We shall only insist on this point, viz. that the dark chamber, megascopes, magic lanterns, and phantascopes are all based on the formation of real images, by means of converging lenses. Such is also the principle of the solar microscope, fHUMlil JK^ which is not less interesting than the instruments before described, and certainly more useful for the study and teach- ing of science. The solar mi- croscope is used to project the image of a small object, in a considerably enlarged form, FIG. 231. Plmntascope. FIG. 232. Solar microscope ; complete. CHAP. VI.] REFRACTION OF LIGHT. 305 on a screen. It is a megascope with the advantage of easy use, and of showing the enlarged object to a great number of spectators. To this end, the object is placed a little beyond the principal focus of a lens of short focus. The enlargement is more considerable as the distance of the object from the focus decreases. But the image will be formed at a much greater distance from the lens ; and, the greater the magnifying power, the more will the light be diffused, and consequently enfeebled ; hence the necessity of illuminating the object as brightly as possible, so that the image may retain a sufficient degree of distinctness. This is why either the rays of the sun, or those of a very intense source of light, such as the electric light, are used. A mirror reflects and projects the rays of light on FIG. 233. Section of the solar microscope. a lens of large aperture, which causes them to converge for the first time ; a second lens concentrates the rays still more ; and at the focus the object, the details of which we desire to examine, is placed. Figures 232 and 233 represent the solar microscope and its internal construction. The gas microscope is that in which Drummond's light is used to illuminate the object ; and the photo-electrical one that in which the brilliant voltaic arc supplants the solar rays. Nothing is more curious than to see the magnified images of the various organs of the smallest animals ; the infusoria which live in a drop of fermenting liquid ; the decomposition of water into gaseous globules of oxygen and hydrogen ; the crystallization of salts ; and the structure of animal and vegetable tissue. 30C . PHYSICAL PHENOMENA. [BOOK in. CHAPTER VII. COLOURS: THE COLOURS IN LIGHT SOURCES, AND IN NON- LUMINOUS BODIES DISPERSION OF COLOURED RAYS. White colour of the sun's light Decomposition of white light into seven simple colours ; solar spectrum Recomposition of white light by the mixture of the coloured rays of the spectrum Newton's experiment ; unequal refrangibility of simple rays Colours of non-luminous bodies. THE light which physicists take as a type of all others as regards colour is that of the sun. That the light of the sun is white may be proved by a very simple experiment. If in the interior of a dark room, tne solar light, after passing through a hole in the shutter, is received directly on a piece of white paper, the image of the sun on the paper will be found to be a round white spot. If this experiment were not made in a dark room it would be inconclusive, because the paper would receive, in addition to the solar rays, rays reflected from the surface of other bodies differently coloured. But this white light is not simple. It is composed of a multitude of colours or tints, which are themselves simple colours. This has been proved beyond doubt by a series of experiments which have been made under diverse conditions, and which are principally due to Newton. We will indicate the most striking of these. If we place in the path of the solar rays, after their passage through the round hole of the shutter of a dark room, a triangular flint- glass prism in such a manner that its edges are placed horizontally (Fig. 234), and that the beam enters it obliquely by one of its surfaces, we shall see on the screen, at a certain distance abcrve the point where the spot of light appeared before the interposition of the prism, a pro- longed luminous band, formed of a series of extremely bright colours ; this band is called the solar spectrum. The following is the order in which the colours succeed each other when the prism has its base CHAP, vii.] THE COLOURS IN SOURCES OF LIGHT. 307 upwards ; the order is the reverse when the base is turned down- wards. At the lower extremity of the spectrum is a bright, full red, to which succeeds an orange tint, and this passes by imperceptible gradations into a magnificent straw-yellow. Then comes a green of remarkable purity and intensity ; then a greenish blue tint ; and then a decided blue colour, which becomes eventually indigo. After the indigo succeeds violet ; the palest shade of which ends the spectrum. Fio. 234. Decomposition of light by the prism. Unequal refrangibility of the colours of the spectrum. Plate II., Fig. 1, shows the series of colours of the solar spectrum as obtained by a prism filled with bi-sulphide of carbon. Thus a ray of white light is, as we have before stated, the reunion of a series of coloured rays, of which we have mentioned only the principal ; for the transition of one colour into another is made in such an imper- ceptible manner, that there is no abrupt change of colour nor solu- tion of continuity. 1 Such is the phenomenon of the decomposition, or analysis, of white light, which is also called the dispersion of the coloured rays. 1 Except by the very fine black lines, of which we shall speak further on 308 PHYSICAL PHENOMENA. [BOOK in. The dispersion of light by refraction is manifested to us every day by numerous phenomena, some of which the ancients also ob- served, but without suspecting the true cause. Precious stones, such as diamonds, emit lights of different colours ; and the decomposi- tion of light by one of its facets is not one of the least beauties of this precious substance. The rainbow is a phenomenon due to the same cause, as we shall show when we come to the description of meteors. It is the same with the various colours which tint the clouds and atmospheric strata at the time of the sunrise or sunset. Lastly, in glass vessels containing transparent liquids, and in pieces of glass cut as lustres, we see in certain directions iridescent fringes, presenting the colours of the spectrum in all their purity. A second experiment proves that each of the colours of the spectrum is simple, and that the degree of refrangibility increases from the red to the violet. This experiment consists in allowing a narrow beam of the coloured light to pass through a small hole made in the screen, at the point where the red light falls, for instance ; when this is received on a second screen (Fig. 234), it forms a red image at a point which is carefully noted. If, instead of receiving it directly on this screen, a second prism is interposed, the luminous beam is again deviated to a higher point than before. But the new image is red like the first, and of the same form if the prism is properly placed > therefore, the red light of the spectrum cannot be decomposed. The same experiment, repeated with other colours, gives analogous results. All the colours of the solar spectrum then are undecomposable or simple ; but their refrangibility increases, for it is noticed that the distances between the direct images of the colours on the screen and the images obtained by refraction in the second prism are greater as the colour is nearer the extreme violet of the spectrum. If, instead of a prism formed of flint-glass, we use prisms of other solid or liquid refractive substances, we obtain spectra more or less brilliant, and more or less elongated; if the prisms are colourless, the spectra are composod of the above colours, arranged in the same order ; but their proportions that is, the spaces occupied by each of them vary according to the nature of the substance, whilst the order of the colours remains the same. Flint-glass, among solids, gives the most extended spectrum, especially at the violet end, and bi-sulphide of carbon among liquids. CHAP. VII.] THE COLOURS IN SOURCES OF LIGHT. 309 The angle of the prism also influences tha length of the spectrum produced, which is greater as the angle is more obtuse. This fact may be easily proved experimentally, by the aid of prisms having various angles, of which we have spoken above. Thus, white light is decom- posed by refraction into rays differently coloured, and the colour of each of the rays corresponds to a particular degree of refrangibility. This is the analysis of light. But, if such is indeed the composition of light, white light ought to be produced by uniting all the colours of the spectrum in proper proportions. Various experiments confirm this consequence of the analysis FIG. 235. Recompoaition of light by a lens. of light. Most of them are due to Newton, who described them in his " Optics," and they are reproduced in the present day with very slight modifications. The most simple experiment of this nature consists in receiving on a converging lens the solar spectrum produced by a prism. On placing a screen of white paper at the focus where the rays of the different colours are brought to a point (it is the conjugate focus of the point whence the rays emerge from the prism) a white image of the sun is- seen (Fig. 235). By bringing the screen nearer to the lens, the separated coloured rays again reappear, brighter as the screen is gradually brought nearer the lens. On the other hand, if the screen is moved away from the lens, starting from the 310 PHYSICAL PHENOMENA. [BOOK in. point of convergence, the colours again appear, so that the red, for- merly at the bottom, is now at the top ; and the violet, which was at the top, now occupies the lower portion of the coloured band. By using two prisms of the same substance and angle, but placed in reverse positions, as in Fig. 236, the beam of white light which falls on the first prism is divided into differently coloured divergent rays ; but refraction brings them to parallelism on their emergence from the second prism, and, instead of a spectrum, a beam of white light, produced by the reunion of the differently coloured rays, is seen. But the upper edge of the image received on the screen is red, and the lower one violet ; because, among all the rays of white light forming the beam, the mean rays alone give rise to spectra the colours of which reunite, while the extreme rays of the spectrum are not super- posed on any other colour, and recomposition can- not be effected at these points. Two spectra obtained Fio. 236.-Recomposition of light by prisms. by meang Qf fcwQ different prisms and projected in inverse directions on a screen give white light at the place where the colours are superposed. If the spectrum given by one prism is observed with a second prism, a position may be found in which the image received by the eye is round and white. All of these experiments, and others also, are described by .Newton with admirable clearness and simplicity. " Hitherto," he sa,ys, " I have produced white by mixing the colours produced by prisms. Now, in order to mix the colours of natural bodies, take water slightly thickened by means of soap, and agitate it until it becomes frothy. When this froth has come to a state of rest, if you examine it attentively, you will see various colours on the surface of each bubble of which the froth consists. But if you remove to such a distance that you cannot distinguish the various colours, the froth will appear perfectly white." (" Optics," Book I.) CHAP. V1T.] THE COLOURS IN SOURCES OF LIGHT. 311 He also tried to obtain a white tint by the mixture of certain proportions of various coloured powders. Orpiment (orange-yellow sulphide of arsenic) mixed with purple, green, brown, and blue, gave him a composition of an ash-coloured grey, which, when exposed to sunlight and compared with a piece of white paper of the same size placed by the side of the mixture and in the shade, appeared of a brilliant white. Newton explains the grey colour of mixtures of this kind by the absorption of light, and it was to obviate this diminution of brightness that he thought it better to illuminate the composition strongly by the solar rays. Lastly, if a disc, divided into sectors coloured with the prin- cipal colours of the spectrum, is caused to revolve rapidly, in pro- portion as the rotation increases, the indi- vidual colours disap- pear from the eye. The disc ultimately assumes a tint which approximates to white according as the true proportion of the dif- ferent colours has been the better observed. It will be understood that when the succes- sive impressions of the different colours on the retina are confused, in consequence of the rapidity of the movement, it is as if the rays made their impres- sion simultaneously, and the sensation which is produced is that of white. The same experiment can be very simply shown by spinning a top, the surface of which is divided into sectors, in the direction of meridional lines, and painted with the colours of the spectrum. This will appear white or a greyish-white in proportion as its rotation is the more rapid, and the colours will gradually reappear as the motion slackens. The phenomena which we have just described are produced FIG. 237. Recomposition of white light by a revolving disc. 312 PHYSICAL PHENOMENA. [BOOK in. by solar light. But it must not be forgotten that by this term must be understood not only the light due to the rays which arrive directly from the sun, but also all light originating from this body . that of clouds, the atmosphere, and the light of the moon and planets. Analysed by means of a prism, these give spectra of very variable brightness, but their composition as regards coloured rays is precisely the same as that of the solar spectrum. FIG. 238. Unequal refrangibility of various colours. Lights proceeding from other sources, stars, artificial flames, the passage of electricity, either in physical apparatus or in storms, all produce spectra, in which the colours are disposed in the same order as the colours of the solar spectrum. But generally speaking the phenomenon is less brilliant, and, as we shall soon see, it happens in some cases that certain colours are not seen, and are found to be replaced by dark lines. CHAP. VII.] THE COLOURS IN SOURCES OF LIGHT. 313 The experiments which serve to show that the different colours of the spectrum give, by their reunion, white light, are as conclusive when we use the coloured rays of the spectrum, as when the colours of illuminated bodies are employed. This is in itself sufficient to prove that these latter colours are, like those of luminous sources, unequally refrangible. But Newton made direct experiments on this difference by examining with a prism a piece of paper, the two halves of which were differently coloured, the one being red, the other blue. The prism and the paper were placed in front of a window, as shown in Fig. 238, and he noticed that the two halves of the paper appeared unequally deviated, the blue half being lower than the red, so that the paper appeared divided into two parts, the one . no longer a continuation of the other; the reverse happened when the angle of the prism was placed in the contrary direction ; therefore blue is more refrangible than red. FIG. 239. Unequal refrangibilities of simple colours. Newton's experiment. By receiving on a screen of white paper placed behind a lens the images of the same paper illuminated by a candle, Newton like- wise discovered that the screen must be placed at different distances to obtain clear images of the blue half and the red. A black silk cord which was twisted round the paper enabled him to determine with greater facility the place where the image of each colour was formed with distinctness, for, in other places, the images of the threads were confused. For the blue half the distance of the image to the lens was less than in the case of the red half, which again proves that the blue is more refrangible than the red. These two experiments are the first described by Newton in his " Optics." That which we call the natural colour of a body is the colour B B 314 PHYSICAL PHENOMENA. [BOOK in. which is presented to us when it is illuminated by a very pure white light, as by sunlight. If its surface has the property of absorbing all the coloured rays of the spectrum with the exception of one, red for example, the body appears to us red, because it only reflects to our eye the red rays of the spectrum. If this surface absorbs but a limited number of coloured rays, the colour of the body will be that which proceeds from the mixture of the non-absorbed rays ; and this explains the considerable number of colours and shades of bodies, which indeed are much more varied that those of which the spectrum itself is composed. That substance which is able to reflect in an equal proportion all the colours which compose white light, is itself white, and it is brighter according as this proportion is greater. On the other hand, as this proportion diminishes, the white colour diminishes in intensity, and becomes a deeper and deeper grey, lastly attaining black, when the absorption of all the coloured rays of the spectrum is as complete as possible. Black bodies are therefore those whose molecular constitu- tion is such, that all the rays which constitute white light are absorbed by their surface ; whilst white bodies are those which reflect them all, and coloured bodies are those which reflect certain rays and absorb others. If this explanation is true, it is susceptible of many experimental verifications. Let us take a white body and arrange it so that it only receives the yellow rays of the spectrum. This is easily done by placing it in a dark chamber, and admitting only the yellow rays of the spec- trum obtained by means of a prism. The body will appear yellow. It would be red, green, blue, &c., if it were lighted up by red, green, or blue rays. On the contrary, a black body will remain black whatever the colour by which it is illuminated. Lastly, a red body will appear of a deep red, if it is lighted up with the light proceeding from the red rays of the spectrum, whilst it will appear black if we expose it to the rays of other colours. Experiment confirms these results. It is observed, however, that coloured bodies take the tint of the rays which illuminate them, even when these rays are not of the colour of these bodies ; and that this tint is much brighter where there is greater analogy between their own colour and that of the rays with which they are illuminated. Thus " vermilion placed in red appears of a most brilliant red ; in CHAP, vii.] THE COLOURS IN SOURCES OF LIGHT. 315 the orange and yellow, it seems an orange and yellow, but its bright- ness is less. The green rays also give it their colour, but, on account of the great inaptitude of the red to reflect the green light, it appears dark and dull ; it becomes still more so in the blue, and, in indigo and violet, it is nearly black. On the other hand, a piece of dark blue or Prussian blue paper takes an extraordinary brilliancy when exposed to the indigo rays. In green it becomes green, but not very bright ; in red, it appears nearly black." (Sir John Herschel.) Newton's theory must therefore be thus understood : that the sur- faces of coloured bodies are generally apt to reflect the rays of a certain colour in a much greater quantity than those of other rays ; and that gives them their predominant colour. These surfaces, never- theless, do not entirely absorb the other rays, and that prevents them from being perfectly black when they are illuminated by coloured lights different from those which they generally reflect. The colours of bodies are seldom identical with those composing the solar spectrum, as they are principally composite ; evidence of which can be obtained by submitting them singly to analysis by the prism. This analysis gives a spectrum formed of various simple colours, the mixture producing the particular colour observed. It is sufficient to look at a coloured object, as a flower or a piece of dyed stuff, through a prism, to see that the edges of the image, parallel to the edge of the prism, are banded like the rainbow. If, instead of illuminating a coloured body by the white light of the sun, or by one or other of the simple colours of which this light is composed, we use other luminous sources, such as the light of a lamp or artificial flames, the colour is found to be altered. Thus we all know that green appears blue by the light of a lamp. But let us first finish what we have to say of Newton's theory concerning the colours of non-luminous bodies. In endeavouring to penetrate more deeply into the causes of this phenomenon, Newton supposed that the incident light is decomposed at the surface ; one part is absorbed, extinguished in opaque bodies and transmitted in transparent ones ; the other part is reflected by the superficial molecules, at a very little depth in opaque bodies, and at any depth in transparent ones. This explains why, in the latter, the colour of transmitted light is generally different from that of reflected light. For example, we have seen that gold reduced to extremely B B 2 316 PHYSICAL PHENOMENA. [BOOK in. thin leaves allows a greenish blue light to pass through it, while its reflected colour is yellow, or reddish yellow. " Halley, having descended to a depth of several fathoms in a diving bell, saw that the upper part of his hand, on which fell the solar rays after passing through a glazed opening, was of a crimson colour ; the under part, which was illuminated by light reflected from deep water, appeared green; whence Newton concluded that water allowed the red rays to pass through it and reflect the violet and blue." (Daguin.) We must distinguish between light reflected regularly, or specu- larly, and that diffused light which is scattered from the surfaces of bodies. The first has nothing to do with the colour of bodies ; and indeed we know that perfectly polished bodies represent the images of the bodies they reflect, coloured like the bodies themselves; while their own colour remains unperceived. To what modification is light which is diffusely reflected sub- mitted ? How does the structure of bodies act on the different coloured rays, so as to reflect some and extinguish others ? Is it the form, density, refractive power of the molecules, or, rather, is it these united elements which give place to the phenomenon of various colorations? These are excessively subtle questions, which cannot be answered with exactitude in the present condition of science. CHAP, viii.] COLOURS. 317 CHAPTER VIII. COLOURS. Classification of colours- Tones and scale of the colours of the solar spectrum, after the method of M. Chevreul Chromatic circles of pure and subdued colours ; tones and scales Complementary colours. THE white light of the sun, decomposed by means of a prism, produces a series of colours which correspond, as we have seen, to different degrees of refrangibility. These colours are, so to speak, infinite in number, as they pass from one end of the spectrum to the other by imperceptible shades; but it is customary to distinguish seven principal colours, the names of which, taken in their natural order, form a crude Alexandrian verse : Violet, indigo, blue, green, yellow, orange and red. Some physicists, believing in the possibility of reproducing some of these colours by the mixture of others, green, for example, being obtained by the juxtaposition of yellow and blue, violet by that of blue and red, and so on, have endeavoured to prove that the spec- trum is only formed of three elementary colours. According to Brewster these colours would be red, yellow, and blue ; according to Young, red, green, and violet. The proportions in which they are mixed in the different parts of the spectrum would account for the variety of shades of which ifc is composed. In the present day, these theories are rejected ; the experiments by which they were supported having been proved to be inexact. All the colours of the spectrum are therefore simple colours, the number of which can be considered as infinite ; although, in practice, they are reduced to seven principal colours. White is not a simple colour, but, on the contrary, the most complex of the composite colours. Black is not a colour; it is 318 PHYSICAL PHENOMENA. [BOOK m. the complete absence of all light. As to the composite colours which natural bodies present to us, they are due to combinations, in various proportions, of all the elementary colours. A very simple experiment proves that the combination of all the rays of the spectrum is necessary to produce perfect light. It consists in intercepting a certain portion of the spectrum before it falls on the lens which is used for the recomposition of the light. Thus, if the violet be intercepted, the white will acquire a tinge of yellow ; if the blue and green be successively stopped, this yellow tinge will grow more and more ruddy, and pass through scarlet to orange and blood-red. If, on the other hand, the red end of the spectrum be stopped and more and more of the less refrangible por- tion thus successively abstracted from the beam, the white will pass first into pale, and then to vivid green, blue-green, blue, and finally into violet. If the middle portion of the spectrum be intercepted, the remaining rays, concentrated, produce "various shades of purple, crimson, or plum-colour, according to the portion by which it is thus rendered deficient from white light ; and, by varying the intercepted rays, any variety of colours may be produced ; nor is there any shade of colour in nature which may not thus le exactly imitated with a brilliancy and richness surpassing that of any artificial colouring. The number of composite colours, obtained by the combination of simple colours, or the different coloured rays of the spectrum, increases to an almost indefinite amount. But we shall presently see that it is possible to increase them still more, either by the addition of a certain quantity of white light, or by the mixture of black in various proportions. Two colours which, by their combination, produce white are called complementary colours. There is a very simple method of determining the groups of colours which possess this property : it consists in the interception, as it issues from a lens, of a portion of the convergent beam about to meet at the focus. This portion received on a second prism will be deviated, and will give a colour which will be evidently complementary to the colour produced at the focus of the lens, as before their separation they formed white. Helmholtz discovered, by a different process, which consisted in CHAP, viii.] COLOURS. 319 receiving the spectrum colours through slits in a screen and then concentrating them by a lens, that there is an indefinite number of groups of two colours susceptible of forming, by their mixture, perfect white. The following are some of the results obtained by that physicist : Complementary Colours. Intensities of the two Colours. Violet greenish yellow ..... 1 10 Indigo yellow 1 4 Blue orange 1 1 Greenish blue red 1 0'44 The numbers which follow these groups measure the relative in- tensities of each of the colours and refer to a bright light; they vary when the incident light itself varies in intensity. Helmholtz has devised an extremely simple method of studying the resultant of the mixture of two colours, which are placed on two adjacent discs. When an unsilvered glass is placed vertically between them, one of the discs is seen directly ; the other through the transparent plate. Moreover, the first is seen a second time, by reflection. If it is then placed in such a position that its image appears superposed upon the disc seen through the glass, the two colours will be found naturally blended, and one can easily judge of the shade produced by their composition. Thus, also, two discs, coloured, the one by chrome yellow, the other by cobalt blue, produce pure white ; which proves that these colours are complementary. To sum up, a simple or composite colour always has its comple- mentary colour ; moreover, it has an infinity of them, for if to the complementary colour we add white light in variable proportions, the resultant can only be white. But this rule can only be applied to clear colours, that is to say, those which are not altered by any proportion of black ; in this case, instead of perfect white, a grey or greyish- white would be obtained. Lastly, the mixture of complementary colours only produces white when it is not a material mixture ; if material colours are used, moistened in whatever way, or even in a pulverulent state, the mixture will only give a more or less decided grey. If the colours, whether simple or composite, are indefinite in number ; if the mix- ture in different proportions of white or black again multiplies that 320 PHYSICAL PHENOMENA. [BOOK in. number ; it is no less true that the eye can only appreciate a limited quantity. Yet, if it were possible to collect in one scale all the shades of colours presented to us by Nature, arid to distinguish them from each other, we should be astonished at the richness and magnificence of that palette. The leaves and flowers of plants, the skins of animals, the brilliant colours which the feathers of birds possess, the wings of butterflies and other insects, shades of different minerals and shells, would furnish elements of the innumerable series of natural colours, and would pass from one shade to another by imperceptible gradations. Thus we could have a classification of colours derived from natural objects. Colours used in the arts are probably much more restricted ; we can nevertheless form an idea of their number by this fact that the Komans used, it. is said, more than 30,000 tints in their mosaics. But even this number, precisely because it is considerable, causes the want to be felt of a proper classification of colours and their shades, which would enable them to be defined by showing their relationship to a fixed type, determined once for all. We all know that, in industries and the arts, the nomenclature of colours is very arbitrary or, at least, varies in one art or industry from another : the names are borrowed from natural objects, minerals, flowers, fruits, and animals, but there is no line of gradation between them. In order to obviate the inconveniences resulting from this confusion, M. Chevreul, celebrated for his chemical labours and his study of colours, proposed a classification of colours and their shades. The principles and basis of this we will now describe. According to M. Chevreul, a substance possessing any one of the colours of the spectrum can only be modified in four different ways : 1. By white, which reduces it in intensity. 2. By "black, which diminishes its specific intensity. 3. By a certain colour, which changes the specific property with- out rendering it less bright. 4. By a certain colour which changes the specific property and renders it less bright, so that if the effect is carried to the highest degree, it results in black or normal grey, represented by black mixed with white in a certain proportion. To express all these modifications, M. Chevreul uses the following- expressions, which once defined can no longer be equivocal : CHAP, viii.] COLOURS. 321 He calls the tones of a colour the different degrees of intensity of which this colour is susceptible, according as the matter which presents it is pure or simply mixed with white or black ; the scale, the whole of the tones of the same colour ; the shades of a colour, the modifications which it undergoes by the addition of another colour which changes it without rendering it less bright ; lastly, the subdued scale, the scale whose light tones as well as the dark ones are tarnished with black. M. Chevreul obtained a scale sufficiently extensive for the principal colours and their tones and shades by the following means : Having divided a circle into seventy-two equal sections, he placed, at equal distances, three patterns of tinted wool, one red, another yellow, the third blue ; as fresh and pure as possible, and of the same intensity of colour. Between these three sections, and at an equal distance from each, he placed orange between the red and yellow, green between this latter and the blue, and violet between the blue and red. By continuing in the same manner succesive intercalations of intermediate colours and shades, he at last ob- tained what he called a chromatic circle of fresh colours, so as to reproduce the spectrum of solar light. When these seventy-two shades were obtained, he took each of them to make a complete scale formed by the addition of increasing quantities of white and black, in order to have ten sub- dued tones and ten tones of the same colour rendered clearer by white. Each scale therefore comprised, from pure white to pure black, which were the extremities, twenty different tones, of which the pure colour is the tenth, starting from white. 1 From, this first combination there are already 1,440 different tones, all deduced from the chromatic scale of pure colours : but in successively subduing the seventy-two tones of this circle by the addition of 1, 2, 3, &c. tenths of black, nine circles of subdued colours are formed ; and each of the seventy-two tones which they comprise becoming in its turn the type of a scale of twenty new ones proceeding from white to black, there follows, for the complete series, a scale of 14,400 tones, to which must be again 1 " Des Couleurs et de leurs Applications aux Arts industriels d 1'aide desCercles chromatiques." The text of this work is accompanied by twenty-seven steel engravings, coloured by Eene Digeon. C 322 PHYSICAL PHENOMENA. [BOOK in. added the twenty tones of normal grey, which make 14,420 different tones. It is evident that such an extensive scale ought to suffice for most of the scientific and industrial applications, and will most frequently exceed the wants of artists. Unfortunately, the rigo- rously exact material reproduction of all these colours is of great difficulty, and it is no less difficult to preserve the types when once they are obtained. The chromatic construction of M. Chevreul must be reproduced in unalterable colours, for instance, in pictures enamelled on porcelain. Scientific research would not be less interested than the arts to possess fixed types, to which the colours of natural objects, so often changed by time, would be brought back again by the help of the order of numbers, and thus made easy of reproduction. M. Eadde has recently patented a colour gauge, with about 10,000 shades of colour, and he claims for it: 1. That he can reproduce the colours in it with absolute accuracy. 2. That as the colouring material is worked into the texture of the substance in which it appears, it is indestructible and unalterable. CHAP, ix.] LINES OF THE SOLAR SPECTRUM. 323 CHAPTER IX. LINES OF THE SOLAR SPECTRUM. The discoveries of Wollaston and Fraunhofer ; dark lines distributed through the different parts of the solar spectrum Spectral lines of other luminous sources Spectrum analysis ; spectrum of metals ; inversion of the spectra of flames Chemical analysis of the atmosphere of the sun, of the light of stars, nebulas? and comets. "VTEWTON", in studying the different parts of the solar spectrum, -L^ by means first of circular and afterwards of elongated apertures, could not distinguish any indication of the precise limits of its various colours : they appeared to blend witli" one another in an imperceptible manner and without interruption. He was persuaded^ however, by his experiments, that the coloured rays which constitute white light possess, from the extreme red to the extreme violet, all possible degrees of refrangibility, and he regarded each of these rays as simple and homogeneous, imagining that the light de- composed by the prism was spread out in' a continuous manner throughout the whole spectrum. It is curious that Newton did not go further that he did not reduce the aperture to a fine line of light, in which case the colours would have been seen in all their purity, and would not have been mixed and confused by the overlapping of each colour on its neighbour. This step in advance was reserved for the beginning of the present century, and then a great discovery was made. It was found that here and there in the different colours there were gaps in the light ; in other words, that there were dark lines in the sun's spectrum. This was first detected by Wollaston in 1802, but the discovery was independently made and largely elaborated by Fraunhofer. C o 2 324 PHYSICAL PHENOMENA. [BOOK in. Joseph Fraunhofer, who was born in 1787, at Straubing, a little town in Bavaria, was the son of a glazier. He was at first a worker in glass, but, by labour and perseverance, he succeeded in meriting the reputation of being the most ingenious and learned optician of our century. Fraunhofer was not satisfied with bringing the con- struction of optical instruments to a perfection then unknown ; but, being a consummate observer, he employed the instruments which he manufactured, to make various discoveries, amongst which, that to which we have referred is one of the most curious and most fruitful in its results. In the attempt to measure the refractive indices of the coloured rays, and to find particular points in the spectrum capable of being used as marks, Fraunhofer discovered the great fact, that the light of the solar spectrum is not continuous, but that it is divided by a multitude of fine black lines, which form so many sharp inter- ruptions in the luminous band. In this experiment, which requires the most delicate manipula- tion, he made use of a prism of pure flint-glass, free from striae, upon which a beam of sunlight, which had previously passed through a very fine slit parallel to the edge of the prism, was caused to fall. The spectrum thus obtained, when observed by means of a magnifying glass, showed him, instead of a continuous band in which the colours blended into each other without interruption, a ribbon crossed in the direction of its width, with numerous dark and black lines very unequally spread over the spectrum. The distribution of these lines did not appear to have any relation to the tints of the principal colours. Fraunhofer varied this experiment in a variety of ways ; but, as long as the luminous source was sunlight, either direct or re- flected, the same dark lines always appeared, and they preserved the same relations of order and intensity. If, instead of a flint-glass prism, a prism of any other substance, liquid or solid, be employed, the distances between the lines vary, but otherwise they always occupy the same positions relative to the colours of the spectrum. The illustrious optician of Munich studied this remarkable phenomenon with infinite care : he determined, with great precision, the positions of 580 dark lines, and, for use as marks and com- parison, he distinguished among this number eight principal lines, CHAP. IX.] LINES OF THE SOLAR SPECTRUM. 325 which he called by the first letters of the alphabet. The solar spectrum of Plate II. shows the position of these lines, as they were obtained with a prism filled with bisulphide of carbon. The lines A, B, c, are all found in the red, the first at the extremity of the spec- trum, the second at the middle of the red, and the third at a little distance from the orange. The double line D forms nearly the limit of the orange near thegreen ; E in the middle of this last colour ; F at the middle of the blue ; G and the double line H are, one at the end of the indigo towards the blue, the other at the end of the violet. Since 1817, when Fraunhofer observed the lines which bear his name, new dark lines have been no- ticed, and, at the pre- sent day, more than 2,000 have been mapped by Kirch- hoff and Angstrom. FIG. 240. A fragment of the solar spectrum. 326 PHYSICAL PHENOMENA. [BOOK m. The more recent researches of Rutherford and Lockyer have in- creased the number of the definitions indefinitely. We obtain some idea of this multitude of lines in examining Fig. 240, which reproduces a portion of the solar spectrum, com- prised between the principal lines D and E. Sir David Brewster, who was much occupied in these researches, in addition to the usual precau- tions indispensable in obtaining a clear and pure spectrum, increased the sensibility of his sight by using ammonia gas, the dissolving action of which destroyed the fluid veil which covers the surface of the eye. Fraunhofer did not confine himself to the study of the lines which break the continuity of light in the solar spectrum ; he also applied his beautiful method of observation to the spectra of other sources of light. And at first, as was to be supposed, he found the same lines in the bodies which reflected solar light to us, such as clouds or pure sky, moon and planets : the lines were the same, but they possessed less intensity. By observing the spectrum of the brightest star, Sirius for example, he found it also crossed by dark lines : but much less numerous and not distributed in the same manner as in the solar spectrum; moreover, he discovered that the lines varied in the various stars. Lastly, he applied the same method of observa- tion to the electric light; and, instead of dark lines, he saw in this spectrum a certain number of bright lines. Such are the celebrated experiments which served as starting points to a series of brilliant discoveries, the whole of which now constitute one of the most important branches of optics, and aid chemistry by the most ingenious and delicate method of analysis. We will now endeavour to give some idea of this method, known as spectrum analysis. Solar and stellar spectra are, as we have seen, striped with dark lines which indicate interruptions in the emission of light, and prove, contrary to what was at first believed, that in the light proceeding from these light sources there are not rays which possess every possible degree of refrangibility. The contrary effect takes place in the spectra of all incandescent bodies, either in the solid, liquid, or densely gaseous condition : the spectra of these lights are continuous : there are no breaks in the spectrum. Vapours and gases, however, which are not dense give different results. If we introduce into an artificial flame, such as a jet of gas CHAP. IX.] LINES OF THE SOLAR SPECTRUM. 327 or a spirit-lamp, certain metallic substances, which the high tempera- ture of the source can convert into vapour, continuous spectra are no longer observed, but bright lines separated by wide, comparatively dark, intervals : Fraunhofer had already remarked this. Gases also, rendered incandescent by the electric spark, give similar spectra. Since his time, the fact has been studied in all its phases and by various methods. It has been discovered that the bright lines of metallic vapours, and gases when not very dense, vary, in number FIG. 241. Spectroscope. and position, according to the metal or gas ; and the spectra change as the pressure of the gas is altered. To study spectra of this kind, physicists employ instruments called spectroscopes. Fig. 241 represents one of these. The flame of a gas-lamp is placed in the axis of a lens to which light pene- trates through a narrow slit ; the slit and lens forming what is called the collimator. The slit being in the focus of the lens, the light passes through the prism in a parallel beam. The light which 328 PHYSICAL PHENOMENA. [BOOK in. passes through the refractive medium is made to form an image of the slit at the focus of another lens, which image is examined by an eyepiece. This arrangement, which is a great improvement upon that adopted by Fraunhofer, is due to an English optician of great celebrity, Mr. Simms. To obtain the spectrum of the vapour of a metal, for instance that of sodium, we introduce into the flame of a lamp a platinum wire, impregnated with a concentrated solution of salt, of which this metal forms the base, sea-salt (chloride of sodium) for instance. We soon perceive a yellow ray of great intensity and sharp out- line. This is the only line of the sodium spectrum. (Plate II.) The vapour of lithium gives two principal lines, one a pale yellow, the other red and bright; potassium gives two characteristic lines, red and violet, accompanied by yellow and green lines ; calcium gives a very bright green line, one orange, and one blue ; strontium gives eight lines, six of which are red, one orange and one blue ; barium, two green lines ; thallium, one green line, remarkable for its brilliancy. The vapours of a great number of simple bodies have thus been studied, the bright lines of their spectra discovered, and their position fixed. No two vapours or gases have the same spectrum. Hence results a new method of analysis, which is so delicate that a millionth part of a milligramme of sodium is sufficient to show immediately the characteristic yellow ray of the spectrum of this metal. Two German chemists and physicists, MM. Kirchhoff and Bunsen, were the first to bring spectrum analysis to a high degree of precision. " I take," says M. Bunsen, " a mixture of the chlorides of alkaline metals and earths, sodium, potassium, lithium, barium, strontium, and calcium, containing at most a hundred thousandth of a milli- gramme of each of these substances ; I place this mixture in the flame and observe the result. At first, the intense yellow line of the sodium appears on a background of a continuous very pale spectrum ; when it begins to be less sensible and the sea salt is volatilized, the pale lines of the potassium appear ; they are followed by the red line of the lithium, which soon disappears, whilst the green rays of the barium appear in all their intensity. The salts of sodium, potassium, lithium, and barium are therefore entirely volatilized ; a few instants after, the calcium and strontium CHAP ix.] LINES OF THE SOLAR SPECTRUM. 329 lines come out, as if a veil has been removed, and gradually attain their form and characteristic brilliancy. By the help of spectrum analysis, the presence of sodium' has - been, determined in the air and the dust floating about in a room/ The sensibility of the reaction of this metal is so great, that spectro- scopic observers are obliged to take all kinds of precautions to prevent the appearance of the sodium line ; even if we dust a book near the instrument, the yellow sodium line immediately appears. Five new metals have been discovered by this method : the two first, csesium and rubidium, by MM. Bun sen and Kirchhoff ; the third, thallium, by Mr. Crookes and M. Lamy ; the fourth, indium, by MM. Eeich and Eichter; the fifth, gallium, so recently that it is difficult to say to what family of elements it belongs. Prof. Odling's discourse at the meeting of the British Association at Plymouth in 1877, contains the latest information with reference to it. The name caesium is given from the two blue lines in its spectrum ; rubidium from the red lines which characterize the spectrum of this metal; the name thallium recalls a beautiful green line, and that of indium a blue line near the indigo. In these various lines then we have the power of detecting the gases and the vapours of the various elements ; but this is not all Eecent researches undertaken by Frankland and Lockyer have shown that certain spectra undergo great changes by varying the pressure, and that some lines in various spectra widen out, and become diffused from increase of pressure, which also, when long continued, changes -a typical gaseous spectrum hydrogen, for instance into a perfectly continuous one, similar to those of solids or liquids. Erankland and Lockyer have also shown that the various spectra produced by varying the pressure can be, to a certain extent, repro- duced by varying the quantity of any given vapour in a mixture. Such researches as these give us ground for hoping that in time this method of analysis may be employed quantitatively as well as qualitatively, and explain Bunsen's experiment to which we have before referred. But we do not confine the power of the spectroscope to terres- trial matter ; it has gone further : problems can be investigated and solved by its means which had appeared inaccessible to human in- vestigations ; the study of the chemical composition of the heavenly 330 PHYSICAL PHENOMENA. [BOOK in. bodies, that of the sun and stars these suns so prodigiously distant from us ; of nebulae, which telescopes show us plunged in the abysses of the ether at such distances that the imagination can scarcely fathom the depth, and of comets. Let us show in a few words how this has been done. If we place a jet of gas before the slit of a spectroscope, and lessen it so that it is scarcely perceptible, and burns with a bluish flame, we observe that, in this condition, it will give no spectrum ; there is complete darkness behind the prism. But, if a metallic salt is introduced into the flame, sea-salt for instance, the yellow ray of the sodium immediately appears, as we have just seen. If, at the same time, and in the same instrument, we introduce a solar ray in such a manner that the sodium spectrum and the solar spectrum are superposed, a perfect coincidence will be noticed in the position of the sodium yellow ray, and Fraunhofer's double dark line D. Now, for the sunlight let us substitute the intense light known as Drummond's light obtained by heating a piece of lime in a gas burner into which a current of oxygen gas is introduced. The spec- trum of this light, seen alone, shows a bright spectrum of perfect continuity ; that is, containing none of the dark lines of the solar spectrum. But if we interpose between the Drummond's light and the slit of the spectroscope a sodium flame, the yellow sodium line now gives place to a black line occupying precisely the same posi- tion as the bright line did when the brighter light source was not behind it. It is this phenomenon which M. Kirchhoff calls the "inversion of the spectra of flames." It has been proved in regard to a great number of metallic spectra. " If we cause," he says, " a solar ray to pass through a flame of lithium, we see in the spectrum, in place of the usual red line, a dark line, which rivals by its sharpness the most characteristic of Fraunhofer's lines, and which disappears on removing the lithium. The reversal of the bright lines of other metals is not so easily effected ; nevertheless, M. Bunsen and myself have been fortunate enough to invert the brightest lines of potassium, strontium, calcium, and barium. . . ." Now, what inference is to be drawn from this singular fact ? It CHAP, ix.] LINES OF THE SOLAR SPECTRUM. 331 is that metallic vapours, endowed with the property of abundantly emitting certain coloured rays, in preference to others, absorb these same rays when they emanate from a more intensely luminous source and traverse them. Thus, sodium light, which emits yellow rays, absorbs the yellow rays of Drummond's light on their passage through it. Hence results the black line, which occupies the same position in the continuous spectrum which the bright sodium line previously held. If this absorption is a general fact, it must be concluded that the black lines observed in the solar spectrum indicate the reversal of as many bright lines by metallic vapours in the atmosphere of the sun. This atmosphere, to us, acts the part of the sodium flame, and the bright light of the sun's body that of the Drummond's light in the same experiment. This magnificent discovery, which has at one bound enabled us to become familiar with the constituents of the atmospheres of all the stars of heaven which are bright enough to show a spectrum, is generally accorded to Kirchhoff and Bunsen, but the credit of it is really due to an Englishman, Professor Stokes, who taught it as early as 1852, while Kirchhoff and Bunsen did not announce their discovery till 1859. The observational and experimental foundations on which Pro- fessor Stokes rested his teaching were as follows : 1 (1) The discovery by Fraunhofer of a coincidence between his double dark line D of the solar spectrum and a double bright line which he observed in the spectra of ordinary artificial flames. (2) A very rigorous experimental test of this coincidence by Professor W. H. Miller, which showed it to be accurate to an astonishing degree of minuteness. (3) The fact that the yellow light given out when salt is thrown on burning spirit consists almost solely of the two nearly identical qualities which constitute that double bright line. (4) Observations made by Stokes himself, which showed the bright line D to be absent in a candle-flame when the wick was snuffed clean so as not to project into the luminous envelope, and from an alcohol flame when the spirit was burned in a watch-glass. And 1 See Sir W. Thomson's Address as President of the British Association in 1871. 332 PHYSICAL PHENOMENA. [BOOK m. (5) Foucault's admirable discovery (EInstitut, Feb. 7, 1849), that the voltaic arc between charcoal points is " a medium which emits the rays D 'on its own account, and at the same time absorbs them when they come from another quarter." The conclusions, theoretical and practical, which Professor Stokes taught, and which Professor Thomson gave regularly afterwards in his public lectures in the University of Glasgow, were : (1) That the double line D, whether bright or dark, is due to vapour of sodium. (2) That the ultimate atom of sodium is susceptible of regular elastic vibrations, like those of a tuning-fork, or of stringed musical instruments; that, like an instrument with two strings tuned to approximate unison, or an approximately circular elastic disk, it has two fundamental notes or vibrations of approximately equal pitch ; and tbat the periods of these vibrations are precisely the periods of the two slightly different yellow lights constituting the double bright line D. (3) That when vapour of sodium is at a high enough temperature to become itself a source of light, each atom executes these two fundamental vibrations simultaneously ; and that therefore the light proceeding from it is of the two qualities constituting the double bright line D. (4) That when vapour of sodium is present in space across which light from another source is propagated, its atoms, according to a well-known general principle of dynamics, are set to vibrate in either or both of those fundamental modes, if some of the incident light is of one or other of their periods, or some of one and some of the other ; so that the energy of the waves of those particular qualities of light is converted into thermal vibrations of the medium and dispersed in all directions, while light of all other qualities, even though very nearly agreeing with them, is trans- mitted with comparatively no loss. (5) That Fraunhofer's double dark line D of solar and stellar spectra is due to the presence of vapour of sodium in atmospheres surrounding the sun and those stars in whose spectra it had been observed. (6) That other vapours -than sodium are to be found in the atmospheres of sun and stars by searching for substances producing CHAP, ix.] LINES OF THE SOLAR SPECTRUM. 333 in the spectra of artificial flames bright lines coinciding with other dark lines of the solar and stellar spectra than the Fraunhofer line D. Studying from this point of view the dark lines of the solar spectrum, Bunsen and Kirchhoff were enabled to prove the coin- cidence of a great number of them with the bright lines of certain metals. For example, the seventy bright lines of iron, different in colour, width, and intensity, coincide, in every point of view, and precisely in the same way, with the seventy dark lines of the sun ; which makes it impossible to doubt that, in the solar atmosphere, iron exists in the state of vapour. In Fig. 240, a certain number of these lines are seen, marked Fe. The same savants discovered the presence of nine other simple bodies in the atmosphere of the sun, hydrogen, copper, zinc, chromium, nickel, magnesium, barium, calcium, and sodium; and it is probable that to this list we may add cobalt, strontium, and cadmium. This work has recently been o extended by the researches of Angstrom and Thalen. From the absence of the characteristic lines of other metals, such as gold, silver, platinum, &c. in the solar spectrum, it was believed, at first, that these bodies are not found in the sun, at least in the outer strata which form its atmosphere ; but this conclusion is too absolute, as is shown by new researches due to M. Mitscherlich, which may probably be explained by the observations of Frankland and Lockyer before alluded to. We sum up then what we have stated, as follows : Solids, liquids, and vapours and gases when dense, give us con tinuous spectra without bright lines. Vapours and gases when not dense give us continuous spectra with bright lines. Changes in the lines composing the spectrum, and in the thickness of the lines, are brought about by changes of pressure. Gases and vapours absorb those rays which they themselves emit if a brighter light source is behind them ; this absorption is continuous or selective, as the radiatimi is continuous or selective. This is one among many results brought about by employing many prisms to give considerable dispersion, and therefore a very long spectrum. There is another which reads almost like a fairy tale ; so impossible does it at first sight appear, that we can thus measure the velocities of the stars in their paths, or the rate at 334 PHYSICAL PHENOMENA. [BOOK in. which solar storms travel by such means : but of this, more presently. One of the recent advances in the application of the spectroscope to the examination of the celestial bodies arises from the following considerations : The light from solid or liquid bodies is scattered broadcast, so to speak, by the prism into a long band of light, called a con- tinuous spectrum, because from one end of it to the other the light is persistent. The light from gaseous and vaporous bodies, on the contrary, is most brilliant in a few channels ; it is husbanded, and, instead of being scattered broadcast over a long band, is practically limited to a few lines in the band in some cases to a very few lines. Hence, if we have two bodies, one solid or liquid and the other gaseous or vaporous, which give out exactly equal amounts of light, then the bright lines of the latter will be brighter than those parts of the spectrum of the other to which they correspond in colour or refrangibility. Again, if the gaseous or vaporous substance gives out but few lines, then, although the light which emanates from it may be much less brilliant than that radiated by a solid or liquid, the light may be so localized, and therefore intensified, in one case, and so spread out, and therefore diluted, in the other, that the bright lines from the feeble light source may in the spectroscope appear much brighter than the corresponding parts of the spectrum of the more lustrous solid body. Now here comes a very important point : supposing the continuous spectrum of a solid or liquid to be mixed with the dis- continuous spectrum of a gas, we can, by increasing the number of prisms in a spectroscope, dilute the continuous spectrum of the solid or liquid body very much indeed, and the dispersion will not seemingly reduce the brilliancy of the lines given out by the gas : as a consequence, the more dispersion we employ the brighter relatively will the lines of the gaseous spectrum appear. Let us apply this to the prominences seen round the sun in an eclipse. The reason why we do not see the prominences every day is that they are put out by the tremendous brightness of our atmosphere near the sun, a brightness due to the fact that the particles in the CHAP, ix ] LINES OF THE SOLAR SPECTRUM. 335 atmosphere reflect to us the nearly continuous solar spectrum. There is, as it were, a battle between the light proceeding from the promi- nences and the light reflected by the atmosphere, and, except in eclipses, the victory always remains with the atmosphere. We see, however, in a moment, that by bringing a spectroscope on the field we might turu the tide of battle altogether, since the prominences are gaseous, as the reflected continuous spectrum is dispersed almost into invisibility, the brilliancy of the prominence lines scarcely suffering any diminution by the process. This reason- ing was first successfully put to the test by a distinguished French physicist, M. Janssen, in 1868. Is it not wonderful, that the dispersion of light not only explains with such accuracy the chemical composition of the bodies whence it emanates, and preserves, after a passage of millions upon millions of miles, the traces of absorption of various rays, a certain indi- cation of the presence of simple bodies suspended in an atmosphere which astronomers only suspected, and the existence of which is thus confirmed, but enables us to measure velocities, and even to study the meteorology of our sun ? as we shall see shortly. Spec- trum analysis thus applied to sun, stars, planets, nebulae, comets, furnishes valuable indications as to the intimate constitution of these bodies, and solves problems which the most powerful optical instruments would doubtless never have unravelled. 1 It is thus that the sciences mutually help each other: progress realized by one of them is nearly sure to promote new discoveries in others. 1 For fuller particulars on this branch of the inquiry see " The Heavens," a companion work to this. 336 PHYSICAL PHENOMENA. . [BOOK in. CHAPTEE X. SOLAR RADIATIONS. CALORIFIC, LUMINOUS, AND CHEMICAL. Divisions of the spectrum ; maximum luminous intensity of the spectrum Obscure or dark rays ; heat rays : chemical rays Fluorescence, calorescence. THE different parts of the solar spectrum are distinguished not only by the unequal refrangibility of the rays which produce them, by their colours, and by the greater or less vividness of their brilliancy, but by their warming or calorific action, as well as by their power of modifying, to different degrees, certain substances in a chemical point of view. When the luminous intensities of the seven principal colours are compared together in the same spectrum, we at once perceive that the brightest portion is found in the yellow. From this point the brightness diminishes towards the red and the violet. We see, moreover, that the colours can be naturally divided into two classes : the first comprising the more luminous colours, red, yellow, and green; the second, the darker colours, blue, indigo, and violet ; there are continuations of the spectra in both directions which are invisible to the eye. Thus we have the ultra-red and the ultra-violet rays. In fact we must look upon the spectrum as composed of heat-rays, light-rays, and chemical rays, the second only of which are completely visible to us. A very simple experi- ment enables us to judge of the difference which exists between the illuminating powers of different colours : if we take the pages of a book, and receive the spectrum on the printed portion of the paper, we shall find that the characters can be easily read in the orange, yellow, and green; whilst it is scarcely possible to read those which receive the other colours. According to Fraunhofer, who studied photometrically the CHAP, x.] SOLAR RADIATIONS. 337 luminous intensities of the colours of the spectrum, the maximum brightness is found between the lines D and E; but this point is nearer D, and its distance from that line is about the tenth part of the total interval D E. More precise methods have deter- mined numerically the illuminating power of the spectrum at the points where it is cut by the eight principal lines of Fraunhofer. Taking the maximum brightness at a thousand, the following are the luminous intensities : Colours. Luminous intensities. Lines. Extreme red imperceptible A Red 32 B Red . . 94 Orange 640 D Yellow 1000 Green 480 E Blue 170 F Tndigo 31 G Extreme violet 6 H This refers only to the relative intensities of the colours of the solar spectrum, not to those of other spectra, nor to the similar colours of various substances. These are pure colours, without mixture of white or black: mixtures of black with primitive colours include, as we have seen in explaining the classification of colours by M. Chevreul, all the category of dark colours called browns, the tints of which are no longer those of the corresponding ones in the spectrum : the same holds with clear and bright colours obtained by increasing proportions of white. Some time ago the question arose whether the heat of the solar rays was equally distributed throughout the whole length of the spectrum, or if, on the contrary, the differently coloured rays, be- sides their difference of luminous intensity, also possessed unequal calorific powers. Some experiments made by the Abbe Eochon led to the belief that the most luminous rays were also the most calorific, so that the maximum heating was in the yellow; but other physicists asserted that this maximum was in the red, or rather beyond the extreme red. According to Seebeck (1828), all these opinions are true, because heat, transmitted by the coloured rays, being unequally absorbed according to the nature of the prism, the D D 338 PHYSICAL PHENOMENA. [BOOK m. position of the maximum calorific rays must depend on the sub- stance of this latter ; and indeed, this physicist showed that the most intense calorific rays are those of the yellow, orange, red, or extreme red, according as the solar light is dispersed by the aid of prisms formed with water, sulphuric acid, ordinary glass, or English flint-glass. As rock-salt absorbs little or no heat, either dark or luminous, the calorific powers of the differently coloured rays can be best compared by using a prism of this substance. Working thus, Melloni proved that the temperature of these rays increases in passing from the violet to the red; and that the maximum calorific effect is produced beyond the red, at a distance from the extreme limit of the red equal to that which exists between this and the yellow. Beyond this point the heat decreases; but it is still per- ceptible when it has reached a distance from the red equal to the whole extent of the luminous that is, the visible spectrum. This remarkable result acquired a fresh degree of importance when the solar rays were studied from another point of view. We all know the influence of sunlight on material colours, when these colours are given either to stuffs, paper, wood, or other organic substances. Coloured curtains fade with daylight ; yellow cotton or linen is bleached when exposed to the sun. We understand, in the present day, how necessary light is to the complete develop- ment of health, and even to the life of vegetables and animals. Now, these multiple influences, to which we shall have occasion to return, consist in a series of chemical actions in the decomposition or combination of substances. Chlorine and hydrogen, which in the dark have no action on each other, combine when exposed to the light, forming hydrochloric acid. If the flask which contains them is exposed to the diffused daylight, the combination is effected slowly; in the solar rays, it takes place suddenly, and explosion is the result. Light decomposes salts of gold, silver, and platinum. Heliography, which was discovered by Niepce and Daguerre, and all actual processes of photography, are based on the chemical action of luminous rays, either from the sun, moon, or other suffi- ciently intense luminous source. We shall describe these further on ; we will now indicate the phenomena themselves. Mr. Eutherford, who has photographed the spectrum with unequalled success, has deter- mined that the maximum chemical effect lies near the line G. CHAP, x.] SOLAR RADIATIONS. 339 The same question presents itself here as in regard to the illuminating and heating effects. We require first to know if the different regions of the solar spectrum are endowed with the same faculty of chemical action, or if this efficacy varies in different parts of the spectrum. Now Scheele, who in 1770 had ascertained the action of light on chloride of silver, discovered also that the coloured rays of the spectrum act unequally in producing this decomposition. It was afterwards discovered, not only that the chemical rays increase in intensity in passing from red to violet to such a degree that the chloride in question blackens- in a few minutes, when it receives the concentrated rays of the violet part of the spectrum, whilst it requires several hours, if it receives rays between and including the green and red rays, but that beyond the extreme violet, in the dark portion of the spectrum, chemical action con- tinues at a considerable distance beyond the luminous portions. The intensity of chemical radiation, which varies for one substance according to the position of the rays in the spectrum, does not attain its maximum at the same point for different substances. This maximum is not the same for salts of silver as for salts of gold, nor for the latter as for salts of potassium. The following phenomenon is worthy of remark : the spectrum which may be called chemical, to distinguish it from the luminous and heat spectrum, possesses rays like the luminous spectrum. In the dark portions of a spectrum photographed by means of chloride of silver, white lines may be observed which indicate an interruption of chemical action, and their position coincides precisely with Fraun- hofer's lines. But, beyond the violet, other lines exist, which naturally have no corresponding ones in the luminous spectrum. 1 Professor Stokes, by enabling us to see these invisible rays, has given us the reason why they are ordinarily invisible. If we receive these rays on a screen washed with a solution of sulphate of quinine, they are at once visible as blue light ; we have the phenomenon of fluorescence, which can also be rendered visible by other means. The explanation of the phenomenon of fluorescence is that the ultra-violet rays, which move too rapidly for our eyes, have their 1 Nevertheless, the most refrangible rays, like the violet, are not completely invisible. According to J. Herschel, the ultra-violet rays, acting on the retina, give a shade called by him lavender-grey. D D 2 340 PHYSICAL PHENOMENA. [BOOK in. velocity retarded toned down when they fall on and are reflected from sulphate of quinine and are thus brought within the range of visibility and known colour. The heat rays have been similarly rendered visible by Professor Tyndall in the phenomenon of calor- escence, in which the obscure heat rays have their velocity increased. Thus, the solar spectrum is more complete than was at first believed, from studying only the impressions produced on the eye. It appears to be formed of three superposed spectra ; one giving light and colours ; another, the action of which is sensible to the ther- mometer, revealing to us the warning or calorific property of the solar rays; and the third teaching us how much their chemical activity varies. But, do three kinds of rays exist, as was at first supposed ? Delicate experiments, among which we only quote that which implies the identity of the rays of the luminous spectrum and those of the chemical spectrum, prove that there is identity between the different radiations. The same rays produce, in one place, varied colours ; in another, varied luminous intensities : here, unequally distributed intensities of heat; there, chemical combinations and decompositions. Only, a ray, which is endowed with considerable calorific and chemical power, does not excite in us the luminous sensation, or rather, only exercises on our retina an inappreciable influence. Thus, as there are sounds in Nature to which our ears are not attuned, so are there colours in the spectrum which will for ever remain invisible to us. CIJAP. XL] PHOSPHORESCENCE. 341 CHAPTER XL PHOSPHORESCENCE. Phenomena of spontaneous phosphorescence Animal and vegetable phosphores- cence Glow-worms and fulgurse ; infusoria and medusae Different conditions which determine the phosphorescence of bodies Phosphorescence by insola- tion Becquerel's phosphoroscope. WE have already alluded to fluorescence ; there is another curious phenomenon which differs from fluorescence in this, that it remains for long after the exciting source of light is withdrawn. The history of the discovery of phosphorescence is as follows : In 1677, an alchemist of Hamburg, named Brandt, discovered by a process which he at first kept secret, 1 a new body endowed, among other singular properties, with the property of emitting a continuous luminous smoke when it was exposed to the air. Hence the name phosphorus (from <&>?, light ; , to bear) applied to this substance, which is one of the sixty-four simple bodies now recognised. If we trace characters on a wall with a stick of phosphorus, they will appear as luminous lines in the dark, and will not cease to shine until after the complete disappearance, either by slow combustion or evaporation, of the phosphorescent matter. Long before the discovery of this body, the name of phosphori was given to all substances which, like it, emitted light without being accompanied by sensible heat ; such as wood, decomposed by the action of moisture ; dead salt-water fish not yet putrified, the shining of which is communicated to the water itself, when it is agitated for some time; and lastly, a great number of mineral 1 A few years after Brandt, Kunckel discovered the means of obtaining phos- phorus. A century later, in 1769, Scheele proved that it exists in abundance in the bones of men and animals. 342 PHYSICAL PHENOMENA. [BOOK in. substances, when they are submitted to blows or to mechanical friction, or when they have been exposed to the solar rays. It is to this emission of spontaneous or artificial light that physicists have given the name of phosphorescence. Phosphorescence is not peculiar to inorganic or lifeless matter. When, on a warm evening in June or July, we walk in the country, it is not uncommon to s.ee in the grass and under the bushes a multitude of small lights, which shine like terrestrial stars : these are the lampyres, or glow-worms, a species of coleoptera, the larvae of which, like the perfect insect, but in a less degree, possess the property of emitting a greenish blue light. The fulgura or lantern fly, and the cucuyos of Mexico and Brazil, shine during the night with a light sufficiently bright to enable one to read. Certain flowers, like the flowers of the marigold, nasturtium, and Indian rose, have been considered as phosphorescent, but it how appears to be proved that this is a mistake ; it is certain that fifteen phanerogamic plants, and eight or nine cryptogamic ones, emit light ; but only in the evening after they have been receiving the sun's light ; so that exposure to the sun appears to be to them a condition essential to phosphorescence. The phosphorescence of the sea is produced by myriads of animalculse, which, like the lampyres and fulgurae, emit a light sufficiently bright to give to the waves the appearance of fire. It is now infusoria, now medusae, starfishes, &c., which diffuse, some a blue, others red or green lights, or even give the sea a whitish tint, to which sailors give the name of sea of snow or sea of milk. Calcined oyster-shells become luminous when they are exposed to the light of the sun ; this property is due to the sulphide of calcium; it is also possessed by the sulphides of barium and strontium. 1 Phosphorescence can be induced in a great many substances by mechanical or chemical action; this may be noticed on break- ing sugar, the light being produced at the moment of rupture. 1 Canton, an English physicist, discovered in 1764 the phosphorescence of calcined oyster-shells ; hence the sulphide of calcium is called Canton's phosphorus. V. Calciarolo, a workman of Bologna, discovered the phosphorescence of calcined sulphate of baryta ; hence the name Bologna phosphorus which is given to sulphate of barium. CHAP, xi.] PHOSPHORESCENCE. 343 Similar effects are produced by rubbing two pieces of quartz against each other, also chalk, or chloride of calcium, or on separating plates of mica by cleavage. Elevation of temperature also pro- duces phosphorescence. Fluorspar, diamonds and other precious stones, chalk, sulphate of potassium and quinine, emit light when they are placed in contact with warm substances. We shall see further on, that electricity is able to produce the same effects in bodies which are bad conductors. Thus we have a series of phenomena in which the production of light is neither the result of rapid combustion at a high tem- perature, nor that of a vivid illumination which disappears as soon as the source ceases to be in the presence of the illumined object. All the bodies which we have mentioned, and which peculiar circumstances render phosphorescent, acquire, for a limited, but often considerable time, the property of being luminous by themselves, of emitting light perceptible in the dark, and strong enough to illuminate objects lying near them. Phosphorescence appears to be due to multiple causes: in organized and living beings, the mode of producing light is nearly unknown. We only know that the will of the animal plays a certain part, that a moderate temperature is necessary to the emission of the light, as also is the presence of oxygen gas. A sharp cold or intense heat both cause it to disappear. In phos- phorus, decayed wood, dead fish, &c., the production of light is doubtless due to chemical action, that is, to slow combustion ; for, in vacuo, all phosphorescence ceases. It follows therefore, from the facts above stated, that exposure to the sun, elevation of temperature, electricity, and mechanical action, in which elec- tricity and heat doubtless take part, are, in many cases, favourable conditions to the development of phosphorescence. This singular mode of production of light has recently been the subject of very interesting studies by MM. Biot, Matteucci, and principally by M. Edmond Becquerel. We will rapidly glance at some of these. It has long been known that phosphorescence is a property which can be momentarily acquired by a number of bodies, especially in a solid or gaseous state : paper, amber, silk, and a multitude of other substances of organic origin ; oxides and salts of alkaline and earthy metals, and of uranium ; and a great many 344 PHYSICAL PHENOMENA. [BOOK in. gases. But no other metals, nor their compounds, nor any other kind of liquid, has up to the present time manifested the slightest trace of this phenomenon. The tints of phosphorescent light vary according to the nature of the body which emits it: thus precious stones emit a yellow or blue light; sulphides of strontium, barium, and calcuim give all the shades of the spectrum, from red to violet. But a singular fact proved by M. Ed. Becquerel is, that the tint and brightness of the light do not depend alone on the temperature, but also 011 the mode of producing the sulphides, and, what is still more singular, on the molecular state of the salts whence they have been produced. Thus, having taken different carbonates of lime, spar, chalk, &c., and having treated them with sulphur, he obtained six sulphides of ^calcium which, exposed to the sun, became phosphorescent, and in darkness presented the following tints: Tint of the Light. Iceland spar Orange yellow Chalk . . . . ; V . , . Yellow. Lime . . . . ;v . . . Green. Fibrous arragonite .... Green. Marble . . ^ . .' : Rose violet. Arragonite of Vertaison . . Eose violet. " If I may be allowed the comparison," . says M. Edmond Becquerel, in regard to these facts, " I could say that these last bodies, on account of their luminous effects, are analogous to the sonorous cords which produce different sounds according to their tension." Elevation of temperature accelerates phosphorescence, but it also exhausts it quickly : for the light obtained does not last long. It has also the effect of modifying the tints ; thus sulphide of strontium, blue at the ordinary temperature, passes to a blue violet, clear blue, green, yellow, and lastly to orange, when its temperature is raised from 20 degrees below zero to 150 degrees above. It will be of much interest to study the manner in which the different rays of the spectrum act on bodies in determining their phosphorescence, from the chemical rays situated in the dark part of the spectrum beyond the violet, to the heat-rays beyond the red. In order to observe this, the spectrum is projected on a band covered with various phosphorescent substances, and the Sulphides of Calcium obtained from CHAP. XT.] PHOSPHORESCENCE. 345 luminous effects produced are examined in the dark at different distances, that is to say, in the regions covered by the prismatic rays. Thus, it is possible to ascertain which of the rays produce the most intense luminous effects. It is found that the maxi- mum of action depends on the bodies influenced ; but in every case, the chemical rays nearest the violet, and consequently the most refrangible, produce phosphorescence : the heat-rays do not excite it ; but they are endowed with the property of continuing the action of the chemical rays. These results explain the feeble FIG. 242. M. Ed. Becquerel's phospnoroscope. action of the flames of candles, or gas, in producing the phosphor- escence of bodies, and, on the other hand, the efficiency of the electric light : this latter abounds in chemical and ultra-violet rays, whilst the former, although rich in heat-rays, are very poor in chemical rays. The bright light of magnesium rivals, as M. Le Eorey proves, the electric light. It is sufficient to burn a wire 346 PHYSICAL PHENOMENA. [BOOK in. of this metal in presence of a tube inclosing, for example, some sulphide of calcium, to obtain prolonged phosphorescence, as may be shown by carrying the tube into darkness. M. Edmond Becquerel invented, for the study of these phenomena, an instrument which he calls the phosphoroscope. The following is a short description of it : Two blackened discs are each pierced with four openings in the form of sectors, and can be caused to revolve on a common axis : but as the openings of one do not cor- respond with the openings of the other (as may be seen in Fig. 243), it follows that a ray of light cannot pass through the system of the two discs, whatever may be the rate of rotation. They are both inclosed in a blackened box, which remains fixed, and in the sides of which are two openings. The solar light passes through one of them, falls on the body, the phosphorescence of which is to be Fio. 243 Disc of the phosphoroscope. T i -i i i r> -i -i studied, and which is nxed between the two discs, in the axis of -the outer openings of the box ; but, as we have said, it cannot pass through the other side. The phosphorescent light induced in the body passes, on the contrary, through the opposite opening every time the rotatory movement brings one of the movable windows in front of the outer opening. The action of light on the body is thus produced four times during each revolution. If the velocity is sufficient, the developed phosphorescence is continuous, and the sensation produced in the eye of the observer is equally so. The phosphoroscope, thus constructed, gives to the body observed a constant quantity of light, whatever the rotatory movement may be ; the quantity of phosphorescent light which reaches the eye is also constant ; but the duration of the constant action of the light on the body varies with the velocity, as it is equal to the time that an opening takes to pass before it : this duration is easily measured when one knows the dimensions of the opening and the number of turns that the system of the two move- able discs makes in one second. To sum up : the more rapid the rotation, the shorter the duration of the light, but the interruptions CHAP. XL] PHOSPHORESCENCE. 347 in this action are shorter, so that there ought to be a certain velocity for which the maximum brilliancy is obtained. By the aid of the phosphoroscope, M. Becquerel, besides the result we have already described, has been able to prove the existence in some bodies of luminous emissions, the duration of which does not exceed the ten- thousandth part of a second. Others, like the green sulphide of strontium and calcium, remain phosphorescent for thirty-six hours. Diamonds shine for many hours. He has been able to study the law according to which, the phosphorescent bodies lose their light by successive emissions. The light emitted by various vegetable and animal phosphor- escents has been submitted to spectrum analysis; and it is found that the spectra of these lights are continuous, as neither dark nor bright lines can be distinguished. 348 PHYSICAL PHENOMENA. [BOOK in. CHAPTEE XII. WHAT IS LIGHT? Hypotheses concerning the nature of light Newton's emission theory Huyghens' undulatory theory ; vibrations of the ether Propagation of luminous waves ; wave-lengths of the different rays of the spectrum. TTITHERTO we have described luminous phenomena as studied by _L_L observation, without indicating any hypothesis regarding the particular nature of the agent which induces the perception of these phenomena by our organs. All that we know is, that the various substances in Nature can be ranked in two classes : in the first are placed light-sources, or bodies capable of producing light directly and of themselves ; in the second, bodies which transmit in divers ways the light MLing on them, but which, in their actual state, cannot directly emit it. Among light-sources, there are some, like the sun and most of the stars, which appear to be constant, at least their emissive power has not decreased for thousands of years : probably we ought to count by millions of centuries, if we wish to measure the probable duration of this power. But they doubtless do not differ essentially from temporary luminous sources which we have at our disposal on the surface of the globe. These latter owe their state either to a very high temperature, to chemical combinations conducive to the disen- gagement of light, such as a furnace, or to a state of electric tension producing the same result take the electric light. All that we know of the physical constitution of the sun, and say, a white-hot cannon- ball or any mass of metal, tends to prove that they are globes in a state of incandescence. We have already seen that, among the substances of the second class, there are many which can momen- tarily acquire, under the influence of temperature, e^osure to the CHAP, xir.] WHAT IS LIGHT? 349 sun, or certain chemical or mechanical actions, the property of emitting light, which is called phosphorescence ; and that without being in a state of incandescence or vivid combustion. We know also that light is not transmitted instantaneously, but that it requires a definite time to pass from one point to another in a word, that it has a particukr mode of movement. We have now, therefore, to inquire in what this movement consists ; that is, whether light is a substance incessantly emitted by luminous bodies, or an impulse produced in a special medium, and propagated through space. These are questions of such great interest, that they necessarily force themselves upon the mind ; their examination will also have the advantage of furnishing us with an explanation of various phenomena to be hereafter described. The time has therefore arrived for us to indicate the nature of a theory now generally received by physicists, and by the help of which all optical phenomena are found to be consequences of a single principle. At the same time, we may give certain details concerning another hypothesis, which for a length of time had the privilege to share with the first a common applic- ability to optical phenomena. We will first consider the older theory, known as the emission theory. According to Newton, who first reduced this theory to a system, light is formed of material molecules of extreme tenuity, which are perpetually emitted by luminous bodies, and which the latter project through space with a uniform velocity; the impact of these pro- jectiles on the retina agitates the optic nerves, and produces in us the sensation of light. These particles are endowed with attractive and repulsive forces, which are manifested in the neighbourhood of the molecules of bodies, and produce the attractive forces of interior refraction and reflection, and the repulsive forces of exterior reflec- tion. There are as many kinds of particles as colours, and each kind possesses a particular refrangibility. Successive particles which follow the same right line form a luminous ray ; but they may be separated by great intervals. The luminous impression has been proved to remain on the retina about one-tenth of a second; it is therefore sufficient that ten luminous particles should arrive at the eye in a second, in order that the impression caused by one of them should not be effaced before the arrival of the next; or, which is the same, in order that there shall 350 PHYSICAL PHENOMENA. [BOOK in. be a continuous sensation. Supposing them situated at equal dis- tances, they should follow each other at a distance of 18,600 miles from each other. Supposing they follow each other at the rate of a hundred a second, there would still be an interval between them of 1,860 miles. We understand, therefore, how, according to this hypothesis, the luminous rays emanating from different sources can intersect each other in various directions without obstruction. But we must suppose that the mass of each of them is of such small weight, that our imagi- nation can scarcely realize the idea. Sir J. Herschel assisted it by the following comparison. He says : " If a molecule of light weighed one grain (0*065 gramme), its effect would be equal to that of a cannon-ball of 150 Ibs. (56 kilogrammes), animated by a velocity of 305 metres (330 yards) per second. "What, then, must this tenuity be, if a thousand million of molecules, attracted by lenses and mirrors, have never been able to communicate the least movement to the most delicate instruments invented expressly for these experiments ! " (Treatise on Light, vol. i.) Sir John Herschel lived indeed before the discovery of the Radiometer. "We have just stated that, to explain the phenomena of reflection and refraction of light, Newton imagined that each molecule is either repelled or attracted by the molecules of bodies. The intensity of these forces, which are exerted in infinitely small spheres, is pro- digious ; it is proved that they exceed the intensity of gravity at the surface of the earth to such a degree, that it is necessary, in order to express their value in numbers, to multiply this latter intensity by the figure 2, followed by forty-four zeros. In the theory which is now adopted, the undulatory theory, we find numbers which submit somewhat to precedent ; it is not difficult, therefore, to conceive that it has been preferred to the theory of emission. We owe the first exact exposition of the undulatory theory to Huyghens, who numbered among his partisans, in the last centuries, Hooke and Euler ; and among those who have developed and per- fected it in the present century, Young and Fresnel. We will endeavour to explain the undulatory theory in its essential elements. The hypothesis of emission requires that the interplanetary celestial spaces be void of matter, in order to give free passage to CHAP, xii.] WHAT IS LIGHT? 351 the motion of the luminous molecules, or rather these spaces must be free from all matter, save the molecules themselves. On the other hand, according to the undulatory hypothesis, these same spaces are filled with an extremely thin and eminently elastic fluid, which is called the ether. This medium penetrates all bodies, and is diffused throughout all the inter-molecular spaces. Luminous bodies are those whose molecules, in a state of continual vibration, communicate impulses to the ether, which, in its turn, propagates the same vibratory movement from place to place and in all directions, with a uniform velocity of 186,000 miles per second. The velocity of propagation of the lumi- nous waves is the same for all the rays of light, whatever their intensity or colour. It is uniform and constant in a homo- geneous medium ; but it varies in passing from one medium to another ; and, as it is admitted that it is dependent on the connection which exists between the elasticity of the ether and its density, it must be inferred that this connection itself changes in different media; that is to say, the distribution of the molecules of ether is not the same in interplanetary media as in heavy bodies ; and in these it varies with the nature of the substances and their density. Let us try to understand the nature of the vibrations of the ether. Each molecule of a luminous source executes a series of very rapid vibrations ; that is to say, of backward and forward move- ments across a position of equilibrium. These vibrations are communicated to the ether, the different molecules of which assume the vibratory movements similar to those of the light-source, and communicate them spherically from place to place. During the time which a molecule of ether requires to make a complete oscillation round its position of equilibrium, its movement is communicated, in the direction of the propagation of light, to a stream of molecules, the most distant of which is at a fixed distance from the first : it is this distance which is called the wave-length, and the luminous wave is nothing more than the series of movements effected during a complete oscillation of a molecule of ether. As the same dis- turbance which has its origin at one point of the source of light is thus propagated in the ether which fills space, with uniform velocity, it follows that all points of the surface of a sphere, 352 PHYSICAL PHENOMENA. [BOOK m. having for its centre the luminous point, are at the same instant in the same phase of vibratory movement. All the points of any of these spherical surfaces are called the surface of the wave. In certain media, the surface of the wave can be ellipsoidal. Lumi- nous waves have, therefore, great analogy with sonorous waves; like them, they are isochronous, and they move with uniform velo- city. They consist in alternating movements of an elastic medium across a position of equilibrium ; but, whilst the vehicle of sound is a tangible medium, as the air, or any other gaseous or liquid or solid body, the vehicle of light is a substance, if not imponderable, at least intangible. The sonorous wave is propagated through the air, travelling in a right line 330-6 metres per second ; the luminous wave, in the same time, travels 186,000 miles, and, whilst the length of an un- dulation varies, for perceptible sounds, between one-fifth of an inch and eleven yards, the maximum length of an undulation of ether does not attain the twenty-five thousandth part of an inch. But between these two modes of vibratory movement there exists, as Fresnel has shown, an important difference; for, whilst sonorous vibrations are made in the same direction as their propagation, luminous vibrations take place in a direction perpendicular to that of the movement of propagation, that is, parallel to the surface of the waves. It is difficult to imagine the vibrations being effected per- pendicularly to the direction of their propagation. A comparison will explain this kind of movement. If we take hold of the end of a very long cord placed in a straight line along the ground, and give it a shake in a vertical direction, there follows a series of undulations which are propagated to the other extremity, all of which are effected in a direction perpendicular to that of the cord, just as we see undulations which succeed each other on the surface of the water caused by the throw of a stone, or any other heavy body, on the liquid. There is, between these two phenomena and the movement of the ether, one resemblance more ; that is, that the propagation of the waves takes place without there being any transport of the molecules which undergo the vibration. We shall presently understand how the wave-lengths of luminous vibrations can be measured, and how it was discovered that these lengths vary in passing from one colour to another. They are, as SPECTRA OF THE METALS OF THE ALKALIES & ALKALINE EARTHS. From the Drawings of BUNSEN & KiRCHHOFF. 10 20 30 40 SO 60 70 80 90 100 110 120 130 1-13 1C 3 1CD 170 Ka Lia Sr3 Rb K.0 CHAP, xii.] WHAT IS LIGHT ? 353 the following table shows, excessively small, their mean value scarcely ever exceeding the half of a thousandth of a millimetre. When these wave-lengths are once known, an easy calculation gives the number of vibrations which the ether performs in a second, when it gives rise to the different colours of the spectrum. As light travels over an interval of 298,000 kilometres (186,000 miles) in one second, it is sufficient to divide this last number by each wave-length, in order to find how many of these vibrations take place in a second. Here are the results for the seven principal colours of the sola.r spectrum : Ked, mean 620 ..... 514,000,000,000,000 Orange, 583 .' . . ft 'V 557,000,000,000,000 Yellow, 551 "". '. .-'/ ; .' 548,000,000,000,000 Green, 512 .... . 621,000,000,000,000 Blue, 475 ....>. 670,000,000,000,000 Indigo, t1 449 ..... 709,000,000,000,000 Violet, 423 ... ."''; ' 752,000,000,000,000 l This determination of wave-lengths, combined with wide dis- persion, enables us, by reason of the high velocity of some of the motions of the heavenly bodies, a velocity comparable with that of light itself, and the existence of bright and dark lines in their spectra, to determine the rapidity of the various movements of many of the stars. Let us endeavour to give an idea how this result is arrived at, begging indulgence for a gross illustration of one of the most supremely delicate of nature's operations. Imagine a barrack, out of which is constantly issuing with measured tread and military precision an infinite number of soldiers in single or Indian file; and suppose yourself in a street seeing these soldiers pass. You stand still, and take out your watch, and find that so many pass you in a second or minute, and that the number of soldiers, as well as the interval between them, is always the same. You now move slowly towards the barrack, still noting what 1 These numbers are deduced from the new determination of the velocity of light ; they exceed by about ^ those given in treatises on physics before the result of M. Foucau It's experiments was known. E E 354 PHYSICAL PHENOMENA. [BOOK in. happens. You find that more soldiers pass you than before in the same time, and, reckoned in time, the interval between each soldier is less. You now move still slowly from the barrack, i.e. with the soldiers. You find that fewer soldiers now pass you, and that the interval between each is longer. Now suppose yourself at rest, and suppose the barrack to have a motion, now towards you, now from you. In the first case the men will be paid out, so to speak, more rapidly. The motion of the barrack-gate towards you will plant each soldier nearer the preceding one than he would have been if the barrack had remained at rest. The soldiers will really be nearer together. In the second case it is obvious that the interval will be greater, O and the soldiers will really be further apart. So that, generally, representing the interval, between each soldier by an elastic cord, if the barrack and the eye approach each other by the motion of either, the cord will contract; in the case of recession, the cord will stretch. Now let the barrack represent the hydrogen in Sirius or the sun, perpetually paying out waves of light, and let the elastic cord represent one of these waves; its length will be changed if the hydrogen and the eye approach each other by the motion of either. Particular wave-lengths with the normal velocity of light are represented to us by different colours. The long waves are red. The short waves are violet. Now let us take the case of the hydrogen in the sun and fix our attention on the green wave, the refrangibility of which is indicated by the F line of hydrogen. If any change of wave-length is observed in this line, and not in the adjacent ones, it is clear that it is not to the motion of the earth or sun, but to that of the hydrogen itself and alone, that the change must be ascribed. If the hydrogen is approaching us, the ivaves will be crushed together; they will therefore be shortened, and the light will incline towards the violet, that is, towards the light with the shortest waves ; and if the waves are shortened only by the 1Qu ^ ouo th of a millimetre, we can detect the motion. CHAP. XTI.] WHAT IS LIGHT ? 355 If the hydrogen is receding from us, the waves will be drawn out; they will therefore be longer, and the green ray will incline towards the red. In Sirius there is hydrogen, and by this means Mr. Huggins has determined the velocity of that star's movement in the heavens. Now, in the case of the sun, bear in mind that there are two different circumstances under which the hydrogen may approach or recede from the eye. Take a globe, which we will consider to represent the sun. Fix your attention on the centre of the visible hemisphere of this globe : it is evident that an uprush or a downrush is necessary to cause any alteration of wave-length. A cyclone or lateral movement of any kind is powerless ; there will be no motion to or from the eye, but only at right angles to the line of sight. Next fix your attention on the edge of the globe the limb, in astronomical language : here it is evident that an upward or down- ward movement from the centre of the globe outwards is as powerless to alter the wave-length as a lateral movement was in the other case, but that, should any lateral or cyclonic movement occur here of sufficient velocity, it might be detected. So. that we have the centre of the disc for studying upward and downward movements from the centre of the globe outwards upward or downward as they would seem to a spectator standing on the sun, and the limb for studying lateral or cyclonic movements, if they exist. Now the hydrogen lines in the solar spectrum are observed to change their places, while the lines near them remain at rest, so that they may be looked upon as so many milestones telling us with what rapidity the uprush and downrush takes place ; for the twistings in the hydrogen lines are nothing more or less than alterations of wave- length, and thanks to Angstrom's map, we can map out distances along the spectrum from F in jowooo^h 8 ^ a millimetre from the centre of that line; and we know that an alteration of that line io;ooo ( ooo tns f a millimetre towards the violet means a velocity of 38 miles a second towards the eye, i.e. an uprush ; and that a similar alternation towards the red means a similar velocity from the eye, i.e. a downrush. To sum up : these are the two theories proposed for the explana- tion of luminous phenomena. Both explain with equal facility the E E 2 356 PHYSICAL PHENOMENA. reflection and refraction of light ; but, whilst the system of emission requires that the velocity of propagation should be greater in refractive media, the undulatory theory, on the other hand, supposes that this velocity is less, according as the medium is endowed with more con- siderable refractive power. To decide between them, it is therefore only necessary to determine the velocity of light in different media, to settle, for instance, the following question : Is light propagated through air more or less rapidly than through water ? Now, this important problem has received a definite solution during the last few years. M. Foucault and M. Fizeau, each in his turn, by a very ingenious process, the principle of which was first employed by Wheatstone for calculating the velocity of electricity, 1 has succeeded in proving that light is propagated with less rapidity through water than through air, as the theory of undu- lation requires. Other phenomena, which we will now describe, are equally favourable to this theory ; whilst, on the emission theory, no satis- factory explanation of them can be found. It is no longer doubtful that the preference ought finally to be given to the theory wliich makes light not a particular substance projected through space by luminous bodies, but a vibratory movement propagated through a medium which fills space ; not only that space which is usually called the interplanetary space, but that which is occupied by the interstices of the molecules of ponderable bodies. 1 F. Arago conceived the idea of using Wheatstone's revolving mirror to com- pare the velocities of light through different media. CHAP, xni.] INTERFERENCE OF LUMINOUS WAVES. 357 GHAPTEE XIII. INTERFERENCE OF LUMINOUS WAVES. PHENOMENA OF DIFFRACTION. GRATINGS. Dark and bright fringes due to very small apertures Grimaldi's experiment Interference of luminous waves ; experimental demonstration of the principle of interference Phenomena of diffraction produced by slits, apertures of dif- ferent form and gratings Coloured and monochromatic fringes. IN 1665 Pere Grimaldi published at Bologna a curious work entitled " Physico-Mathesis de Lumine," in which he described for the first time appearances to which he gave the name, which they still bear, of diffraction phenomena, which physicists have since studied and multiplied until they form an important branch of optics. Having introduced a beam of light into a dark room through a very small aperture, Grimaldi noticed that the shadows of narrow opaque bodies exposed to this light were spread out much more than they should have been. Besides, these shadows were edged with coloured fringes, parallel to themselves and to the edges of the opaque bodies. The phenomenon disappears if, instead of a narrow aperture, the pencil of light passes through a wide hole. If we substitute for the opaque body a very small circular hole, made for instance in a metallic plate, and receive the light which has passed through it on a screen, concentric rings with, coloured fringes are obtained, some situated within the geometric image of the aperture, others beyond ; that is to say, within the limits of the shadow of the plate. Thus, two apertures placed near together give two series of rings, which partly overlap each other; and, moreover, three series of dark rectilinear fringes or bands are perceived, which disappear directly one of the holes is moved (Fig. 244). This last experiment caused great astonishment in the philosophic world, as it 358 PHYSICAL PHENOMENA. [BOOK m. upset all the ideas then conceived as to the nature of this luminous agent. And, indeed, it seemed to show, that light added to light produces, in certain cases, DARKNESS ! Newton studied the phenomena of diffraction discovered by Grimaldi; and he added fresh observations, and endea- voured to explain the cause of diffraction by a deviation when the edges of opaque bodies are subjected to the rays of light. Fraunhofer, Young, and Fresnel suc- ceeded in discovering the laws, and the last-named connected them in the most happy manner with the undulatory theory. Before continuing the description of the phenomena, let us endeavour to form some idea of what Young called the principle of interference the theory of which he has clearly explained on the undulatory hypothesis, and which Fresnel afterwards demonstrated by the famous experiment of the two mirrors. Let us suppose that two rays of light follow the same direction, A B ; that they have the same intensity, and that the wave-lengths of each of them are equal, in which case the vibratory movements of the ether will have the same amplitude for the same phases. If the FIG. 244. Grimaldi's experiment. Dark and bright fringes produced by a system of two small circu- lar holes. / FIG. 245. Interference of luminous waves. waves of the first ray coincide with those of the second, it is clear that their intensities will become united ; the quantity of light will be increased by their union. But if one of them is behindhand precisely half the length of a wave, the molecules of ether situated along the line A B will be drawn from one side by forces the intensity CHAP, xiii.] INTERFERENCE OF LUMINOUS WAVES. 359 and direction of which will be represented by the curve a a a .... and from the other side by equal and contrary forces represented by the curve a a a'. ... Every molecule, such as m, will then remain at rest under the action of these opposed forces : the vibratory move- ment will cease, and darkness will succeed to light. It is then said that the luminous waves or rays interfere. The same result is produced if the retardation is f , J . . . and generally, odd numbers of half undulations. If it be an even num- ber of half undulations, the result is the same as if there had been coincidence. Thus, between these two extreme cases, the luminous intensity is sometimes increased and sometimes diminished, but in neither case is there an absolute destruction of light. Theoretically, this reasoning, which is a necessary consequence of the undulatory theory, perfectly accounts for Grimaldi's experi- ment, and all those in which dark and bright fringes or bands appear. It nevertheless had to be proved by observation, and this Fresnel accomplished, mainly by the experiment of the two mirrors we have already mentioned. This experiment is too important for us to neglect here. The nature and limits of this work do not permit us to touch upon theoretical explanations of many phenomena, but the principle in this instance must at least be described with sufficient clearness to enable the reader to accept the inferences with confidence. Two plane mirrors, o N, o M (Fig. 246), of metal or black glass, are placed vertically in a dark room, so as to form an angle much more obtuse than in the figure. In front of these mirrors a beam of sunlight is brought to a focus at s by a spherical or cylindrical lens, so that it can give either a point or a luminous line. Two images are thus formed, one in each mirror ; that in s for the mirror o N, the other in s for the mirror M. We have thus two sources of light which present this peculiarity, that, as they emanate from a common source, they are in the same state of vibration. If we now place a vertical screen in front of the mirrors, in such a way as to receive the luminous beams from the two images, a bright band will be perceived on the screen in the pro- longation of the line o A, and, on each side of this band, a series of alternate dark and bright fringes. If one of the mirrors is taken away, the fringes instantly disappear, and the screen is evenly illuminated. 300 PHYSICAL PHENOMENA. [BOOK in. It is thus seen that the phenomenon is the same as in Grimaldi's experiment of the two openings, and it remains for us to explain how light added to light can produce darkness ; or, as we have seen, that whenever dark fringes occur, it is due to the interference of luminous waves emanating from two sources, and that, on the other hand, we have the same phase of undulation whenever bright fringes or FIG. 246. Fresnel's experiment of two mirrors ; experimenal demonstration of the principles of interference. bands are seen. Figure 246, in which we observe concentric waves emanating from s and s' , explains this. These two sys- tems of waves cross and cut each other at different points. Now, such of these points which, like a, are situated on the perpendicular A o to s s , are in the same phase of undulation in both systems, since the rays s a, s a, being of the same length, the same paths sia and si' a are followed by the two luminous waves emitted CHAP. xui.J INTERFERENCE OF LUMINOUS WAVES. 361 from the one source s, and reflected by both mirrors. The same takes place with regard to the points a a a' . . . situated in the vertical plane passing through A 0. The luminous intensities are therefore united in this plane ; hence the central bright fringes. In positions such as n, n' , the difference of path of the waves which cross each other is from ,... wave-lengths ; in other words, an odd number of half undulations : hence interference ensues, and consequently a dark band. It is so also for the points mm'.... wherever a dotted arc cuts a plain arc in the figure. Further on, the points & b' . . . c c . . . belong to rays each of which is delayed an even number of half wave-lengths behind the other ; hence bright fringes . . . and so on. In order to try this admirable experiment, Fresnel used in suc- cession lights of all the simple colours ; he found fringes of each of these tints, but they became narrower as he got farther from the red in the series of prismatic colours. Violet gave the nai> rowest bands. By measuring with great precision the distances of the bands, this illustrious physicist succeeded in deducing the wave-lengths of light of different colours, and afterwards the number of vibrations executed by the ether in the short interval of a second the wonderful numbers we have already seen. Fringes pro- ceeding from white light ought therefore to be formed of fringes coloured by each of the spectrum tints superposed upon each other, so that the violet would be by the side of the central bright band. Observation proves this. Thus, by this memorable experiment the truth of the undulatory theory is confirmed; mathematical analysis has also drawn from it a crowd of inferences, some already known by observation, others outstripping observation and serving as a guide to it. The names of Huyghens, Young, and Fresnel will remain for ever attached to this beautiful theory, as is that of Newton to the theory of universal gravitation. Let us now return to the phenomena of diffraction, all of which flow from this principle of interference of luminous waves. They are so numerous that we can only choose some of the most remarkable. Newton, while repeating and varying Grimaldi's experiments on the enlarged shadows of fine bodies, such as hairs, thread, pins, and straws, became convinced that the deviation of the luminous rays was F F 362 PHYSICAL PHENOMENA. [BOOK in. not due, as was at first believed, to a refraction in a thin stratum of denser air surrounding the bodies. He saw also that the formation of fringes did not depend on the nature of the substances used. Whether metals, stones, glass, wood, or ice, &c. were used, he always recognised three fringes succeeding each other and starting from the shadow. The interior fringe was violet, deep blue, light blue, green, yellow, and red; the exterior one, pale blue, pale yellow, and red. He also observed that monochromatic lights produce fringes of unequal width. But all his experiments led him to the conclusion, that the rays of light undergo, in passing by the edges of a body, inflections which are stronger the nearer they graze the surface. This was a natural hypothesis, in accord- ance with the . emissive theory ; but we shall presently understand the true explanation. The very numerous experiments which have been since performed in connection with this subject may be arranged under two heads. The first comprises phenomena of diffraction produced by rectilinear edges ; for instance, by one or by several very narrow slits, in the form of parallelograms, or by a very fine screen, a metallic thread, or a hair : the second comprises phenomena obtained when the diffraction is produced by means of one or more extremely small apertures, either square, triangular, circular, or by the edge of a circular screen of small dimensions. Of the systems of fringes pro- duced under these varied circumstances, some are coloured, proceeding from white light ; others, monochromatic, from light of a single colour, for instance, red light. We see, in many cases, fringes accompanied by a multitude of small spectra like the rainbow, the bright colours of which add to the beauty of the phenomenon. Sir J. Herschel observed curious diffraction effects by placing in front of the object-glass of an astronomical telescope diaphragms of different forms, and then observing single and double stars. With an annular opening, he saw coloured rings surrounding the images of luminous points, which then presented discs similar to those of the planets. Triangular diaphragms gave, on the contrary, stars with six rays ; an aperture formed by twelve concentric squares gave a star with four rays. Lastly, by piercing in a regular manner equilateral triangles on the diaphragm, he obtained a series of cir- cular discs, arranged on six lines, on which they diverged, starting cu AP. xni.] INTERFERENCE OF LUMINOUS WAVES. 363 from a central colourless and very bright disc; they were, more- over, each surrounded by a ring more or less coloured, and spread into spectra as they extended farther from the centre. These phenomena are of great interest; the magnificent colours which are presented to the eye form, as it were, so many pictures, the variety of which equals their splendour. But to the eyes of the physicist they present still greater interest, inasmuch as they are so many confirmations of the beautiful theory of the undulations of the ether. Mathematical analysis applied to the different phenomena of diffraction produces results which agree, in a marvellous manner, with those -of observation. We have already said that they some- times outstrip it, and of this the following is a remarkable example. Fid. 247. Effects of diffraction in telescopes. (Sir J. Herschel.) The geometer Poisson, having submitted to calculation the problem which has for its object the determination of the nature of the shadow and the fringes produced by an extremely small opaque disc exposed to the light which diverges from a luminous point, found that the centre of the shadow ought to be as brilliant as if the disc did not exist : this light was an effect resulting from the diffraction of luminous waves on the edge of the screen. Such a result was so opposite to preceding observations, that Poisson pre- sented it as a serious objection to the undulatory theory. But Arago having made the experiment with requisite care, by using a very small metal disc cemented on a diaphanous and perfectly homogeneous F F 2 3G4 PHYSICAL PHENOMENA. [BOOK ITT. glass plate, found that the luminous point appeared as calculation had indicated. It was as if the shadow was produced by a screen pierced at the centre. This experiment evidently affords one of the most beautiful triumphs of the theory, a decisive proof in favour of the undulatory theory of light and of the existence of the ether. Fraunhofer, whose beautiful experiments on the lines of the spectrum we have already described, introduced into the study of the phenomena of diffraction the excessive precision which so eminently distinguished him. After having observed the images produced by a very limited number of small openings, he conceived the idea of examining the effect produced when light traverses a grating formed of a multitude of very fine threads either parallel or crossed. He first used a grating of brass wire, composed of numerous very fine wires, stretched on a rectangular frame by means of screws suitably arranged. Then, to obtain a greater regularity and delicacy in the intervals through which the light passed, he traced parallel and equi- distant lines on plates of glass covered with gold leaf; then engraved them with diamonds on the glass itself, thus forming more than 1,000 divisions per millimetre. Each of the striae is an opaque screen, and the interstices left by the striae allow the light to pass through. However, a much smaller number of divisions makes the grating more regular, as it is almost impossible to secure that the thickness of the lines or intervals between them shall be even approximately constant in the finer gratings, and thirty- eight lines in a millimetre, 1,000 per inch, are sufficient to show the phenomena. Beside the parallel-line grating, Fraunhofer studied gratings with square meshes, formed by two series of lines crossing each other at right angles ; also those of circular and other forms of mesh. In this manner he obtained a number of figures, in which the fringes and spectra are distributed with wonderful symmetry ; but he did more ? he studied the laws of this distribution laws which M. Babinet has proved to be necessary consequences of the principles of interference. The following are the phenomena resulting from the passage of light through a grating with parallel lines : at the centre is a bright line, then two rich dark intervals followed on each side by two spectra the violet of which is nearest the centre, and so pure that the dark lines are easily distinguished. Beyond this there are two CHAP, xiii.] INTERFERENCE OF LUMINOUS WAVES. 365 fresh dark bands ; and lastly, two series of superposed spectra, paler and more and more extended. A grating with square meshes gives us, besides the bright central line and two series of spectra more extended than those of the grating with parallel meshes, in the four right angles a multitude of small spectra radiating towards the centre. Newton had a glimpse of the phenomena of diffraction through small apertures and gratings, as the following passage in his " Optics " shows : " On looking at the sun through a piece of black ribbon held close to the eyes, we perceive several rainbows ; because the shadows which the fibres or threads throw on the retina are edged like coloured fringes." A beautiful effect is produced by the diffraction of solar light through the grating formed by the broad part of a bird's feather. Fringes of a like nature can be equally observed by the light of a candle, with the eyes nearly closed, the lashes, on joining, forming meshes of irregular form. It is by the interference of luminous rays that physicists ex- plain the bright colours which are noticed on certain bodies whose surfaces are covered with a multitude of very fine striae : the feathers of several birds, and the surface of mother-of-pearl, for in- stance, are formed of numerous striae which reflect all the pris, matic colours. Sir David Brewster, having occasion to fix mother-of-pearl to a goniometer with a cement of resin and wax, was greatly surprised to see the surface of the wax bright with the prismatic colour of the pearl : he repeated the experiment with dif- ferent substances, realgar, fusible metals, lead, tin, isinglass, and in each case he saw the same colours appear. An Englishman, Mr. John Barton, applied this property of striated surfaces to the arts ; he worked very fine facets on steel buttons and other objects which, in the light of the sun, gas, or candles, exhibit designs brilliant with all the colours of the spectrum. " These colours," says Brewster, " are scarcely surpassed by the fire of the diamond." 366 PHYSICAL PHENOMENA. [BOOK in. The following is another phenomenon which seems to belong to the phenomena of interference, as it is explained by M. Babinet ; the description of which we take from the account given by the observer, M. A. Necker : " To enjoy the sight of this phenomenon/' he says, " the observer should stand at the foot of a hill, interposed between himself and the spot where the sun sets and rises. He is then completely in the shade ; the upper edge of the hill or mountain is covered with woods, trees, or detached bushes, which appear black against a perfectly clear and bright sky, except at the place where the sun is on the point to appear or disappear. There the whole of the trees and bushes which crown the summit branches, leaves, trunks, &c. appear with a bright and pure white, and shine with a dazzling light although projected on a background, which is itself luminous and bright as the part of the sky near the sun always is. The smallest details of the leaves and little branches are preserved in all their delicacy ; and it might be said that the trees and forests are made of the purest silver, with all the art of the most skilled workman. Swal- lows and other birds, which fly across this region, appear as sparks of dazzling whiteness." To those who know how to observe, Nature has a magnificence which the skill of the most ingenious experimenter can never ap- proach. That which makes the merit of the inquirer is not so much to reproduce her to multiply the phenomena, the pictures of which she shows us as by dint of patience, sagacity, and genius, to discover the reasons of things and the laws of their manifestations. From this point of view, natural philosophy is one of the grandest studies which the human mind can pursue. CHAP, xiv.] COLOURS OF THIN PLATES. 367 CHAPTER XIV. COLOURS OF THIN PLATES. The soap-bubble Iridescent colours in thin plates Newton's experiment on coloured rings ; bright and dark rings Laws of diameters and thicknesses- Coloured rings are phenomena of interference Analysis of the colours of the soap-bubble. THE most beautiful and brilliant phenomena are not always those which require the most costly and complicated instru- ments to produce them. Who among us, in his childhood, has not amused himself, with a pipe or straw and soap and water, in blowing and throwing into the air bubbles of the most perfect form and the most delicate and varied colours ? At first, when the sphere of the bubble is of small diameter, the pellicle is colourless and transparent. By degrees, the air which is blown into the interior, pressing equally on all parts of the concave surface, increases the diameter while it diminishes the thickness of the envelope; it- is then that we see the appear- ance, at first feeble and then brighter, of a series of colours arising one after the other, and forming by their mixture a multitude of iridescent tints, until the bubble, diminished in thickness, can no longer offer sufficient resistance to the pressure of the gas which it incloses. Black spots then present themselves at the top, and soon the bubble bursts. It is always at the upper portion of the liquid sphere that the black spots which announce its disappearance may be observed. This simple experiment and childish recreation, which offers so much attraction to the eye of the lover of colours, is not less beautiful or interesting to the man of science. Newton made it the object of his studies and meditations, and, since the time 368 PHYSICAL PHENOMENA. [BOOK in. of this great man, the colours of the soap-bubble hold a legitimate place among the most curious of optical phenomena. Moreover, this is one particular instance of a whole series of phenomena, observed whenever light is successively reflected and refracted by surfaces which bound thin plates of transparent bodies. Solids, liquids, and gases are equally suitable for this kind of experiment. Crystals which can be reduced to very fine laminae by cleavage, like mica, gypsum, talc, glass blown into extremely thin bulbs, the surface of annealed steel which retains a thin, coating of oxide, show iridescent colours similar to those of a soap-bubble. The bright shades which ornament the membranous wings of dragon-flies, those seen on pieces of glass after exposure to damp, and on the surface of oily water, belong to the same series of phenomena. They are studied in physics under the common denomination of the colours of thin plates. Before speaking of the cause of this decomposition of light into its constituent colours, we will endeavour to give an idea of the conditions under which it is produced, and the laws which govern the succession of tints, at first sight so changeable and mobile. Let us follow Newton in his celebrated experiments. The starting-point of this great physicist was the following observation. He says, in his " Optics," that " having pressed two prisms strongly together, so that their sides touched each other (which were perhaps very slightly convex), I perceived that the place where they were in contact became quite transparent, as if there had been here only a single piece of glass. For, when the light fell on the air comprised between the two prisms so obliquely that it was totally reflected, it appeared that at the place of contact it was entirely transmitted. Looking at this point, a black and obscure spot was seen, like a hole, through which objects placed beyond it would distinctly appear." Newton, having turned the prisms round their common axis, saw the gradual appearance around the transparent spot of a series of rings alternately bright and obscure, and coloured with different tints. To account better for the production of these rings, he used two glasses, one plano-convex, the other convex on both sides; and both of great radius of curvature. He then placed one over the other, and pressed the convex side gently on the plane side; CHAP. XIV.] COLOUES OF THIN PLATES. 369 in this position the two glasses had between them, around the central point of contact, a layer of air, a very thin meniscus, the .ssniaiiiiB Fio. 249. Thin plate of air comprised between two glasses, one plane, the other convex. (Newton's experiment of coloured rings.) thickness of which, at the centre nil, continued to increase imper- ceptibly. The following are the phenomena which he observed : Eeceiving the reflected light in a direction nearly normal to the plane surface of the layer of air, he saw around the central Fio. 250. Newton s coloured rings. point of contact a series of differently coloured concentric rings becoming narrower as they were further from the centre. Each colour appeared, at first, as a circle of uniform tint, which circle 370 PHYSICAL PHENOMENA. [BOOK m. expanded as the pressure on the upper glass was increased, until a new colour issuing from the centre transformed it into a coloured ring. Lastly, at the centre itself, there appeared a black spot. The following is the order and colour of the rings represented in Fig. 250. The colours indicated start from the centre : From o to A, black, blue, white, yellow, red ; A B, violet, blue, green, yellow, red ; B c, purple, blue, green, yellow, red ; c D, green, red ; D E, greenish blue, red ; E F, greenish blue, pale red ; F G, greenish blue, reddish white. If, instead of receiving the light reflected on the two surfaces of the thin plate, we look at ordinary light through a system of two similar lenses, a series of coloured rings will be seen, but their colours will be feebler than those of the rings seen by reflection. Moreover, the order of the colours is entirely different, and, instead of a black spot at the centre, a white spot is seen. The following is the series of the various tints forming the coloured rings seen by transmission : White, red-yellow, black, violet, blue ; White, yellow-red, violet, blue ; Green, yellow-red, green-blue, red j Bluish green ; Ked, bluish green ; Bed. If we compare this second series with the first, we see that the tints which occupy the same order in the two systems of rings are precisely complementary, so that the transmitted light and the reflected light at any one point of the layer of air produce white light when re-united. This consequence of the two experiments has been verified by Young and Arago, who, having placed the two glasses in such a manner as to cause both the reflected and transmitted lights to reach the eye with the same intensity, saw the rings disappear. In order to observe the rings, Newton used the various simple colours of the spectrum. In this instance he perceived, by reflec- tion, rings which were alternately black and bright, the latter CHAP, xiv.] COLOURS OF THIN PLATES. 371 presenting the tint of the simple colour used. But the diameters of the rings varied in size, according to the colour of the light, and they widened on passing from the violet to the red. We can therefore understand how it is that the rings obtained with white light are iridescent. The different colours of which white light is formed, produce each its series of rings ; but as the dimensions are different, the superposition is not exact; the dark rings disappear because they are again covered by other shades of light, except at the centre, and only when these shades are blended together in a proper proportion does the one ring of white light before observed appear. When we introduce water be- tween the glasses, the rings are still visible, but they are smaller and narrower, and the tints are fainter. Lastly, if, instead of a gaseous or liquid medium, the space between the two glasses is a vacuum, coloured rings are still seen, showing no perceptible difference from those given by air. Newton, with his accustomed sagacity and precision, could not confine himself to the proving of these facts and others into the details of which we cannot enter here ; he sought out the law of the production of the rings, and thus he succeeded in tracing to the same principle the different phenomena described at the commencement of this chapter, the iridescent colours of soap-bubbles and thin plates in all solid, liquid, and gaseous masses. He carefully measured the diameters of the successive rings obtained with mono- chromatic light, at the moment when the black spot of the centre in- dicated that the surfaces were in contact. From it he deduced the geometrical ratios, which gave the relation of the diameters to the thicknesses of the thin plate, and these thicknesses themselves ; and he determined the following laws : The squares of the diameters of the bright rings, seen by reflection, are related in the ratio of the odd numbers, 1, 3, 5, 7, 9. The squares of the diameters of the dark rings are as the even numbers, 2, 4, 6, 8. In regard to the rings seen by transmission, as they occupy pre- cisely inverse positions, each obscure ring being replaced by a bright ring, and each of those by a dark ring, their diameters evidently follow the same laws, and the series of numbers is inverted. So much for the relative dimensions of the bright and dark rings. 372 PHYSICAL PHENOMENA. [BOOK m. As to the thicknesses of the layer of air interposed between the glasses, they continue to increase from the centre towards the extremi- ties ; but we find that the values which correspond to the rings of the different orders are odd numbers for luminous rings, and even numbers for black or obscure rings. These laws, although so simple, are general. . Newton concluded that the phenomenon of coloured rings depends on the variable thickness of the thin plate interposed between the two surfaces, and the nature of the substance of which it is composed, but not at all on that of the glasses between which it is interposed. He endeavoured to connect it with the emission theory of light, supposing that the luminous rays, on being propagated, undergo periodical changes "fits of easy transmission arid easy reflection" which sometimes render them apt to be reflected and sometimes apt to be transmitted ! In the present day, as the undulatory theory is admitted, the coloured rings are explained in a simpler way on the principle of interference. A ray of light which penetrates to the first surface of the plate is partly reflected and partly transmitted; transmitted as far as the second surface, where it is again reflected. The two rays, thus reflected on each surface, interfere, as we have already seen, and the luminous effect is destroyed or augmented according as the delay of the second equals an odd number of half-lengths of wave, or an even number of these same lengths. Hence, darkness in the first case, and light in the second, or, in other words, dark rings and bright rings. Analysis applied to this interesting case of the undulatory theory also proves the laws of the diameters and thicknesses, which Newton first discovered by experiment. As the lengths of the waves vary according to the nature of the simple light, and diminish in passing from red to violet, we see that the rings of this latter colour must be narrower than the red rings. Now, in what way is this theory applicable to the phenomenon of the soap-bubble colours, colours so variable and changing, and which are continually mixed and blended with each other ? Newton showed the identity of the coloured rings obtained by means of glasses, and those which appear on bubbles. To study these, he took the precaution of protecting the blown soap-bubble from the influence of the external air, which, earning the thickness CHAP. XIV.] COLOURS OF THIN PLATES. 373 to vary irregularly, changes the colours one into the other, and thus prevents them from being exactly observed. He says, "As soon as I had blown one, I covered it with a very transparent glass; and by this means its different colours ap- peared in regular order, like so many concentric rings surrounding the top of the bubble." When these pre- cautions are taken, the coloured rings visible at the top of the bubble are seen slowly spreading out, in, proportion as the flow of the water towards the bottom of the liquid sphere renders this thinner, and, after having descended to the base, each disappears in its turn. Fig. 251 shows the disposition of these coloured bands. The phenomenon thus regulated loses its beauty from an artistic point of view, but in the scientific it gains in interest Usually the zones of several rings can be seen, in spite of the irregu- larity of colour and their mixture. By degrees, the bubble becomes so thin at the top that the black spot makes its appearance, often mixed with smaller and darker spots ; and almost immediately afterwards the bubble bursts and disappears. According to Newton, the following is the exact order in which the coloured rings succeed each other from the first coloration of the bubble until its disappearance : Eed, blue ; red, blue ; red, blue ; red, green ; red, yellow, green, purple ; red, yellow, green, blue, violet ; red, yellow, white, blue, black. Now, if we compare this series with that of the coloured rings Fia 251> ~ Colours of thin plates m 374 PHYSICAL PHENOMENA. [BOOK m. obtained by means of the two glass surfaces in the first experi- ment, it will be noticed that they are arranged exactly in the opposite order, and this is as it should be, if the same cause pro- duces both these effects. At the commencement the bubble is too thick for the appearance of colours; it is colourless. Then its thickness diminishes more and more, so that at last the black corresponding to the least thickness appears exactly like the black spot of the first ring, which is found at the point where the two glass surfaces are in contact. This refers to colours seen by reflection. The bubble, once formed, ought to be observed in such a manner that it can reflect towards the eye the light of a whitish sky ; and, in order better to distinguish the rings and colours, a black ground should be placed behind it. But the soap-bubble may also be observed by looking at ordinary light through it. Coloured rings are again formed ; but they are of small bril- liancy, and their successive colours are complementary to those given by reflected light. It is easy to assure oneself of this fact. If we examine the bubble by the light of clouds reflected to the eye, the colour of its circumference is red; at the same instant, another observer, looking at the clouds through the bubble, will find that its circumference is blue. On the other hand, if the contour of the bubble is blue by reflected light, it appears red by transmitted light. Now, it is easy to understand why the soap-bubble, observed in the open air, presents in the iridescent colours of its surface that irregularity, that mobility, that perpetual mixture of tints which causes it to be one of the most beautiful phenomena due to the decomposition of light by interference. The agitation of the air around the bubble, added to the want of homogeneity in the soapy water in different parts, and to the evaporation which takes place in a very unequal manner, produces numerous currents in the liquid pellicle, which, opposing the action of gravity in every direction, prevent the water from descending by regular zones towards the base of the bubble. Its thickness thus varies from one point to another, and, as it is on this thickness that the production of the different tints depends, these are distributed in the most varied manner. On the other hand, in a closed flask the air being saturated with vapour, evaporation and the agitation CHAP, xiv.] COLOURS OF THIN PLATES. 375 due to the external air no longer exist, and the rings appear with the regularity indicated by calculation. We have forgotten to mention that the laws discovered by Newton regarding rings furnish a means of calculating the thickness of the liquid film of any given colour. At the point where the black spots are situated this thickness is the least ; and it is then about the two hundred and fifty-thousandth .part of an inch. . Hence it follows that, if one could produce a soap-bubble uniformly of this thickness, it would be completely invisible. 376 PHYSICAL PHENOMENA. [BOOK in. CHAPTER XV. DOUBLE REFRACTION OF LIGHT. Discovery of double refraction by Bartholin Double images in crystals of Iceland spar Ordinary and extraordinary rays ; principal section and optic axis Positive and negative crystals Bi-refractive crystals with two axes, or biaxial crystals. T71 RASMUS BARTHOLIN, a learned Danish doctor, who lived at J-J Copenhagen towards the middle of the seventeenth century, on examining some crystals which one of his friends had brought him from Iceland, was surprised to observe that objects appeared double when seen through them. He noticed this singular phenomenon in 1669, and described the circumstances of the case in a special memoir. Twenty years later, Huyghens undertook the study of what has since been called double refraction ; he determined its laws, and propounded a theory in accordance with the principles of the undulatory theory of which he had laid the foundations. Since Bartholin's discovery and Huyghens* observations, these phenomena have been studied in all their phases, and the whole now constitutes an entire branch of optics. Before describing the principles of these phenomena, we will call to mind what happens when a beam of light falls on the surface of a transparent medium like water or glass. On reaching the surface, part of the luminous beam is reflected regularly, so as to give an image of the object ; another portion is reflected irregularly in all directions. Thus part of the light returns on its path. The other portion of the ray penetrates into the transparent substance, where it is propa- gated without altering its direction, if the incidence is normal; whereas it is refracted, if the ray falls obliquely on the CHAP, xv.] DOUBLE REFRACTION OF LIGHT. 377 surface. In both cases the ray generally remains simple ; it is still simple when it emerges from a transparent medium, so that the eye which receives it only sees a single image of the luminous source. This, however, is by no means always the case ; certain substances act upon a ray of light in its passage through them and split it up into two, whence two images of the object, instead of one, are seen, as Bartholiri first proved. In lodes and metamorphic limestones and clays, a mineral is found which crystallizes in the form of a solid rhombohedron with six parallel sides, which is very transparent arid colourless; its chemical composition shows it to be a carbonate of lime with traces of protoxide of manganese. The most beautiful specimens come from Iceland, and attain a thickness of several inches ; the mineral is known under the name of Iceland spar. FIG. 252. Specimen of Iceland spar. Crystals of this kind are split with the greatest ease in certain directions, so that an exact geometrical form can be given them, which is more convenient for the study of their optical properties. The rhombohedron is then bounded by six lozenges equal among themselves. Each of these lozenges has two obtuse angles, measuring 101 55', and two acute angles of 78 5'. Of the eight solid angles which form the summits of the crystal, six a-re formed of an obtuse angle and two acute angles ; the two others, of three obtuse angles. Let us imagine that these two latter are joined by a straight line : this diagonal of the rhombohedron is of great importance in reference G G 378 PHYSICAL PHENOMENA. [BOOK in. to the phenomena of which we are about to speak ; this is called we shall presently see why the optic axis of the crystal. We will now describe the phenomena of double refraction, which can be easily observed by means of a specimen of Iceland spar. Let us take a piece of this crystal ; place it on a line of writing, and look through it: we witness the phenomenon which struck BarthoKn. Each letter is doubled. Let us, also, notice that each separate image is not so black as the letter itself : it has a greyish tint, and that this has nothing to do with the absorption of light by the crystal is evident, because the tint is black where the two images are superposed. The edges of the crystal itself seen by refraction appear double ; and a straight line traced on paper is changed into two parallel lines. If we allow a beam of solar light to fall on one of its sides, the luminous ray issues as a double ray and forms two sepa- rate images on a screen, the distance between them depending on the inclination of the incident ray to the side of the crystal. We will FIG 253. Double images of objects seen through a crystal of Iceland spar. now go farther into the analysis of the phenomenon ; and to simplify the experiment, let us examine one part at a time. Seen through the crystal, the images appear double ; but if we turn the crystal on itself, parallel to the faces of incidence and emergence, we observe that one of the images turns round the other, and when an entire revolution has been described by the crystal, one image returns to its first position, after having described a circle round the other immovable one. When, instead of observing one point, the same experiment is made on a straight line, it will be noticed that in two different positions of the crystal one of the lines, which appears to be moved parallel to the other, attains a maximum digression ; in two other positions, the two images seem to coincide. But this coincidence is only apparent; for if a point on the observed line CHAP, xv.] DOUBLE REFRACTION OF LIGHT. 379 is marked, we see the double image of this point, where the images of the lines are superposed. In fact, the one line has been slid along the other. Thus the rotation of one of the images round the other takes place in this case, as in the preceding one. Let us now see why the name of ordinary image is given to the immovable image, and that of extraordinary image to that which rotates round the first. The reason is, that the refracted ray which produces the immovable image follows during its path the laws of simple refraction, such as they were enunciated by Snellius and Descartes, whilst the other ray does not obey the same laws. 1 This characteristic difference between the two images can be exhibited in many ways. If we cause a ray of light to fall perpendicularly on one of the faces of the crystal, it will be bifurcated in penetrating into the interior; but one of the rays will follow the direction of the incident ray, and will not be refracted on its emergence : this is the ordinary ray, which obeys Descartes' law. The other ray will be deviated from the direction of the incident ray, both on its entrance into and its emergence from the crystal : this is the ray which produces the extraordinary image. When the incidence is oblique, the two rays are refracted ; but the ordinary ray is equally deviated whatever the position of the crystal may be, provided that the lines of incidence and emergence remain parallel to their first position ; in a word, its path is that which it would preserve through a piece of glass with parallel sides. It is not so with the other ray, which gives rise to the extraordinary image, since this image, as we have already shown, turns round the first, if the crystal be caused to revolve parallel to itself. In this movement of the extraordinary image there is a circumstance which must be noted. If the crystal be placed on a sheet of paper on which a point is marked, and the eye be in the plane of incidence, the ordinary refracted ray will be also in this plane, as the law of simple refraction shows, and the ordinary image of the point will be on the line 1 1 of the plane of incidence with the paper (Fig. 254). But it will not be the same with the extraordinary image E, and the lines which join the two images E will make an angle with the line of which 1 In a word, on the one hand, the extraordinary refracted ray is not generally in the plane of incidence ; and, on the other, the relations of the sines of the angles of incidence and refraction do not remain constant. G G 2 880 PHYSICAL PHENOMENA. [BOOK HI. we Lave spoken. Now, we observe that this line o E always remains parallel, during the rotation movement, to the bisector A D of the obtuse angle of the side parallel to the plane of the paper. Also when, owing to this movement, this bisector is placed parallel to I I, the extraordinary image is itself on this line, and the two refracted rays are both in the plane of incidence. FIG. 254. Positions of the extraordinary image in relation 1o the plane of incidence. Principal section. There is then, among the sections which cut the crystal perpen- dicularly to one of its sides, a section of such a nature that if the incident ray were found contained there, the extraordinary ray would obey the first law of simple refraction exactly like the other ray. This plane is called the principal section. Each plane, perpendicular FIG. 255. Principal sections and optic axis of Iceland .spar. to one of the faces of Iceland spar, and parallel to the small diagonal of the lozenge, or to the bisector of the obtuse angle, is one principal section of this face. Each principal section is parallel to the optic axis, and this condition suffices ; so that if an artificial face were cut in the CHAP, xv.j DOUBLE REFRACTION OF LIGHT. 381 crystal, any plane perpendicular to this face and parallel to the optic axis, would also be a principal section of the artificial face. Lastly, if we make an artificial face ABC perpendicular to the optic axis N I, every ray which falls on this face will necessarily be in a principal section, and the two refracted rays will always be in the plane of incidence. In this case observation proves that if the inci- dent ray is normal to the artificial face, the refracted ray alone remains. This is therefore a direction in which the phenomenon of bifurca- tion vanishes: double refraction no longer takes place, when the inci- dent Tay is parallel to the optic axis. Monge made a remarkable ex- periment, very easy to repeat, which shows us the path followed by the rays emanating from a luminous point through the crystal in giving rise to the two images, ordinary and extraordinary, of the point. If we examine the double FIG. 256. Artificial section ]>erpeiidiciuar to the optic axis. Fio. 257. Crossing of the rays which produce the ordinary and extraordinary. image. image of a point s (Fig. 257), situated at some distance from the lower face, and place underneath this face an opaque card, a b, which we slide along from I towards a, we shall notice with surprise that 382 PHYSICAL PHENOMENA. [BOOK in. the most distant image of the point first disappears; and this is explained as follows. A luminous incident pencil, s I, is bifurcated and gives two refracted rays; whence on issuing from the parallel face, two emergent rays arise; they diverge, and one of them can then only penetrate the eye : let us suppose this the one which produces the ordinary image o. An incident pencil, near the first, will also give two emergent rays, one of which will penetrate to the eye and will produce the extraordinary image E. As the faces of the crystal are parallel, each emerging ray is composed of rays parallel to those of the incident ray. As those which produce the image are concentrated in the eye, it is necessary that the corresponding refracted rays should cross each other in the crystal. Monge's experiment is explained thus : the card a b first inter- cepts the pencil which produces the most distant image, and it is this the extraordinary image E which must naturally disappear first. '; V Such are the most remarkable circumstances which constitute the phenomenon of double refraction. The laws which govern this phenomenon are too complex to allow us to explain them in an elementary work like this. But we will endeavour to give, in a few lines, some idea of the difference which exists between simple and double refraction. We have already said that the ordinary ray follows the two laws of Descartes ; in other words, that the refracted ray is always in the plane of incidence, and that if the angle of incidence is changed, the relation which exists between its sines and those of the refracting angle is always constant. The extraordinary ray only follows the first of these laws, if the incident ray is in a principal plane. But it does not follow the second, so that the relation of the sines, which is called the index of refraction, varies according to the angle that the incident ray makes with the optical axis of the crystal. Is this angle nil, or is the incident ray parallel to the optical axis ? In this case only, double refraction disappears ; one of the images is blended with the other : there is equality between the ordinary and extra- ordinary indices of refraction. As the angle increases, so does the inequality of these indices, and it is a maximum if the incident ray is perpendicular to the optic axis. For Iceland spar, the only crystal endowed with the power CHAP, xvi] DOUBLE REFRACTION OF LIGHT. 383 of double refraction that we have hitherto examined, the index of refraction of the ordinary ray is greater than that of the extra- ' ordinary ray. The contrary takes place, if certain other bi-refractive substances are employed, such as rock-crystal. In order to explain the cause of this difference we should be obliged to expound the entire theory of simple and double refraction, according to the undulatory theory, to show that refraction is caused by the difference of velocity which the ether waves undergo in passing from one medium into a more refractive one ; that the ordinary ray acts as if it were in a homogeneous, non-crystallized medium, whilst the extraordinary ray is propagated with more or less facility, according as it is moved in such or such direction relatively to the position of the crystalline molecules. In Iceland spar, the velocity of the extraordinary ray is the greatest ; and the reverse is the case in rock-crystal. Hence the names oi -positive and negative crystals have been given to substances which possess double refraction according as they are included in one or the other category, the type being for the first, rock- crystal, and for the second, Iceland spar. Tourmaline, rubies, emeralds are nega- tive crystals like Iceland spar ; quartz the mineralogical name of rock-crystal sulphate of potassium and of iron, hyposulphate of lime, and ice are FIG. 258.-Roek-crj.tui. numbered with the positive crystals. Double refraction is also pro- duced in a certain class of crystalline substances known under the name of crystals with two axes, or biaxial crystals. Topaz, arragonite, sulphate of lime, talc, feldspar, pearl, and sugar are crystals with two axes : in each crystal of this kind there are two different directions in which the incident ray passes without being bifurcated; these two directions are the optic axes of the crystal. But there is an essential difference between the phenomena of double refraction in crystals with one axis, or uniaxial crystals, and those of crystals with two axes, or biaxial crystals. In the first, one of the two refracted rays follows the laws of simple refraction : in 384 PHYSICAL PHENOMENA. [BOOK in. the others, the two rays are both extraordinary : neither of them follows Descartes' laws. Fresnel's experiment proves the fact very simply. A topaz is divided into several pieces cut in different directions, and these pieces are fastened together by their plane surfaces so that the form of a parallelopiped is given to the whole. Then on looking at a straight line, two images of the line are seen, and each of these images is a broken line of which the different portions correspond to the fragments of the topaz : now, if one of the systems of refracted rays followed Descartes' law, the image produced would be a straight line, for the direction of the rays in the prism would then be independent of the direction of the optic axis in each piece which composes it. Experiment thus proves that the two rays are both extraordinary rays. We shall soon find another means of distinguishing crystals with one or two axes from each other. We may conveniently end this chapter by enumerating the refractive media in which phenomena of this order are not mani- fested, or, iii other words, which are endowed with simple refraction. First there are gases, vapours, and liquids ; then, among substances which have passed from a liquid to a solid state, those whose mole- cules have not taken a regular crystalline form, such as glass, glue, gum, and resins ; lastly, crystals whose primitive form is the cube, the regular octahedron, and the rhomboidal dodecahedron. It must be added that the bodies belonging to these two last categories can acquire the property of double refraction when they are subjected to violent compression or expansion ; also when their different parts are unequally heated. Certain solids belonging to the vegetable or animal kingdom, horn, feather, and mother-of-pearl, are also endowed with double refraction. CHAP, xvi.] POLARIZATION OF LIGHT. 385 CHAPTER XVI. POLARIZATION OF LIGHT. Equal intensity of the ordinary and extraordinary images in a double refracting crystal Natural light Huyghens' experiments ; variations of intensity with four images ; polarized light Polarization of the ordinary ray ; polarization of the extraordinary ray : the two planes in which these polarizations take place Polarization by reflection. WHEN a luminous object is viewed through a double refracting crystal, a rhombohedron of Iceland spar for instance, we know that two distinct images are seen ; one ordinary, following the law of simple refraction, the other extraordinary, the properties of which we have indicated in the preceding chapter. The latter is easily recognised as it revolves round the other, when the crystal is made to rotate in a plane parallel to the faces of incidence and emergence of the rays. It is now necessary to remark that, in all these posi- tions, the relative intensity of the two images has not varied : the brightness of each of them is the half of that of the luminous object, as can be easily proved by direct observation. Let us suppose that we examine a small white circle on a black ground. In all parts where they are separated, the two images, ordinary and extraordinary, of the circle present a greyish tint of the same intensity, and the brightness equals that of the object when the two images are super- posed. Indeed, the same phenomenon always takes place, whatever the respective colours of the object and ground may be. The same result is also shown if we allow a ray of solar light to fall on the crystal and receive the two refracted rays on a converging lens, the two images being projected on a screen (Fig. 259). If the crystal is made to revolve parallel to the face of incidence, the two images are displaced, each describing a circumference of a circle, and we 386 PHYSICAL PHENOMENA. [BOOK in. observe that in every position the luminous intensities are equal. If the two images are partly superposed, the brightness of the super- posed parts will be double that possessed by the separate parts, as shown in Fig. 260. FIG 259. Propagation of ordinary ami extraordinary images of a double refracting crystal. Equal intensity. An old and beautiful experiment, due to Huyghens, proves that the rays which emerge from Iceland spar have acquired new and remarkable properties after their deviation in the crystalline medium, properties which they did not possess before passing through the crystal. This experiment consists in receiving the ordinary and extraordinary rays, after their emergence from the first rhombo- hedron, on a second crystal, and examining the relative intensities of the images which they produce, when the second crystal is caused to revolve over the first. The following is a very simple method of observing the phenomena which are thus produced; it is that which Huyghens himself devised. Let us place the first ciystal on a black spot on a white ground ; there will be two images of equal in- tensity. We will now place a second piece of Iceland spar on the first, and it must be placed so that their principal sections coincide; in order that this condition may be realized, the faces of one must be placed parallel to the faces of the other: there will be only two images of the FIG. 260. Equal intensity of ordinary and extraordinary images. CHAP, xvi.] POLARIZATION OF LIGHT. 387 same intensity as before. Only, the two images, ordinary and extra- ordinary, will be more separated than by one crystal. The same effect would take place if the principal sections of the two rhombohedra remained in the same plane, or in parallel planes when even the two opposite faces of the crystals were not parallel ; and it is not necessary that, in the first position, the two rhombohedra should touch each other. We observe then, already, a difference between the luminous ray before its refraction by Iceland spar, and each emerging ordinary or extraordinary ray ; whilst the first is bifurcated in penetrating the crystal, it appears that the two others remain simple in penetrating a second crystal. Fis. 261. Huyghens' experiment. Variations in intensity of the images seen when one prism of Iceland spar is rotated over another. Let us now slowly turn the upper crystal, so that the principal section makes greater and greater angles with that of the first. We then see four images appear ; each of the two first will be divided, but the equal intensity which characterized them is not retained in the others. Of these four images, arranged at the angles of a lozenge with regular sides, but with unequal angles, two proceed from double refraction, in the upper crystal, of the ordinary emergent 388 PHYSICAL PHENOMENA. [BOOK m. ray ; the two others proceed from the double refraction of the extra- ordinary ray. But an important difference to be indicated is that, in general, each couple is characterized by a difference in the lumi- nous intensity of the images. Fig. 261 represents their relative positions and intensities for angles comprised between and 180 of the principal sections of the two crystals. If the principal sections are at right angles, only two images are seen : if they make an angle of 180 and the crystals have the same thickness, the two images are superposed ; in the latter case, the deviations made by each crystal being in opposite directions, there is only one image. It already follows from this first experiment that each ray of light which has passed through a doubly refracting crystal, no longer possesses, after its passnge, the same properties in all directions ; for in certain directions it is no longer susceptible of undergoing a new FIG. '262. Polarization of the ordinary ray ly double refraction. bifurcation, and in others, the two rays into which it is divided have no longer the same luminous intensity. To distinguish these new properties, it is said that light which has passed through a doubly refracting crystal is polarized liyht. But it in important to point out precisely the phenomena just described. Let us suppose that a ray of solar light, s I (Fig. 262), is allowed to fall on the first crystal of Iceland spar, its principal section being vertical. This ray is divided in the plane of the section into two rays: the one ordinary, IK; the other extra- ordinary, I E'. If we intercept one of the two by a screen, and allow the other to pass through a second piece of Iceland spar, the luminous ray, on traversing the second crystal, will undergo double refraction : it will be divided into two rays, i', K, which is the ordinary ray, and i', R', which is the extraordinary one. Lastly, CHAP, xvi.] POLARIZATION OF LIGHT. 380 by the help of a lens, we will project the emerging rays on a screen, and examine what will happen if the second crystal is turned so as to produce at its principal section every possible angle with that of the first, from to 360. Fig, 263 shows the relative intensities of the two images if the ordinary ray from the first crystal has traversed the second as in Fig. 262; Fig. 264 shows on the contrary what these intensities are when the extra- ordinary ray emergent from the first is allowed to pass through the second prism. Fin. 263. --Division of the ordinary ray. Variable FIG. 264. Division . Tlicriuoiiiutricul scales. 426 PHYSICAL PHENOMENA. [BOOK n. seven or eight times more than glass, and this fact renders the mercurial thermometer possible. But from this we learn that it is not the expansion of the mercury which causes the level to vary, but the difference between the expansions of the liquid and that of the enve- lope; in a word, it is the apparent dilatation of the mercury, not its absolute dilatation. But it is no less evident that the different ther- mometers, constructed and graduated as we have just stated, must always be comparable between themselves, whatever the dimensions of the tubes and reservoirs and the quantity of mercury in each of them. Only, as different kinds of glass are not equally expansible, especially at high temperatures, in order that there should be cor- respondence between the indications of the instruments submitted to the same conditions, it is necessary that they be made of glass having the same composition. The sensibility of a mercurial thermometer, that is to say, the rapidity with which it assumes the temperature of the surrounding medium, is greater as the mass of mercury in the reservoir is less, and as the surface of the envelope is greater. In order to fulfil this second condition in the best manner, the cylindrical or even spiral form is given to the reservoir, as it is preferable to a spherical bulb. This kind of sensibility is especially desirable for ascertaining variations of temperature which quickly succeed each other. There is another kind of sensibility no less useful than the first: it is that which allows very slight variations of the level, corresponding to very slight variations in the temperature, to be manifested, so as to allow the indication of the smallest fraction of a degree. This quality is ob- tained by giving larger capacity to the reservoir, and small diameter to the tube, so that for the expansion indicated by one degree the level varies considerably. Mr. Walferdin has constructed thermo- meters, to which he gives the name of melastatic, in which the hundredth part of a degree can be detected : whenever these instru- ments are used, it is necessary, on adding or taking away from the mercury, to regulate their course for the variations of temperature to be ascertained. The mercurial thermometer cannot be employed for temperatures higher than 360 above zero, because at this point the liquid boils and would break the tube. In like manner, below 35 or 36 the mercury is near the temperature at which it solidifies, and then contracts irregularly, so that it would furnish CHAP, i.] THERMOMETERS. 427 inexact indications. Beyond either of these two limits, thermometers of a different kind, which we shall briefly describe, are employed. Let us commence with the alcohol thermometer, which is used to measure very low temperatures. This instrument does not differ in form from the mercurial thermometer; but it is graduated by com- parison with a standard mercury thermometer, that is to say, the two tubes are plunged simultaneously into baths, the temperature of which is made to vary. The points at which the level of the alcohol becomes stationary are marked for each temperature which is deter- mined from the mercurial thermometer, and the intervals are divided into as many equal parts as there are degrees from one to the other. But even with these precautions, it is seldom that alcohol thermo- meters agree between themselves, or with the standard thermometer, which is explained by the irregularity of the expansion of this liquid at different temperatures. For lower temperatures than that of melting ice, it would be preferable to use thermometers filled with common ether, as this dilates with much greater regularity than alcohol. Thermometers are also constructed of gas, based for example on the expansion of air. Fig. 286 represents two of these instruments, the first that were invented for the measure- ment of variations of temperature. Galileo invented the first: it consists of a tube and FlG . 28 6.-Air thermometers of , ,, ,. ., , Galileo and Cornelius Drebbel. reservoir, enclosing a small liquid column or index, A, which separates the air of the reservoir from the outer air ; as the temperature increases, the air contained in the bulb of the thermo- meter is warmed, dilates, and forces the index towards the open end of the tube. The other instrument is also formed of a tube and reservoir similar to the first, but its open end is immersed in a liquid contained in an open vessel ; by cooling, the air decreases in volume, and its elasticity becomes less, so that the liquid, which is always submitted to the exterior atmospheric pressure, rises to a greater or less height in the tube. This instrument, which was much in request during the last century, was invented by a Dutchman named Cornelius Drebbel. These two thermometers are now graduated by 428 PHYSICAL PHENOMENA. [BOOK iv. comparison with a mercurial thermometer. The points are marked at which the liquid becomes stationary at two different temperatures, and the interval is divided into as many equal parts as it comprises degrees. But they are both also affected by changes of atmospheric pressure, and are therefore not capable of much precision ; their chief value consists in the rapidity of their indications. Leslie and Eumford invented two thermometers based on the expansion of air; but not possessing the same inconveniences as the preceding ; in other words, they are uninfluenced by pressure. FIG. 287. Differential thermometers of Leslie and Eumford. They both consist of a tube, bent twice at a right angle, and ter- minated at each extremity by a bulb or reservoir. In Leslie's ther- mometer (Fig. 287) the tube encloses a column of sulphuric acid coloured red ; the level is the same in each limb, when the tem- perature of the two bulbs is equal ; this common level is marked 0. If now one only of the reservoirs is warmed, the air which it contains, in expanding, presses against the liquid ; the level of the corresponding limb falls to I, whilst it rises in the other to a ; and the height above zero marks the differences of temperature of the reservoirs, if this instrument has been graduated by comparison with a mercurial thermometer. Eumford's air thermometer differs from the preceding, inasmuch CHAP, i.] THERMOMETERS. 429 as the liquid column is replaced by an index which occupies the centre of the horizontal portion of the tube, when there is equality of temperature between the two reservoirs. If one of these is warmed more than the other, the expansion of the air causes the index in the horizontal part of the tube to move towards the colder bulb, and the difference of the temperature is measured by the number of divisions which this index passes over from zero. These two instruments thus mark differences of temperature, and they are therefore known as differential thermometers. But they can also indicate absolute temperatures, if the graduation has been effected with this object in view. The expansion of solid bodies may also be employed to measure temperatures. The instruments which we have described above are based on the unequal expansion of liquids, gases, and of the \ FIG. 288. Unequal expansion of two different metals for the same elevation Of temperature. vessels which contain them ; this inequality, perceptible in liquids, becomes considerable in gases. The construction of the metallic thermometers represented in Figs. 289 and 290 depends on the inequality of expansion of different solid bodies. Two metallic plates for example, one of copper and the other of zinc sol- dered together lengthways, so as to form a straight bar, expand unequally when the temperature is raised ; the bar then bends, as in Fig. 288 ; the zinc, which is the more expansible of the two metals, forms the convex side, and the copper the concave. When the bar has returned to its primitive temperature, it assumes its rectilinear form, to bend again in the contrary direction if it is afterwards subjected to cooling. 430 PHYSICAL PHENOMENA. [BOOK iv. The metallic dial thermometer (Fig. 289) is composed of a curved plate of copper and steel soldered together ; one of the extremities of this is fixed, while the other is supported by the small arm of a lever, the large arm of which, in the form of a toothed sector, works in the pinion of an index. Variations of temperature increase or diminish the curvature of the plate, and thus cause the lever and consequently the index to move, sometimes in one direction and some- times in the other. The dial is divided into degrees, by observing the indications of a mercurial thermometer. In Bre'guet's metallic ther- mometer (Fig. 290) the plate is formed of three ribbons of silver, gold, and platinum, soldered together and formed into a spiral : the silver, being the most expansible of the three metals, forms the inner surface of the spiral. This is suspended vertically, and its lower extremity FIG. 289. Metallic dial thermometer. FIG. 290. Breguet's metallic thermometer. supports a horizontal index, which moves over the divisions of the dial. When the temperature rises, the curvature of the spiral diminishes under the influence of the greater expansion of the silver, and the needle moves in one direction : it moves in the contrary direction if the temperature falls. As the bulk of the spiral is extremely slight, it very rapidly acquires equilibrium of temperature with the surrounding air. Breguet's thermometer is therefore very sensible, and useful for noting rapid variations of temperature. We can only allude to pyrometers, instruments which are used for measuring very high temperatures, such as those of blast-furnaces, forge-fires, &c. ; some are based on the expansion of solids, others on the contraction of clay. The trials which have been made in order to CHAP, i.] THERMOMETERS. 431 compare the indications of pyrometers with those of mercurial thermometers have not given very accurate results. When great precision is desired, air pyrometers are used for measuring high temperatures, a description of which will be found in more detail in many treatises on Physics. The various thermometers which we have recently described determine the variations of their own temperature, by the different expansions and contractions of their own substance. But the object which is proposed in constructing them is to measure the temperature of various media, whether solid, liquid, or gaseous which in each instance requires particular precautions. If it is a question of the temperature of the air or a gas, or again of a liquid, the thermometer is immersed in it; and if the instrument be of great sensibility, if its mass be very small in com- parison with that of the medium, the temperature indicated by the thermometer, when the level of the mercury or the index is at rest, may be taken without sensible error for that of the medium itself. If it is a question of a solid body, a cavity large enough to receive the reservoir of the instrument is made, or, still better, this cavity is filled with mercury ; after a short time, the temperature of this liquid is in equilibrium with that of the body, and the thermometer is then immersed. It is always necessary that the mass of this . be very small compared with that of the body ; indeed, as there is exchange of heat between them, the indication no longer relates to the original temperature of the body, but to that which is established at the end of this change, and on the hypothesis that the mass of the instrument is very large, the difference would be considerable. Hence it is evident, that this cause of error can never be entirely avoided ; the effects can only be lessened, in order that the result may not be perceptibly altered. 432 PHYSICAL PHENOMENA. [BOOK iv. CHAPTEK II. MEASURE OF EXPANSION. Effects of variations of temperature in solids, liquids, and gases Applications to the arts Eupert's drops Measure of the linear expansion of solids Expansion of crystals Contraction of iodide of silver Absolute and apparent expansion of liquids All gases expand to the same extent between certain limits of temperature. A BODY expands when its temperature increases : this is the universal fact which we have stated, and which is employed to measure changes of temperature. But to what extent does the volume increase, and by what fraction of the primitive volume is it increased for one degree of the centigrade thermometer ? Does this fraction vary in different substances, and does it remain the same at every temperature ? Such are the questions which naturally present themselves to physicists when they have deter- mined by observation the effects of variation of temperature. Before indicating the results at which they have arrived, let us show by a few examples the practical utility of the precise knowledge of these effects, and the necessity which often arises of correcting or foreseeing them. If a fragile body which is a bad conductor of heat is subjected to quick changes of temperature, the effect produced will be the breaking of the body. Thus, if a red-hot bar is placed on a piece of cold glass the glass cracks ; the same thing happens with a piece of very hot glass if it is suddenly placed in contact with a piece of cold iron. In the first instance, sudden expansion is produced in the portions of the glass touched by the hot iron, and the surrounding portions, which have not had time to become warmed, break violently from the first hence the rupture. In the second instance, on the CHAP, ii.] MEASURE OF EXPANSION. 433 other hand, the portions first touched are contracted before the other parts have had time to cool, and rupture is again the conse- quence of this sudden molecular movement. We all know that boiling water cannot be poured into a cold glass vessel without breaking it by the quick expansion of the sides in contact with the liquid. During hot summers the expansion of metals used in buildings and their contraction by cold in winter, produce effects which are the more apparent when these metals are united to materials whose expansibility differs from their own. The following is a curious example, quoted by Tyndall in his work on Heat, the observation and explanation of which is due to Canon Moseley: "The choir of Bristol Cathedral was covered with sheet lead, the length of the covering being sixty feet, and its depth nineteen feet four inches. It had been laid on in the year 1851, and two years afterwards it had moved bodily down for a distance of eighteen inches. The descent had been continually going on from the time the lead had been laid down, and an attempt to stop it by driving nails into the rafters had failed; for the force with which the lead descended was sufficient to draw out the nails. The roof was not a steep one, and the lead would have rested on it for ever, without sliding down by gravity. What then was the cause of the descent ? Simply this. The lead was exposed to the varying temperatures of day and night. During the day the heat imparted to it caused it to expand. Had it lain upon a horizontal surface, it would have expanded all round ; but as it lay upon an inclined surface, it expanded more freely downwards than upwards. When, on the contrary, the lead contracted at night, its upper edge was drawn more easily downwards than its lower edge upwards. Its motion was therefore exactly that of a common earthworm: it pushed its lower edge forward during the day, and drew its upper edge after it during the night, and thus by degrees it crawled through a space of eighteen inches in two years." From this example we learn how important it is to note the changes of volume in solids which are used in building or the arts. Railway lines lengthen in summer and shorten in winter; it is necessary, therefore, on laying them, to give them a certain play which allows the lengthening to take place freely, otherwise the L L 434 PHYSICAL PHENOMENA. [BOOK iv. heat would force the bolts from the sleepers, or would contort the line. The damaged line which occasioned the Fampoux accident 011 the Northern Railway of France was apparently caused by a contortion of this nature, as the ends of the rails had not a sufficient interval between them. , ^ Stones held together by iron clamps are often broken, either by the expansion or contraction of the metals, both being greater than that of the stone. The force with which the molecules of bodies are sometimes separated and sometimes drawn together, one against the other, by change of temperature, is enormous. A bar of iron a metre (39'3 inches) long expands lengthways 1*17 mm., when its tem- perature is raised from to 100 ; it contracts to the same amount in passing from 100 to 0. Now, it has been calculated that in order to overcome this molecular movement, a force equal to the pressure of 2,450 kilo- grammes 5,000 Ibs. must be employed, if the section of a bar of iron is a square cen- timetre six to the square inch and 245,00-0 kilo- grammes if the section is a square decimetre. This force has been employed for the holding together of the lateral walls of a gallery in the Con- FIG. 291. Boom of the Conservatoire des Arts et Metiers. Servatoire deS Artset Metiers, which the pressure of the roof had driven out of the vertical. Two bars of iron were placed so as to cross the two walls at the upper part ; they were terminated on the outside by screws furnished' with nuts. The whole of their length was quickly heated, which produced a lengthening, and the nuts were then screwed up close against thick pieces of wood placed on the outside of the roof walls whilst the bars were still hot. On cooling, the bars contracted, and by degrees the force of contraction drew the walls nearer together. By repeating the same operation several times they were at last brought to a vertical position. Cartwrights utilize the contracting force of cooling iron to bind CHAP. n.J MEASURE OF EXPANSION. 435 together the spokes of carriage wheels. The iron tire is forged in such a way as to surround the wood, when it is heated to rather a high temperature ; on cooling, it binds the parts of the wheel strongly together. Dutch tears, or Kupert's drops, are drops of melted glass which have been suddenly solidified in cold water. On breaking the fila- ment of glass with which they are terminated, the whole mass instantly becomes powder, with such a force that if the drop has been previously plunged into a flask filled with water the shock transmitted to the water is sufficient to break the flask. A similar effect is produced in very thick glass flasks which have been cooled suddenly after having been blown. A grain of sand thrown into the vessel is sufficient to cause the bottom to fall out (Tyndall). The cause of this is the same in this last example as in the Dutch tears. The exterior of the glass drops cools first, imprisoning the in- terior mass, which has not yet solidified; when this cools in its turn, it contracts, and the effect of the contraction being exercised evenly on the outer envelope, it remains in equilibrium. But the molecules are in a state of violent tension, , ,, . , , , ., . FIG. 292. Dutch tears. and the least rupture suddenly destroys the equilibrium in one point, and at the same time destroys it in the whole mass. The expansion of liquids is generally greater than that of solids, and the expansion of gases is the greatest of all. We have seen how this is proved ; it now remains for us to show by what means the expansions are measured, by what methods the so-called co- efficient of expansion of a solid, liquid, or gas is determined. The unit of volume of the body being given, let us imagine that the temperature is raised one degree centigrade : expansion or increase of vol ume will of course result. This increase, expressed in numbers referred to this same unit, constitutes the co-efficient of expansion of the substance for the temperature employed. In a more general sense, we may say that it is the fraction of the primitive volume added to the volume of any body when its temperature is raised one degree. Thus a litre or cubic decimetre of mercury heated from to 1 becomes a litre plus 179 millionths, or 1 -0001 79 decimetre, L L 2 436 PHYSICAL PHENOMENA. [BOOK iv. The fraction 000179 is the co-efficient of expansion of mercury at zero. The numbers of which we here speak vary with the nature and physical condition of the substances. Moreover, the co-efficient of expansion of one body generally varies for different degrees of the thermometric scale, even when its physical condition does not change. In liquids and gases the cubic expansion, or expansion of volume, is considered ; but in solids it is possible to determine the increase of one of the dimensions, that is to say, the linear expansion, or, in the case of two dimensions, superficial expansion. As a solid of any form generally expands equally in every direction, so as to retain its original form at all temperatures, the increase of its volume can be deduced from that of one of its dimensions; besides, it is proved that the co -efficient of cubic expansion is perceptibly to all intents and purposes triple of the co-efficient of linear expansion ; for this reason, in the case of solid bodies, this last co-efficient is alone determined. FIG. 293. Measure of the linear expansion of a solid, by the method of Lavoisier and Laplace. Let us now consider the nature of the method devised by Lavoisier and Laplace for measuring the linear expansion of a solid bar. The bar A B is fixed at A, so that it can expand only at the extremity B ; on expanding through the space B B' it forces the rod OB, which is fixed and can revolve on the point o, into the position OB'. The telescope LL, originally horizontal, moves with the rod to L'L, so that, in place of being opposite the point c of the vertical scale C (/, it is then opposite c'. By this means they substitute for the difficult measure of the smaller space B B' that of a space c c', the ratio of which to the space B B', through which CHAP. If.] MEASURE OF EXPANSION. 437 the rod has expanded, is equal to the ratio of o c to OB. Fig. 294 shows the arrangement of the apparatus employed in the preceding method. The metallic bar s, whose expansion is to be measured, is immersed in a trough filled with water, beneath which is placed a fire to raise the temperature ; at one end it is in contact with a fixed glass rod B', immovably fixed to the pillars; at the other end it presses against the movable glass rod B, which com- municates its motion to the telescope. The water in the trough being first at 0, the observers note the division of the scale with which the micrometric wire stretched horizontally across the field of the telescope corresponds. Then, after having replaced the iced water by water raised to a temperature of 100 that is, to the boiling PIG. 294. Laplace and Lavoisier's instrument for the measure of linear expansion. point the division of the scale is again observed. By a simple pro- portion the relation of the elongation of the bar to its original length is determined; in other words, the expansion for 100 of temperature. Operating thus on solid bars of different substances and between different limits of temperature, Laplace and Lavoisier determined, for the co-efficients of expansion of solids, numbers which vary for different substances, but which are sensibly constant for the same substance for the different degrees of the thermometric scale, between the temperatures and 100. The following are some of the 438 PHYSICAL PHENOMENA. [BOOK iv. results determined by various observers either by the method just described or by other processes. Iron. . . ...... ,,.,.... 0000012 Copper 0-000017 Tin 0-000022 Lead .' 0-000029 Zinc OO00032 Silver , 0-000019 Gold 0-000015 Platinum G'000009 Steel 0-000011 Aluminium 0'000022 Bronze 0-000019 Wood charcoal O'OOOOll Granite 0'000009 White marble '000008 Building stone 0'000009 Glass , 0-000008 Ice . , 0-000053 The preceding co-efficients of expansion apply only to the speci- mens which were used to determine them; according to some observers, the same substances are found to possess totally dif- ferent co-efficients, dependent on the particular molecular conditions in which the substances used by each of them exist. Thus, wrought iron, iron wire, and cast iron have not the same co-efficient of ex- pansion ; and a similar remark applies to other metals. Solid bodies which have not a homogeneous structure in every direction expand unequally in different directions. Thus the expansion of dried wood is not the same in the direction of the fibres and perpendicular to their direction. All doubly- refracting crystals have unequal co-efficients of expansion in different directions. According to Mitscherlich and Fizeau, there are even some which, when they in- crease in length by heat in one direction, contract in another. Such is carbonate of lime or Iceland spar : for while, on raising the temperature one degree, this crystal expands 29 millionths in the direction of the optical axis, it contracts perpendicularly to the axis, and this contraction amounts to nearly 6 millionths. A similar phenomenon is observed in the emerald and in orthic feldspar. The differences of crystalline structure in different directions, which we have seen indicated in those substances by the curious CHAP, ii.] MEASURE OF EXPANSION. 439 effects of double refraction, are here shown under another form which is not less interesting. Moreover, as we have just stated, these anomalies are not real exceptions to the law of expansion of solids by heat, because when the whole expansion is considered there is increase of volume. This is not the case however with iodide of silver. From some very interesting researches by M. Fizeau on this substance, it appears that it undergoes a real contraction in proportion as it increases in temperature between limits rather extensive, since they embrace 80 degrees of the thermometric scale ; and further, that the co-efficient of contraction which physicists call the negative co-efficient of expansion becomes greater as the temperature in- creases. For some time it was believed that ice or solidified water was contracted by an elevation of temperature, thus forming an ex- ception to the general phenomena of expansion of solids : this how- ever is not the case, and Brunner found that its density increased with the fall of temperature. The co-efficient of expansion of ice, as we have seen in the table at page 438, rises as high as 53 ten- millionths, higher, in fact, than that of zinc, the most expansible of all metals. Wood, and the greater number of organic substances, diminish in volume when they are warmed, if they are not com- pletely desiccated ; but this is only an apparent exception. Heat induces evaporation of the water which these bodies contain, and in diminishing in volume they also lose in weight ; besides, on returning to their original temperature by cooling, they do not re- sume their primitive volume. Clay, although completely dried, also contracts when it is submitted to an increasing temperature, and it is on account of this property that clay pyrometers have been constructed ; these instruments indicate the temperature of large kilns : but it has been proved that the contraction is owing to the commencement of vitrification or chemical combination of the ele- ments of the clay ; besides which, on cooling, the clay no longer assumes the former volume. The expansion of liquids is greater than that of solids. We have already seen that the construction of ordinary thermometers is based on the difference of the expansion of glass and mercury. As the liquids, the expansion of which we desire to measure, 440 PHYSICAL PHENOMENA. [BOOK iv. are necessarily enclosed in solid vessels or envelopes, which them- selves change in volume when the temperature is changed, it follows that we must distinguish between absolute expansion, that is to say, the real increase of volume of the liquid, and apparent expansion, as it is observed by the aid of a thermometric tube divided into parts of equal capacity. The absolute expansion of a liquid is evidently equal to its apparent expansion, plus the expansion of the envelope. The following is the process employed for the measurement of the absolute or real expansion of liquids. The absolute expansion of mercury was first determined by a process which we cannot here describe; then, on subtracting from the number found the apparent expansion of the same liquid, the expansion of the glass was obtained. This being once known, the expansion of any liquid can be deduced from it by a reverse operation, that is to say, by first measuring the apparent expansion and adding to it the expansion of the glass or envelope. Kesults have shown that liquids not only expand more than solids, but that these co-efficients of expansion this refers to cubical expansion are not constant. Let us take some examples. M. Kegnault, by perfecting the method invented by Dulong and Petit, has obtained the following numbers, which represent the co-efficient of absolute expansion of mercury, for an elevation of one degree centigrade: Co-efficients of cubic expansion of mercury. Mean between and 100 0*00018 170 at 100 0-00018305 at 200 0-00018909 at 300 0-00019413 at 350 0-00019666 We perceive that the co-efficient increases with the temperature, but between and 100 it is sensibly constant, and then equal to -g-eVrj- ; while at it is TVST* Such is the fraction by which any volume of mercury expands at the temperature indicated. Water and alcohol expand more than mercury between and the temperatures 100 and 80, which are their boiling points. Moreover, the former of these liquids offers an anomaly which deserves attention. Between the temperature of melting ice and 4 6 , water, CHAP. II.] MEASUEE OF EXPANSION. 441 instead of expanding, diminishes in volume ; at this temperature it attains its maximum density. Heated above 4 it continues to expand till it reaches 100 C. M. Despretz, who has made a complete study of the expansion of water and its contraction near 0, has given the following volumes and densities of water at different temperatures: Temperatures. Volumes. Densities. 10001269 0-999873 1 1-0000730 0-999927 2 1-0000331 . . . . . 0-999966 3 1-0000083 VW , . 0-999999 4 1-0000000 .... . 1-000000 5 1.0000082 ..-.--.-. 0-999999 6 1-0000309 &v.j . . . 0-999969 7 1-0000708 ... , ... . 0-999929 8 1-0001216 . . *.'.". 0-999878 100 1-0431500 0-958634 The contraction of water heated from to 4 can be proved very simply. A cylinder of glass, full of water at a temperature above 4 C., is surrounded, midway between the top and bottom, by a tray containing ice. The upper stratum of water gradually and continuously cools, and the thermometer which is immersed in it falls from 4 to 0, whilst the lower thermometer, after having fallen to 4, remains stationary. This ex- periment proves that the upper stratum on cooling to 4, becoming heavier than the lower ones, falls to the bottom of the glass FlG . 295 .__ Exp e^pTvin g the vessel, and is replaced by those, which are contraction of wate in turn cooled down by the ice. But when the temperature is lower than 4, the water remains at the upper part, as the indications of the two thermometers prove. Gases expand much more than solids and liquids under the action of heat : a thin glass sphere, or a balloon of gold-beater's skin filled with air, or any other gas, bursts when it is slightly heated. As according to Mariotte's law, the volume of a gas is changed by pressure, it is necessary, in order that its co-efficient of expansion, may possess a definite value, that care be taken to indicate to what M M 442 PHYSICAL PHENOMENA. [BOOK iv. pressure it has been submitted. These co-efficients are ordinarily taken at an atmospheric pressure of 760 mm. Gay-Lussac determined a great number for temperatures comprised between and 100, and arrived at the remarkable result, that the co-efficient of expansion is the same for all gases, simple, mixed, or combined. According to this illustrious physicist, a volume of gas, on being heated 1 C., increases the 267th part of its volume : a cubic decimetre of air, passing from to 100, therefore expands 375 cubic centi- metres, that is, more than a third of its volume at 0. The number which we have just mentioned is a little too high, as the beautiful researches of M. Eegnault have proved ; and he has at the same time shown that Gay-Lussac's law is not absolute. Air, nitrogen, hydrogen, and carbonic oxide have nearly the same co-efficient of expansion, which is 0*00366, which is equal to the fraction ^ T . But those of other gases are different : thus, in the case of cyanogen, it is equal to '00388, or to the fraction |g-. Moreover, the less the pressure to which the different gases are submitted, the more do their co- efficients of expansion approach equality; thus verifying Gay- Lussac's law. We shall see hereafter that the expansion of air and gases by heat explains many meteorological phenomena. It is also the principle of numerous applications, among which we may quote air balloons, hot-air stoves, and hot-air engines. CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 443 CHAPTER III. EFFECTS OF VARIATIONS OF TEMPERATURE : CHANGES IN THE STATE OF BODIES. The passage of bodies from a solid to a liquid state : fusion Return of liquids to the solid state : solidification or congelation Equality of the temperatures of fusion and solidification Passage of liquids into gases : difference between evaporation and vaporization Phenomenon of ebullition : fixed temperature of the boiling-point of a liquid under a given pressure Return of vapours and gases into a liquid condition : liquefaction and congelation of carbonic acid and several other gases A permanent gas defined. WE all know that a mass of water which is liquid at certain temperatures is capable of passing into the solid state when its temperature falls below a certain limit ; in a word, it becomes a piece of ice without changing its nature, that is to say, without ceasing to be formed of the same chemical elements. On returning to its original temperature, it again resumes the liquid condition ; and if it is then heated to 100, under an atmospheric pressure of 760 mm., it is converted into vapour. The greater number of liquids are like water in this respect, and can exist in either the solid, liquid, or gaseous condition. Bodies which are solid at ordinary temperatures, metals for example, change their condition when they are submitted to a sufficiently intense heat; they are then liquefied, and sometimes vaporized. Cooling produces opposite phenomena, and causes a gas to pass into a liquid, and then into a solid. These various changes of condition are effected under circum- stances which vary with the nature of the substance, but which nevertheless conform to certain common laws, which we shall now discuss. First, however, let us enumerate the changes of condition M M 2 444 PHYSICAL PHENOMENA. [BOOK iv. in solids, liquids, and gases, which can be produced under the influence of variations of temperature. An increase of temperature produces, in solids, a change to a liquid state, which is called fusion ; in liquids, it gives rise to a gaseous state, or vaporization : we shall see, further on, the distinction which must be made between vaporization and evaporation, which also designates the change of a liquid into gas, or into vapour. Cooling causes gases to become liquid : this is liquefaction ; and in liquids, a return to the solid state, which is sometimes called solidification, and sometimes congelation or freezing. The fusion of solid bodies takes place at temperatures which differ from each other considerably. Thus, whilst ice melts at 0, sulphur at 125, and lead at 322, a temperature of 1,500 is neces- sary to melt iron, and nearly 2,000 to melt platinum. But all solids have this common property, that the temperature of fusion is definite for each of them; moreover, during the time that the change from the solid to the liquid condition is taking place, the temperature of the mass remains the same, whatever may be the intensity of the heat which produces the fusion. We may remember that it is this property which has been utilized in determining a fixed point of the thermo- meter. The only effect which is produced by an increase in the energy of the source of heat is a greater rapidity in the fusion of the solid. The passage to a liquid state of the greater number of solids is made suddenly; thus ice, sulphur, and metals assume their fluidity in a moment. Other substances, on the contrary, begin by being softened ; and they become viscous, before becoming quite fluid. Glass affords an example of this condition, which gives great facility to its working, and enables it to be blown and worked into various forms. Formerly we were not able to produce a temperature sufficiently high for the fusion of certain bodies : hence they were called refrac- tory or fixed. In the present day the number of these substances is considerably diminished, and the fusion of numerous rocks, which used to be considered infusible, has been effected. M. Despretz has even succeeded in producing an incipient fusion in charcoal, the most refractory of all known bodies. Other solids are infusible, because heat decomposes them ; such are chalk, pit-coal, and marble : never- CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 445 theless, by enclosing a piece of marble in an iron cylinder, hermetically closed, and then submitting it to a high temperature, a certain portion of this body can be fused. The heat at first decomposes part of the marble into carbonic acid and lime, and the gas, by its elastic force, prevents the continuance of decomposition, and the remaining marble is partially fused. The expansion which a solid body undergoes when submitted to increments of heat, generally continues until the commencement of fusion ; at this juncture it takes place still more rapidly, so that the liquefied mass has a greater volume than that of the solid which produced it. There are some exceptions to this law, and we shall have occasion to return to this subject in speaking of the solidifica- tion of liquids. A foreseen relationship exists between the latter phenomenon and that which we have just studied : for they are both effected for the same substance, at a fixed temperature : in a word, the point of solidification is the same as the point of fusion. Thus, water becomes ice when its temperature reaches 0; lead is solidified when cooled to 322, sulphur to 115, iron to 1,500, platinum to 2,000. And we have another similarity in the fact that the temperature of the liquid mass remains constant during the whole time of solidification; a more intense removal of heat renders the passage to the solid state more rapid, but it does not lower the temperature of the mass. The term congelation or freezing is more particularly applied to solidification which takes place at a low temperature, for example, below 0. Water congeals at 0, mercury at 39 below ; many liquids, such as bisulphide of carbon and alcohol, have not yet been solidified, although by using refrigerating mixtures their tem- perature has been lowered to 80 below 0. We thus see that the temperature of the fusing point of solids is the same as the temperature of solidification. Nevertheless it is possible, under certain circumstances, to lower the temperature of a liquid mass below this point without producing solidification. Water, for example, when enclosed in a vessel and sheltered from the agita- tion of the air, can remain liquid at a temperature 20 below 0. In this experiment it must be very limpid, in order that it may be kept at perfect rest, and the cooling must be effected gradually. But when it is in this condition, the slightest agitation, or the throwing in of a 446 PHYSICAL PHENOMENA. [BOOK iv. small piece of ice, is sufficient to cause congelation to take place instantly throughout the whole mass. Then a remarkable result occurs, for there 'is a disengagement of heat, and freezing takes place at a temperature of 0, as under ordinary circumstances. A solid, on melting, expands quickly, and the reverse phenomenon ought to take place when a liquid mass is solidified. Experiment, indeed, has shown that there is a diminution of volume. But this is not a general law, as there are exceptions, such as water, cast-iron, bismuth, and antimony. These substances expand on solidifying, and this property is utilized in the arts, in the case of molten iron, and allows the reproduction in a very perfect form of the interior of the moulds in which this substance flows. We have already learnt that water expands on cooling from 4 to 0, so that the sudden expansion which it undergoes on congealing appears to be the continuation of the same phenomenon, and renders the explanation which is given to it probable : the phenomenon is explained by the new disposition which the molecules take in the vicinity of the point where this crystallization is effected. When the passage to the solid state is effected, the expansion is sudden, and is performed with an irresistible force, as shown, by the following experi- ment, the description of which we take from Tyndall's " Treatise on Heat :" " But to give you an example of this energy, a quantity of water is confined in this iron bottle. The iron is fully half an inch thick, and the quantity of water is small, although sufficient to fill the bottle. The bottle is closed by a screw firmly fixed in its neck. Here is a second bottle of the same kind, prepared in a similar manner. I place both of them in this copper vessel, and surround them with a freezing mixture. They cool gradually, the water within approaches its point of maximum density ; no doubt at this moment the water does not quite fill the bottle, a small vacuous space exists within. But soon the contraction ceases, and expansion sets in ; the vacuous place is slowly filled, the water gradually changes from liquid to solid ; in doing so it requires more room, which the rigid iron refuses to grant. But its rigidity is powerless in the presence of the atomic forces. These atoms are giants in disguise, and the sound you now hear indicates that the bottle is shivered by the crystallizing molecules, the other bottle follows, and here are the fragments of the vessels, showing their thickness, and impressing CHAP. III. EFFECTS OF VARIATIONS OF TEMPERATURE. 447 you with the might of that energy by which they have been thus riven." Two bombs filled with water, the fusee holes being closed firmly by an iron stopper, were exposed to intense frost : in one instance the stopper was projected to a distance of 500 feet on freezing, and a long cylinder of ice issued from the opening (Fig. 296) ; the other bomb was split open, and a sheet of ice was forced through the crack. This experiment is given in M. Daguin's "Traite" de Physique," and was made by Major Edward Williams, of the Artillery in Quebec. FIG. 296. Effects of expansion produced by the freezing of water. Similar results have been obtained with bismuth. An iron bottle rilled with melted metal, and closed with a screw-stopper, bursts when the metal begins to solidify ; the rapid expansion which determines the changes of condition develops an expansive force so considerable that the envelope cannot resist it, and is broken. The expansion of water at the moment of congelation explains the bursting of water-pipes during a frost ; the accident is not per- ceived until a thaw, because as long as the water remains as ice in the pipes no escape can be manifested, but when the thaw commences, the water flows through the cracks in the pipes. The greater number of solids must be liquefied before they pass into the state of vapour. Nevertheless, camphor, arsenic, and some other substances diminish in weight when exposed to the air, without becoming liquid. Snow and ice do the same. Every one can observe 448 PHYSICAL PHENOMENA. [BOOK iv. this fact during dry weather and hard frosts : pieces of ice and heaps of snow perceptibly diminish in volume, or quite disappear, without even partial fusion having taken place. As regards liquids, they pass spontaneously for the most part into vapour, at varying temperatures. Water 011 being placed in an open vessel gradually disappears ; wet things dry with much greater rapidity when the temperature is high and the surrounding air not humid ; and again, when placed in a current of air, the water with which they are saturated is converted still more quickly into vapour. Mercury evaporates at ordinary temperatures ; a fact which was placed beyond doubt by Faraday, by means of the following experi- ment : he suspended a piece of gold leaf in a flask containing mercury, and after some length of time he found that the leaf was whitened. The mercury had thus amalgamated itself with the gold, which could not have resulted unless evaporation had taken place. This first mode by which liquids pass into the state of gas is called evaporation. It is characterized by the fact that it is effected at any temperature whatever, and solely at the superficial stratum of the liquid. Vaporization, on the other hand, is the conversion into vapour under the influence of a rise of temperature at the moment when this temperature attains a fixed limit, determinate for each liquid, and constant for the same external pressure. The liquid is then in ebullition, that is to say, its mass is agitated by the passage of the bubbles of vapour which have escaped from the bottom of the vessel which contains it, and the specific lightness of which causes them to ascend to the surface. The temperature at which a liquid enters into ebullition is, as we have just said, constant for the same pressure : that is, if the liquid is always contained in a vessel of the same substance. Water boils at 100, at the barometric pressure of 760 millimetres, in a metallic vessel ; in a glass vessel, however, it scarcely boils at 101, as proved by Gay-Lussac : this probably proceeds from a stronger adhesion of the liquid molecules to the glass than to the metal. Moreover, the temperature of ebullition remains constant during the whole time that the vaporization of a liquid mass continues ; only if a more intense heat is used, the passage into the vaporous state is effected more rapidly. The following are the temperatures at which vaporization (which CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 449 v.-- always accompanies ebullition) takes place in the case of several liquids : Ether 35 Alcohol. ........ 80 Water . 100 Concentrated sulphuric acid . 325 Mercury 350 Sulphur 400 Let us now study more closely the curious phenomena of the ebullition or boiling of liquids, taking for our example that liquid which is most easy to observe, viz. water. When the temperature of a vessel containing water is raised by placing it on the fire, the bottom and sides of the vessel receive the first influence of >- : L xV~\ the heat. The heat is then communicated to the contained liquid, which is at first evaporated at the surface, this evaporation being greater as the temperature of the water approaches nearer to ebullition. At length the moment arrives when vapour is produced on the inner surfaces and at the bottom of the vessel. The bubbles there formed have an elastic or expansive force, which, added to their specific light- ness, causes them to rise to the surface of the liquid. But the weight of the strata of water and the atmospheric pressure are opposed to this ascent, which does not effectively take place until the elastic force of the vapour is equal to the sum of these two pressures. Then a tumultuous movement com- mences, which is due to the passage of bubbles which burst at the surface of the liquid. A little before ebullition, a peculiar noise is heard : it is then said that the water sings. The pro- duction of this noise may be explained as follows: when the first bubbles of vapour rise to the surface, they traverse strata more or less warm, the vapour of which they are formed is cooled and condensed, and the surrounding water immediately fills the spaces FIG. 297. Ebullition In open air. 450 PHYSICAL PHENOMENA. [BOOK iv. which result. But the upper strata of the water soon attain the temperature of the strata at the bottom, and the noise ceases, because the cause of the condensation of the bubbles has disappeared. The appearance of the bubbles of vapour confirms this explana- tion ; they at first rise under the form of cones which taper off at the upper part; when ebullition is complete they rise, on the contrary, as cones widened at the top, because, instead of being condensed* they are expanded in proportion as they overcome the diminishing pressure of the liquid above them. Experiment proves that, during the whole time of boiling of a liquid, the elastic tension of the vapour which is formed is precisely equal to the external pressure ; and because, as we shall presently see, this tension increases with the temperature, it follows that the temperature of ebullition of a liquid is lowered as the external pres- sure decreases, and, 'on the contrary, that it is raised as the external pressure increases. Thus, under a pressure of 760 mm. water boils at 100. De Saussure, having boiled water on Mont Blanc, found 86 to bo the temperature of ebullition, the barometric pressure being 434 mm. ; Bravais and Martins made similar experiments, and found the temperature of ebullition at the Grands- Mulets, on the sides of the samemountain, 90, under a pressure of 529 mm., and at the top of Mont Blanc 84 '4, with a pressure of 424 mm. In an apparatus called (after its inventor) Papin's Digester, the temperature of ebullition of water is raised at will, by increas- ing the pressure on the surface of the liquid. The increased pressure is produced by the vapour, which accumulates in large quantity above the surface, and raises the boiling-point of the liquid. Papin's FIG. 298. Papin's Digester. CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 451 Digester is composed of a cylindrical vessel made of iron or bronze, with thick and excessively strong sides ; it is closed by a cover of the same metal, which a pressure-screw presses against the edges of the opening (Fig. 298). A hole in the cover allows the vapour to escape whenever its tension exceeds a certain limit, which can be fixed at pleasure by the following means: the hole in the cover is closed by the arm of a lever, at the extremity of which is a weight acting with a force proportional to its mass and the length of the arm of the lever. The limit of the elastic force of this vapour, or, in other words, that of the temperature of the water contained in the vessel, can thus be regulated beforehand. Water can be boiled at a constant tem- perature far exceeding 100, a temperature capable indeed of melting tin, bismuth, and lead. Papin's Digester is used to dissolve or boil in water substances which require a higher temperature than that of ebullition in free air, at the ordinary pressure of the atmosphere. We have mentioned that the ebullition of liquids takes place at temperatures which are lower as the pressure decreases ; now, on placing under the receiver of an air- pump a vessel containing water at a temperature below 100, this liquid is seen to enter into ebullition as soon as, on rarefying the air, the pressure falls to that of the elastic force of steam at this temperature ; the vapour thus formed accumulates above the surface of the liquid, and by its increasing pressure ultimately stops the ebullition. If the receiver is now cooled by means of a wet cloth, the fall of temperature condenses a part of the vapour, and thus diminishes the pressure, and ebullition recommences. This experiment can be tried without the aid of an air-pump. FIG. 299, Ebullition of water at a temperature lower than 100. 452 PHYSICAL PHENOMENA. [BOOK iv. Water, contained in a bulb with a long neck, is submitted to a lengthened ebullition, in order that the air may be completely ex- pelled by the vapour which is formed ; the flask is then corked and removed from the fire, and in order to prevent the entrance of air, the neck is immersed in water (Fig. 299). The vapour which remains above the liquid has a tension sufficient to prevent ebullition; but if the bulb is cooled by pouring cold water over it, or by putting it in contact with ice, the vapour is condensed and ebullition recom- mences : it seems as if water is boiled by being cooled. To understand thoroughly the con- ditions under which the last change of state the liquefaction of gases which remains to be studied takes place, it is indispensable for us to know the laws which regulate the formation of vapours in vacuo, the experimental demonstration of which is due to the physicist Dalton. The following is an account of them : If we introduce into the Torri- cellian vacuum a certain volume of any liquid, for instance, a cubic centi- metre of alcohol, the level of the mercury is seen to be depressed, and to stop at a point I (Fig. 300) ; and its distance from the level of a barometer, immersed in the same basin as the first tube, measures the tension or elastic force of the vapour formed. We see at once that in vacuo liquids pass spontaneously into vapour. Let us suppose that a thin stra- tum of liquid is floating on the mercury : if the tube is now raised without lifting the lower end out of the mercury, the level will be observed to remain at I, that is FIG. 300. Spontaneous evaporation of a liquid in the barometric vacuum. First law of Dalton. CHAP, ni.] EFFECTS OF VARIATIONS OF TEMPERATURE. 453 to say, at the same height as before. But the liquid stratum of alcohol diminishes in thickness in proportion as the space occupied by the vapour increases ; a fresh quantity of vapour is formed with- out a change of tension ; and thus it continues until the whole of the liquid is evaporated. If we now continue to raise the tube, that is, to increase the space which the vapour occupies, the level of the mercury will rise, which proves that the tension of the vapour diminishes. The tube being again lowered, the level falls and comes back to the point I; but if then the same movement be con- tinued, the level remains constant, while an increas- ing portion of the vapour resumes the liquid form. Figure 301 represents three barometric tubes, the cham- bers of which are filled with the vapour of the same liquid; as long as this re- mains in contact with the liquid itself, its tension does not vary, which is proved by the equal height of the mercury in the three experi- mental tubes. From this first experi- ment Dalton concluded : 1st. That a liquid placed in a vacuum vaporizes spontaneously. 2nd. That the vapour thus formed attains a maximum degree of tension which remains invariable whilst an excess of liquid remains in contact with the space filled with vapour. It is then said that the space is saturated with vapour. If we make the experiment with liquids of various kinds water alcohol, ether, &c. we find that the maximum tension varies with different liquids at the same temperature ; this is proved by the different levels of the mercury in the barometer tubes shown in FIG. 301. Invariability of the maximum tension of the same vapour at the same temperature. Dalton's second law. 454 PHYSICAL PHENOMENA. [BOOK iv. Figure 302. If the temperatures are caused to vary, these phenomena are produced in the same order, but the maximum tension increases rapidly. The following table gives the tensions of aqueous vapour in a vacuum, at different temperatures, expressed either by the number Fio. 302. Inequalities of the maximum tensions of different vapours at the same temperature. Dalton's third law. of millimetres of mercury which it supports in a barometric tube, or by the number of atmospheres of 760 millimetres. Temperatures. Tensions. Temperatures. Tensions. mm. 10 2-1 + 120 2 atmospheres. 4-6 + 134 3 + 10 9.2 + 144 4 >j + 20 17-4 + 152 5 5J + 30 31-5 + 180 10 )> + 40 .55-0 + 212 20 ?> + 50 92-0 + 252 40 JJ + 100 760-0 + 266 50 By this table it is seen that at the ordinary temperatures, between 10 and 30 for instance, the maximum tension of aqueous vapour in vacuo does not exceed 3-2 millimetres. A pressure higher than* 32 CHAP, in.] EFFECTS OF VARIATIONS OF TEMPERATURE. 455 millimetres, at the temperature of 30, will cause a part of the vapour to return to the liquid state. Nevertheless, we see water spon- taneously vaporized in the open air, under a much greater pressure, the mean being 760 mm. This is an apparent anomaly, which proves the tendency which gases possess to rise by virtue of the expansive force which belongs to them ; the air truly presses on the surface of the water, but as air is a porous body, its molecules having spaces between them, the molecules of aqueous vapour fill these intervals, and thus mix with the gas of which the atmosphere is formed. The laws of the mixture of gases and vapours were studied by Gay-Lussac, who demonstrated that, if a space full of gas is saturated with the vapour of any liquid, the maximum tension of this vapour is precisely that which it possesses in a vacuum at the same tempera- ture. The more the temperature is raised, the more vapour will a space, whether vacuous or filled with gas, require to. saturate it. Thus in summer, in very warm weather, there is often more aqueous vapour in the air than in winter, during a damp and cold season. This fact astonishes many people, who consider that clouds and fogs are formed of aqueous vapour; but this is a mistake, for aqueous vapour is always perfectly invisible and transparent. The very minute drops of which fogs and clouds are formed are water in the state of liquid, not of vapour ; in other words, they are aqueous vapour which the lowness of the temperature has condensed. There are, it is true, substances whose vapours are visible for example, iodine ; but this results from the fact that this vapour is not colour- less like that of water, for it is of a beautiful purple-violet. Again, the vapour of chlorine is visible, on account of its greenish-yellow colour, that of bromine for its brownish-red colour. When a gas or vapour is contained in a closed space, its lique- faction can be produced by two methods viz. either by lowering its temperature or diminishing its volume. But, in ordei that the liquid may appear, it is necessary that the space be previously saturated ; and it is also by this same means of cooling or compression that the state of saturation is obtained. By vapour is understood the condition of a substance which was before in a liquid state. There is no difficulty in liquefying any vapour, if we place it under the conditions of temperature and pressure which it possessed when it existed in the liquid state. 456 PHYSICAL PHENOMENA. [BOOK TV. The liquefaction of gases presented many difficulties which by degrees have been overcome. Ammonia gas, chlorine, carbonic acid gas, and protoxide of nitrogen have been liquefied and even, with the exception of chlorine, solidified thanks to the use of vigorous processes of compression and refrigeration. Five gases now alone remain which have not been liquefied by any known means ; these are, hydrogen, oxygen, nitrogen, carbonic oxide, and binoxide of nitrogen a temperature of 110 below zero, combined with a pressure of from 30 to 50 atmospheres, has left them still in the gaseous state : for this reason they are called permanent gases. But induction authorizes us to believe that it would be possible to reduce them, like other gases, to the liquid state by using more powerful means, for in a recent research Dr. Andrews of Belfast has shown it to be probable that the various states of matter are continuous, the liquid state forming a link between the solid and gaseous states a link however at times suppressed when the solid passes at once into the gaseous or vaporous form and he holds that the gaseous and liquid states are only distant stages of the same condition of matter, and are capable of passing into one another by a process of con- tinuous change. CHAP, iv.] PROPAGATION OF HEAT. 457 CHAPTER IV. PROPAGATION OF HEAT. RADIANT HEAT/ Heat is transmitted in two different ways, by conduction and by radiation Examples of these two modes of propagation Radiation of obscure heat in vacua Radiant heat is propagated in a straight line ; its velocity is the same as that of light Laws of the reflection of heat ; experiments with conjugate mirrors Apparent radiation of cold Burning mirrors Refraction of heat ; burning glasses Similarity of radiant heat and of light Study of radiators, reflectors, absorbing and diathermanous bodies Thermo-electric pile ; experi- ments of Leslie and Melloni. WHILE describing the effects of heat on matter, effects which modify its volume, or change its physical condition, we have said nothing of the manner in which the passage of heat from the heat-source to the heated body is effected. When two bodies are in the presence of each other, either in contact or at some distance apart, experiment proves that an interchange of heat takes place between them, how little soever their temperatures may differ; so that each of them becomes a source of heat to the other: but we more frequently reserve the term heat-source for that one of the two bodies which possesses the higher temperature. We shall now study the different modes of transmission of heat when it passes from a heat-source to a body which is more or less distant, or when it is transmitted through various media. Experiment has shown us two principal modes of propagation of heat, and the following examples may be easily multiplied by adding our own daily observations. When a cold iron bar is held in the hand by one of its extremities, the other end being placed in the fire, a certain time elapses before the heat of the fire, which is gradually transmitted along the bar, is perceptible to the touch ; the shorter the bar, the less time does the heat take to travel along N N 458 PHYSICAL PHENOMENA. [BOOK iv. it; moreover, the intensity of the heat thus propagated increases from the moment of the first impression, if the bar still remains in the fire. Here, the heat has travelled along the metal, and from molecule to molecule ; it is by the intervention of material particles that it has thus been conducted from one extremity to the other of the iron bar, and lastly communicated to the hand by contact. This is an example of the propagation of heat by conduction. It is in this way that the temperature of the exterior walls of a vessel is raised, when hot water has been poured into the interior. The same mode of transmission does not obtain, however, when the heat of the fire is communicated to the face of a person who removes a fire-screen quickly from before him, and thus becomes exposed to its influence. In this case the rapidity of the impression proves that it is not by warm air interposed between the fire and the face that the heat of the fire has been propagated, but by a movement analogous to that of light emanating from a luminous source. The heat is then said to be propagated by radiation, and radiant heat is that which is emitted from a source of heat and thus transmitted to a distance. Thus, when a source of heat is in the presence of, and at a cer- tain distance from, a body, it can raise its temperature in two ways : either by gradually warming, molecule by molecule, all the material parts which are interposed between the body and the source, or by warming the body directly, without an elevation of temperature of the intermediate parts being a necessary condition to the elevation of the temperature of the body. Heat is propagated by conduction in the first instance, by radiation in the second. As all other methods of transmission of heat may be included in one or other of these, or by their combination, we shall study them separately, and we shall commence with radiant heat. Tbe action of the solar rays, which make themselves felt at a distance of 91 millions of miles, proves that heat does not require a medium of a ponderable nature for its propagation ; and, indeed, when, after having traversed the interplanetary spaces, it enters the atmosphere, and ultimately reaches the earth, it warms this latter directly, without having raised to a perceptible degree the temperature of the upper strata of the atmosphere, to which the cold which exists in high regions of the air, on the summits of lofty mountains, testifies. CHAP. IV.] PROPAGATION OF HEAT. 459 Heat radiates from all the incandescent bodies which may be observed on the face of the earth, in the same way as it emanates from the sun. Obscure heat also possesses the same property, that is to say, it is propagated from its source to any distance by direct radiation, without warming the intermediate space, as during con- duction. Eumford's experiment has placed this result beyond doubt. He constructed a barometer, the tube of which was ter- minated at its upper extremity by a large bulb, in the centre of which a thermometer was placed ; the bulb thus formed the vacuous chamber of the instrument, so that it was entirely void of ponderable matter (Fig. 303). Having then closed the orifice of the stem, and sealed off the bulb from it, he plunged the lower part of this latter into boiling water; the mercury in the thermometer rose immediately an effect which could be attributed only to the radiation across the vacuum of the heat communicated by the water to the mercury in the bulb. Thus obscure heat radiates from calorific sources in the same manner as luminous heat. We will now show a more complete analogy be- tween the phenomena of radiant heat and light ; the same laws regulate both, so that luminous and calorific effects appear to be produced by movements of the same nature, for we are already aware of the existence of heat-rays beyond the red end of the solar spectrum Like light, radiant heat is transmitted in straight lines through homogeneous media; if therefore we interpose, between a source of heat and one of the ,,, / -r T i T/V i ji Fl - 303. Radiation bulbs of Leslies differential thermometer, a series of obscure heat i VdC'UO, of screens, each pierced with a hole, the instrument will mark the elevation of temperature only so long as the holes of the screens remain in a straight line. This experiment proves that bodies exist of such a nature that radiant heat does not pass through them : they are called adiathermanous substances. Other substances which are traversed with more or less facility by heat- rays are called diathermanous : these latter are generally transparent substances, such as air and other gases; but there are also opaque bodies which permit the passage of radiant heat, and are hence diathermanous. N N 2 460 PHYSICAL PHENOMENA. [BOOK iv. The velocity of propagation of radiant heat is as great as the velocity of light. The first series of experiments proved that there is no appreciable interval between the moment when a screen, inter- posed between a source of heat and a very sensitive thermoscope, is removed, and that in which the instrument marks the elevation of temperature. Mariotte worked thus at a distance of more than 100 metres : Pictet at 23 metres. But these experiments only prove that the velocity of radiant heat is great, without giving its measure ; it has since been proved that there is a perceptible difference be- tween the velocity of the dark heat-rays of the solar spectrum and of light rays. FIG. 304. Reflection of heat; experiments with parabolic conjugate mirrors. Radiant heat is reflected from the surface of bodies, like light, and in accordance with the same laws. We can assure ourselves of this identity, by showing that the effects of a radiating source are analogous to the luminous effects of reflection. Thus, if we place two parabolic mirrors opposite to each other, so that their axes coin- cide (Fig. 304), a source of heat placed in one of the foci will transmit, to the nearest mirror, rays which will be reflected parallel to the common axis, and after falling on the second mirror will, after this new reflection, be reunited in its focus. This is what ought to take place if the laws of the reflection of heat are the same as those CHAP, iv.] PROPAGATION OF HEAT. 461 of light ; and we find that such is the case. In one of the foci we place an iron basket containing burning coals, and in the other focus some gunpowder, tinder, gun-cotton, or any other inflammable substance, it takes fire instantly. This experiment will not succeed, if the source of heat or the inflammable body be displaced, however little, from their respective foci. An experiment of Sir H. Davy has proved that the laws of the reflection of radiant heat are the same in vacua as in air. Moreover obscure heat is propagated like heat which radiates from incandescent sources, which may be demonstrated by the experiment of the conjugate mirrors by means of a vessel filled with boiling water. This vessel is placed in one of the foci and the bulb of a thermometer in the other, which immediately indicates a rise of temperature. The same thermometer placed away from the focus manifests no perceptible change. We will now speak of a curious experiment which would lead us at first sight to believe that cold can be radiated as well as heat. If a piece of ice is substituted for one of the sources of heat, of which we have just spoken, and if it is placed exactly in the focus of one of the mirrors, the thermometer in the other focus falls, as if a reflection of cold had taken place. The fact in this case is, as in the others, that there are two bodies of unequal temperature in the presence of each other, both of which radiate heat. Each of them suffers a loss of heat, which is partly compensated for by the gain which follows from the radiation of the other. In the first experiment, the thermometer received more than it lost, and there- fore there was an increase of temperature and an elevation of the mercurial level. In the ice experiment, the thermometer on the con- trary loses more heat than it receives; its temperature diminishes, and the mercury sinks. The laws of radiant heat have been utilized in obtaining a heat of very great intensity at the focus of a spherical concave mirror exposed to the solar rays. With an apparatus of this kind, which is then called a burning mirror (Fig. 305), and which possesses a large diameter and considerable curvature, metals have been melted, bricks and stones vitrified, &c. Buffon obtained this effect from spherical mirrors, by placing 100 silvered plane mirrors in such a manner that each, of them was a tangent to the same sphere ; each mirror turned on a hinge, and he thus increased or diminished the 462 PHYSICAL PHENOMENA. distance of the focus at will. By means of this mirror he melted lead at a distance of 140 feet (45'5 m.), and silver at 100 feet (22'5 m.). The rays of heat which fall on a body are not all reflected. They are generally divided into two groups. The first group consists of the rays which are reflected from the surface of the body according as we have just stated, to the laws of reflection of light ; there are also other rays which are diffused in every direction; but none of these rays penetrate into the substance of the body. The second group is formed of the rays which are absorbed by this substance, and produce in it an elevation of temperature, being propagated by conduction throughout the whole mass: and, lastly, rays which pass through the body, and issue in the same manner as light traverses and issues from transparent media. The proportion of these differ- ent fractions of incident heat rays varies according to the nature of the body which re- ceives them, the state of its surface, &c. Hence the expres- sions, reflecting, diffusive, absorb- ing, and diathermanous powers, to designate the properties which correspond to these different modes of radiation of heat by various bodies. We shall speak of these hereafter. At present we will confine ourselves to the pheno- mena of the transmission of radiant heat through diathermanous media, and to the laws of its propagation, because we shall find an analogy between heat and light in this respect. Heat-rays, when they enter a diathermanous medium, undergo the deviation which we have studied in light under the name of refraction. If the calorific beam falls perpendicularly on the surface of the medium, there is no deviation. But at another incidence the ray is deviated, and approaches the normal at the point of incidence, in Fio. 305. Burning mirror. CHAP. IV.] PROPAGATION OF HEAT. 46$ passing from one medium to another of a greater density ; in a word, the laws of refraction of heat have been demonstrated to be like those of the refraction of light. This fact has been proved experi- mentally by using convergent spherical lenses to concentrate the calorific rays which accompany the luminous rays of the sun. At the focus, where the light is most intense, the heat is also the greatest ; and every one can verify the truth of this fact, by setting fire, by the aid of a magnifying-glass, to even a slightly inflammable substance by the rays of the sun tinder, linen, wood, paper, &c. This refers, it is true, to sources of luminous heat ; but Melloni has proved by using FIG. 306. Refraction of heat. prisms and lenses of rock-salt which substance absorbs a smaller amount of heat than any other that obscure heat is refracted in the same manner as that proceeding from an incandescent source. The refraction of heat has been used, like its reflection, to produce a very intense heat by the concentration of the rays of the sun. The name of burning glass is given to every kind of lens constructed for this purpose, whatever the diathermic substance may be. The power of a burning glass increases with its diameter, and with the shortness of the radii of the spheres to which the surfaces of the lens belong. Tschirnhausen, celebrated for the construction of burning mirrors of great power, made burning glasses nearly a metre in diameter, with which he succeeded in melting metals and vitrifying mineral 464 PHYSICAL PHENOMENA. [BOOK iv. substances. Buffon obtained the same results with an echelon lens, that is, a lens, one surface of which is plane, while the other is cut into concentric rings. The curvature of each of these rings is calculated so that all the solar rays falling on the surface con- verge to the same point (Fig. 307). In an apparatus of this kind, the thickness of the glass being less than in an ordinary lens of the same aperture, less heat is absorbed, and the calorific effect at the focus is consequently more intense. Burning glasses have also been constructed with various liquids, the lens being formed of two convex glasses, enclosing a cavity which contains the liquid employed. Of these we must quote the burning glass con- structed in the last century by Bernieres and Trudaine ; it was four feet (1/33 m.) in diameter, and had a focal length of eight feet : when filled with turpentine and exposed to the solar rays, calorific effects of extra- ordinary intensity were ob- tained. We have most of us heard that sailors, during voyages to the frozen regions of the poles, have been able to use lenses of ice to procure fire. In England very interesting experiments were made with an ice lens of great diameter (3 metres), which proved the possibility of igniting powder and paper at the focus of this novel kind of burning glass. From the foregoing remarks we see that radiant heat is propa- gated according to the same laws as light; its velocity is of the same kind and degree; its direction is rectilinear in homogeneous media; it is reflected and refracted similarly. The analogy has become still more striking since the discovery that heat undergoes FIG. 307. Echelon lens. CHAP, iv.] PROPAGATION OF HEAT. 465 double refraction in bi-refractive media ; and lastly, that it is also polarized by reflection, and by simple and double refraction. It is probable, therefore, that the calorific radiations do not differ essentially from luminous radiations, that doth are due to the same cause, viz. to vibrations of the ether ; but, whilst the disturbance produced by the motion of the luminous waves affects the organ of sight alone, that which proceeds from heat-waves, instead of giving us the sensation of light, produces the sensation of heat. Calorific and luminous radiations have even been considered as possessing no other difference, except a greater or less rapidity of the vibratory movement which gives rise to them. Thus the longest undulations or the least refrangible rays these expressions are equivalent would constitute the heat-rays, the obscure radiations ; then increasing from a certain limit of rapidity, the vibrations, without ceasing to produce heat, would impress the retina in the form of light. The theoretical ideas which assign a common origin to phenomena apparently so different, and which are so, indeed, to our senses, are becoming more and more plausible. The old hypothesis, which made heat, light, electricity, and magnetism so many real and distinct agents having a separate existence, is almost abandoned. We shall soon see, in regard to heat, other proofs in favour of the new theory, which show that heat is transformed into motion, and motion into heat; a transformation incapable of being explained by the hypo- thesis that caloric is a substance. All bodies, whatever may be their temperature, emit or radiate heat. We have described the experiment which proves that this emission takes place with obscure heat as well as with luminous heat. If, then, two or more bodies are in the presence of each other, they will mutually radiate one towards the other, and we know that the heat, received thus by each of them, will be partly reflected or diffused, partly transmitted through its substance, and partly ab- sorbed. It is this last portion only of the heat which has fallen on the surface of a body which, being transmitted from molecule to molecule, that is by conduction, influences its temperature. When bodies which are near together and confined in a small space are of unequal temperatures, experiment shows that the hottest gradually cool while the others become warmer. At the end of a 466 PHYSICAL PHENOMENA. [ROOK iv. certain time equilibrium of temperature is established, which proves that the interchange of heat ceases, or rather that it results in an exact compensation between the losses and gains undergone by each of them : the quantities of absorbed and of radiated heat are then equal to each other. This last hypothesis, which is generally admitted, is expressed by saying that the absorbing power and the emissive or radiating power of a body are equal to each other. Moreover, the hypothesis has been verified by experiment as regards temperatures not exceeding 300. Of this more presently. The temperature of a source of heat influences the rapidity with which it is cooled by radiation. Generally speaking, the higher the FIG. 308. Measure of the emissive powers of bodies. Experiment with Leslie's cube. temperature, the more considerable is the emission, other circum- stances remaining the same. This result may be proved by enclosing the source of heat in a vacuum or in a space filled with a gas, provided that the temperature be higher than that of the walls of the enclosure, the rapidity of the cooling being also greater as the excess of temperature itself is greater. Emissive power depends also on the nature of the surface by which the radiation is effected. Leslie proved the inequality of the emissive power of different bodies in the following manner : As sources of heat, he took hollow cubes, the lateral faces of which were formed of the substances whose emissive powers he desired to compare; he then filled them with boiling water, which CHAP, iv.] PROPAGATION OF HEAT. 467 was kept at a temperature of 100 by the heat of a spirit-lamp. Each face of the cube A (Fig. 308) was turned successively towards a concave mirror M, at the focus a of which was placed one of the bulbs of his differential thermometer. To limit the rays of heat which fell on the mirror, Leslie placed two screens, B, c, pierced with wide apertures in the common axis of the mirror and cube, as shown in Tig. 308. The action of the radiated heat produced a difference of level in the two limbs of the differential thermometer, which became stationary at the end of a few seconds. Operating in the same manner with the different faces of its cubes, Leslie proved that the nature of the radiating surface has a considerable influence on the emissive power; and, as it has been proved that the emissive powers of two bodies are proportional to the excess of temperature of the two bulbs of the apparatus, he could form a comparative table of their values for one temperature of the heat-source. Since Leslie's time, the radiating powers of a great number of bodies have been measured with other apparatus, and his result, that lamp-black and white lead are the two substances which possess the greatest amount of radiating power, has been verified. If we represent the emissive powers of these substances by 100, the emissive powers of the following substances, at the temperati*re of 100, are as follows : Lamp-black . . . White lead. . . . Paper 100 100 98 Steel Platinum .... Polished brass 17 17 7 Glass 90 Red copper .... 7 Indian ink .... Gum-lac .... 85 72 Polished gold . . . Polished silver . . 3 3 We thus see that the metals . possess the least emissive power. It was once imagined that bodies of bright colours radiated heat to a less extent than those of a dull and dark colour, but the foregoing table disproves this ; for white lead radiates as much as lamp-black. The degree of polish of the surface of a body, a metal for instance, influences its radiating power : in the case of a beaten or laminated plate, if it is roughened its radiating power is increased ; on the contrary, it is diminished if the plate is of cast metal ; which leads to the supposition that the emissive power is in the inverse ratio of the density of the superficial strata. 468 PHYSICAL PHENOMENA. [BOOK iv. The preceding results account for a fact, which is easily proved, that polished metal vessels, especially silver ones, preserve the heat of the liquids contained in them for a long time ; but if this surface is unburnished, and especially if it be covered with lamp- black, the radiation becomes very intense, and the cooling of the liquid takes place rapidly. From a consideration of the radiating power of different sub- stances let us pass to their reflecting power. And in the first place we may remark that, in the case of a body which is not transparent to heat or which is adiathermanous, of 100 heat-rays falling on its surface, perhaps 20 will be absorbed; while all the others, to the number of 80, will be reflected. Now, as the absorbing power is itself equal to the emissive power, by a very simple calculation the reflecting powers of bodies can be found without having recourse to experiments. At the same time we must not forget that experiment has led to the preceding reasoning ; and in physics, it is always more instructive to learn anything experimentally, both as regards the explanation of facts and the verification of laws. Leslie compared the reflecting power of different substances, by modifying the apparatus which he used for the study of their radiating powers ; but we prefer the apparatus used by Melloni, as many other researches connected with heat can be made with it. The following is a description of it : A series of bars of different metals, usually bismuth and anti- mony, B, A, . . . are soldered together at their extremities, and they are arranged in such a manner that all the even junctures are on one side, and all the odd ones on the other, as in Fig. 309. The two extreme bars of the series, one bismuth and the other antimony, are connected by a A BA BA BA BA B t A i - Vio. 309.-Elements of the thermo-electric pile. metal Wire ; thlS form S a thermO- electric pile. Whenever there is a difference of temperature between the even and the odd joints, an electric current is produced, either in one direction or the other, but always passing from the bismuth to the antimony, on the side which is at the highest temperature. Generally a" certain CHAP. IV.] PROPAGATION OF HEAT. 469 number of similar elements are united in a bundle, to which the form of a rectangular prism is given, so that both faces are visible, one formed by the even number of joints, the other by the uneven. Whenever one or other of the faces of the pile is heated by calorific radiation, the current will be produced ; and we must now consider how its existence can be proved. The two conducting wires are wound round the frame of a galvanometer the desciiption of which will be found in Book VI., which is devoted to Electricity and the current acts on the magnetic needle, causing it to deviate either in one direction or in the other, according to the direction of the FIG. 310. Thermo-electric pile for the study of the phenomena of heat. current. The extent of the deviation can then be read on the dial of the galvanometer, and this shows the intensity of the current, and, afterwards, the difference of temperature of the two faces of this pile. The thermo-electric pile thus constituted is an instrument of great sensibility : if we touch one of the faces with the finger, or blow a puff of warm air upon it, it is sufficient to cause the needle of the galvanometer to be considerably deviated ; on touching the same face with a cold body, deviation takes place in the contrary direction. Melloni employed the thermo-electric pile for the measure- 470 PHYSICAL PHENOMENA. [BOOK iv. ment of the reflecting powers of different bodies, in the following manner : At A (Fig. 311) a Locatelli lamp, which is a heat-source of constant intensity, was placed ; B and c are two screens, one entirely opaque, the other having an aperture or diaphragm, thus allowing heat-rays from the lamp to pass through it, when the screen B is removed. On the stand D, a plate of the reflecting substance to be examined is placed, and at E is the thermo-electric pile, moving on a scale H H', which can be moved round the point H, so that the face of the pile can be placed in the direction of the reflected calorific rays. Before placing the plate on its stand, the scale is turned round the point FIG. 311. Apparatus used by Melloni to measure the reflecting powers of bodies. H, and placed in a line with a scale which supports the pieces A, B, c. The screen B is then lowered, and the deviation of the needle of the galvanometer is measured, which gives the intensity of a ray of heat radiated directly from the lamp to the pile, at a distance equal to the total lengths of the scales. When the first measure- ment has been effected, a second is made in order to give the intensity of the reflected ray, and for this purpose the different parts of the apparatus are placed as shown in the figure, the reflecting plate being on its support, and the pile protected from direct radiation by means of a large screen. On lowering the screen B, the rays emanating from the source fall on the plate, are there reflected, and strike against the face of the pile, after having traversed the same CIIAP. iv.] PROPAGATION OF HEAT. 471 distance as the direct rays did in the first experiment. The needle of the galvanometer is deviated to a certain extent, and the relationship of the two deviations gives the reflecting power of the substance. MM. La Provostaye and Desains have continued Melloni's re- searches, and experimented on a great number of substances ; they have measured their reflecting powers under different incidences, varying the natures of the source of heat. They have discovered that with any one body the reflecting power remains nearly constant, from the normal incidence to an incidence of 30; but afterwards it increases rapidly, in proportion as the angle of incidence increases. The reflecting powers of metals remain nearly constant for each of them, in whatever manner their surfaces have been worked, pro- vided that the degree of polish is the same. If the intensity of the incident ray of heat be represented by 100, that of the reflected ray is given by the following numbers, which refer to an incidence of 50 : Reflecting powers. Radiating powers. Polished silver ... 97 ..... 3 Gold ....... 95 3 Red copper 93 7 Polished brass .... 93 7 Platinum 83 17 Steel 83 17 Glass 10 90 Lamp-black .... 100 By comparing these numbers with those which measure the radiating or emissive powers of the same substances, shown in the second column, we find a proof of what has been before stated, viz. that the radiating and absorbing powers of a body must be equal; for the radiating, like the absorbing, power is the com- plement of the reflecting power, at least for bodies which are not transparent to radiant heat, and if we make due allowance for the diffused heat. Polished metals possess the greatest amount of reflecting power ; when their surfaces are unburnished or rough, the heat-rays are reflected in every direction, and the proportion of heat reflected in a regular manner diminishes considerably as the proportion of diffused heat increases. This phenomenon is analogous to that observed under the same conditions in the case of light. 472 PHYSICAL PHENOMENA. [BOOK iv. Leslie and Melloni also compared, by means of the two appa- ratus before described, the absorbing powers of bodies ; that is to say, the proportion of heat emitted from a constant source which enters them and raises their temperature. They found that, in this respect, the order of classification of the various substances is the same as if they had been arranged according to their emissive powers ; a result which confirms, to a certain extent, the equality of these two powers proved by the reasoning adopted in the case of equili- brium of temperature. We owe to Leslie the experimental determi- nation of the fact that good reflectors of heat are bad radiators. What has been aptly termed the Theory of Exchanges of radiant heat, a branch of the subject which has been investigated by Prevost, Provostaye, Desains, Balfour Stewart, and Kirchhoff, may be stated as follows : I. If an enclosure be kept at a uniform temperature, any sub- stance in it will at last attain that temperature. II. All bodies are constantly giving out radiant heat indepen- dently of the temperature of the bodies which surround them. III. Therefore, when a body is kept at a uniform temperature, it receives back as much heat as it gives out, i.e. its absorption is equ,al to its radiation. This theory not only applies to the quantity of heat, but to its quality. That is, it holds good not only in the case of dark rays, but of par- ticular rays located in a particular part of the spectrum of a body visibly luminous, as the spectrum of the light emitted by such a body is built up of both heat-rays and light-rays, as we have seen. Hence to these statements we must now add, according to the researches of Balfour Stewart and Kirchhoff: IV. Bodies when cold absorb the same rays which they give out when hot. It will be seen that this is the same statement which we have already made concerning light; it is in fact the basis of spectrum analysis. The influence of colour on the absorption of heat-rays has been shown by Franklin's experiments. This illustrious physicist CHAP, iv.] PROPAGATION OF HEAT. 473 placed pieces of differently coloured stuffs on the snow, and left them for some time exposed to solar heat ; they absorbed the heat-rays, became warm, melted the snow beneath them, and thus sank to various depths, and deeper in proportion as the colour was darker. From this result it was thought that bodies of light colour are bad absorbers, and this again justified the supposed identity of rays of light and rays of heat. But Tyndall has recently proved that this conclusion is not quite exact. According to this physicist, the nature of the source of heat must be taken into account ; obscure heat-rays are not affected in the same way as luminous heat-rays. The diathermanous power of substances must also be considered. Thus, having taken two cards, one covered with white powdered alum and the other with black powdered iodine, and having exposed both to the fire, he found that the iodized card scarcely warmed at all, while the card covered with alum became extremely warm ; he explains this difference by the diathermanous property which iodine possesses to such a high degree ; the radiant heat penetrates the powder and is reflected on the limiting surface of the molecules, without being absorbed by them. Moreover, a piece of amorphous, and almost black, phosphorus, placed at the focus of the electric light, cannot be ignited, whilst the same arrangement nearly instan- taneously raises platinum to a white heat. Tyndall attributed this curious effect to the diathermancy of the phosphorus. This last property, possessed by certain substances, in virtue of which they can be traversed by heat-rays without absorbing them, in other words without their temperature being raised, exists in the most marked manner in rock-salt. Of 1,000 rays which reach the surface of a plate of this substance, 923 are transmitted; the 77 rays which do not pass are reflected from the two faces of the plate ; consequently, there is no absorption. This remarkable result, discovered by Mel- loni, remains the same, whatever may be the nature of the heat-rays, whether luminous or obscure. Alum and glass are only diathermanous as regards the radiations of luminous heat ; they arrest rays of obscure heat : this is also the case with Iceland spar, rock-crystal, and ice. The thickness of the plates has an influence on the absorption as on the trans- mission of heat-rays; but this influence does not increase in pro- portion to the thickness. Thus of 100 rays which reach two o o 474 PHYSICAL PHENOMENA. [BOOK iv. diathermanous surfaces, one 'having double the thickness of the other, 62 rays pass through the thinner, and 58 through the other; a plate quadruple the thickness of the first allows 55 rays to pass. FIG. 312 Mclloni's apparatus for measuring the diathermanous power of bodies. The comparison of the diathermanous powers of different sub- stances is made by means of Melloni's apparatus, arranged as in Tig. 312. A plate of the substance the diathermanous power of FIG. 313. Cube of boiling water. FIG. 314. Plate of blackened copper heated to 400. Fio 315. Incandescent spiral of platinum. which is to be measured, is supported on a stand D. The thermo- electric pile is placed at E, in the direction of the rays of heat which traverse the aperture made in the screen c. The deviation of the CHAP, iv.] PROPAGATION OF HEAT. 475 needle of the galvanometer, produced by the direct rays without the interposition of the plate, is first ascertained ; the plate is then placed on its stand, and the deviation produced by the same rays traversing the plate is noted. The relation of these two deviations gives the diathermanous power of the substance. To study the influence of the nature of the heat-source, Melloni substituted in place of Locatelli's lamp a cube of boiling water, a plate of blackened copper, or an incandescent spiral of platinum. These different heat-sources are represented in Figs. 313, 314, and 315. In the experiments he made on this subject, Melloni took care, in order to compare the results, to place these different sources at such distances from the pile, that the direct rays of heat produced the same deviations on the needle of the galvanometer. The following table shows the influence of the nature of the source of heat on the transmission or on the diathermanous power of different substances : Locatelli's lamp. Cube of water Copper Incandescent at 100. at 400. platinum. Direct radiation . . . Eock-salt . . 100 , 92 39 39 37 . 9 ', 6 , . 100 , , . 92 , , . 28 . . . 24 . . 28 , 2 . > .100 . . , . 92 .. 6 . . 6 . . 6 . . . . 100 92 Iceland spar .... Glass Rock-crystal .... Aliun. Ice , From these experiments we conclude that, as there are different rays of light, so also there are different rays of heat which bodies absorb and transmit in different proportions, nearly in the same way as transparent bodies absorb some colours and allow others to pass. Speaking of this property, Melloni used the word thermochroism, derived from two words, the first signifying heat and the second colour. In terminating the foregoing remarks concerning radiant heat, we may enunciate the following law relating to the decrease of in- tensity with an increase of distance. As with light, the intensity of radiant heat varies inversely as the square of the distance. A very simple experiment, which we have borrowed from Tyndall's work on Heat, proves the truth of this law, which may be deduced by calculation. o o 2 476 PHYSICAL PHENOMENA. [BOOK iv. One face of the thermo-electric pile is furnished with a cone which limits the dimensions of the sheaf of heat-rays, and which, covered on the inside with black paper, can only reflect the heat which falls obliquely on its inner surface. For the source of radiant heat, a tin vessel filled with boiling water is used, one face of which is covered with lamp-black ; this surface we use to prove the law, by radiation towards the pile. The pile furnished with its cone is placed opposite the vessel, at a given distance s o (Fig. 316); the needle of the galvanometer is deviated to a certain extent ; the -pile is then removed to double the distance s' 0; the positio'n of the needle of the galvanometer remains constant ; and this is the case for any other distance. For each of these positions, the total FIG. 316. Intensity of radiant heat. Law of the squares of the distances. effect of radiation is therefore the same ; but the parts of the surface of the vessel which send out rays of heat into the cone are greater and greater ; these are circles whose diameters A B, A' B, increase in proportion to the distance of the pile from the vessel, and whose surfaces from that time continue to increase as the squares of these same distances. It is therefore necessary that the intensity of radiation should diminish in the ratio of these same squares, in order that the effect produced on the pile may remain constant. In a word, the augmentation of the efficacious radiating surface is exactly compensated for by the diminution of the intensity with the distance ; it is thus that the law has been proved. CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 477 CHAPTER V. TRANSMISSION OF HEAT BY CONDUCTION. Slow transmission of heat in the interior of bodies Unequal conductivity of solids Conductivity of metals, crystals, and non-homogeneous bodies Pro- pagation of heat in liquids and gases ; it is principally effected by transport or convection Slight conductivity of liquid and gaseous bodies. WE have already seen that, if we hold a bar of iron, one end of which is placed in the fire, in the hand, the heat of the fire is communicated to the metal, and is transmitted from molecule to molecule along the bar; after a short time the temperature rises so high that it commences to burn our hand, and obliges us to remove it from the bar. If, instead of being iron, the bar, still of the same diameter and length, is of another metal, a similar effect would be produced ; but we observe that the length of time which the heat takes to travel along the bar, and to heat it at any given distance from the end to the same, temperature, varies with the nature of the bar. The following simple experiment will prove the difference which we have pointed out : Let us take two bars of equal dimensions, one of copper, the other of iron, and fix small balls of wood by means of wax at equal distances from the extremities of each ; if we place the bars, end to end, and heat the extremities in contact by means of a flame of a spirit-lamp placed at the point of junction, we shall see the balls fall one after the other, as the wax is melted by the heat which is transmitted by means of conduction along each of the bars. But at the end of a certain time, the number of balls which have fallen from the copper bar will be found to be greater than the number of balls which have fallen from the iron bar. Moreover, two balls situated at 478 PHYSICAL PHENOMENA. [BOOK iv. the same distance from the source of heat but on different bars, do not fall at the same instant. We will for the present leave the consideration of the rapidity with which heat is transmitted along each bar, and study the first effect, viz. the comparative distance at which a certain degree of temperature (here it is that of the fusion of wax) can be most quickly Fio. 317. Unequal conductivities of copper and iron. attained by the two metals. Copper, in which we have found this distance to be first attained, is said to be a better conductor of heat than iron. pipf FIG. 318. Ingeiihouz' apparatus for measuring conducting powers. Fig. 318 represents an apparatus invented by Ingenhouz and modified by Gay-Lussac, which is used to compare the conducting powers of solids. Cylindrical rods of each of the substances to be compared are covered with layers of wax of equal thickness, and are placed horizontally, so that one of their extremities is immersed in a bath of oil or boiling water, while the other passes through the sides of the vessel which contains the liquid. The heat of the liquid is transmitted along each rod, and melts the wax at distances which are greater as the conductivity of the substance increases. Other processes have been devised for the measurement of the conducting powers of solids; but the one we have just described is sufficient to show how different bodies can be arranged in the order of their CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 479 conductivity. The following is the order and degree of conductivity of the principal metals : Silver 1,000 Copper- Gold . Brass . Zinc . Tin 776 532 236 190 145 Iron 119 Steel 116 Lead 85 Platinum 84 Palladium 63 Bismuth . 18 Of all solid bodies metals are the best conductors of heat, always excepting bismuth. Stone, glass, and marble are much less so than metals ; lastly, wood-charcoal prepared at a low temperature, that is to say not calcined, and organic substances generally, pulpy fruits and plants, and the tissues of animals and vegetables, are bad conductors. The preceding numbers indicate the great difference in the conduc- tivities of metals. This difference may be illustrated in a very simple way, by plunging two spoons, one of German silver and the other of pure silver, into the same vessel of hot water. After a little time the free end of the silver spoon is found to be much hotter than that of its neighbour ; and if pieces of phosphorus be placed on the ends of the spoons, that on the silver will fuse and ignite in a very short time, while the heat transmitted through the other spoon will never reach an intensity sufficient to ignite the phosphorus. This fact is accounted for by the difference between the con- ducting power of the silver and that of the German silver ; for the first is represented by 1,000, the second by 60. The following experiment demonstrates that the conductibility of a substance does not depend on the rapidity with which heat is transmitted through its interior. Two short cylinders of the same volume, one of iron, the other of bismuth, have each one of their extremities coated with white wax; they are then placed on the cover of a vessel filled with hot water, their waxed ends being uppermost. The heat of the vessel is transmitted through each cylinder, and the wax on both will melt ; but that which covers the bismuth will melt first. Nevertheless the conductivity of bismuth, according to the foregoing table, is six times less than that of iron. What therefore can be the reason of the phenomenon described? It is due to the fact, that to raise the two metals of the same weight to 480 PHYSICAL PHENOMENA. [BOOK iv. Fig. 319. Experiment on the conductivity of iron compared with that of bismuth. the same temperature, about four times more heat is required for iron than for bismuth ; the heat received by the iron is therefore in great part expended in raising its temperature, and this explains the relative slowness with which the transmission through its mass takes place. To rightly observe the dif- ference between the conducting powers of iron and bismuth, it is necessary to take two bars of the same diameter, to measure the dis- tances from the source of heat of the points which possess the same temperature at the moment of equilibrium, and to take the squares of the numbers which measure these distances, which will give the relative conducting powers. The foregoing remarks refer to homogeneous bodies. In solids whose structure is not the same in every direction for example, doubly refracting crystals, Iceland spar, quartz, &c. the conductivity varies with the direction of transmission of the heat. There is a complete analogy be- tween the mode in which heat is propagated in these bodies, and that which relates to the movement of light. Thus, let us take two plates of quartz, one cut parallel and the other perpendicular to the optic axis ; coat both of the sections with wax, and pierce them with a hole, through which a wire heated by F IG. 32o.-unequai conductivity -i , , . T . . , of quartz in difierent directions. an electric current is passed: on passing the current we observe that the wax melts around the wire ; but whilst the stratum limiting the melted wax is an ellipse in the first plate, in the second it is a perfect circle (Fig. 320), which proves the unequal conductivity in the two directions. The conductivity of wood is greatest in the direction of the fibres, and much less in a direction perpendicular to this. The unequal conductivity of different solids is utilized in many ways. Tools and metal utensils, which require to be submitted to a CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 481 high temperature, are furnished with non-conducting handles of wood or ivory, for instance which almost entirely stop the transmission of heat. Cotton, silk, and especially woollen fabrics, are bad conductors ; they are therefore useful for preserving the body from excessive heat or cold. In summer, they prevent the external heat from penetrating to our bodies ; and in winter, on the contrary, the heat of the body is retained on account of the difficulty of its transmission through thick clothes. Moreover, it is not alone the substance of which they are composed which gives this property to the fabric, for the mode of manufacture also influences it. Between the threads, air is inter- posed, which remains at rest, and, like all gases in a state of rest, it conducts heat very badly ; heat therefore passes with great difficulty through the fabric. Eider down preserves heat much better than a closely made and heavier woollen coverlet would do. We might multiply these examples to any extent, but will confine ourselves to two or three curious experiments based on the differences of conductivity of solids. A metal ball is tightly wrapped up in fine cloth, in such a manner that the contact is close ; we then take a coal from the fire and place it on the ball so enveloped. The fabric will remain intact ; and if, to increase its combustion, the coal is blown upon, the cloth will not be burnt. The reason of this is that the heat received by the linen is immediately monopolized by the highly conducting metal, and disseminated through its mass. If before lighting a gas-lamp, a piece of fine wire-gauze is placed above the jet, and the gas then turned on, it will spread below and above the gauze. If it is lighted underneath, the combustion remains confinecL to the lower part of the jet of gas; if, on the contrary, it is lignted above, the upper part of the jet will alone continue to burn (Fig. 321). In both instances, the interposition of the wire-gauze is sufficient to limit the combustion, and the reason is obvious : the meshes of the gauze form an excellent conductor of the heat developed, which spreads rapidly over the wire, and does not allow a sufficiently high temperature for the existence of flame on the other side of the gauze. An important application of this pro- perty of metallic gauzes exists in Davy's safety lamps, which are used by miners. The metallic netting which envelops the light prevents the ignition and explosion of the fire-damp the dangerous gas which escapes plentifully into coal-pits. P P 492 PHYSICAL PHENOMENA. [BOOK rv. Asbestos and amianthus are two silky mineral substances, noted for their incombustibility. They are very bad conductors of heat, and with a glove of amianthus a red-hot ball may be held in the hand without danger. In this instance, the heat cannot be transmitted, it is intercepted ; in the preceding example it is, on the contrary, rapidly absorbed ; in both cases its transmission by means of conduction is limited. The experiments which have been made in order to measure the conductivity of liquids and gases prove that it is very slight. Never- theless, heat is transmitted with some rapidity through these media ; it is, however, transmitted not by conduction but by convection, that is to say, by direct transport of the heated parts. The cause of these move- ments may be easily understood ; when a liquid is heated, its density Fio. 321. Property of metallic gauze ; obstacle which it opposes to the propagation of heat. diminishes; then, as a consequence of the principle of Archimedes, it tends to rise and to displace the denser strata above it. This happens, when a liquid is heated at the bottom of the vessel which contains it ; if the liquid is heated laterally, the "currents which are established start only from the sides, instead of starting from all parts of the bottom 'of the vessel ; the heating in this case is much less rapid. The existence of currents is easily proved, if a material of the same density as the liquid is mixed with it, such, for example, as sawdust. This remains suspended in water, and on heating the vessel the movement of the particles can be traced from top to bottom and from bottom to top, proving the existence of currents : the ascending currents proceed from the heated parts, which rise, while the descending currents are due to the denser parts, which take the place of the former. Heat is therefore diffused through the whole liquid, and it is in this way that it is transmitted. CHAP, v.] TRANSMISSION OF HEAT BY CONDUCTION. 483 Nevertheless, liquids possess some proper conductivity, as has been proved by M. Despretz, who heated a liquid contained in a cylindrical vessel from above. Twelve thermometers, the bulbs of which were placed at different heights in the liquid, with their stems outside, indicated decreasing temperatures from the upper strata to the middle of the vessel, which was a metre in height ; the six lower thermometers did not rise perceptibly. The conductivity of liquids is thus established, but, as before stated, it is very slight. The proper conductivity of gases has not been established ; all that we know is, that they are certainly very bad conductors of heat. Gaseous masses are heated like liquid masses, by transport or convec- tion : in virtue of their great dilatability, as soon as a portion of a gaseous mass is heated, either by radiation or contact, its volume increases, and movements, which quickly heat the different strata, result. The heat is thus conveyed as in liquids, but with still greater rapidity. Again, if the movements of which we speak are confined by enclosing the gas in the interstices existing between thin pieces of fibrous substances, like cotton, wool, unspun silk, down, &c., the gas acquires heat with difficulty, as has been proved by many experiments of Thomson. Wo have already seen that it is partly owing to the fact of gases being bad conductors of heat when at rest, that clothes preserve the body from losing heat during cold weather. 484 PHYSICAL PHENOMENA. [BOOK TV. CHAPTER VI. CALORIMETRY. SPECIFIC HEAT OF BODIES. Definition of a unit of heat Heat absorbed or disengaged by bodies during vari- ations in their temperature Specific heat of solids Latent heat of fusion Ice-calorimeter Latent heat of vaporization of water. WHEN a body is heated or cooled through a certain number of degrees, we say that it gains or loses a certain quantity of heat ; but the thermometer which shows us these variations indicates nothing as to the value of this quantity : we must not therefore give the pre- cise etymological sense to the word thermometer. The thermometer measures temperatures, not quantities of heat. We shall find, indeed, that the heat necessary to raise a given weight of a body through a certain number of degrees varies with the nature and physical condi- tion of the body ; beyond certain limits of temperature, it varies also for the same substance. Before proceeding further we must explain what is meant by quantity of heat. We know nothing of the intimate nature of heat ; the analogies which we have endeavoured to establish between radiant heat and light have induced physicists to imagine that calorific phenomena, like luminous phenomena, are produced by the vibrations of the ether ; but the manner in which these vibra- tions, after penetrating into the interior of bodies, produce changes of volume and condition is a question which science has not yet solved, and which has only been answered by conjecture. Nevertheless, researches of great importance have placed beyond doubt the im- portant fact that heat can be produced by mechanical means, and, conversely, that it can be transformed again into mechanical work susceptible of being accurately measured ; in a word, that heat can CHAP, vi.] CALORIMETRY. 485 be assimilated to force and measured like other physical forces. We shall hereafter endeavour to explain what is understood by the mechanical equivalent of heat. Without passing beyond the domain of heat itself, we will now state how it is possible to compare the quantities of heat which are absorbed or disengaged during variations in the temperature as well as in the changes of condition of solid, liquid, and gaseous bodies. This division of the science of heat is known as calorimetry. A unit of heat, or calorie, is the quantity of heat necessary to raise from to 1 centigrade one kilogramme (in England one pound) of water. It is evident therefore that, if a certain number of calories are requisite to raise the temperature of the unit of weight a certain number of degrees, 2, 3, 4, .... more would be required to raise the temperature the same number of degrees of a weight 2, 3, 4 times greater. Therefore the quantities of heat are proportional to the weights. It is also considered as established, that the heat requi- site to raise the temperature of a given weight through a certain number of degrees, is equal to that which it disengages on returning to its initial temperature. A very simple experiment also proves to us that the quantity of heat absorbed during a certain elevation of temperature is sensibly constant, whatever may be the initial temperature. Into a vessel which has been heated to 25, a kilogramme of water at is poured, and a second at 50 ; then, after having rapidly stirred the mixture, a thermometer on being plunged into it shows the temperature of the mixture to be 25. Thus the heat, transferred by the kilogramme of water at 50 to the kilogramme at 0, raises the temperature of the second kilogramme to 25 ; at the same time, the loss of heat undergone by the first has lowered its temperature from 50 to 25. Finally, this experiment proves that the heat necessary to raise a definite weight of water from to 25, would raise the same weight of water from 25 to 50. The initial temperature has therefore no influence on the quantity of heat absorbed. This, however, is only true within certain limits, which vary with different substances : thus, two kilogrammes of mercury, one at 200, the other at 0, mixed together, give two kilogrammes of mercury, not at 100, the mean temperature between the two extremes, but at 102'85, a higher temperature than the mean. Beyond 100, mercury 486 PHYSICAL PHENOMENA. [BOOK iv. absorbs or disengages more heat for a like variation of temperature than below 100. Lastly, a third experiment shows that the quan- tities of heat which we have just compared, vary with the nature of the substances. If we mix separately one kilogramme of water at with a similar weight of mercury or essence of turpentine at 100, or place in it a kilogramme of copper at 100, a gain of heat for the water and loss for the other substances will, as in the previous instances, result ; and in each experiment it will be obvious that the gain will be equal to the loss. But in the first instance the tempera- ture of the mixture will be 3'2, in the second 30, and in the third case 8*6. We see therefore how much heat is requisite to produce the same variation of temperature in equal weights of different sub- stances. This is explained by saying that every substance has a calorific capacity, or specific heat, belonging to it, and specific heat may be defined as the quantity of heat which is necessary to raise the temperature of a kilogramme (or pound) of a substance from to 1. This quantity of heat is expressed in calories or heat- units, which evidently amounts to taking for unity the specific heat of water. Various methods have been employed by physicists for the measurement of the specific heat of solids. One of these the method of mixtures consists in plunging the body, the tempera- ture of which is known, into a bath of water or any other liquid at a determined temperature : when the temperature of the mixture has become stationary, it is measured, and, by a simple calculation, 1 the relation of the specific heats of the solid and liquid is obtained. This method is applied equally to liquids. Certain precautions are taken when the bodies placed in contact exercise a chemical action on each other ; moreover, the heat absorbed by the vessel is noted, that absorbed by the thermometer itself is allowed for, and lastly the losses caused by radiation are estimated. The following is a table giving the specific heats of different solid, liquid, and gaseous bodies ; it proves that water 1 This calculation consists in solving an equation the first part of which expresses the quantity of heat lost by the body, and consequently transferred to the bath and vessel : the second comprising two terms the first, the heat gained by the liquid ; the second, the heat gained by the vessel which contains it. It is evident that, patting aside the external radiation of the liquid and vessel, the loss and the gains are compensated ; hence the equation and solution of the problem. CHAP, vi.] CALORIMETRY. 487 of all substances (with the exception of hydrogen, the specific heat of which is three times that of water) absorbs or disengages the greatest quantity of heat for equal variations of temperature : Substances. Specific heat. Water 1*000 Hydrogen 3'294 Essence of turpentine 0*426 Air 0-207 Sulphur 0203 Glass 0-198 Iron 0-114 Copper 0-095 Silver ." . . . . 0'057 Tin 0-056 Mercury .;.-. : .-; ." . . 0'033 Gold 0-032 Platinum . . -, 0*032 Lead. . . ; : ' '. ...'.. 0-031 Bismuth 0-031 But we must not forget that these numbers represent the quan- tities of heat necessary to raise equal weights of these bodies from to 1, and that they only remain constant within certain limits of temperature. They vary but little from to 100; but this is no longer the case at higher temperatures. The specific heat of mercury, for instance, which is 0*033 within these limits, becomes 0-035 beyond 100. The physical condition of bodies also causes the specific heat of the same substance to vary ; in the solid state it is less than in the liquid state, and in the gaseous state it regains sensibly the value which it had in the solid state : thus the capacity of ice, which is nearly equal to that of steam, is scarcely half that of water. When the density of a metal is increased, by hammering for example, its specific heat is diminished. This explains, to a certain extent, a result deduced from the preceding table, viz. that the densest bodies have generally the smallest capacity for heat. Dulong and Petit discovered a remarkable law, which has been verified by M. Regnault in his beautiful researches on the specific heats of bodies. It is well known that chemists consider simple bodies as formed of irreducible parts or atoms, the weight of which is called the chemical equivalent of the body. The weight of the atom of hydrogen being taken as unity, that of an atom of mercury 488 PHYSICAL PHENOMENA. [BOOK iv. is 100, that of sulphur 16, and so on. This being granted, let us now inquire what quantity of heat will be necessary to raise the tem- perature of an atom of sulphur 1 ; and what quantity likewise will be absorbed by an atom of mercury to raise its temperature 1. It is evident from the foregoing, that we must multiply the weights 100 and 16 of each atom by the specific heat of the simple body to which it belongs ; that is to say, by 0'033 and 0-203 : the products will be proportional to the quantities of heat sought. Now, 100 x 0'033 gives 3'3, and 16 x 0'203 gives -3'248 : the products are thus sensibly equal, and the same happens if we take any other two simple bodies. This law may be enunciated as follows : the same quantity of heat is required to raise the temperature of an atom of any simple body the same number of degrees ; or, again, the atomic specific heat is the same for all substances. We have seen that the specific heat of water is nearly four times greater than that of air; thence it follows that 1,000 kilogrammes of water, on being cooled 1, disengage an amount of heat sufficient to raise the temperature of 4,000 kilogrammes of air 1. But 4,000 kilogrammes of air occupy, under the normal barometric pressure and at 0, a volume 770 times that ,of a like weight of water; that is to say, a volume of 3,080 cubic -metres: the con- sequences of which fact are thus explained by Tyndall in his work on Heat: " The vast influence which the ocean must exert, as a moderator of climate, here suggests itself. The heat of summer is stored up in the ocean, and slowly given out during the winter ; hence one cause of the absence of extremes in an island climate. The summer of the island can never attain the fervid heat of the continental summer, nor can the winter of the island be so severe as the continental winter. In various parts of the Continent, fruits grow which our summers cannot ripen ; but in these same parts our evergreens are unknown ; they cannot live through the winter cold. Winter in Iceland is, as a general rule, milder than in Lombardy." In quoting these remarks, we must not forget that the particular facts related by Tyndall do not depend only on the vicinity of the ocean and the high specific heat of water, but also on the elevation of temperature in Iceland by the great lukewarm current of water known as the Gulf Stream. CHAP, vi.] CALORIMETRY. 489 In describing the phenomena of the fusion of solids, and the vapori- zation of liquids, we insisted on the general fact, that the temperatures of the melting and of the boiling point are fixed for each body, independently of the intensity of the source of heat which determines the result, or the rapidity with which these changes of condition are effected. These temperatures are the same, moreover, as those of the inverse phenomena of solidification of liquids and liquefaction of vapours. Thus, when a piece of ice melts, its temperature remains con- stant at 0, and all the heat furnished by the fire, whatever may be its intensity, is consumed in reducing the ice to the liquid condition and in maintaining this condition. We have here, therefore, a quantity of heat absorbed by a body which does not raise its temperature, and consequently does not become sensible to the thermometer. On this account it is called latent heat. It is the latent heat of fusion or liquidity, or, better, the latent heat of elasticity, according as it refers to the passage from the solid to the liquid condition, or to the passage from the liquid to the gaseous condition. It is very evident, therefore, that the heat which is absorbed in these two instances is disengaged when the substance returns to its primitive condition. The latent heat of different substances has been determined by methods analogous to those which are employed in the case of specific heat. We shall confine ourselves here to the results obtained in the melting of ice, because it will enable us to describe another process for determining the specific heat of bodies. It has been found that the latent heat of fusion of ice is 79'25 calories ; that is to say, that the quantity of heat absorbed by a kilo- gramme of ice during melting, would be sufficient to raise 79*25 kilogrammes of water from to the temperature of 1 ; or again, to raise a kilogramme of water from to 79'25. Therefore, when a kilogramme of ice at is melted in a kilogramme of water at 79 0< 25, the two kilogrammes of water produced possess a temperature of 0. The knowledge of this result permits the determination of the specific heat of a body by ascertaining experimentally the weight of the ice which can be melted by lowering its own temperatu-re to 0. The following is the process : A cavity is made in a compact and homogeneous block of ice, the sides of which are carefully dried ; a piece of the substance whose specific heat is sought, the temperature of which is above 0, is then 490 PHYSICAL PHENOMENA. [BOOK iv. introduced ; a thick plate of ice is then placed over the cavity, to which it serves as a covering (Fig. 322). During the act of cooling, the substance melts a portion of the ice with which it is in contact, and the resulting water is collected and weighed. Let us suppose that the result is 100 grammes of water, it is evident that the heat disengaged by the body during its cooling to 0, has been the tenth part of 79'25 calories or *7'925 calories. By hypothesis the body weighed 2 kilo- ^^ and was at first at the temperature 350 . then dividing 7.925 by 35> and after . calorimeter. wards by 2, the quantity of heat disengaged by 1 kilogramme for a variation of 1 will be found ; that is to say, the specific heat of the FIG. 323. Measure of tlie specific heat of bodies by the ice calorimeter of Laplace and Lavoisier. body. In the particular case we have chosen it would be 0113, the specific heat of iron. CHAP, vi.] CALORIMETRY. 491 Instead of ice cavities, the ice calorimeter invented by Laplace and Lavoisier may be preferably employed. Fig. 323 represents it in section and elevation. It is an instrument formed of three vessels, which are placed one within the other, while the spaces between them are filled with pounded ice. The heated body is placed in the smallest vessel ; during cooling it melts a certain amount of ice, and the water is collected by a stopcock at the bottom of the vessel. The ice between the two outer vessels prevents the fusion, by external heat, of that which is in contact with the heated body. These methods do not give very exact results ; if we have preferred them to more perfect methods, it is because our aim is principally to explain the possibility of measuring quantities of heat. Those who desire to extend their knowledge on this subject must have recourse to special works, among which we may mention the beautiful Memoirs of M. Eegnault on the specific heats of vapours and gases. A kilogramme of water, at the boiling-point, or 100, requires 536 calories in order to convert it into steam. During the condensation of the steam thus formed, it will disengage the same quantity of heat ; the application of steam to the warming of buildings is based on this fact. In the arts, the latent heat of steam is also employed to raise the temperature of large masses of liquid. 492 PHYSICAL PHENOMENA. [BOOK iv. CHAPTER VII. SOURCES OF HEAT. Solar heat ; measure of its intensity at the surface of the earth, and at the limits of the atmosphere ; total heat radiated by the sun Temperature of space Internal heat of the globe Heat disengaged by chemical combinations ; combustion Heat of combustion of various simple bodies Production of high temperatures by the use of the oxyhydrogen blowpipe Generation of heat by mechanical means ; friction, percussion, compression. IT follows from our foregoing study of calorific phenomena, that two or more bodies when in the presence of each other make a mutual and continuous exchange of heat, either by radiation at a distance, or by conduction. From this point of view, a piece of ice at C. is a source of heat to a body which is at a lower temperature than its own. However, in general language, this expression " source of heat," or " heat-source," is more particularly reserved for bodies which possess high temperatures, and which emit in a continuous manner a certain quantity of heat for a limited or even for an apparently indefinite time. Incandescent solids and gases, fire and flame, are sources of heat according to this view: in the same category may be placed bodies which emit obscure heat at a high temperature, for instance boiling water. Lastly, the expression " source of heat " is also given to the different modes of production of heat: in this sense, friction, per- cussion, electricity, and combustion that is to say, certain physical or chemical actions are sources of heat. The heat which organized and living bodies emit, is of the same order. Sometimes sources of heat are classed as temporary and accidental, natural and artificial, cosmical and terrestrial ; but these distinctions, CHAP, vii.] SOURCES OF HEAT. 493 which are not based on the nature of the heat-sources, teach us nothing more than that there may be a particular study of each kind. We will therefore review them one after the other, beginning with the sun, the most important of all, at least to the earth. The appearance presented to us by the sun is probably due to an enormous layer of cloud built up of solid or liquid incan- descent particles, the layer being surrounded by an absorbing gaseous atmosphere; as is proved by the analysis of the solar spectrum. The opinions of men of science are divided as to the nature of the nucleus : some regard it as an incandescent solid or liquid, others as a gaseous mass likewise incandescent. "We know nothing of the way in which the immense amount of light and heat is renewed and maintained : it radiates in every direction into space, and its intensity does not appear to have sensibly varied for thousands of years. The intensity of the solar heat, as it reaches the surface of the earth, has been calculated by Sir J. Herschel at the Cape of Good Hope, and M. Pouillet in Paris. The instrument used by the latter for this determination, which he called the pyrkeliometer, is repre- sented in Fig. 324. At the upper part we notice a very thin silver cylindrical vessel, the face of which is turned towards the sun and is covered with lamp-black ; this vessel is filled with water, and the temperature of the liquid is indicated by a thermometer whose bulb is immersed in the interior of the cylinder, and whose tube is protected by a brass tube pierced longitudinally with a groove so that the level of the mercury can be seen. At the other end of the tube is a disc of the same diameter as the cylindrical vessel, which receives the shadow of the latter, and indicates whether the black- ened surface is exposed normally to the direction of the sun's rays ; this is the case when the lower disc is exactly covered by the circular shadow of the upper one. The temperature of the instrument in first noted ; its blackened face is then exposed to a portion of the sky without clouds, but in such a manner that it does not receive the solar rays : at the end of five minutes its radiation has produced a certain lowering of temperature. The instrument is then directed towards the sun ; the blackened face receives the solar heat falling perpendicularly upon it for another five minutes. The elevation of temperature is now noted, and the instrument is again caused to 494 PHYSICAL PHENOMENA. [BOOK iv. radiate its heat for five minutes in its first position ; the final cooling must then be observed. The first and third observations are neces- sary for the calculation of the quantity of heat lost by radiation by the instrument during its exposure to the sun, this quantity being a mean between the two observed coolings. By adding to it the heating due to direct exposure to the sun, the total elevation of temperature will be obtained ; and consequently the number of calories can be calculated which have been absorbed during a minute by a surface equal to that of the blackened disc. FIG. 324. M. Pouillet's Pyrheliometer. This quantity of heat depends, as a matter of course, on the eleva- tion of the sun above the horizon ; for before reaching the surface of the earth, the heat-rays of the sun traverse the atmospheric strata, which absorb a certain proportion increasing with their thickness. M. Pouillet has studied the law which regulates the calorific intensity of the sun according as its height varies, and he has de- termined the absorption due to the atmosphere if the sun were at CHAP. VIL] SOURCES OF HEAT. 495 the zenith. This absorption varies to a certain extent according to the purity of the atmosphere, and may rise to 0'25 ; that is to say, to one-fourth the amount of heat which would reach the earth if the atmosphere did not exist. Considering the total heat received by an entire hemisphere, and consequently at every possible degree of obliquity, it is found that the proportion absorbed by the atmosphere is comprised between four and five tenths of the heat emitted by the sun, if the sky were entirely without clouds. The surface of the earth therefore scarcely receives more than one-half of the solar heat, this being distributed unequally according to the obliquity of the rays ; the other half warms the atmosphere. Supposing the heat received by the earth to be uniformly dis- tributed, M. Pouillet has calculated that a square centimetre receives O441 calorie per minute ; that is to say, a quantity of heat sufficient to raise the temperature of 441 grammes of water 1. In one year, each square centimetre receives 231,675 calories : the quantity of heat received in a year by the entire earth would be sufficient to melt a layer of ice 100 feet in thickness surrounding the globe. From the quantity of heat received annually by the earth, the total amount of heat radiated by the sun into space can be deduced. This may be done by calculating how many times the surface of a great circle on the earth, i.e. an area equal to a section of the earth, is contained in the surface of a sphere which has the centre of the sun for its centre, and the distance from this body to our globe for its radius. An easy calculation gives 2,150.000,000, so that the heat intercepted by the earth is only ^ T^O.^OO-.TTOTT P ar ^ f tne en tire solar radiation. " The heat emitted by the sun," says Tyndall, " if used to melt a stratum of ice applied to the sun's surface, would liquefy the ice at the rate of 2,400 feet an hour ; it would boil, per hour, 700,000 millions of cubic miles of ice-cold water. Expressed in another form, the heat given out by the sun per hour is equal to that which would be generated by the combustion of a layer of solid coal ten feet thick, entirely surrounding the sun ; hence the heat emitted in a year is equal to that which would be produced by the combustion of a layer of coal seventeen miles in thickness." Such is the calorific intensity of the immense body which furnishes the earth and the other planets with their supply of heat, and, as we 496 PHYSICAL PHENOMENA. [BOOK TV. shall presently see, their provision of life and mechanical force. We do not yet know how this prodigious activity is maintained ; never- theless, several ingenious hypotheses have been made concerning it, but these, we must remember, rest mainly on conjecture. The earth also receives heat-rays emitted by the stars, which are heat-sources similar to that of which we have just spoken. At the almost infinite distance of the stars, the heat radiated by them is so feeble as to be all but inappreciable : indeed, it is almost impossible to measure it. Nevertheless some successful attempts have been made by means of large telescopes which grasp a large number of these radiations, and delicate thermo-electric piles. Thus Mr. Stone has found that the heat received from Arcturus is equal to the radiation of a Leslie cube of boiling water at a distance of 383 yards. The whole of these distant radiations, that of the sun excepted, determines what is called the temperature of space, which has been estimated by many savants. According to Fourier, this temperature is 60 C. ; M. Pouillet states that it is much lower, and can scarcely exceed 140 C. The surface of the ea,rth also receives heat from its interior heat which belongs to the terrestrial globe itself, as Fourier has proved. At a certain depth below the surface, a stratum is found with a constant temperature which is nearly the mean temperature of the place. Below this stratum the temperature increases, and its mean augmentation is about 1 for 100 feet. If this increase of heat, which has been proved to a depth exceeding 2,400 feet, continues in the lower strata and in the same proportion; at 2 miles the temperature would already reach the boiling-point, and at 25 miles most of the known minerals would have attained their melting points. But it remains to be asked whether the enormous pressure to which the terrestrial strata are subjected at this latter depth, is not an obstacle to their liquefaction: the incandescence of the terrestrial nucleus thus remains in an hypothetical state. There are mechanical reasons, as Sir William Thomson has shown, for believing that the whole earth must be as rigid at least as a solid globe of glass, so that the theory of a fluid central core seems incredible. The sun is the most abundant and economic source of heat : but CHAP. TIL] SOURCES OF HEAl 497 we cannot adapt it at will to our purposes, and, when it is clouded over, or invisible, we most require heat : and unless it is concentrated by expensive apparatus, it only produces comparatively low tem- peratures. Civilization would be impossible if man had only the solar heat at his command, and had not discovered artificial sources of heat. Combustion, that is to say, the chemical combination of certain bodies with oxygen, constitutes one principal source of this kind, and the term artificial heat-sources is applied to those which can be used at will, and the intensity of which can be regulated according to the wants of the moment. Generally speaking, whenever substances enter into combination, heat is disengaged. Thus, a mixture of water and sulphuric acid, and of water and a certain quantity of quicklime, is accompanied by a considerable rise of temperature. The combination of oxygen, one of the constituents of . our atmo sphere, with certain solid or gaseous elements, gives rise to a very intense disengagement of heat accompanied by light, and frequently produces the phenomenon of vivid combustion. But in order that a combustible body may burn, either in the air or in pure oxygen, one of its parts must first be brought to a high temperature ; in fact, it must be lighted. When once the combination has commenced, the heat disengaged by it is communi- cated in succession until the com- bustible gas is entirely extin- guished, or the body with which it is combined is completely con- sumed. It is thus that We Obtain F IG - 325. Combustion of iron in oxygen. fire in our stoves and the light of our candles and lamps ; and we know by experience that these sources of heat and light only last so long as they are kept up, that is to say, while they are furnished with the two elements necessary for the combustion. When combustion takes place in pure oxygen, it is much brighter than in air. On plunging a steel spiral furnished with a piece of burning tinder into a bell-jar filled with this gas (Fig. 325), a very Q Q 498 PHYSICAL PHENOMENA. [BOOK TV. bright combustion of the metal is produced, and it sends out a number of sparks in every direction. The phenomenon of combustion is complex, but we can only say here that the flame proper must be distinguished from the solid incandescent portions. In order that a body may burn with a flame there must be a disengagement of certain gases under the influence of a high temperature; and these gases, becoming luminous, produce a moveable light. In the flame of a candle or jet of gas there are three distinct portions in which the heat and light are associated in different proportions. The exterior layer is the seat of the most active combustion and of the highest temperature, 1 but the light of this region is not intense ; next comes a very luminous stratum where the combustion is always less complete, and the heat less intense, but which shows great brilliancy : whether this is on account of the very fine particles of incandescent carbon of which it con- sists, or on account of the density of the vapours, is not yet decided. Lastly, at the interior of the flame, there is a dark space, at a much lower tem- perature, because, as the oxygen of the air cannot penetrate to it, the gaseous matters which fill it are not burnt. It is only on reaching the top of the flame that these matters are burnt in their turn : when the combustion is incomplete, they rise in the form of smoke. If the flame of a candle is blown upon quickly, we all know what happens, the light is extin- FIQ. 326. Fiame of a guished ; and the reason is simple: by the act of blowing, cold air is introduced into the inflammable gas, which cools on being diffused into a quantity of cold air ; the temperature then falls to such an extent that combustion ceases. If, after having blown out the flame, the wick remains incan- descent, by blowing it lightly it is again lighted, because the 1 A spectroscopic examination of a candle-flame affords a very beautiful proof that the outer flame is the hottest, for this region gives us the bright line of sodium, which would be a dark line, when the spectroscope is directed to the brighter part of the flame, if the outer flame were not the hottest. CHAP. VII.] SOURCES OF HEAT. 499 oxygen necessary for the combustion is introduced, and the gas again disengages itself, and is inflamed at the point of contact of the solid, incandescent parts. Several physicists among others, Laplace, Lavoisier, Rum ford, Despretz, Dulong, Fabre, and Silbermann 1 have endeavoured to measure the quantities of heat which are disengaged during chemical combinations, and especially during ordinary combustion. The number of calories which are disengaged when a unit of weight of a combustible body is burned, is what is called the heat of combustion of that body. We cannot describe the methods which have been employed in these important researches, and shall only give some results which show to how great an extent the elements differ in this respect. Whilst the heat of combustion of 1 gramme of native sulphur is 2,260 calories (the calorie is in this case the quantity of heat necessary to raise 1 gramme of water 1 C.), that of 1 gramme of carbon in the state of dia- mond is 7,770 calories; the same body in the state of natural graphite is 7,796 ; and lastly, as charcoal, 8,080 calories. Hydrogen burning in chlorine disengages 23,783 calories, and the same gas burning in oxygen 34,462. The heat of combustion of hydrogen is the most intense of all; it has been calculated that it corresponds to an elevation of temperature of 6,800 ; which has led to the employment of this extreme heat for the production of extremely high temperatures. MM. H. Sainte-Claire-Deville and Debray, by using the oxy- hydrogen blowpipe, have fused considerable masses of platinum ; a kilogramme of this metal requires for its fusion, and for keeping it in a state of fusion during the time of refining, a consumption of 70 litres of oxygen and 120 litres of hydrogen. 1 Andrews of Belfast has made very accurate experiments on this subject. Q Q 2 Fio. 327. Oxyhydrogen blowpipe. 500 PHYSICAL PHENOMENA. [BOOK iv. Mechanical action, friction, percussion, and compression, develop heat, just like the more intimate motions which constitute the phe- nomena of chemical combinations. There are numberless examples of this transformation of motion into heat, and we can each observe them for himself. We will mention some of them. When a metal button is quickly rubbed against cloth or any solid body, it becomes warm, and finally very hot : schoolboys well under- stand this experiment. The friction of a saw against the piece of wood which it is dividing, that of a razor or knife which is being ground, of a file against the metals which it wears away, raises the temperature of the objects subjected to these violent motions, the molecules of which are thus disturbed. The sparks produced by horses' shoes on the pavement, or by the friction of the steel on the wheel of a grindstone, or those which set light to tinder in the flint and steel method, all proceed from the high temperature produced by friction; very fine metallic particles are detached, and the heat developed is sufficient to set the little masses on fire. 1 Very dry pieces of wood rubbed against each other become heated ; smoke is disengaged, and, if we may believe the stories of - travellers, savages by these means procure fire. Turners sometimes produce black bands on the objects which they are making by pressing a piece of wood against the spot which they wish to char. The heat which follows from this pressure, joined to the rapid rotatory movement of the lathe, is strong enough to carbonize the wood on the circumference of the object. The pivots of machines, the axle of carriages and railway carriages, become strongly heated by the friction which results from a rapid and prolonged rotation ; indeed they would take fire, or get red-hot, if care were not taken to lubri- cate or grease them. We may quote here, as an example of the enormous quantity of heat which can be disengaged by the friction of two solids against each other, the celebrated experiment made by Eumford in 1798 ; this experiment had been suggested to $iat celebrated physicist whilst he was superintending the boring of some pieces of cannon at Munich. 1 " Before the discovery of Davy's safety -lamp, the fire-damp was the great trouble of mines ; and many mines remained unexplored and inaccessible on account of the presence of this invincible enemy. As common lamps could not be used, the passages were illuminated by means of a steel wheel which was caused to turn against a gun-flint." SIMONIN, La Vie Souterraine CHAP, vii.] SOURCES OF HEAT. 501 Struck by the great quantity of heat disengaged during this operation, he wished to measure it as exactly as possible ; accordingly he placed a metal cylinder, destined for the operation of boring, in a wooden case filled with water, the temperature of which was shown by an immersed thermometer. An hour after the friction of the blunt borer against the cylinder had commenced, the temperature of the water, at first 16, rose to 46. At the end of two hoars, it was 81, and again, half-an-hour later, the water completely boiled. "It would be difficult," said Eumford, " to describe the surprise and astonish- ment expressed in the faces of the assistants at the sight of such a quantity of water (about two gallons) heated and caused to boil without any fire." The friction of solids against liquids and gases also develops heat. Joule's experiment, to which we shall presently refer, proved the heating of a liquid when agitated by metallic paddles turning on an axis. The incandescence of aerolites is due to friction against the atmosphere, which they enter with considerable velocity. The eleva- tion of temperature caused by the friction of a gas against a solid is placed beyond doubt by a very simple experiment made by Tyndall in his Lectures on Heat : by means of a pair of bellows he caused a current of air to impinge on one of the faces of a thermo-electric pile ; the needle of the galvanometer was immediately deviated, and the direction of the deviation indicated that the face of the pile had been heated by the moving air. We will end this enumeration of phenomena which prove the generation of heat by mechanical force, by quoting an important experiment of Davy's; This illustrious physicist, by rubbing two pieces of well-dried ice together, succeeded in melting a certain quantity. Now, to explain the disengagement of heat produced by friction, the partisans of the material theory of heat, who considered it a fluid contained in the interstices of bodies, reasoned thus : Friction changes the calorific capacity of different bodies ; it diminishes this capacity so that the heat which was retained before the mechanical actions can no longer remain within the body after the molecular change which agitates it: it is this heat which is disengaged by friction, and, before latent, now becomes apparent." The experiment of Davy renders this explanation impossible ; let us bear in mind that water has double the calorific capacity of ice ; 502 PHYSICAL PHENOMENA. ' [BOOK iv. after the fusion of a certain quantity of ice, the water produced by it contains more latent heat than before : hence it would be impossible to understand, in accordance with the material theory, whence the heat proceeds which has caused the ice to pass into water. From this it is concluded that the mechanical force brought into play in friction is transformed into heat, that is to say, into a force of another kind : that there is transformation of visible motion into molecular or atomic motion. Percussion and compression develop heat like friction. Thus, when a nail is driven into a piece of wood with a hammer, not only is the nail heated, an effect which could result partly from the friction against the wood, but the hammer itself undergoes an elevation of temperature. An iron bar, beaten with successive strokes, can be made red-hot. Plates of gold, silver, and copper, compressed under the coining press which is used to stamp money, become heated, but the elevation of temperature is not the same in different metals. Generally speaking, the quantity of heat developed by mechanical action depends on the nature of the substances submitted to these actions, on the state of their surface, and on the pressure exercised. The compressibility of liquids is very slight: nevertheless, by submitting liquids to considerable pressure for example, of from 30 to 40 atmospheres the disengagement of heat can be established. Very great compression can be effected in gases, and a considerable elevation of temperature can be obtained, when a gaseous mass is suddenly compressed into a limited space. This fact illustrates the principle of the pneumatic syringe which we have described in the First Book of this work. The expansion of a gas produces an effect contrary to that of compression,^-that is to say, a fall of temperature results ; carbonic acid gas, first liquefied by compression under 40 or 50 atmospheres in a receiver, produces so much cold by expansion on escaping into the air that it passes into the solid state ; and then takes the form of flakes, white as snow, of solidified carbonic acid. Their temperature is then 93 degrees below zero Centigrade. The same phenomenon of cooling takes place, when steam issues in a jet from the valve of Papin's digester. Its sudden expansion is accompanied by a cooling which condenses it as mist : on plungiDg the hand into the jet of steam, a sensation of coolness is felt which at first seems strange. Great care must be taken in this experiment CHAP, vii.] SOURCES OF HEAT. 503 when the vapour contained in the boiler has only the ordinary atmospheric pressure ; on escaping into the atmosphere, at this pressure, it retains the temperature of 100 C., and the hand may be terribly scalded. In order to complete what we have said concerning heat-sources, we have to mention those which life maintains in organized beings, vegetable and animal. It seems to be proved that animal and vege- table heat has its origin in a series of chemical actions more or less complex, which constitute the phenomenon of nutrition, respiration, and assimilation of food. 504 PHYSICAL PHENOMENA. [BOOK iv. CHAPTEE VIII. HEAT A SPECIES OF MOTION. What we understand by the mechanical equivalent of heat Joule's experiments for determining this equivalent ^Reciprocal transformation of heat into mechanical force, and of mechanical force into heat Heat is a particular kind of motion. IN the study of the science of heat, we have considered two classes of phenomena. On the one hand, we have described the many effects produced by the variations of heat in bodies ; and, on the other, we have reviewed the different processes by which heat can be engendered. We have now to indicate the relations which exist between these two orders of phenomena, the reciprocal dependence of which, being now proved, constitutes the mechanical theory of heat. We have seen that one of the effects of heat is to expand bodies, that is to say, to produce molecular movements which increase the distances of the molecules from each other; and, thus considered, expansion is nothing more than a mechanical effect. When the increase of heat attains a certain limit, there is a change of state, a passage from the solid to the liquid condition, and from the liquid to the gaseous : this is also a mechanical effect, for it does not appear doubtful that these modifications in the aspect of a substance are due to variations in the respective distances of the molecules, and after- wards in the actions which they exercise on each other. We have also seen that increase of heat confers on vapours and gases the elastic force which, in modern machines, so advantageously replaces the old motive forces. In all these cases, heat is transformed into mechanical work ; or, in other words, a certain quantity of heat is consumed in CHAP, vni.] HEAT A SPECIES OF MOTION. 505 producing work, although in many cases this work is not susceptible of measurement in the present state of science. It is not less evident, however, that whenever heat is pro- duced, a certain quantity of work is expended ; this is most certain in the case of heat engendered by friction, percussion, and compression : that which is disengaged by chemical action is f believed to be produced by the molecular movements which con- stitute the combinations. This relation between the forces which give rise to the pheno- mena of heat and the other mechanical forces, had been long sus- pected : but it was reserved to our own time to transfer it from a state of vague hypothesis to that of a theory proved and verified by experiment. Dr. Mayer, of Heilbronn, a little town in Germany, had the honour of giving the first definite formula to the theory and of developing the consequences : in 1842 he calculated the mechanical equivalent of heat, which was experimentally determined a year later by an English physicist, Dr. Joule, who was at that time unacquainted with the researches of the German physicist. Mayer's theory was not however satisfactory, and the real honours of the discovery undoubt- edly belong to Joule. Many other physicists may be referred to as having aided to establish the theory; it will be sufficient for us to mention MM. Kegnault and Him in France, Clausius in Germany, Thomson, Clerk- Maxwell, and Rankine in England. We will now endeavour to give an idea of the mechanical equivalent of heat, and of some of the experiments by which it has been determined. Let us first recall to mind the meaning of the term work in mechanics. When a power is employed in a machine in motion to overcome a resistance with which it is in equilibrium, it has been proved that there is always an equality between the products obtained, by multiplying, on the one hand, the power by the path passed over by its point of application ; and, on the other hand, the resistance by the path over which the point of application of this latter passes. For example, if a power equal to 10 kilogrammes produces equili- brium with a resistance of 30 kilogrammes, and the path traversed by this according to its direction be 1 metre, the path traversed by the power during the same time will be 3 metres ; there will then 506 PHYSICAL PHENOMENA. [BOOK iv. be equality between the two products 10 x 3 and 30 x 1. The name of work is given to each of these products ; the first is work spent on the machine, and the second work done by the machine. It is con- venient to take as a unit of work or dynamic unit, the work developed by raising a weight of 1 kilogramme to a height of 1 metre. This unit is designated a kilogram-metre. On the other hand, we have seen that quantities of heat are measured in calories ; by calorie is under- stood the heat necessary to raise from to 1 Centigrade the tempe- rature of 1 kilogramme of water. The problem which presented itself to 'physicists was : To determine by experiment and calculation the number of kilogrammetres necessary to engender the quantity of heat represented by a calorie. (English men of science use a different unit, called a foot-pound, instead of a kilogrammetre.) FIG. 328. Joule's experiment. Determination of the mechanical equivalent of heat. We deal first with the heat which raises 1 kilogramme of water 1 C., and then determine the mechanical work necessary to produce the same result. It is this number which Mayer and Joule have called the mechan- ical equivalent of heat. The experiments which have been made with a view of determining this important number consist essentially in the production of a certain quantity of heat by the aid of mechanical action, and in measuring carefully the heat produced, and the work consumed in the operation, of course taking into CHAP, viii.] HEAT A SPECIES OF MOTION. 507 account losses of heat and of mechanical work. The following are some of Joule's experiments. He compressed air, by means of a force-pump, into a metallic vessel in the water of a calorimeter. After a certain number of strokes of the piston, the pressure of air having attained a certain number of atmospheres, he observed the elevation of temperature of the water, and deduced from it the quantity of heat communi- cated to it. The heating was not entirely due to the compression of air, but also to the friction of the piston. He therefore re- commenced the operation by allowing the receiver to communicate with the atmosphere, that is to say without compressing the air. The heat produced by this fresh operation was evidently due to the friction in the first operation. Joule found by this method 444 kilogrammetres for the mechanical equivalent of the heat. By turning a paddlewheel in water or in mercury (Fig. 328), the same physicist observed the elevation of temperature of the liquid, and likewise deduced the number of calories caused by the friction. On the other hand, he easily measured the work expended in producing the rotation. The final result arrived at by Dr. Joule gives, as the mechanical equivalent of heat, 772 foot-pounds ; that is, the force expended in raising 1 pound through 772 feet will raise the temperature of the pound of water 1 F. To sum up, it has been shown by a great number of experiments made by various physicists, that the mechanical equivalent of the heat necessary to raise 1 kilogramme of water 1 C. is about 425 kilogrammetres. Or, according to the definition given above, that the quantity of heat necessary to raise the temperature of a kilogramme of water 1 C. is capable, if it could be entirely ex- pended in mechanical work, of raising a weight of 425 kilogrammes to a height of one metre, or 1,390 pounds, to the height of a foot. Eeciprocally, when work equal to 425 kilogrammetres is completely transformed into heat, the heat produced is capable of raising the temperature of a kilogramme of water 1 C. Thus the transforma- tion of mechanical force into heat and of heat into mechanical force, is not only a fact acquired by science, but an important demon- stration which throws light on the nature of the cause to which we must attribute the phenomena which we have studied in this Fourth Book. 508 PHYSICAL PHENOMENA. [BOOK iv. The study of the laws of radiant heat had already induced us to assimilate heat-waves with luminous waves, and to regard heat itself as produced by certain vibrations of the ether. In penetrating the interior of bodies it is probable that the heat communicates to their molecules certain movements which, transformed in different ways, sometimes change the volume of the bodies, sometimes modify their physical condition, and sometimes produce intimate effects of such a nature as to alter the mode of association of the elementary atoms. These movements, on being propagated by our nerves, produce in us the sensation of heat. BOOK V. MAGNETISM. BOOK V. MAGNETISM. CHAPTEE I. MAGNETS, Phenomena of magnetic attraction and repulsion Natural and artificial magnets ; magnetic substances Poles and neutral line in magnets Action of magnets on magnetic substances ; action of magnets on magnets Law of magnetic attraction and repulsion Direction of the magnetic needle ; declination and inclination ; influence of the terrestrial magnet Process of magnetization Attractive force of magnets. II /TINEKALOGISTS gave the name of magnetic oxide of iron, or -LT-L magnetic iron, to an ore of this metal, which is found in large quantities in the mines of Europe and America, particularly in Sweden, in the Isle of Elba, and in the United States. It was worked for some time at Bona (Algeria) ; and lastly, according to ancient writers, it was formerly found in Asia Minor, near the two towns of the same name of Magnesia. The mineral to which we refer is composed of protoxide and sesquioxide of iron ; its colour is generally black or brown, and sometimes greyish, with a metallic brightness. Some specimens possess the property, known to the ancients, of attracting pieces of iron which are placed near one of their points : these are natural magnets, or, as they are more commonly called, lode-stones. We shall presently see how the attractive power of the natural magnet can be communicated to tempered steel: the pieces or bars of steel thus prepared are called artificial magnets. 512 PHYSICAL PHENOMENA. [BOOK v. Iron is not the only substance capable of being attracted by a magnet ; the same effect takes place with other metals : cobalt, nickel, chromium and manganese, cast iron, steel, and all specimens of oxidized iron, which are not themselves magnets, are also attracted. These bodies are ranged under the same head of magnetic substances}- The phenomena which we are about to describe remained unknown for centuries, like those of electricity ; yet the ancients were aware of the two .principal facts which, in the hands of modern observers, have been the starting-points of these two branches of physics which are now united. The attraction of light bodies by yellow amber, and the attraction of iron by the lode- stone, were only amusements in their eyes, or singularities of nature ; in the present day they are, among thousands of others, two particular manifestations of an agent unusually diffused through, and continually in action in, the physical world. The attractive power of magnets, natural or artificial, for magnetic substances is easily proved. The following are some of the processes used for this purpose : If a magnet is immersed in a quantity of iron filings, we observe on removing it that at certain parts of its surface numerous particles of the metal are attached in the form of tufts (Fig. 329), and on placing small pieces of iron, such as nails, near the same points, they will be seen to move forward to the magnet, and to adhere with a FIG. 329,-Attraction of iron filings by a natural f rC6 the Strength of which Can be determined by the effort neces- sary to remove them. By means of the magnetic pendulum, which consists of an iron ball or any other magnetic substance suspended 1 The words magnetism and magnetic come from one of the Greek names of the magnet, fiayvrjTrjs, which the ancients themselves believed to be derived from the names of the two towns of Magnesia in the neighbourhood of which lode- stones were first found. Aristotle called the magnet simply \i0os, the stone, par excellence. It was also termed Lydian stone, Hercules stone rjpan\fia \i6os. According to M. Th. H. Martin, this last term was wrongly interpreted as synonymous with the Heraclea stone, one of the names of the town of Magnesia, which induced the ancients themselves to give the name of fjLayvr'jTrjs to the magnet ; which name the Romans retained. CHAP. I.] MAGNETS. 513 by a thread, the attraction which the magnet exercises on the sub- stance is even more easily proved. The same apparatus also shows that the attraction, which is nil at the points where the iron filings are not attached, is at a maximum where the largest tufts have been formed. Moreover, the attraction of magnets for magnetic substances is reciprocal. Thus, a piece of iron brought near a mag- netized bar rendered moveable by being suspended, as represented in Fig. 331, attracts the bar, and causes it to move round the axis of suspension. This last experiment also proves that magnetic attraction is exercised at a distance, and increases in intensity as the distance FIG. 330. Magnetic pendulum. diminishes ; we shall see further on in accordance with what law this takes place. But at the same distances this action is scarcely weakened by the interposition of bodies, either liquid or solid, pro- vided they are not magnetic. Thus when a magnet is moved beneath a sheet of paper, or cardboard, a plate of glass, wood, or porcelain, pieces of iron placed on the surface of these sheets or plates will follow the motion of the magnet. Although magnets, either natural or artificial, and magnetic substances, are reciprocally attracted, this does not prove that the properties of both are alike. There is an important difference, which R R 514 PHYSICAL PHENOMENA. [BOOK v. we must observe, viz. that substances which are simply magnetic do not attract each other : a piece of iron which attracts a magnet has no action on iron, if it is not in the vicinity of a magnet. There is another important difference, viz. that a piece of iron undergoes attraction at all points, whilst in a magnet the attractive property is unequally distributed : we have already seen that it does not exist at certain points and is at maximum at others. The experiments which follow will show this characteristic difference between magnetic substances and magnets. FIG. 331. Attraction of a magnetic bar by iron. By examining a magnet which has been placed in iron filings (Fig. 329), the latter are not only seen to be attached more particu- larly to the two opposite parts, but the arrangement of the particles takes a special direction, as if in each part where the attraction is strongest there were a centre of attraction. Towards the middle of the bar, on the contrary, a part will be noticed where no particle of iron has attached itself. The two extreme points of the magnet are called the poles, and the middle section of the magnet the neutral line or equator. The following is an experiment which shows in a still more striking mariner the existence of the poles and the neutral line : On the bar which serves as a magnet a sheet of cardboard is placed, CHAP. I.] MAGNETS. 515 upon which very fine iron filings have been sifted. The particles are now seen to dispose themselves in a regular manner round the poles of the magnet, and to form lines which are convergent and symmetrical with respect to the neutral line ra m (Fig. 332). Sometimes a magnet FIG. 332. Magnetic figures. Distribution of iron filings on a surface. possesses more than two poles : besides the extreme poles, the existence of which we have proved, intermediate points are observed to which the iron filings attach themselves, and which are also separated from FIG. 333. Consequent points, or secondary poles of magnets. each other by neutral lines, as is shown in the. magnetic figures repre- sented in Fig. 333. These are called consequent poles. It is easy now to explain the difference which exists between magnets and magnetic substances. The latter have neither poles nor neutral lines : whichever of their points is presented to the poles of a magnet there R I? 2 510 PHYSICAL PHENOMENA. | BOOK v. is always reciprocity of attraction, whilst a magnet acts only at its poles. Let us take two or more magnetic bars and suspend them at their centres, and successively approach the two poles of any one of them to the two poles of the others ; we observe, on presenting a given pole of the first to the two poles of the second magnet, that attraction takes place by one of them and repulsion by the other : the same pheno- mena will take place with the others. All the poles attracted by the pole M of the trial bar are said to be poles of the same name ; let us mark them with the letter A : while all the poles repelled by the same pole M are also poles of the same name, because on them the action is in the same direction under the same circumstances ; let us mark them with the letter R. If now the opposite pole N of the trial bar is presented to each of the poles of the other magnetized bars, it will be found that it repels all the poles A and attracts all the poles R : thus in every way the two opposite poles of the same magnet are poles of contrary names. Let us see now how two poles of the same name act on each other : to this end we will place near each other any two FIG. 334. Attraction and repulsion of the J poles of magnets. ^ Q p "[ es ^, or again any two of the poles R ; in both cases we shall find that they repel each other. If, on the contrary, we present two poles of contrary names, a pole A and a pole R, they will be seen to attract each other; which proves that in the preceding experiment the pole M of the trial bar is of the same name as the poles R, and the pole N of the same name as the poles A. We may sum up these observations as follows : Opposite poles of the same magnet are of contrary names; if the fiction of one of the two on a given pole of a magnet is attractive, the action of the other is repulsive. The poles of the same name of any two magnets repel each other, while poles of contrary name attract each other. We here have a distinction which radically separates magnetic substances, such as soft iron, from artificial or natural magnets, and enables us to determine whether a steel bar or a specimen of oxide of iron is a magnet or not. It is sufficient to observe in what manner a CHAP. I.] MAGNETS. 517 magnet comports itself in the presence of the bar, or of a piece of lodestone. If there is attraction at every puint, it is not a magnet ; but if there is attraction at one extremity and repulsion at the other, it is a magnet, not simply a magnetic substance. Magnetization is the condition of a substance which has the pro- perty of attracting iron and other magnetic bodies, and which sub- stance possesses two poles and a neutral line. This property may be permanent or temporary : it is permanent in natural magnets or steel bars magnetized by processes of which we shall soon speak. The following experiment proves that it is temporary in magnetic sub- stances which are in contact with one of the poles of the magnet : A small cylinder of soft iron can be raised by means of a magnet ; this is magnetized by the influ- ence of the magnet, for on approaching a second cylin- der of iron to its extremity, it undergoes an attraction and is also raised. Thus what is called a magnetic chain can be formed at the end of the bar, composed of pieces of iron which attract and support each other. But if the magnet in con- tact with the first piece of soft iron is removed, in an instant all the others fall, thus losing the temporary magnetism with which the presence of the magnet had endowed them. Each piece of soft iron becomes for the time being a magnet with two poles and a neutral line, and this is proved by the fact that if magnetic figures are formed during the contact of the magnet and the iron cylinder, the iron filings arrange themselves in a manner which corresponds to that of the magnet itself. It will also be noticed that the neutral line is nearer the pole next to the magnet than to that which is more remote. Magnetic attraction does not require absolute contact ; it is only necessary that the distance be sufficiently small between FIG. 335. Magnetization by the influence of magnetism. 518 PHYSICAL PHENOMENA. [HOOK v. the pole of the magnet and the piece of soft iron which momentarily acquires the polar magnetism, and the distance depends on the strength of the magnet employed. *9m -- FIG. 336. Magnetization by influence at a distance. When a magnetic bar is broken into two or more pieces, each piece, however small it may be, becomes a complete magnet with two poles and a neutral line ; only, its magnetic power is no longer so strong as in the first magnet, as may be proved by the weights of soft iron which eacli is competent to lift. The magnets which proceed from this rupture have their poles of contrary names end to end ; that is to say, situated at the two extremities of the pieces near each other which were joined before the rupture, as in Fig. 337. l> (I , FIG. 337. Rupture of a magnet; disposition of the poles in the pieces. A magnetic needle is a lozenge-shaped piece of steel endowed with the property of a common magnet ; that is to say, having a pole at each extremity and a neutral line at its centre. A magnet of this kind suspended horizontally in a loop of paper by an untwisted fibre of silk, or well mounted on a pivot with an agate centre (Fig. 338) in such a way that it can turn freely in every direction, after some oscillations always assumes a certain direction in a horizontal plane ; at least, it undergoes variations of but slight amplitude. CHAP. 1.] MAGNETS. 519 This property of the magnetic needle to turn one of its poles towards the northern horizon, has been utilized for centuries by navigators. 1 It is not often, however, that the needle turns to the true North, so that the vertical plane passing through its poles does not coin- cide with the meridian plane of the place. The angle of the two planes is called the declination of the mag> netic needle, or, simply, declination. We shall see, when speaking of ter- restrial magnetism, that the declina- tion is not the same in esrery part of the world ; in some places it is nil, in other regions it is to the east and in some to the west : more- over, in the same place it varies in the course of centuries. At the present time, at Paris, the declina- tion is west, and about 18 30', that is to say, the vertical plane passing through the poles of the magnetic needle a plane called the mag- netic meridian makes with the geographical meridian plane an angle of 18 degrees and a half, At London this declination is about 21. One of the poles of the needle is turned nearly to the N.N.W. This constancy of direction, in freely suspended magnets in a horizontal plane, may be simply put to the test by a mag- netized sewing-needle. On placing it on a cork float on water perfectly at rest, the needle assumes the direction of which we have just spoken. Moreover, between the two poles of the needle there is a very characteristic difference ; for if, when the needle is in equilibrium, it is turned end for end, it does not keep its new position, when even the direction which has -been given to it is 1 It appears certain that from the second century before the Christian era, the Chinese used compasses indicating the direction of the South. These compasses carried a little statuette, which turned on a vertical point, the extended arm of which always pointed to the South, because it contained a magnetic needle, whose south pole was towards the hand and the north pole towards the elbow (Th. H. Martin). The compass with a balanced needle was known to the Arabs, who doubtless transmitted it to Europeans about the twelfth century. FIG. 338. Magnetic needle. 520 PHYSICAL PHENOMENA. [BOOK v. FIG. ;9. Magnetic declination in Paris, October 18C4. identical with the first ; it will be seen to turn on itself, describe a semi-circle, and again assume its original position, so that the same pole is always turned to the North. If instead of placing the magnetic needle so that it can turn freely in a horizontal plane, it is suspended by its centre of gravity round a horizontal axis, it will be able to turn freely in a vertical plane. Let us suppose this plane the magnetic meridian. Then the one of the two poles turned towards the north is inclined, and dips below the horizon, making with this plane an angle which is called the magnetic inclination. In some parts of the earth, near the equator, the inclination is nil ; it increases generally in proportion as the latitude increases, and near the poles there are points at which it is at a right angle : the magnetic needle there assumes a vertical position ; these are the magnetic poles of the earth. At Paris, the inclination, which varies slightly from year to year, is at the present time about 66. A magnetic needle may be arranged so that it places itself in the magnetic meridian with an inclination to the horizon such as we have just stated. Fig. 341 shows an arrangement which allows the needle to turn on a horizontal axis passing through its centre, and can then take up the local dip as the axis is suspended by a thread. The system begins by oscillating, until the needle is in the magnetic plane, and then it dips to an extent equal to the inclination at the place. Elsewhere we shall have occasion to describe the instruments by which we accurately measure the inclina- tion and declination of the magnetic needle : to these instruments the name of magnetometers has been given. These experiments prove to us that the terrestrial globe exercises an influence on a magnet similar to that which one magnet exercises on another. It is just as if, at the interior of the earth, there existed FIG. 340. Inclination of the needle at Paris, October 1864. CHAP. I.] MAGNETS. 521 a powerful magnet possessing two poles. Physicists have stopped at this hypothesis, which, moreover, does not imply the existence of a material mass analogous to the natural magnets, and lying in the deep strata of our spheroid, as we shall see when we study the relations which exist be- tween magnetic and electric phenomena. If the earth is compared to a magnet, the pole in the northern hemisphere will naturally be called the northern magnetic pole, and that in the southern hemisphere the south- ern magnetic pole. But, from the preceding we have learnt that poles of contrary names attract each other, while those of the same name repel each otherj.it follows, therefore, that the pole of the magnetic needle which turns to the north is the southern pole of the needle, whilst the pole turned towards the south is its northern pole. When the position of the needle has only to be considered, its southern pole is called the north pole, and its northern pole the south pole. But if the law of the mutual action of the two magnets is well understood, their denominations cannot be equivocal. *\ The inclination and declination of the magnetic needle are subject, in different regions of the globe, to variations, some of which are periodical whilst others appear to be irregular. Sometimes even the needle undergoes perturbation, as if the terrestrial globe was the seat of real magnetic storms ; then we see towards the polar regions luminous phenomena, visible at great distances, known as the northern or southern auroras. The frontispiece represents a polar aurora observed in the north of the Scandinavian peninsula. We shall give a description of this phenomenon in Book VIL, devoted to atmospheric meteors. 8 S FIG. 341. Magnetic needle, showing both the inclination and declination. 522 PHYSICAL PHENOMENA. [BOOK v. Hitherto we have only spoken of the direction of the actions which magnets exercise on each other, or on magnetic substances. The intensities of the forces of attraction and repulsion which reside in the poles of magnets have also been measured. For this purpose Coulomb used an instrument similar to the torsion balance, which enabled him to measure these forces ; this is the magnetic balance represented in Fig. 342. FIG. 342. Coulomb's magnetic balance. A long magnetic bar is suspended by a metal thread placed so that it is in the magnetic meridian without any torsion of the thread : if the thread is now turned in such a way as to throw the bar out of this first position, and to cause it to make a certain angle with it, the force of torsion will be equivalent to the intensity of the action of the terrestrial magnetism which tends to bring back the bar into the magnetic meridian. Coulomb commenced by assuring himself that this intensity is proportional to the angle of displace- ment of the bar, for small deviations. If we then place vertically at the side of the instrument, as shown in the figure, another magnet in the magnetic meridian (shown by the dotted line), and in front of the pole of the same name, repulsion ensues: the sus- CHAP, i.] MAGNETS. 523 pended magnet turns until a position of equilibrium is attained. The repulsive force of the two magnets is measured by the sum of the two forces, the terrestrial magnetic force on the one hand, and the force of torsion developed in the thread on the other. If now, by the rotation of a micrometer situated at the upper part of the instrument, the two poles are gradually brought nearer together, and if, at each operation, the intensity of the repulsive force is measured, the law which Coulomb discovered will be proved : it is as follows : Magnetic repulsions vary in the inverse ratio of the squares of the distances through which they are exercised. By another method, which consists in counting the number of oscillations which a magnetic needle makes when one of its poles is placed in the presence of the pole of contrary name of another magnet, at different distances, Coulomb proved that the same law of variation in inverse ratio of the squares of the distances, applies to magnetic attractions as well as to repulsions. We shall hereafter find that it also governs electrical forces. At the commencement of this chapter we said that masses of steel are capable of acquiring the properties of natural mag- nets. To obtain this result several processes are used, which we shall now describe. The oldest mode of magnetization ^H, ^ is that of single touch, which consists ** r ^ * in placing the pole of a magnet in con- F '- tact with one of the extremities of a tempered steel bar. After a certain time the bar is found to be mag- netized, with a pole at each of its extremities. A more powerful magnetization is obtained by passing the magnet several times from one end to the other of the bar which is to be magnetized (Fig. 343). The touching ought always to be done with the same pole and in the same direction. The pole' a, obtained at the extremity at which the movement begins, is of the same name as the pole A of the magnet which is placed in contact with the steel bar. There are several methods of magnetization discovered about s s 2 524 PHYSICAL PHENOMENA. [BOOK v. the middle of the last century which are distinguished from the first by the term of double touch, because two magnets are used instead of one. We shall only describe the methods of ^Epinus and of Duhamel. The bar to be magnetized, a &, is placed with its two extremities on the contrary poles of two powerful magnets, A 7 B'. Two other FIG. 344. Magnetism by separate double touch. Duhamel's process. magnets, A, B, are then taken, which are inclined from 25 to 30 degrees over the middle of the bar, the two contrary poles are placed opposite to each other, and care is taken that each of these poles is on the side of the pole of the same name belonging to the fixed magnets A' B'. If the movable magnets are passed in the opposite direction several times without changing their inclination, the polar magnetism is developed in the steel bar, which acquires two poles, a I, of contrary names to the poles B B', A A' of the magnets used. This is Duhamel's process ; it gives powerful magnetization, but not at all regular, and it sometimes produces consequent points. The process of ^Epinus only differs from that of Duhamel by the two movable magnets being inclined from 45 to 50 degrees, and after having placed them in contact and bound them together at the middle of the steel bar, both are passed together from one extremity of the bar to the other. The magnetization thus obtained is not only more powerful than the preceding, but more regular. Therefore the separate double touch is preferred when needles are to be magnetized for compasses. Steel, or even- soft iron bars, can be magnetized without the use of artificial or natural magnets, if they are placed and kept for some time in the plane of the magnetic meridian and in the direction of the inclination. In this position a steel bar is magnetized along its whole length, and obtains all the properties of a magnet : a bar of soft iron becomes a magnet, but only a temporary one ; the magnetic action of the terrestrial globe magnetizes by influence, or induction as it is CHAP. I.] MAGNETS. 525 called. If one of the extremities of a magnet thus produced is struck with a hammer, the magnetic force of the bar is not only increased but it becomes permanent. Pieces of wire strongly stretched whilst held in the direction of the dipping needle are magnetized ; and if they are united by their poles of similar name in a single sheaf, a very powerful magnet may be obtained. To magnetize by the action of terrestrial magnetism, it is sufficient to hold the bar of iron or steel vertical while one of its extremities is struck with a hammer. In this manner this bar is in the plane of the magnetic meridian, but without the in- clination of the magnetized needle. This action of the earth well explains how it happens that in shops in which steel and iron are worked, a great number of tools become magnetic, shovels, pincers, iron-work of windows, and generally all the pieces of iron- work which are a long time in a position perpen- dicular to the horizon ; this is also the case with the crosses which FlG _ 345 ._ Magnetization by the method surmount church towers. We shall of ^ pinus - soon have occasion to speak of the magnetism obtained by electric currents, but it was known for a length of time that lightning could communicate magnetic properties to iron. In the article Magnet in D'Alembert and Diderot's Encyclopaedia we read: "One day lightning entered a room in which there was a box of steel knives and forks destined for sea use ; the lightning entered by the southern angle of the room, exactly where the box was placed; several knives and' forks were melted and broken; others which remained whole were strongly magnetized, and became com- petent to lift large nails and iron rings, and this magnetic virtue was so strongly impressed that it was not dissipated when they became rusty." The strength of magnets alters in the course of time : shocks, changes of temperature, and lastly the action of the earth are the causes of this alteration. The strength depends on the volume of the magnet, its form, and the temper of the steel; thus, in two similar magnetized bars, the magnetic intensity is sensibly propor- tional to their size, or, in other words, to cubes of equal dimensions ; 526 PHYSICAL PHENOMENA. [BOOK v. nevertheless, it has been noticed that small magnets are, in pro- portion, more powerful than large ones: some have been made which supported pieces of iron whose weight was a hundred times their own. This suggested the idea of forming magnets by uniting a series of magnetic bars by their similar poles : these are called compound magnets. Fig. 346 shows how these magnets are arranged. In the Koyal Institution of London there is a compound magnet formed of 450 plates, each of which is 2 feet in length. It is sufficiently powerful to lift 110 Ibs. Form also influences the strength of magnets ; thus, with equal weights, a lozenge-shaped mag- netic needle is more powerful than a rectangular bar. The temper of the steel has a great influence on the force of the magnetized bar : tempered steel is magnetized more strongly than non-tem- pered steel; if it is subjected to increasing tem- peratures, the magnetic force is weakened more and more. Coulomb has shown, however, that the result is quite different, if, instead of working with rectangular bars, very fine and long needles are employed ; in this case heating increases their magnetic force. Fl net 346 fwmed lp of D tweive Lastly, temperature has a great influence on magnettoban. tlie force of magne t Sf A magnetic bar when heated to redness loses all its magnetism, the intensity diminishing as the temperature rises, as stated by Coulomb. But if the varia- tions of heat take place within narrow limits, the magnetic in- tensity varies only slightly, and the magnet resumes in cooling the strength which it originally possessed. This refers to polar magnetism, that is to say, to that possessed by magnets ; but it is also the case with simple magnetic substances like soft iron, nickel, &c., which also lose their property when their temperature is raised to a certain degree. Iron is not magnetic if it is heated to a cherry red-heat, and the same happens in the case of cast-iron heated to whiteness. Above 350, nickel is no longer magnetic, and man- ganese only becomes so below zero, about - 20. These last results are due to M. Pouillet. CHAP. I.] MAGNETS. 527 We have now to speak of the means employed to preserve the magnetic force in natural and artificial magnets. Experiment has proved that magnetic bars, united parallel to m each other, two by two, in a box, so that the opposite poles are together, preserve their magnetism, if care is taken to join the contrary poles by bars of soft iron, which are called armatures or keepers. An armature is used to increase the power of a magnet. When these are used it is sometimes curved in the form of a horse- shoe, the armature uniting the two poles. A magnet armed in this way (Fig. 347) carries not only a greater weight than that which a single pole would carry, but double that weight. By uniting two rectangular magnets or compound magnets, turned so that their opposite poles A, B are joined by a similar armature (Fig. 348), a very strong magnet is obtained. Experiments also show that magnets thus arranged keep their magnetic force better if they are left armed FlG 3 4 7 _ Ironhorse ^hoe magnet, with their keepers, or if the charge of iron with its armatl that they are able to lift is suspended on it, always provided that it Fio. 348. Magnet formed of two compound bar magnets. does not exceed that limit ; for then, the keeper being suddenly detached, the magnetic force of the magnet is weakened. 528 PHYSICAL PHENOMENA. [BOOK v. Masses of magnetic oxide of iron, which constitutes natural magnets, have often but feeble magnetism ; but their magnetic virtue has been increased by furnishing them with pieces of soft iron conveniently arranged. Fig. 349 shows how these armatures FIQ. 349. Natural magnet furnished with its armature. are placed : m m are plates of soft iron in which the natural magnet is enclosed, and which are terminated by thicker masses pp, these forming real poles to the magnet; c is the armature or keeper. Finally plates of copper are used to support the plates of soft iron round the mass of magnetic oxide. BOOK VI. ELECTRICITY. BOOK VI. ELECTRICITY. CHAPTEE I. ELECTRICAL ATTRACTION AND REPULSION. Attraction of amber for light bodies Gilbert's discoveries ; electricity developed by the friction of a number of bodies Study of electrical attraction and repul- sion ; insulators, or bad conductors ; good conductors Electrical pendulum Kesinous and vitreous, positive and negative electricity Laws of electrical attraction and repulsion Distribution of electricity on the surface of bodies Influence of points. THE ancients discovered that amber, when it is quickly rubbed with a piece of woollen stuff, and brought near light bodies such as bits of straw, pieces of paper, or feathers, causes them to move towards it, as if attracted by some mysterious force. Thales of Miletus, who lived 600 years before the present era, mentioned this property ; and the Greek philosopher, Theophrastus, speaks of jet as likewise possess- ing it. But to these two facts alone, during more than two thousand years, the knowledge of physicists was confined, so far as this class of phenomena is concerned. Pliny the naturalist, on mentioning the first fact, stated that " friction gives to amber heat and life." About the year 1600, an English doctor, William Gilbert, to whom science owes many discoveries concerning the properties of the magnet, discovered that glass, sulphur, resins, and various precious stones possessed the attractive properties of amber. Since that time a great number of physicists have extended the researches of Gilbert, and 532 PHYSICAL PHENOMENA. [BOOK vi. brought to light many curious phenomena before unknown, and thus contributed to found the branch of physics which, under the name of electricity, has now undergone so much extension and is of so much importance. The word electricity means more particularly the cause, even now unknown, of the phenomena we are about to describe ; it is taken from the Greek name of yellow amber, electron (rjXe/crpov). 1 Nothing is more easy than to produce the phenomena of attraction of which we have just spoken. A stick of amber, glass, or resin, is quickly rubbed with a piece of cloth; if the rubbed parts are held near pieces of straw or paper, at a small distance, these are seen to approach the surface of the glass, very much as iron filings are attracted by the magnet, but as soon as they come into contact with the rubbed surface the attraction is changed into repulsion, and the light substances move away. When the substance rendered electric by friction is passed at a short distance over the face, a sensation is perceived similar to that of a cobweb coming in contact with it. If the rod of resin is rather large, and the friction energetic and pro- longed, a sharp crackling noise is heard, when we place the fingei very near it, and, if the room is dark, a spark will be seen to pass between the finger and the nearest portion of the rod. These various phenomena cease if the hand is passed over the rubbed substance. A body is said to be electrified so long as it shows in any degree the properties indicated in these experiments ; it is in its natural state when it gives no sign of attraction or repulsion. For some length of time it was imagined that, electrically con- sidered, all substances must be ranged into two distinct classes : one comprising those which are susceptible of becoming electric by friction : the other, those which could not acquire this property. It had been discovered, in fact, on repeating the preceding experiments with substances of every kind, that metals, stones, vegetable and animal matter, and the human body, for instance, do not give rise to the same phenomena as amber, resins, glass, sulphur, &c. But Gray, a physicist of the last century, determined the cause of this difference, and showed that it referred only to the particular conditions under which the experiments were made. 1 Yellow amber is a kind of fossil resin, which is found in great abundance on the coasts of the Baltic. It has for a length of time been employed on account of its beauty of colour and transparency as an ornament in dress and jewellery. CHAP, i.] ELECTRICAL ATTRACTION AND REPULSION. 533 Indeed, after rubbing a glass tube closed with a cork stopper, we perceive that the stopper itself is electrified, although the cork rubbed separately does not give any sign of electricity. Gray studied this transmission of electricity, and proved that it could take place through a great distance, through bodies which until then were considered incapable of being electrified by friction. On the other hand, this transmission cannot take place with substances capable of being directly electrified under the conditions previously stated. It follows from these experiments, that different substances FIG. 350. Attraction of light bodies. possess in different degrees the property of conducting electricity once developed : bodies which were before considered as only sus- ceptible of being electrified by friction, are precisely those which conduct electricity the least they are lad conductors. Those, on the contrary, which it had been found impossible to electrify, are good conductors. The consequences of this new distinction are important, and we shall see they are proved by experiment. As glass, amber, resin, &c. are bad conducting bodies, electricity can only be developed in the rubbed portions ; and this is proved by observation. But if they are touched by the hand, which is a good conductor like the rest of the body, electricity passes to the latter, then to the ground, and disappears always at the points where contact takes place. We have seen that it 534 PHYSICAL PHENOMENA. [BOOK vi. quite disappears if the hand is passed over the whole surface of the electrified rod. When a metallic cylinder is rubbed, it will be under- stood that no sign of electricity can manifest itself; and, indeed, as metals are excellent conductors, if electricity is produced, it instantly extends over the whole surface of the metal, and, through the inter- vention of the body of the operator, passes to the ground. If a handle made of some bad conducting body, glass for instance, is fitted to the metallic cylinder, and if this handle is held in the hand whilst the metal is being rubbed, the latter becomes electrified and acquires the properties which we have described above as belonging to glass, resin, and amber. For this reason the name of insulating bodies is given to bad conductors ; by insulating any substance whatsoever, it becomes susceptible of being electrified by friction. These experiments can be repeated under a variety of forms. A person standing on a stool with glass legs is electrified when he is rubbed with the skin of a cat ; on placing the finger near any part of his body sparks will pass from him, and during the whole time of electrization he perceives a singular sensation on the face, like that caused by an electrified rod. Water is a good conductor ; and in the state of vapour it possesses the same property. This is the reason why great care must be taken when electricity is being obtained, not only to insulate the substance operated upon if it is a good conductor, but to wipe and dry the handle or glass supports, or other insulators. This is also the reason why electricity is produced with greater facility in dry than in damp weather ; the room in which the experiments are made must be dried as much as possible previously, so that the air which it contains may contain as little aqueous vapour as possible. To avoid the escape of electricity by the insulating glass supports which are generally employed in electrical apparatus, they are covered with a layer of shellac varnish, the surface of which is not hygrometric like that of glass. Various substances may be arranged according to their order of conductibility in two classes, viz. into good and into bad conductors or insulators, but in each of them the conducting property exists in different degrees, so that no substance is absolutely without it. The following table gives a few substances arranged in the order of their decreasing conductibility : CHAP. I.] ELECTRICAL ATTRACTION AND REPULSION. 535 Good conducting bodies. Metals. Burnt charcoal. Graphite. Acidulated water. Minerals. Water. Vegetable substances. Animal substances. Steam. Powdered glass. Flour of sulphur. Bad conducting or insulating bodies. Ice. Phosphorus. Caoutchouc. Porcelain. Dry air. Silk. Glass. Sulphur. Resin. Amber. Shellac. From this it is seen that electrical conductibility is not influenced by the chemical nature of the substance, so much as by its physical FIG. 351. Electrical pendulum. Phenomena of attraction and repulsion. condition or molecular structure. Thus ice is in the number of the insulators, whilst water and steam are amongst the conductors. Sulphur and glass in large masses are bad conductors: but when reduced to very fine powder they conduct electricity very readily. Coal in the ordinary state is an insulator, but it becomes a conductor when calcined ; carbon crystallized, or in the state of diamond, is a bad conductor, but graphite, which is another mineralogical form of 536 PHYSICAL PHENOMENA. [BOOK vi. carbon, is a good conductor. Heat has great influence on the electrical conductibility of bodies ; a high temperature confers this property upon several bodies which are insulators at the ordinary temperature ; glass, sulphur, shellac, and gases, are among this number. We will now return to the phenomena of electrical attraction and repulsion, and study them in greater detail. We shall for this employ a very simple instrument, to which the name of the electrical pendulum (Fig. 351) has been given. It is a little ball of elder pith suspended by a silk thread to a stand, and is con- sequently insulated, as silk is a bad conductor. By holding near the pith ball a rod of electrified resin, we observe that there is first attraction ; but, so soon as contact has taken place, the ball is repelled from the resin, and this will continue to be the case even when the rod of resin is again brought near to it. In this state, the pith ball is electrified, which is easily seen by holding the finger to it, for then it is attracted ; on touching it with the hand, after contact with the resin, it is neither attracted by the finger nor repelled by the rod of resin ; the electricity which it possessed has passed into the earth, through the body of the operator. If, instead of using a rod of resin, an electrified glass rod is employed, the same phenomena manifest themselves in the order we have just described : there is attraction and contact, then repulsion. So far, no difference has been observed between the electricity developed on the resin and that developed on the glass, when these two bodies are rubbed with a piece of catskin or silk. But let us suppose that after having obtained the repulsion of the pith ball by means of the electrified resin, a glass rod electrified by catskin is brought near the pith ball. The pith ball is now attracted by the glass as strongly as if, instead of having been pre- viously electrified by resin, it had remained in its natural condition. The same phenomena of attraction will be manifested, if, after having electrified the ball by contact with the glass rod, a piece of resin electrified by catskin or silk is placed near it. Thus the electricity developed on the resin and that developed on the glass by friction of the catskin or silk acts under the same circumstances, in an opposite manner; for the one attracts the electrified body which the other repels, and reciprocally. Hence, electricity was distinguished by the earlier experimenters into two kinds, and the names given were resinous electricity and vitreous CHAP. I.] ELECTRICAL ATTRACTION AND REPULSION. 537 electricity. On repeating the preceding experiments with amber, sulphur, wax, paper, &c., it will be seen that these substances act, some like the resin and others like the glass ; and it .is then said that they are charged either with resinous electricity, or with vitreous electricity. These terms are now abandoned, and for the following reason : As all bodies are capable, as we have just seen, of being electrified by friction, it is clear that if one of the rubbed bodies is electrified, the other must be electrified as well ; and this is confirmed by experiment. But it has been shown, besides, that electricity developed on one of the bodies is not the same as that developed on the other ; for example, if two discs are taken, one of polished glass and the other of metal covered with cloth, each furnished with an insulating handle, and if after they have been rubbed against each other they are suddenly separated, the glass disc will be found charged with vitreous electricity, and the cloth with resinous electricity, as may easily be proved on trying the action which each of them exercises on an electrical pendulum, the ball of which has been previously electrified in the same manner in each case. But this is not all ; it will be noticed that the nature of the elec- tricity developed on a body changes according to the body with which it is rubbed ; thus, glass, which we have seen taking up vitreous elec- tricity when it is rubbed with silk, on the other hand takes resinous electricity if it is rubbed with catskin. Shellac becomes charged with resinous electricity if it is rubbed with a catskin or flannel; while it acquires vitreous electricity if it is rubbed with a piece of unpolished glass. By retaining the terms we have just used, a certain confusion may occur, for which reason the names of positive and negative electricity have been substituted for those of vitreous and resinous electricity. However, we must not attach to these words other signification than this : positive electricity is that developed on glass by rubbing it with silk ; negative electricity is that ob- tained on resin by rubbing it with catskin. But the method of action of these two kinds of electricity may be summed up in two very simple laws : 1st, All bodies electrified either positively or negatively attract light bodies in their natural state. 2. Two bodies charged with electricities of contrary names attract each other : two bodies charged with electricities of the same name repel each other. T T 538 PHYSICAL PHENOMENA. [BOOK vi. There is no exception to these laws, but the conditions of produc- tion of one or the other kind of electricity are extremely complex ; the same substance, we have just seen, is sometimes electrified positively and sometimes negatively, according to the substance with which it is rubbed. But modifications, often but slightly apparent on the sur- face of bodies, change the nature of the electricity developed. Thus polished and unpolished glass, both rubbed with catskin, take, the first, positive electricity, the second, negative electricity ; two discs of similar glass rubbed against each other are electrified sometimes in one way and sometimes in another; heat possesses great influence, and most hot substances acquire negative electricity. Many curious experiments have been made as to the conditions which determine one or the other mode of electrization ; but little is as yet known as to the causes of these singular phenomena, and the theories which have been started to explain them have no greater advantage than to classify the facts, and thus render them more easy to fix in the memory. An insulating body, or a bad conductor, can be electrified either by friction or by the contact of another body already electrified. We shall soon see another mode of electrization, which consists in develop- ing electricity, at a distance, by influence or induction. It is in all cases interesting to know how the electricity is distributed in a body ; if it spreads itself through the entire mass or only on the surface if, in every part where its presence is manifested, it exerts the same energy in a word, what is its tension in the different parts of bodies of different form. One of the facts which experiment has already revealed to us is, that in an insulated body, electricity is located on the surface which has been rubbed, or which has been placed in contact with an electri- fied body. This is the case with the most perfect insulators ; in bodies possessing a less degree of insulation, electricity extends to a little dis- tance round the parts of which we speak. The reason of this fact is evidently the same as that which makes these bodies bad conductors of electricity. On the other hand, in good conductors, electricity, in whatever mode it may be produced, spreads itself almost instantane- ously over the whole surface. Experiments which we are about to de- scribe prove that it does not penetrate into the mass of the body, or, at least, that the thickness of the electrified stratum is very small. CHAP. I.] ELECTRICAL ATTRACTION AND REPULSION. 539 A metallic sphere insulated on a glass foot is covered with two thin hemispherical envelopes, which are held in contact with it by two insulating handles ; the whole system is then electrified, and both hemispheres are suddenly withdrawn. On separately presenting to the ball of an electrical pendulum, first the sphere itself, then each of the coverings, we shall observe that these latter are alone electrified. The electricity was not therefore spread out to a greater thickness than that of the envelopes. A hollow metallic sphere, pierced with a hole at the top and placed on an insulating stand (Fig. 353), is charged Fm, 352. Distribution of electricity on the surface of conducting bodies. with electricity ; and in order to ascertain the manner in which the electricity is distributed, a small gilt paper disc is used, furnished with an insulating handle this is called a Carrier QT proof plane and it is applied to any point of the outer surface of the electrified sphere : it is then found that it attracts the pith ball of the electrical pendulum. The proof plane is now touched with the hand ; the electricity with which it was charged passes away, and it returns to its normal con- dition : if it is now applied to the interior of the sphere, care being taken that it does not touch the sides of the hole, no sign of elec- tricity will be shown on withdrawing it and presenting it to the pith T T 2 540 PHYSICAL PHENOMENA. [BOOK vi. ball. The result will be the same if the interior of the sphere is first touched. Faraday made the same experiment by giving to the body the form of a cylinder of metallic network, which he placed on an insulated disc of brass ; the disc was then electrified, and he proved, by the help of the proof plane, that the electricity was located alone on the outer surface of the vessel. The same illustrious physicist also made the experiment with a conical bag of muslin, attached to an insulated metal ring : the latter is electrified ; and a double silk thread, fixed to the top of the cone, FIG. 353. Distribution of electricity on the surface of bodies. enables the bag to be pulled inside out, and it is always found that the electricity is on the outer surface, so that it passes alternately from one surface of the bag to the other (Fig. 354). Thus it is entirely on the outer surface of conductors that elec- tricity is distributed : at least, if it penetrates into the interior, the thickness of the electrified stratum is extremely small. Let us take two spheres, one plain and of metal, the other of shellac, gilt on the outside, both being of the same diameter; and then electrify the first, and measure the electric tension by means of an instrument CHAI>. i.J ELECTRICAL ATTRACTION AND REPULSION. 541 called an electrometer. If the spheres are now placed in contact, the electric tension on each of them is found to be half what it was at first on the single metallic sphere. As the thickness of the electric stratum on the shellac sphere is equal to that of the gold leaf, we must conclude that its thickness is not greater on the solid sphere. We have just spoken of electric tension. It is the intensity of the force with which a given portion of the surface of an electrified body attracts or repels an electrified body exterior to it. Coulomb, under the name of the electric balance, devised an instrument which is used to measure this tension, and by means of it he determined the FIG. 354. Faraday's experiment to prove that electricity is located on the outer surface of electrified bodies. laws according to which electric attractions and repulsions take place under varied conditions. As the principle of this instrument and the mode of observation is the same as in the case of the magnetic balance, described in the preceding Book, we shall content ourselves with simply stating the following laws. The repulsion or attraction of two equal spheres charged with electri- cities of the same or contrary kinds, varies in the inverse ratio of the square of their distances. Af tractive or repulsive forces vary as the products of the quantities of electricity which the two spheres contain. This, it will be remembered, is the law which governs universal gravitation. The tension of electricity spread over the surface of a conducting body is only equal at each point of the surface, when the body has the 542 PHYSICAL PHENOMENA. [BOOK vi. form of a sphere. This is expressed by saying that the thickness of the electric stratum is uniform (Fig. 355). In an elongated ellipsoid, this stratum possesses its maximum thickness at the extremities of the major axis ; in a flattened ellipsoid, the maximum is round the equator. In a flat disc, the electric tension, which is nearly nil at the centre, increases towards the edges, where FIG. 355. Tension of electricity at the different points of a sphere and of an ellipsoid. it attains its greatest intensity. In a conductor formed like a cylinder terminated by two hemispheres, the tension is greatest at the surface of these latter ; and it is nearly nil everywhere else. The dotted lines surrounding the solids represented in Figs. 355 and 356, indicate, by their distances from the adjacent points of the surfaces, the tension of the electricity at each of these points. We see, therefore, what a great (' WMMNMMMIIIDI^^ influence form has on the distri- *-.^ \^/ bution of electricity on surfaces; but nowhere is this influence so perceptible as on the parts of bodies terminated by abrupt edges, Fl*. 356.-Ten,ion of electricity on a flat disc, aCUte an g leS > and C0nical OT and on a cylinder terminated by hemispheres. mi(M pointg< At these electricity accumulates, and acquires sufficient intensity to pass into the surrounding medium, even when this medium is only to a slight extent a conductor. Before experimentally proving what is called the power of points, we may say a word or two on the influence of the medium which surrounds an electrified body, on the preservation or loss of the electricity on its surface. We already know that if this medium is a good conductor, such as water or moist air, the electricity will not remain on the body which has been electrified, but will pass away : this is an obstacle which must be removed, however slight it may be, if we wish to acquire a quantity of electricity. But if the medium is dry air, let us inquire CHAP, i.] ELECTRICAL ATTRACTION AND REPULSION. 543 what will be the influence of atmospheric pressure on the loss of elec- tricity from the surface of a body, and what the influence of tempera- ture ? These questions are very complex, because the causes which act at one time on the loss of which we speak, besides being numerous, are very difficult to study separately. The insulating supports are more or less conductors ; and the same remark applies to electrified bodies. Coulomb and Matteucci studied this interesting and difficult question, and did not always arrive at similar results. Nevertheless, their researches have shown that the loss of electricity in dry air increases with the temperature ; that with a constant temperature it increases rapidly when the pressure of air diminishes, or rather as the air sur- rounding the electrified body is rarefied. Nevertheless, this last law only holds good in the case of strong charges ; so that, if we introduce an electrified body into a vacuum, it immediately loses the greater part of its tension ; but this action is limited, after which the loss goes on very slowly. The greater the rarefaction, the less is the limit, but the loss of electricity becomes less also. We shall hereafter describe some very curious phenomena, which show the loss of electricity in rarefied media. We will now return to the escape of electricity at points. It has been calculated that at the top of a conical point the electric tension is infinite, so that it is impossible to charge a con- ducting body, furnished with such a point, with electricity; this is confirmed by experiment. In proportion as the electricity is developed, it escapes into the surrounding medium and disappears. When the extremity of the point is examined in the dark, a luminous tuft is seen, the form and colour of which we shall hereafter study. If, while the point is in communication with the electric source, the hand is placed before or under it, a wind is felt which indicates a continuous movement of the particles of air; this movement is rendered very perceptible by placing at the end of the point the flame of a candle (Fig. 357). The electric wind is intense enough to cause the flame to bend, or even to extinguish it. This agitation of the air, at the extremity of the points of electrified conductors, was at first attributed to the escape of the electricity, which was compared to a fluid ; but the following explanation appears to us preferable, because it requires no hypothesis as to the nature of electricity, and is, moreover, found to agree with known phenomena. 544 PHYSICAL PHENOMENA. [BOOK vi. The molecules of air, which are in contact with the point electrified to a considerable degree of tension, are charged with electricity of the same name as that of the conductor ; then commences repulsion, and the molecules, on getting further away, give place to others, which Fio. 357. Power of points. Electric wind. are electrified in their turn, and so on. Hence the current of air which observation indicates, and which is only continuous so long as the electric charge is renewed. The force with which the air is driven from a point, engenders a reaction, which must repel the point in a contrary direc- tion ; and if this point does not move, it is because it is not free to do so. The existence of this reaction is proved by using a little instrument called the electric fly (Fig. 358). A system of divergent wires is united by a centre piece, which allows the movement of the system in a horizontal plane ; each wire is curved in and sharply pointed in the same direction. As soon as the conductor on which the fly is placed is charged, the latter takes up a rotary movement in the direction opposite to that of the points. Fio. 358. Electric fly. CHAP. II.] ELECTRICAL MACHINES. 545 CHAPTEE II. ELECTRICAL MACHINES. Electrification at a distance ; development of electricity by induction Distribution of electricity on a body electrified by induction Hypothesis as to the normal condition of bodies ; neutral electricity proceeding from the combination of positive and negative electricities Electroscopes ; electric pendulum ; dial and gold-leaf electroscopes Electrical machines : Otto von Guericke's machine ; Ramaden, or plate-glass machines ; machines of Nairne and Armstrong The electrophorus. WHEN a body is in its normal condition, we have just seen that there are two modes of rendering it electrical, viz. by friction, or by contact with a body previously electrified. The phenomena which we are about to describe prove that, in the latter case, contact is not necessary. Let us take, for instance, an electrified FIG. 359. Electricity developed by influence or induction. body c a metallic sphere mounted on a glass column and let us place in its vicinity, at a short distance from it, an insulated cylin- drical conductor A B, in its natural condition. These two bodies are no sooner in the presence of each other, than the conductor A B shows 546 PHYSICAL PHENOMENA. [BOOK vi. si/ A* 411. Deviation to the left of tho current, vertical current. current. We will leave the reader to find the direction of the needle in the other cases ; a task which has been rendered easy by Ampere's law. The laws which regulate these observations were studied by Biot and Savart and by Laplace. Bearing in mind the fact that the influence of the current depends on its intensity and, conse- quently, on the surface of the couples of the pile employed, it diminishes in pro- portion as the distance from the needle increases. It must not be forgotten that in the presence of a voltaic current, the needle is subjected to two influences at the same time, viz. that of the current itself, and that of the earth, which acts on the needle like a magnet ; the devi- ations observed are, therefore, an effect resulting from these two simultaneous actions. If, by any means, we can render the direction of a magnetic needle independent of the action of the earth it is then called an astatic needle the current deviates the needle to a right angle, what- ever may be its intensity. The deviation then indicates only the presence of the current, without proving its energy. Let us now see how we can utilize the action of electrical currents on the magnetic needle, in the construction of apparatus which serve both to prove the presence of small currents, and to measure their intensity. We will first describe the apparatus called Scliweigger 's multiplier, from its inventor:^ It consists of a wooden frame (Fig. 412) round which a copper wire is wound a great number of times ; this metallic wire '\ is entirely covered with an insulating \- substance, gutta-percha, silk, cotton, &c., so that an electric current entering by one of the extremities of the wire, and issuing from the other, cannot pass from one spiral to another without having traversed the whole length : in a word, it is obliged to pass FIG. 412. Schweigger'8 multiplier. through all the successive windings. If the frame is placed verti- COS PHYSICAL PHENOMENA. [BOOK vt cally on one of its sides, in the plane of the magnetic meridian, and if a magnetic needle is placed in the inside, suspended freely on a vertical pivot, a good instrument will be obtained for showing, by the deviation of the needle, the existence of an electrical current, however slight it may be. To effect this, it is sufficient to attach the extremities of the wire of the multiplier to the two rheophores of the pile or of any voltaic circuit; so soon as the circuit is closed, the presence of the current will manifest itself by a greater or less deviation of the needle. We will now analyse this effect, and examine how the action of the current is multiplied by the arrangement we have just described, and, for this purpose, we may first consider one of the circuits of the wire wound round the frame ; the current passes from M to N, then to Q and P, and at n leaves the needle. Now, if we compare it with Ampere's statement, we shall ^^.^^ see that each of the four portions of the current tends to deviate the southern pole from a to a, consequently towards the east, or, in other words, to the front of the figure; each of them acts like FJO. 413. Concurrent actions of the dif- , . , -> , vi ferent portions of the wire in the an insulated current, or better, like an multiplier. indefinite portion of the current near the needle. The total deviation will be then stronger than if the current only followed one of the sides of the rectangle. ]STow, at the following winding, the current acts again in the same manner, and it is the same for all the successive windings, so that its in- fluence on the magnetic needle is multiplied by the number of the windings of the wire. Hence the name of multiplier is given to the instrument. The magnetic needle is in this experiment, as we have already stated, submitted to two forces : the directive action of the earth, in virtue of which it places itself in the magnetic meridian ; and the action of the current, which tends to cause it to assume a posi- tion at right angles to the first. The deviation of the needle is produced by the resultant of these two actions. To increase the deviation, and to give a greater sensibility to the multiplier, Nobili conceived the idea of substituting for the magnetic needle a system of two parallel magnetic needles, fixed on the same axis, with CHAP. V.] ELECTRO-MAGNETISM. GOO their poles of the same name placed in contrary directions. The suspension being by a silk thread without torsion, if the needles have the same magnetic force, their system will be astatic; that is to say, will remain in equilibrium, whatever may be its angle with the meridian. A system exactly astatic would not fulfil the end which is proposed, which is to measure the intensity of the currents by the deviation, as then the deviation would always attain the maxi- mum of 90, whatever the power of the Fla 414 - s> n Sesf tw astatic current. But if one of the needles, the lower one for example, is a little more magnetized than the upper one, the system will continue to be influenced by the earth ; but this action will be very feeble, and therefore the Fig. 415. Galvanometer. action of the currents through the intervention of the multiplier will be, on the contrary, considerable. The introduction of the compensated needles in Schweigger's multiplier led Nobili to the construction of the galvanometer (Fig. 415), the most delicate 610 PHYSICAL PHENOMENA. [BOOK vi. apparatus for determining the existence, strength, and direction of weak electrical currents. The following is the manner in which this instrument is used : The ivory frame around which the insulated wire is wound, and which is below the dial, can be moved in a horizontal plane by an outside screw ; and it is first brought into a plane of such a nature that the zero of the graduation of the dial corresponds to one of the extremities of the needle. It is now certain that the rounds of copper wire are parallel to the two needles of the system. The apparatus is furnished with levelling screws, so that it can be placed horizontally ; a,nd a glass shade protects the suspending thread and the needles themselves against the agitation of the exterior air. The frame includes a rectangular ivory plate, which has two brass buttons, at each of which terminates the extremity of the two wires of the multiplier. To these buttons, or binding screws, the rheophores of the current, the direction and intensity of which are to be deter- mined, are attached : as soon as the circuit is closed, and the current passes along the rounds of wire, the upper needle is seen to deviate to the right or left of its position of equilibrium; the direction of this deviation indicates, according to Ampere's law, the direction of the current. The intensity of the current is measured by the arc which either of the extremities of the needle has traversed, starting from the zero of the graduation. It has been found that, if the devia- tion does not exceed 20, it is sensibly proportional to the intensity of the current. We have just seen the action of voltaic currents on the magnetic needle, and how this influence has been utilized in constructing an apparatus of extreme delicacy, to show the direction and intensity of a certain current. We may now state that magnets exercise on currents an action equal to that to which they themselves are submitted, but in a contrary direction. Thus, when a strongly magnetized magnetic bar A B (Fig. 416) is placed in a horizontal position below or ahove a metallic wire forming a voltaic circuit, and free to turn round the points of suspension, the wire is seen to set itself across the magnet, in such a manner that the south pole of the bar is always to the left of the current which is nearest to it. When the direction of the current CHAP. V.] ELECTRO-MAGNETISM. 611 is changed by the reversal of the rheophores which terminate the two extremities of the wire, the wire immediately makes a rotation of 180 on itself; the southern pole of the latter is still to the left of the current, according to Ampere's law. We have now arrived at Ampere's beautiful discovery, which immediately followed that of Oersted's, as to the action of voltaic currents on each other. We will confine ourselves to the statement of the principal laws which govern the reciprocal influence of currents, laws the experimental verification of which is easy, in the Repulsions. Attractions. FIG. 416. Action of a magnet on a current. FIG. 417. Law of the attraction and repulsion of a current by a current. numerous particular cases which they comprehend. Ampere has demonstrated that : 1st. Two parallel currents, which pass in the same direction, attract each other: while they repel each other if they pass in a contrary direction. 2nd. Two non-parallel currents attract each other, if at the same time loth approach or recede from the apex of the angle formed ly the ends produced ; they repel each other, if one of the currents approaches the apex of the angle, whilst the other recedes from it. Fig. 417 represents the three cases of attraction and two cases of repulsion to which these laws refer. Thus then, on the one hand, electrical currents act on magnets, and magnets act on currents : while, on the other hand, currents act on each other. Hence, there is 612 PHYSICAL PHENOMENA. [BOOK vi. only a step to assimilate magnets with, currents ; Ampere has indi- cated this, and has brought to the help of theory the control of experiment. He discovered that the earth itself acts on the currents ; that if a rectangular instrument similar to that of Fig. 416 is left to itself, and an electrical current passed through it, the apparatus turns round on its vertical axis and places itself spontaneously across the magnetic meridian ; the ascending portion of the current is carried to the west and the descending portion to the east. M. Pouillet, by some clever arrangements, has shown that an insu- lated vertical current, moveable round an axis which is parallel to it, is transported of itself to the magnetic west or east, according as it is ascending or descending, whilst the action of the earth on the horizontal branches of Ampere's apparatus is nil. To determine the nature of these facts Ampere constructed a static apparatus, this is to say, a magnetic system indifferent to the action of the terrestrial globe ; then causing a fixed current to act on it, placed horizon- tally in a direction perpendicular to the magnetic meridian, from east to west, he saw that the action of this current was precisely the same as the action of the earth. He concluded that the magnetic action of the earth on the magnetic needle is due to electrical currents which continually circulate perpendicular to the magnetic meridian, their direction being from east to west. These various currents, whatever may be their number, may be considered as com- posing a single current ; and experiment shows that, in our latitudes, its position is situated towards the south. Pursuing these beautiful generalizations, Ampere showed that a magnet may be assimilated to an assemblage of circular vertical and parallel currents passing in the same direction. An assemblage of such currents indeed experiment will show us when freely sus- pended so as to be able to turn in a horizontal plane, places itself, when submitted to the action of the earth, in the magnetic meridian ; in fact, it behaves exactly like a magnetic needle. Ampere constructed a helix or electrical magnet in this way : He took a metallic wire and rolled it round a cylinder in equidistant coils, giving it the form represented in Fig. 418 ; he then brought the two extremities of the wires longitudinally above the coils, and curved them in such a way that the whole could freely turn round a vertical axis ; next, he at- tached the two ends of the wire to the rheophores of a pile. When the CHAP. V.] ELECTRO-MAGNETISM. C13 current passes in the direction marked by the arrows, the solenoid the name given to the apparatus by Ampere places itself in a position of stable equilibrium ; each coil is in a vertical plane, its direction being from magnetic east to west ; the axis of the solenoid coincides then with the magnetic meridian, exactly like a magnetic needle. If the direction of the current is changed, the solenoid is seen to be dis- placed ; and after having moved through 180, it places itself in its original position, its longitudinal axis being always in the magnetic meridian, but it is turned about. Lastly, an element of the solenoid, suspended so that it is able to turn freely -round an axis perpendicular Wes North. - East. \8outh. Fio. 418. Direction of a solenoid in the meridian, under the action of the earth. to the magnetic meridian, assumes an inclination which is precisely equal to that of the magnetic needle. Thus, ordinary magnets, and solenoids or electrical magnets, con- duct themselves in the same manner when under the influence of the magnetic action of the earth. But the analogy has been pushed further; Ampere has shown that the extremities or poles of two sole- noids exercise on each other attractions and repulsions of the same nature as the attractions and repulsions of the poles of magnets: poles of the same name of solenoids repel each other ; while poles of contrary names attract each other. Lastly, the same actions manifest themselves, if the pole of a solenoid is presented to one or other of the 614 PHYSICAL PHENOMENA. [BOOK vi. two poles of a magnetic needle. The similarity is complete, and Ampere was able to form his theory of magnetism in all its exactness, a theory which assimilates magnetic phenomena with dynamic electrical phenomena. The following is a brief r6sum6 of this beautiful theory : The terrestrial globe is continually traversed by numerous electrical currents, induced perhaps by chemical action. These various currents, with directions and intensities probably different and variable, pro- duce on magnets the same effect as a single current, resulting from the composition of the elementary currents, circulating from east to west, in a direction contrary to the earth's movement of rotation. A magnetic substance, iron, steel, &c., also becomes the seat of elemen- tary electrical currents, circulating round certain groups of atoms. In soft iron, and in magnetic bodies which are not endowed with polar magnetism, these currents move in all directions, so that the oooo FIG. 419. Particular currents of magnets. FIG. 420. Resulting currents at the surface of a magnet. resulting effect is nil. In magnets, on the contrary, the particular currents have all the same direction ; for example, they circulate as the arrows indicate in Tig. 419, in which is shown a transverse section of a magnetic bar. In the neighbouring or contiguous portions in &, V, a, a', &c., the currents are of contrary directions, and are de- stroyed ; so that the total effect is reduced to the exterior effect, which leads us to consider the contour of each edge as being traversed by a single current. The same effect will take place in all the sections, and the magnet will be constituted as indicated in Fig. 420. We therefore see that, according to Ampere's theory, every magnet may be considered an equivalent to a solenoid. In regard to magnetic substances, such as soft iron, the vicinity of a magnet causes them to momentarily acquire polar magnetism, by the same action that the currents of solenoids exercise on the currents of which they themselves are a part. This influence modifies the direc- tion of these elementary currents, and makes their resultant no longer CUAP. v.] ELECTKO-MAGNETISM. 615 nil; thus is produced induced magnetism. "We shall find, moreovei, that permanent magnetism is perfectly explained by Ampere's theory but in this case, experiments must instruct us, and they will reveal to us phenomena of the greatest interest. In September 1820, Arago, a short time after Oersted's and Ampere's discoveries, made the following experiments : He inserted into a mass of iron filings a copper wire which united the two poles of a pile ; on drawing out the wire without interrupting the current, he saw its surface covered with particles of iron filings, arranged trans- versely ; as soon as the current was interrupted, the particles detached themselves from the copper and fell. To assure himself that this was temporary magnetism, not the attraction of an electrified body for light bodies, he substituted for the iron filings a non-magnetic sub- stance, and the phenomenon did not take place. On placing needles JV^A^V-^.^ ^ Jir^^^A^A^^^ FIG. 421. Magnetization of a steel needle by a solenoid; right-handed and left-handed spirals. of soft iron, and then of tempered steel, very near the copper wire, he noticed that the action of the current transformed them into magnetic needles, having their southern pole always to the left of the current ; this result agreed with the then recent experiments of Oersted. Soon after, Arago and Ampere noticed that the magnetism of soft iron, or that of steel, was developed with much greater intensity by placing the needle in the interior of an electrical helix. The rheophore wire of a pile was coiled round a glass tube ; then, having placed in the axis of the latter the needle to be magnetized, they passed the current through the wire : magnetization was immediately produced, but, as might have been expected, it was temporary in soft iron, and permanent in steel. Glancing at Fig. 421, we see that there are two ways of coiling the wire round the tube. Supposing the tube to be horizontal, the 616 PHYSICAL PHENOMENA. [BOOK vi. wire can be coiled from right to left, each round being coiled from top to bottom on the side of the tube turned towards the operator ; this is the right-handed solenoid; or, again, the wire may be coiled in the same way, but passing from left to right; this is the left-handed solenoid. If the current traverses the coils of the spiral from left to right, as indicated by the arrows, the magnetiza- tion will give a southern pole as to the needle, to the left in the right-handed spiral ; the southern pole will, on the contrary, be to the right in the needle of the left-handed spiral. In both cases, the southern pole is always to the left of the current, according to Ampere's law. By this process of magnetization, so simple and wonderful, secondary poles can be produced at will on bars to be magnetized, which are called, as we have before seen, consequent points. To effect this it is sufficient, after having coiled the wire in one direction round the tube, to coil it in the opposite direction at each of the points when we desire to produce a secondary pole. The whole 3 FIG. 422. Magnetization by a spiral ; production of consequent points. spiral is thus formed of a right-handed spiral, followed by a left- handed spiral, and so on (Fig. 422). We have mentioned that soft iron, surrounded by a magnetized spiral, assumes temporary magnetism. The magnetic force thus de- veloped is more powerful according as the iron is more homogeneous and pure, and as the number of the coils of the spiral is greater. To realize this last condition, the metallic wire is surrounded by an insulating envelope, as in Schweigger's multiplier for example, by a silk thread : it is then coiled round a piece of soft iron, drawing the coils as close as possible, in order to get a great number of rounds. It then becomes what is called an electro-magnet; that is to say, a magnet whose magnetic power subsists during the passage of the current of the pile, and ceases when the current is discon- tinued. The form of a cylinder, bent like a horse-shoe, is usually given to electro-magnets, each branch of \\hich is covered with a CHAP. V.] ELECTRO-MAGNETISM. 617 portion of wire (Fig. 423). The spirals here appear coiled in an opposite direction, but the direction of the coiling is in reality the same in both branches, if we suppose the cylinder of FIG. 423. Horse-shoe electro-magnet. FIG. 424. Electro-magnet. soft iron straightened. We have then at the two extremities, as soon as the current passes, two poles of contrary names. Electro- magnets are also made with two parallel iron cylinders of soft iron, united on one side by an iron plate, and on the other by a FIG. 425. Electro-magnet with its charge. copper plate (Fig. 424). The power of an electro-magnet depends not only on the number of coils of the conducting wire of the current, but also on the intensity of the latter, and the dimensions 3 B G18 PHYSICAL PHENOMENA. [BOOK vi. of the soft iron which forms it. The electro-magnet constructed by M. Pouillet for the Facuite des Sciences of Paris, is capable of supporting a weight of several thousand kilogrammes. Many curious experiments can be made with electro-magnets; we may, for example, form" a magnetic chain, by placing a heap of magnetic substances, iron filings, nails, &c. below the poles. As soon as the current passes, the little bodies are attracted by the poles, which magnetize them by induction, and then get mixed together, as seen in Fig. 426. As soon as the circuit is broken, all the frag- ments of the chain fall simultaneously. FIG. 426. Magnetic chain. The promptitude with which soft iron is magnetized under the influence of electricity, and loses its magnetism as soon as the current ceases, has brought to light numerous and important applications of the electro-magnet. We shall see, moreover, that this property has been utilized in the construction of motive machines, not very powerful, it is true, but valuable for work which requires precision and regularity. In the electric telegraph especially, the electro-magnet acts this important part, proving how well speculations of the most CHAP. v.J ELECTRO-MAGNETISM. 619 profound theories lead to practical applications of the highest social utility. Hereafter we shall do justice to the inventors of the system who have effected this almost instantaneous mode of communica- tion of thought ; bub the names of Volta, Ampere, Oersted, and Arago must be held up to the gaze of the civilized world ; for it is these celebrated men who discovered the principles which have rendered this wonderful invention possible. fi20 PHYSICAL PHENOMENA. [BOOK vi. CHAPTER VI. PHENOMENA OF INDUCTION. Discovery of induction by Faraday Induction by a current ; inducing coil and induced coll Induction by a magnet Machines founded on the production of induced currents Clarke's machine Kuhmkorff's machine Commutator Effects of the induction coil. FARADAY, one of the greatest physicists of our century, in November 1831 discovered a remarkable fact connected with the electric current ; he found that when a current passes through a metallic wire, it produces in a second wire, placed parallel to the first and separated from it by an insulating body, a current which flows in a contrary direction to the first current. The existence of the current thus developed by the influence of induction can be proved by the spontaneous deviation undergone by the needle of a galvano- meter with which the wire communicates. The second current quickly ceases, although the first current continues to circulate in the principal wire ; but if the latter is broken another instantaneous current is produced in a contrary direction in the parallel wire, and again ceases immediately. The original current is called the inducing current ; the current produced when this latter commences is the inverse induced current ; and, lastly, the current which is de- veloped when the induction current is stopped, is called the direct induced current. Magnets, as well as voltaic currents, produce induction currents ; and the same thing occurs with static electrical discharges, as M. Masson proved in 1834. To obtain powerful induced currents a considerable length must be given to the parallel wires. The inconvenience which results from CHAP. VI.] PHENOMENA OF INDUCTION. 621 this is avoided by winding each of the wires covered with silk round a hollow cylinder of cardboard or wood. This is called a coil. The two extremities of each wire are terminated by two metallic but- tons, or binding screws, fixed on one of the bases of the cylinder : these are for the purpose of placing the coil in communication either with the two rheophores of a pile/ or with a galvanometer. If we take two coils, one of greater diameter than the other, so that the smaller can pass within the cylindrical cavity of the larger one, and place the larger, or induced, or secondary coil in communication with a galvanometer, and the other, the inducing coil, into the first ; and if now the latter is placed in communication with the poles of a Bunsen element, we observe that, so soon as the current is closed, the needle of the galvanometer is deviated, because an inverse FIG. 427. Induction by a current. induced current has traversed the wire of the first coil ; but the needle soon returns to zero after slight oscillations, and remains there se long as the current passes. If the induction circuit is now broken, the needle deviates in a reverse direction, consequently indicating the presence of a direct induced current. Then it again returns to zero and stops there until the current is broken. The same experi- ment may be made in another manner. Let us suppose two copper wires wound on the same coil, well insulated from each other by the silk by which they are covered (Fig. 427) : the one communicates by its extremities with a galvanometer G ; the other with the element p of a Bunsen battery. The current which traverses the coil can be interrupted or established at will by raising portions of the wire which are immersed in the 622 PHYSICAL PHENOMENA. [BOOK vi. vessels g and /, filled with mercury. Now, it is easy to prove, by observing the direction of the deflection of the galvanometer, the presence of induced currents, direct and inverse, at the moment when the inducing current commences and ends. The first experiment proves that every voltaic current develops, at the moment of its commencement, an inverse current in the wire near to it ; and at the moment when it ends a direct current ; so that its inducing action is nil during the whole time the induction current is passing. Let the induction coil be in connection with the pile, and the circuit closed before the two coils are brought together, as in Fig. 428 ; if now the inducing and induced coils are quickly brought near each FIG. 428. Induction by the approach of a current. other, an inverse current is produced in the latter, as the deflection of the galvanometer needle indicates. This current quickly ceases ; but if then the induction coil is removed, a direct induced current is developed, and ceases immediately like the first. In a word, every- thing occurs as in the first experiment. If the intensity of the inducing current is increased in the interval which separates the production of the two opposite induced currents, at the moment when this increase takes place the needle of the galvanometer, which had returned to zero, is deflected, and indicates the presence of an inverse induced current. If the intensity of the current, on the contrary, diminishes, it produces a direct current in the induced coil. CHAP. VI.] PHENOMENA OF INDUCTION. 623 The phenomena of induction by a current may be summed up in the following statements : A voltaic current develops, by influence or induction, in a neigh- bouring inducing wire, a current of opposite direction to its own, that is to say an inverse induced current, whenever 1st. It commences ; 2nd. It approaches ; 3rd. It increases in intensity. The same current produces a direct induced current, of the same direction with its own, whenever 1st. It finishes; 2nd. It recedes ; 3rd. It diminishes in intensity. We shall now see that the same phenomena are produced with magnetic currents, that is to say with magnets, and Ampere's theory thus received from Faraday's experiments a fresh confirmation. Let us again take a coil, having its extremities in communication with a galvanometer, and let us place a magnet in the axis of the cylinder and quickly approach one of its poles to the coil : the needle of the gal- vanometer is immediately deflected and then it returns to zero. The direction of the deviation indicates a current opposite to that which, according to Ampere's theory, represents the action of the adjacent pole of the coil; moreover, the induced current soon ceases, and nothing more is manifested so long as the magnet remains present (Fig. 429). If it is removed suddenly, however, the needle of the galvanometer is deflected in a contrary direction, and then returns to zero after a few oscillations ; it has thus showed the presence of a direct induced current. Before approaching the magnet let us suppose that a cylinder of soft iron has been introduced into the coil (Fig. 430). If now one of the poles of the magnet is brought near, in the direction of the axis of the cylinder, induction and the production of an inverse current will take place for two reasons; first, the presence of the FIG. 429. Induction by a magnet. 624 PHYSICAL PHENOMENA. [BOOK vi. magnet suffices to produce the induced current ; secondly, the soft iron is itself magnetized "by induction, and reacts on the coil. This is proved by the fact that the deviation of the needle of the galvano- meter is stronger than in the preceding experiment. The same remark applies to the direct induced current, which the rapid removal of the magnet develops in the coil. Lastly, if -the distance of the magnet from the soft iron is varied, the magnetism of this latter increases or diminishes, and the presence of contrary induced currents FIG. 430. Induction by the approach or removal of a magnetic pole. is proved under both conditions. To sum up, an inverse current of electricity is induced in a conducting wire by a magnet, whenever 1st. The magnetic pole is approached ; 2nd. It comes in contact ; 3rd. Its intensity is increased. On the other hand, a direct induced current is produced whenever 1st. The magnetic pole is taken away; 2nd. It is detached ; 3rd. Its intensity diminishes. The magnetic power of the terrestrial globe, like a magnet, develops induction currents, and the same thing occurs in the case of static electrical discharges. Induced currents are distinguished from ordinary currents pro- duced by a single pile by their tension, which is much more consider- CHAP. VI.] PHENOMENA OF INDUCTION. 625 able than that of the inducing current. They have been utilized in the construction of electro-motive apparatus of great power. We may mention Clarke's machine and the coil, the invention of which is due to M. Masson, but which, having received important addi- tions from M. Euhmkorff, now bears the name of that celebrated instrument-maker. Clarke's machine is represented in Fig. 431 ; it consists of a powerful magnet, AB, composed of several plates in the form of a FIG. 431. Clarke's magneto-electric machine. horse-shoe solidly fixed to a vertical piece of wood, in such a manner that its two poles are brought opposite to two coils, each furnished with a cylinder of soft iron. The two soft-iron cores are connected on the side of the magnet by a copper plate, and on the opposite side by an iron plate, t t f ; the two coils thus arranged constitute in fact an electro-magnet. They are arranged so as to revolve round a horizontal axis,/, which passes 626 PHYSICAL PHENOMENA. [BOOK vi. between the arms of the magnet, and is connected behind the vertical plate with an endless chain and wheel with a handle. When the machine is put in motion, the two coils turn round their common axis, and each of them is presented at each revolution to the poles of the fixed magnet, A B. As the wires of which the coils are formed are wound in contrary directions, one of them being left-handed and the other right-handed, it follows that the induced currents, developed in each of them by the approach of the two contrary poles of the fixed magnet, are in the same direction. The direction of these currents changes when the coils get further from the two poles ; but it changes in both of them at the same time, so that, at each instant, the induced currents are both direct or both reversed. The magnetism of the soft iron moreover produces currents which increase the intensity of the inductive action. The two wires of the coil terminate at a special apparatus called a commutator, which is used at will, either to preserve the current in the same direction during the whole of the movement, or to allow the direction of this current to change alternately at each half revolution. With Clarke's machine all the effects of ordinary electro-motors are produced, but at a much greater degree of tension than that produced by piles. Special arrangements permit the production, sometimes of violent shocks, sometimes of sparks or heating effects, and sometimes of chemical decompositions. In the last case, the current remains practically constant ; in the others, on the contrary, the current must be alternately closed and broken. Euhmkorff's induction machine is represented in Fig. 432. It is composed of two coils : the interior one, formed of wire of a diameter of about 2 or 3 millimetres but of small length, 50 or 60 metres for instance, is the inducing coil ; the two extremities of the conducting wire terminate at / and /' in two little brass binding screws. The induced or secondary coil surrounds the first, which is placed concentrically in its cavity ; it is formed of an extremely fine wire, about a quarter of a millimetre diameter, and a length of sometimes 30 kilometres. The two extremities of the induced wire are attached at the outside to two metallic binding screws, A and B, which are at CHAP. VI.] PHENOMENA OF INDUCTION. 627 the top of two insulating glass columns. Lastly, in the interior of the inducing or primary coil a cylindrical bundle of thick soft- iron wires is placed, terminated at the extremities by two discs of the same metaL Whenever the current of an electro -magnetic machine or voltaic pile is sent through the inducing wire and traverses it, entering at / and coming out at/', an induced current will be generated in the wire of the outer coil, under the double influence of the inducing coil and the magnetism of the bundle of soft iron. Whenever the inducing current is interrupted, it will produce in the induced coil a fresh current of contrary direction to the first. Multiplying the number of the passages of the current and its interruptions, a series of instan- FIG. 432. Ruhmkorirs induction coll. taneous currents will be produced, so near together and so intense that the resulting effect will be superior to that of the most powerful batteries. It remains for us to state by what mechanism these suc- cessive interruptions are obtained. At L we observe, mounted on a metallic column, a metal lever having two branches, one of which has a point on a level with the surface of the mercury contained in a glass, M, whilst the other is terminated by a piece of soft iron, reaching to within a short distance of the bundle of iron wires of the induction coil. When the point touches the surface of the mercury, the piece of iron of the other branch is no longer in contact with the iron core, 628 PHYSICAL PHENOMENA. [BOOK vi. and the reverse of this occurs when this latter contact takes p] ace the point no longer touches the mercury. Let us start from the first position and notice what happens in the apparatus. The current of the pile then passes through the column which carries the glass filled with mercury, follows the liquid, the point in contact with it, and the branch L of the lever descends along the column which supports it, and by means of a metallic band enters the wire/' of the induction coil. The current then passes through the induction coil, returns by / and passes to the other rheophore of the pile ; thus the contact of the point with the mercury allows the induction current to pass. But directly this current enters the coil, the bundle of soft iron is magnetized, attracts the small mass of the lever, whence results the raising up of the branch carrying the point ; this leaves the surface of the mercuryj and the current is broken. Then the magnetism of the bundle ceases, the contact of the piece of soft iron no longer exists ; and the point again touches the mercury. The same phenomena are produced in the same manner as long as the induction coil is in communica- tion with the pilo. The mercury contact-breaker which we have just described 'was invented by M. Leon Foucault. Other contact- breakers produce the same effect by means of a spring. We have said nothing at present about the commutator, c, the object of which is either to change the direction of the induction current, or to interrupt it. Ruhmkorff's commutator (Fig. 433) fulfils both functions at will : it is both rlieotome (interrupter of the current) and rhcotrope (inverter of the current). It consists of a cylinder of wood or glass, the convex surface of which is partly covered with two copper plates, c c', thick in the middle and thinner at the edges. These plates have intervening between them two por- tions of the surface of the insulating cylinder; on each side two springs, //', press laterally against the cylinder, when it is turned so as to bring the thickness of the copper plates in contact with the springs. If, by the use of a milled-head or a handle with which its axis is furnished, the cylinder is turned through 90 degrees, the plates of the springs are opposite the glass or wood, which they need not necessarily touch. In the first position the current passes ; in the second, it is interrupted. Indeed, the current reaches the pile with the binding screw A ; thence, by the spring / it passes to the copper CHAP. VI.] PHENOMENA OF INDUCTION. 629 plate c. This communicates by a screw g with one of the pivots of the cylinder, then with the button D, and traverses the circuit, one of the ends of which is fixed to this latter point. It returns by the other extremity to the button D' to the second pivot of the cylinder, and by the screw (f to the plate c', and lastly, by the spring /', to the binding screw A 7 , whence it returns to the pile. When the springs //' no longer touch the plates C c', the current can no longer pass. This apparatus is then a good interrupter or rheotome. But when the current passes as we have just stated, it is sufficient to turn the button through 180, to change its direction. For then, the "^te c' touches the spring/, and the current passes from D' to D, instead of going from D to D'. Thus the little apparatus of Buhmkorff is also a commutator, that is to say, an inverter of the current, or rheotrope. It forms part of the induction coil ; but it is clear that it can be used when- ever we require to change the direction of a current. When EuhmkorfTs coil is at work, if the two extremities of the wire of the induced or secondary coil are brought sufficiently near, a series of sparks succeed each other with such rapidity that the line of light appears continuous. It is remarkable that, of the two induced Currents Opposite in FIG. 433. Commutator of Ruhmkorff a x machine. Plan and elevation. direction which are generated by suc- cessive interruptions of the inducing current, the direct current alone produces sparks; the tension of the inverse current is not sufficiently strong to allow it to traverse the air. With the first coils, the length of the sparks attained a maxi- mum of 8 millimetres. By degrees, improvements among which we must point out that of M. Fizeau, which consists in interposing a condenser, a Leyden jar for example, in the circuit have led to the production of sparks from 10 to 20 and 30 centimetres. By 630 PHYSICAL PHENOMENA. [BOOR vi. increasing the length of wire of the induction coil to 100,000 metres, M. Euhmkorff was able to obtain sparks of 50 centimetres in length: blocks of glass four inches in thickness have been pierced through and through by the discharge. The physical effects obtained with this powerful machine are extremely remarkable : we may employ it to charge Ley den jars and electrical batteries. It is thus that M. Jamin, having charged a battery of 120 Leyden jars with four coupled coils, each furnished with two of Bunsen's elements, was able to melt and volatilize iron, silver, and copper wires, more than a yard in length. CHAP, vii.] THE ELECTRIC LIGHT. 631 UNIVERSITY CHAPTER VII. THE ELECTRIC LIGHT. Sparks obtained by static electrical discharges ; luminous tufts Light in rarefied gases Voltaic arc ; phenomena of transport ; form of the carbon points Intensity of the electric light Electric light of induction currents Stratifi- cations ; experiments with Geissler's tubes Phosphorescence of sulphate of quinine. BETWEEN the feeble sparks seen in the darkness, when the finger is brought near a rod of resin which has been rubbed with a piece of cloth, and the long and bright flashes of fire which are emitted by the conductors of powerful batteries, or by the dazzling light of the voltaic arc, there is indeed a difference : it is, nevertheless, the same phenomenon. It is also the same light which appears with greater beauty and grandeur in thunder-storms. Let us inquire into the circumstances under which this light is produced. We have seen that, whenever two bodies charged with opposite electricities, at a sufficiently great tension, are near together, with a non-conducting interval, that is, when a resisting medium is interposed between the two bodies, a spark passes. The tendency which contrary electricities possess to unite and constitute a neutral electricity, when they find themselves prevented by the resistance of a non-conducting medium, leads to this transformation of the forces, a transformation of electricity into light and heat. Hence the spark in all its forms. These varied appearances we shall now review, in the case of the discharges of static electricity and of electricity at high tension, and in dynamic electrical currents, which the voltaic pile and induc- tion apparatus have developed to so high a degree of power. With ordinary electrical machines of large dimensions remarkable 632 PHYSICAL PHENOMENA. [BOOK vi. luminous effects may be produced. For tins purpose a metallic plate is employed, which is held in the hand by an insulating handle, and is joined by means of a metallic chain to the friction cushions. By bringing the edge of the plate of the conductor of the machine to different distances, the spark will at first be seen under the form of a rectilinear line of light, of a dazzling whiteness and brightness. If the tension of the conductor is increased by turning the handle of the machine without interruption, the sparks succeed each other with so much rapidity that the line of light appears continuous. The spark; get thinner at their centre, in proportion as the distance of the two conducting bodies increases, and the rapidity of their succession diminishes ; then their rectilinear form gives place to lines more or FIG. 434. Sparks obtained by the discharge of static electricity. less zigzag, or serpent-like in form, as if the resistance which the flow of the electricity undergoes in its passage was unequally distributed. Besides the principal line of light, we perceive, when the dis- tance becomes still greater, luminous branches which issue on all sides, and give to the sparks the forms represented in the drawings of Fig. 435. These long branch sparks are evidently the form of transition between the rectilinear spark and the luminous brushes. To obtain this last form of electrical light produced from the conductors of ordinary machines, the metallic plate must be presented at a much greater distance than when the sparks we have first described pass from the conductor. Then there appears to escape from the conductor a kind of luminous tree which touches the conductor with its trunk, b C CHAP. VIT.] THE ELECTRIC LIGHT. 635 while an infinite number of branches diverges towards the plate. Fig. 436 shows a luminous tuft as obtained by Van Marum. Between the plate and the brush there sometimes exists a dark space ; some- times a mass of light, very narrow, and having its base on the edge of FIG. 436. Electrical brush, according to Van Marum. the plate, joins the top of the brush. In this case we suppose that the conductors charged with positive electricity, and the plate elec- trified by induction is therefore charged with negative electricity. If the reverse took place, the brush with wide ramifications would escape 3 c 2 636 PHYSICAL PHENOMENA. [BOOK vi. FIG. 437 Positive and negative brushes. from the plate and the narrow root from the conductor. Faraday, who studied the forms of positive and negative brushes, showed that this difference results from an unequal tension of the two electricities when the discharge takes place. Negative electri- city requires for its discharge a much lower tension than posi- tive electricity. The electric light can be produced in different media, in air and other gases, and even in bad-conducting liquids: its appearance, that is to say, its form and colour, changes according to the nature of these media ; and when the discharges take place in a gas, they vary with its pressure or degree of rare- faction. In air, at ordinary pressure, we have seen that the spark is a brilliant white. According to Van Marum, who made numerous experiments on this subject, its colour is bluish, tinged with purple, in nitrogen; very white in oxygen; violet red in hydrogen ; greenish in carbonic acid ; reddish-green in carburetted hydrogen gas, and white in hydrochloric acid. The trunk of the positive lumi- nous brushes in air, at the ordinary pressure, is of a violet colour, tinged with purple, whilst the branches are white, this is perhaps because the light is less condensed. In other gases the colour of the brush varies, as Faraday's experiments showed : thus, in hydrogen and in FIG. 438. Light in the barometric vacuum. coal g3S, it is slightly greenish ; ill oxygen it is white as in air, but much less beautiful ; in rarefied nitrogen it is, on the contrary, a magnificent purple ; in carbonic CHAP. VII.] THE ELECTRIC LIGHT. 637 oxide and carbonic acid it is greenish in the first gas, and slightly purple in the second. In the barometric, or Torricellian vacuum, there is no spark, or rather the spark appears between the conductor and the metallic wire which dips in the mercury : at this moment the barometric vacuum is illuminated with a greenish light, as in Fig. 438. For the study of the luminous effects produced by electrical discharges in rarefied gases, the apparatus represented in Fig. 439 is Fiu. 4a. i'lie elueiiie egg. Fio. 440. Electric light in rarefied air. Purple bands. employed: this is called an electric egg. The two metallic rods, each terminated by a ball, and communicating with the conducting caps of the apparatus, can be approached or separated at will. The egg can be detached from its stand and screwed on the plate of an air-pump, so that the air can be rarefied at will, a vacuum made and a gas introduced at any pressure. In air, at ordinary pressure, the spark obtained between the two balls is similar to that we have described at the beginning ; but in 638 PHYSICAL PHENOMENA. [BOOK vi. proportion as the air is rarefied, the light changes in appearance and escapes from the positive ball as a branched sheet ; at a pressure of 60 mm. it presents the appearance shown in Fig. 440. It then appears to be composed of a number of luminous bands of a purple colour, some diverging laterally, others terminating at the negative ball, which is itself enveloped in a thick sheet of violet light. When the pressure is reduced to a few millimetres, the bands unite into a luminous sheaf, in the form of a spindle. The various luminous phenomena we have just described are produced by static electrical discharges. Between the two approxi- mated ends of the rheophores of a pile with a very large number of ele- ments, brilliant sparks may be obtained which succeed each other with rapidity. We have stated above that the phenomenon is much finer, and the light more intense, when it is caused to pass between two carbon points terminating the extremities of the rheophores : we then obtain what is called the voltaic arc. By making use of induction currents, extremely remarkable luminous effects may be obtained without the necessity of a pile with a great number of elements. The following are some details of the voltaic arc : We have already said that, in order to produce the luminous arc, it is necessary to place the carbon points very near to each other ; but when once the current has conquered the resistance of the interposed air and produces the light, the points can be further separated : Davy, working in rarefied air, obtained with his pile of 2,000 couples an arc of light of seven inches in length. The luminous intensity of the voltaic arc is so considerable that the eye can scarcely endure its brightness. According to some ex- periments made by MM. Fizeau and Foucault, this intensity is nearly fifty times greater than that of Drummond's light, that is, the brilliant light produced by directing an ignited jet of oxy-hydrogen gas on a piece of lime; solar light has scarcely an intensity triple that of the voltaic arc. These two experimenters worked with a Bunsen's battery of 92 couples arranged in two series. In studying the very interesting phenomenon of the voltaic arc, it has been noticed that the electrical current passing continuously between the two points transports from one to the other minute particles of carbon : this transport of matter is made with greatest CHAP. VII.] THE ELECTRIC LIGHT. 639 readiness from the positive to the negative pole, so that the points become unequal in size : the negative point increases at the expense of the other. Fig. 441 shows the appearance of the two points, as seen by projection on a screen, in an enlarged form. We will leave the description of it to the learned physicist to whom we owe FIG. 441. Carbon points of the electric light and the voltaic arc between them. this drawing. M. Le Roux, at a lecture on the application of electricity to lighthouse illumination, given by him at the Societe cF 'Encouragement pour V Industrie nationale, described it as follows : " In order to directly examine what passes in the voltaic arc, great care must be taken to place the eye in 640 PHYSICAL PHENOMENA. [BOOK vi. safety from the considerable intensity of the light, but this same intensity allows us to observe the whole of the smallest details of the carbon surfaces. It is sufficient to interpose between them and the screen a lens with a proper focus : you will thsn perceive the image of the carbon points enlarged a hundred times ; this projection enables you to examine, without fatigue, the whole of the phenomena. Here are some carbon points between which the continuous current of a Bunsen's pile passes. You see one of the points increases at the expense of the other: this one, which is the most used, is the positive point ; it is this which communicates with the carbon end of the pile ; if it is more pointed than the other, it is because it loses material which the other acquires. We can, indeed, reverse the direction of the current : you then see the carbon point which was just noW the most pointed, increases, whilst the other becomes more slender ; besides, from time to time some larger patches detach themselves, traverse the space under the form of little incandescent masses^ and indicate the direc- tion of transport. You see little globules boil up here and there on the surface of the carbon ; these are globules of melted silica : you will remark that these globules do not appear on the carbon points where the temperature is highest ; they are volatilized at the outset. Now we are in a very impure vein, and a considerable quantity of these silica globules show themselves ; the brightness of the arc suffers; blowing lightly against the carbons, the current of air inclines the arc and shows us its development. We now reach a part of the carbons where their purity leaves nothing to be desired. You see how quiet the arc is, the progress regular, the points clearly terminated. You will see the quiet, bluish light of the arc contrast- ing with the bright white of certain parts of the points ; the arc forms a kind of truncated cone swollen in the middle, the two bases of which are the carbons: these two bases are the brightest por- tions, the temperature is the highest in them, the molecules trans- ported by the current strike them." When a space filled with gas or very rarefied vapours is traversed by induction currents, the luminous effect presents par- ticular characteristics of great interest. If the air contained in an electrical egg is rarefied to a pressure CHAP. VI 1.1 THE ELECTRIC LIGHT. 641 of two or three millimetres, and if the interior balls are placed in communication with the poles of a BuhmkorfFs coil, a magnificent luminous sheaf is seen, of a beautiful red, starting from the positive ball, whilst the negative baU and rod are enveloped in a sheet of light of a bluish purple. If the direction of the current is reversed with a key, or commutator, the two lights are inverted ; the sheaf issues from the lower ball, whilst the violet aureole envelopes the upper ball FIG 442. Luminous sheaf in rarefied air. Discharge of induction cuirents. FIG. J. -Stratified light in rarefied gas. If, before rarefying the air, vapours of different substances are intro- duced, for example, alcohol, phosphorus, or .essence of turpentine, the luminous sheaf assumes a particular aspect which was discovered nearly at the same time by Ruhmkorff, Grove, and Quet. The red light of the sheaf is interrupted transversly by very narrow dark bands, so that it is alternately formed of dark and bright stria?. From the middle of the sheaf, where the stria? are rectilinear, they are curved in two opposite directions, each facing the balls concavely. 642 PHYSICAL PHENOMENA. [BOOK vi To this phenomenon is given the name of stratification of the electric light. Since the time of this discovery, different forms have been given to the vessels which contain the rarefied vapours suitable for the production of the stratifications. The most curious effects of the kind are produced in tubes known as Oeisslers tubes. The beauty of these luminous effects is again enhanced by the phenomena of phosphor- escence which the electric light produces in uranium glass, and in certain salts (notably sulphides) of strontium and calcium, and also in sulphate of quinine. BOOK VII. ATMOSPHERIC METEORS, 3 D 2 BOOK VII. ATMOSPHERIC METEORS. Optical meteors ; mirage, rainbow Tension of aqueous vapour in the atmosphere ; hygrometry Clouds and fogs Dew, rain, snow Crystals of snow and ice Variations of barometric pressure Measure of maxima and minima tempe- ratures Electrical meteors ; thunderbolts, thunder and lightning Auroras boreales. THE reader who has occupied himself with the studies of which we have spoken at some length, though in a very incomplete manner, will find that all the physical phenomena of nature arrange themselves in one or other of the categories which correspond to the six Books of this work : Weight, Sound, Light, Heat, Magnetism, and Electricity. We have seen moreover that electricity and magnetism have the same cause that they are, in fact, two modes of action, at first sight different, but really the same, resulting from the same physical agent. The more science advances, the more are the divi- sions of which we speak effaced; in other words, the more evident does it become that one principle will probably some day or other account for the varied phenomena perceived by our senses, and of which the world presents a perpetual development. Moreover, in nature these phenomena are not isolated: the separation which science is obliged to make, without which separation indeed science would not be possible, does not exist in reality ; not only do the phenomena co-exist, but they act and re-act one on the other; they strive with, interpenetrate, and modify each other in a thousand different ways, and these are the innumerable actions which become to the observer or contemplater of the universe the source of all the contrasts and of all the harmonies which he observes. 646 PHYSICAL PHENOMENA. [BOOK vn In this concluding Book it is impossible to present a sketch of the immense picture the magnificent panorama which results from the concourse of physical phenomena ; but we cannot omit showing the ties by which some of them are bound to the facts which we have studied, and which the physicist reproduces on a smaller scale in his laboratory. Let us for this purpose consider some of those phenomena which are called atmospheric, the place of their produc- tion being the aerial envelope with which the terrestrial globe is surrounded. They may be arranged in three principal classes : luminous or optical meteors / aqueous meteors, the production of which is due to the modification undergone by aqueous vapour under the influence of variations of pressure and temperature ; and lastly, electrical or magnetic meteors. The refraction of the luminous rays which have to pass through either the entire strata of the atmosphere, or a part of them, gives rise to numerous phenomena, amongst which we have already de- scribed the apparent elevation of objects above their real position, which is called atmospheric refraction. Mirage is a phenomenon due to the same cause ; it is observed chiefly on the surface of plains of sand, when the ground has been strongly heated by the sun's rays. The traveller who crosses these plains then sees objects which are raised above the ground, reflected as if on a liquid expanse ; the illusion is so strong that those who are, for the first time, witnesses of the phenomenon, cannot help believing in the real existence of a lake spreading its waters along the horizon. The French soldiers in the Egyptian expedition were more than once deceived by this false appearance. Overcome with fatigue and thirst, they saw the longed- for lake recede as they approached, renewing for them, under a form not less deceptive, the tortures of Tantalus. Monge, one of the men of science of the Egyptian Institute, was the first to give a complete explanation of the mirage, which, however, is not alone observed in the African deserts. The following is his theory of the mirage. The solar rays, on reaching the surface of the sandy stratum, heat it strongly, whilst they have passed through the superposed strata of air without much raising their temperature, the absorbing power of gases being very small compared with that of solids. But the heat of the ground is !' I.!, 1 ! ||||||l UiU Illll HI "I 1 !'!!, BOOK vii.] ATMOSPHERIC METEORS. 649 communicated by direct contact to the lowest stratum of air and from that successively to these above it ; and expanded air rises in virtue of its specific lightness ; but if the ground presents a nearly horizontal level, and if the atmosphere is calm, equilibrium is retained, and feeble currents produced by some inequalities in the expansion of the different portions of the lower air are alone produced. Hence it follows that, towards the middle of the day, the strata of the air nearest the ground are arranged, from top to bottom, in the order of decreasing density. Let us now imagine a luminous beam sent obliquely to the ground from the point M, a tree in our sketch (Fig. 445) ; on passing from the rarer into the denser stratum, it will deviate from the vertical, from a to d, and this deviation will increase in proportion as it encounters strata more and more refrac- tive, until falling at A on a stratum with the surface of which FIG. 445. Fxplanation of a mirage. it makes an angle equal to its limiting angle, it will undergo total reflection. Starting from this point, it will follow a contrary path, getting nearer and nearer to the vertical, falling on o in the observer's eye, who then sees an image of the point M in M'. The same path being applied to all the points of the object here it is a tree, it will appear reflected as in a mirror, and the observer will see it as a reversed image. The sky is reflected in the .same manner, whence the brilliancy of the ground at a certain distance from the object, and the appearance which causes the belief in the presence 'of a liquid between the eye and the object. 650 PHYSICAL PHENOMENA. [BOOK The phenomenon of the mirage takes place also on the surface of the sea, when the water has a higher temperature than that of the air, and the explanation is the same as that of the mirage on land. When the strata of the air are unequally heated, instead of being separated by horizontal surfaces, they are more or less oblique and we get the lateral mirage which is observed principally in mountainous countries, or in the vicinity of buildings : in this last instance, the objects appear reflected as in a vertical mirror. It even happens, as is sometimes observed at sea, that the mirage of the object, as a vessel, for instance, is formed above it. The son of a celebrated navigator and physicist, Scoresby, witnessed in the polar seas this last phenomenon, which was then called the inverted mirage. One day he perceived in the air the inverted image of the ship which his father commanded, and from which a sudden storm had separated him, and the image was so clear that he could recognise the vessel, although it was completely hidden below the horizon. To explain this phenomenon, the existence of horizontal strata of air, the density of which rapidly diminishes from below upwards, must be supposed at a certain height in the atmosphere. The mirage is a phenomenon of simple refraction. The rainbow , halos, and parhelia are luminous meteors produced by the dis- persion of light during its passage through rain-drops, the very small drops of which form the clouds or haze which float in the atmosphere. We shall confine ourselves to a statement of the theory of the rainbow, propounded by Antonio de Dominis in 1611, elaborated by Descartes, and lastly perfected by Newton. We all know that the rainbow or iris is seen opposite to the sun, " through the clouds which are turned into rain, and that it is some- times simple and sometimes accompanied by an outer bow less brilliant than the first. The principal or interior bow forms a circular band in the width of which the various colours of the spectrum are seen in order from violet to red, starting from the inside of the bow. The secondary bow is wider than the first and shows the same colours arranged in a reverse order, so that the red is inside, next to the red of the principal bow. To account for the conditions \\hich produce the phenomenon, let us trace the path of a solar ray, which falls on the surface of a YJI.] ATMOSPHERIC METEORS. 651 spherical drop of rain. On arriving at the surface of the sphere, the luminous ray is refracted and approaches the normal at the point of incidence. On meeting the interior surface of the liquid sphere it is divided ; part of it emerges and the other part is reflected. The same Fio. 446. Paths of the effective rays through a drop of rain after a single internal -reflection. effect takes place at each of the meetings of the reflected ray with the surface of the drop, the intensity of the reflected light diminishing in proportion as the successive reflections are accomplished. Knowing the angle of incidence of the luminous ray, the angle at which it FIG. 447. rath of the effective rays after two interior reflections. leaves the liquid sphere, after one, two, or any number of interior reflections, can be calculated. Instead of a single ray of light, if we imagine a beam such as s I, the angle of incidence of the rays which compose the beam, not being the same for all, the emerging rays will 652 PHYSICAL PHENOMENA. FBOOK emerge generally in diverging from the sphere, in such a manner that if dispersed through space they could not act on the eye or produce an image on the retina at any distance. Nevertheless, calculation proves that for certain incidences the emergent rays form a cylindrical beam, the intensity of which will remain sensibly the same at a considerable distance. Newton gave the name of effective rays to those which possess this property. Let us recall to mind that the different coloured rays of which a beam of white light or solar light is composed have not the same re- frangibility. The incidences which correspond to the effective rays of each simple colour are therefore not the same ; hence it follows that on emerging from the liquid sphere the incident beam will be divided into as many separate rays as there are colours in the spectrum. On calculating the angles of incidence for the rays of the extreme simple colours, the violet and the red, after a single internal reflection we find : For the violet rays, an angle of incidence of 58 40'; for the red rays, an angle of incidence of 59 23'. Therefore the angles which the emerging rays make with the direction of the incident rays are 40 17' for the violet rays, and 42 2' for the red rays. In the case of two internal reflections, in A and B, the angles of incidence of the effective rays are : For the violet, 71 26'; for the red, 71 50'; and the deviations undergone by the rays, after this emergence from the liquid sphere, are 50 59' for the red rays, and 54 9' for the violet rays. By means of these data, it may be seen that the principal rainbow is produced by the solar rays which have undergone a single reflection in the interior of the liquid spheres composing the rain-drops. The secondary rainbow is produced by the rays which have passed through two successive reflections. Let o z be a line parallel to the direction of the solar rays, and passing through the eye of the observer who turns his back on the sun. Looking in the direction o , so that the angle a o z is that of the deviation corresponding to the effective violet rays, the observer will receive on his eye a violet ray pro- ceeding from the solar ray s a, which has been once reflected in the rain-drops, when they pass successively in their fall by the point a. Indeed the parallelism of the lines o z and s a conduces to the equality of the angles Sao and a o z ; now this last is by hypothesis equal to VII.] ATMOSPHERIC METEORS. 653 the angle of deviation which corresponds to the effective violet rays. The ray s a will then find a rain-drop, whose position will be that which agrees with the calculated incidence and emergence ; and the observer will see a violet point. About 2 degrees higher, at b, he will see a red point, and in the interval a b all the shades of the spectrum comprised between the violet and the red ; that is to say, indigo blue, green, yellow, and orange. But the same thing will evidently occur in every direction making with o z the same angles as those of which we have spoken. The observer will then see bands of all these colours, projected on the sky under the form of concentric circles Fio. 448. Theory of the rainbow ; formation of the principal am ] secondary arc. having their centres on the line o z, in a point diametrically opposite to the sun. So much for the solar rays which penetrate the rain- drops and emerge after a single reflection. Those which have under- gone two reflections will arrive at the eye forming with the line o z angles of 50 59' if they are red rays, and 54 9' if they are violet rays. The effective rays of the intermediate colours will be comprised between these extreme rays ; but in this case the red will be at the inside and the violet at the outside of the arch. These results are deduced from calculation, according to the 654 PHYSICAL PHENOMENA. [BOOK laws of reflection and refraction of light, and the index of refraction of water. Now, the angular dimensions of each rainbow, the width of the zones, and that of the interval which separates them, are so many consequences of the preceding data, and, if the theory is correct, observation ought to verify the truth of it ; and indeed the explanation given by Newton, and by all observers after him who have studied the rainbow, has been verified. When the sun is at the horizon, the line o z is in this plane ; the centre of the arcs is then itself at the horizon, and the rainbow is seen under the form of a semicircle ; and it presents this form both at the rising and the setting of the sun to an observer situated in the plain. For different heights of the sun, the rainbow has an amplitude less than a semi-circumference, which gets less as the sun gets higher. Lastly, if the observer were situated on a very high mountain and on a narrow peak, he would be able to see more than a semi-circum- ference, and even a complete circle, if the rain fell at a considerable distance. It must not be forgotten that the rainbow is a phenomenon the production of which depends only on the position of the observer relatively to that of the sun and of the cloud which is converted into rain. Therefore if two persons at a distance from each other see a rainbow at the same time, they do not see the same arc. If the arc were the same everywhere an observer situated obliquely would see it in perspective, and in the form of an oval or ellipse, not as a circle. Theory and observation agree in showing that this is never and can never be the case. We have often heard persons, to whom we have mentioned having seen a rainbow, reply that they had seen the same rainbow; unless they are precisely in the same position, no two persons ever see the same bow at the same instant. Aqueous meteors are those caused by the transformations which the vapour contained in the air undergoes, under the influence of variations of temperature. Clouds, fogs, rain, snow, dew, white frost and hoar frost, are the different forms under which the atmo- spheric water is presented to our view, which therefore assumes these three conditions : the gaseous condition, when its exists as invisible vapour ; the liquid condition, when the lowering of temperature vii.] ATMOSPHERIC METEORS. 655 condenses it into drops ; lastly, the solid condition, if a still greater cooling congeals the drops which then fall in the form of white flakes, or arrange themselves into crystals on the surface of the ground. The complete description and detailed explanation of these different phenomena would take US' beyond the limits of our space. We shall therefore confine ourselves to an indication of the physical laws which relate to their production. Analysis proves that the air is a mixture of two permanent gases, oxygen and nitrogen, with which variable quantities of aqueous vapour and carbonic acid are mixed. But while the proportion of oxygen and nitrogen remains constant, that of the aqueous vapour varies perpetually and depends on numerous atmospheric conditions, such as temperature, direction and force of the wind, &c. It is very important to the science of meteorology to know how to determine, at a given instant, the hygrometric state of the air. By this term we understand the relation between the tension of the aqueous vapour, which is actually contained in it, and the maximum tension which the same vapour would possess if, at an observed temperature, the air were saturated with it. This relation is deduced from the indications of instruments called hygrometers, constructed on different principles, among which we shall only describe the hair hygrometer, which bears the name of De Saussure, its inventor. It is based on the property which hairs, like many other animal substances, possess, of being very sensible to variations of atmo- spheric dampness. A hair previously washed in sulphuric ether, which frees it from the oily matter which it contains, lengthens when it absorbs aqueous vapour and shortens when it loses the absorbed moisture. The following is the manner in which these changes of dimensions are rendered sensible : The hair is fixed by its upper extremity, and passes round a pulley at the centre of which there is a needle moving on a divided circle. A small weight keeps it on the pulley ; and as this forms with the needle a system of unstable equilibrium, the least variation in the length of the hair turns the pulley, and therefore the needle, in one direction or the other. The hygrometer is graduated by taking, for the fixed points, the extreme dryness or dampness of the air, by'the following method : 656 PHYSICAL PHENOMENA. [BOOK vii- The instrument is placed under a bell-jar, the air of which is dried by chloride of calcium, and when the needle stops at a fixed posi- tion, it is marked 0; the apparatus is then placed under another bell-jar, the interior of which is moistened with water : the air con- tained in this jar is thus saturated with vapour. The needle passes in the contrary direction, and ends by stopping at a point which corresponds to the state of the air saturated with vapour. This point is marked 100, and the interval comprised between the two fixed points is divided into 100 equal parts or degrees. The hygrometer thus constructed and graduated shows well if the air is more or less damp ; but to conclude, from a marked hygrometric degree, the tension of the vapour with regard to the ten- sion of the air saturated at the same temperature, one must construct and calculate empirical tables which give this relation. A thermometer is generally added to a hair hygrometer, the utility of which will be understood after what we have just said. Hair hygrometers present this incon- venience, that their indications are not exactly comparable; hairs belonging to different indi- viduals have not in the same degree the pro- perty of absorbing dampness. The hygrometric state of the air can also be deduced from the temperature to which it must be lowered, in order that the vapour which it retains may be sufficient to saturate it. The instruments which serve to determine this temperature are condensing hygro- meters, thus named because the vapour condensed on the surface of a polished metal indicates the saturation of the air produced by an artificial falling of the temperature : these instruments are pre ferred by meteorologists on account of their precision. The quantity of atmospheric aqueous vapour generally increases with the tempera- ture ; it is greater at sea and on the coast than far inland. It varies according to the hours of the day, increasing in proportion as the temperature rises. . It also varies in the various seasons of the year; the warmest are those in which the air contains the greatest absolute FIG. 449. De Saussure's hair hygrometer. FIG. 4 JO. Forms of snow crystals (Scorosby). 3 K BOOK vii.] ATMOSPHERIC METEORS. 659 quantity of vapour. The contrary, however, happens for relative damp- ness ; it is generally during the night, or during the cold season, that it exists in greatest quantity, that is to say, that the air is nearest saturation. Lastly, the direction of the wind has also a great influence on the hygrometric condition of the air, but it is impossible to give an idea of this influence without entering into extremely complex details, since the atmospheric conditions change, so to speak, in different regions of the globe. Dew is nothing more than a deposition of the vapour contained in the air, which the cooling of objects situated on the surface of the ground has condensed into fine drops during the night. Dew appears especially during the serene nights of autumn and spring : because, at these periods, there is a great difference between the warm temperature of the day and that of the night. The atmosphere then contains, during the day, a sufficient quantity of vapour ; and, if the sky is not covered with clouds, the ground radiates into space a quantity of heat, without the air in itself being cooled as much in its upper strata : but the contact of the ground will cause the tem- perature of the lower strata to fall. As these contain a good deal of vapour, the point of saturation will soon be reached, and their vapour will be deposited in the form of dew on bodies, the more freely, the worse conductors of heat and the better radiators the bodies are. Clouds prevent radiation from being so intense ; and, moreover, between them and the ground an exchange of heat takes place : this explains why there is little or no dew in dull weather. When the temperature of the night falls below freezing-point, the dew deposited on the ground is congealed, crystallizing in the form of very fine icicles : this phenomenon is known as white or hoar frost. When the condensation of the atmospheric vapour is determined by a fall of temperature in the upper strata of air, very small drops of water produced by this condensation, collected in a space more or less great, interfere with the transparency of the air, and form either clouds or fogs. Fogs differ from clouds only by their proximity to the ground. Clouds continually change in form ; but it is not alone the influence of aerial currents which modify them : sometimes 3 E 2 660 PHYSICAL PHENOMENA. [BOOK they are dissipated, because they meet -with strata of a higher tem- perature, and part of the water which forms them passes into the state of vapour; sometimes, on the other hand, they increase by a fresh condensation, and then, if the drops assume a more consider- able volume and weight, they fall to the ground as rain. A change of wind often brings rain, either because the cold masses of air are thus mixed with air charged with vapours, and, reducing its tem- perature, bring it to saturation point ; or, on the other hand, because the masses of warm air charged with vapour are then mixed with a colder atmosphere. In winter, when the temperature is low enough for the drops of water, forming clouds, to be congealed, snow falls intead of rain. Snow-flakes are formed by the agglomeration of small crystals, FIG. 451. Dissection of a block of ice by the solar rays. Crystalline structure of ice. deposited in a star-like form, with a symmetry which is really wonderful. We have reproduced in Fig. 450 the various forms which the navigator Scoresby has described, and figured in the account of his voyages to the Arctic seas. It has been remarked that the greatest number of them are hexagonal polygons stars With six points ; all the small facets forming the crystals making angles of 60 or 120. Sometimes drops of water from the clouds are agglomerated, on congealing, into little irregular masses more compact than snow. They then fall as sleet, or hail. The crystalline form assumed by atmospheric water on congealing also belongs to the compact and transparent masses of ice which the low temperatures of winter produce on the surface of ponds, lakes, and rivers. On examining ice with the naked eye, its structure appears confused, but Tyndall has succeeded in proving its crystalline VII.] ATMOSPHERIC METEORS. 661 texture by a very curious experiment, which consists in passing a beam of solar or electric light through a block of ice. The heat of the beam is partly absorbed by the molecules of which the block is composed, and the return to the liquid state is gradually produced. Fio. 452. Ice-flowers (Tyndall) By examining what is passing in the interior of the block by means of a magnifying-glass, or by projecting its image on a screen by means of a lens, the work of decomposition of which we speak is rendered evident. Here and there we see star-flowers with six rays, with serrated edges ; at the centre of each a spot is seen present- ing the lustre of burnished silver, and Tyndall has shown that this 662 PHYSICAL PHENOMENA. [BOOK spot is a vacuum, the production of which is due to the diminution of volume undergone by the ice as it passes to the liquid condition, so that this curious phenomenon proves the contraction of water during its passage from the solid to the liquid state. The various phenomena we have just rapidly described, and which we have placed under the common denomination of aqueous meteors, because water in its different states forms the substratum of them all, have for their cause the variations of temperature. This last element has therefore great importance in meteorology; moreover its influence is very great on organized and living beings, both animal and vegetable, on their production and development, in a word, on the life on the surface of the globe ; it acts in such a continuous manner on the health of man and his auxiliaries, that the problem which consists in determining its variations, periodicity, and anomalies, is surely one of the most interesting in meteorological ! " J -j - *| ,.! FIG. 453. Rutherford's maximum and minimum thermometers. science. But its complexity is such, that it is not possible to touch upon it here or even to glance at it ; we shall content ourselves with describing the instruments used in the observation of the temperature of the air. We already know the nature of the different kinds of thermometers used for this purpose : it only remains for us to speak of the form given to them, when we desire to know the highest or lowest temperature which the air has attained during a certain interval of time. These are termed maximum and minimum ther- mometers. Fig. 453 represents an instrument of this kind invented by Rutherford ; it consists of two thermometers, one of mercury and the other of alcohol, placed horizontally on a wooden frame. In the interior of the first tube, a little cylinder of steel or enamel is in contact with the surface of the mercury, which the liquid forces before VII.] ATMOSPHERIC METEORS. 663 it as long as the temperature rises ; but which it leaves in its place, at the most distant point of its course, when the temperature falls- The end nearest the mercury evidently indicates the maximum tem- perature. In the tube of the alcohol thermometer is an enamel cylinder which the alcohol moistens and leaves in its place when the temperature rises, and which it draws with it when it falls. The minimum is then given by the end of the cylinder furthest away from the reservoir. When the instrument is adjusted for an observation, care must be taken to bring the two indices to the extremities of each liquid column ; one is in contact with the mercury, and the other is immersed in the alcohol, the end most distant from the reservoir being on a level with the surface of the liquid. To observe maximum and minimum temperatures at great depths, in the sea, or lakes, or Artesian wells, upright thermometers are used, among which we may describe those of M. Walferdin. The maximum thermometer is constructed like a common mercurial thermometer ; but the ex- tremity of the tube is brought to a point, and con- nected with a lateral reservoir which contains a certain quantity of mercury. When an observation is to be made, the reservoir is heated until the mer- cury entirely fills the tube, then the instrument is reversed, the reservoir being uppermost ; the mercury in the lateral reservoir is now on a level with the point, and on cooling to a lower tempera- ture than that of the maximum to be determined the tube remains always filled with mercury. The instrument, thus prepared, is placed in the medium to be observed. As long as the tem- perature rises, the mercury flows into the reservoir, and at the moment of the maximum the tube will be still filled. The instrument being removed from . the medium and reversed, the maximum tempe- rature will be found by heating the thermometer in water until the column of mercury is again on a level with the passage leading into the lateral reservoir. minimum thermometers of M Wulferdin. 664 PHYSICAL PHENOMENA. [BOOK For meteorological observation, self-registering thermometers are now constructed which mark all variations of the temperature by means of photography, the exact time of observation being determined by interruptions of the record at known intervals. The variations of atmospheric pressure are not less valuable for the knowledge of meteorological laws than those of temperature ; we will say a few words on this subject before describing electrical and magnetical meteors. In Chapter VIII. of Book I. we have seen how barometers show, by variations in the level of a column of mercury, the corresponding variations of the pressure of the atmosphere. These oscillations of the barometric column have very complex accidental causes. If the atmospheric column which rests upon any certain surface were always at rest, the pressure would only depend on the weight of air of which this column is composed, to which must be added the pressure resulting from the elasticity of the vapour which is mixed with it ; but this state of equilibrium never exists on any part of the globe. The reasons for it are easily understood, and, moreover, proceed more or less directly from the same cause ; namely, the action of solar heat. The sun warms the surface of the ground and the strata of super- posed air in any place very unequally, according to the hour of the day and the time of the year. The more considerable this heating action is, the more is the air expanded, and the more readily does it rise by diminution of density. But as, at the same instant, the regions more or less distant from the first are in different conditions, there ceases to be equilibrium : then the highest strata of air pass from the warmest region towards the coldest, and a movement in a contrary direction takes place below, that is, a passing of the denser and colder strata of air towards the warm region. This transport of masses of air from one place to another is the cause of winds. Now, it is clear that at the commence- ment of this movement a diminution in the barometric pressure will be produced when the air has been expanded by the eleva- tion of temperature; then also an augmentation will result when the temperature is lower, the weight of the air being increased by the whole weight of the strata which are spread out 011 the vii.] ATMOSPHERIC METEORS. 665 upper surface of the atmosphere. But it must not be forgotten that the heating action of the sun produces at the same time a contrary effect. The vapour contained in the air increases its elasticity as the temperature rises, so that if the barometric column falls when the density of the air diminishes, at the same time it rises under the influence of the increase of tension of the aqueous vapour. The difference of these two contrary movements produces the barometric variation. Lastly, it is probable that atmospheric currents act in another manner on the column of mercury of the barometer. For instance, if an aerial current is propagated from above downwards, its influence will depend not only on its weight, but also on the velocity with which the gaseous mass will be moved, just as if, as M. Marie'-Davy has well said, the winds have for their original cause a difference of pressure occasioned by the inequalities of temperature ; they react on themselves, producing variations of pressure. It has been noticed, that, at the same place, the baro- metric column undergoes diurnal oscillations and variations which follow the seasons of the year: both are subjected to a periodicity which agrees with the preceding explanations. But this same height is subjected to irregular variations, the causes of which are extremely complex. Thus, the barometer rises or falls according to the direction of the prevailing wind. At Paris and over a great portion of Europe, the barometric pressure is generally higher with the north, north- east, and east wind than with the south, south-east, or south-west wind. In the southern hemisphere, the contrary takes place. We will conclude this explanation of the causes which produce the principal atmospheric phenomena, by a short description of electric and magnetic meteors. In 1735, Gray pointed out the analogy which exists between lightning and the noise of thunder during storms, and the spark and sharp sound produced by an electrical discharge. But it is to Franklin that the honour belongs of having established by decisive experiments the identity of the causes of these two phenomena. In 1749, this illustrious physicist, after having noticed all the similarities between thunder and electricity, which had been hinted 666 PHYSICAL PHENOMENA. [BOOK at by preceding observers, conceived the possibility of utilizing the power of points to preserve edifices from lightning. At the same time he gave all the indications necessary for detecting by experiment the electrization of thunder-clouds. Three years later, he used a . kite surmounted by a metallic point to draw sparks from the string wetted by the rain. Nearly at the same time Dalibard realized, in his celebrated experiment at Marly-la- Ville, the conditions which Franklin had proposed, and De Eomas raised an electrical kite at Nerac. During a slight storm, this last observer was able to draw sparks 4 metres (13 feet) in length from the extremity of a cord, by means of a discharger ; the explosions might be compared to those of fire-arms. Lastly, De Saussure discovered by an electroscope surmounted by a metallic rod, that thunder-clouds are electrified sometimes positively and sometimes negatively. When two clouds charged with contrary electricities come together, the violent combination of the two elec- tricities gives rise to the production of a spark, which is lightning. If the discharge takes place between a cloud and the earth, the same luminous phenomenon is seen; but then the thunder is said to fall, and the lightning is called a thunderbolt. The form of lightning is sometimes that of a sinuous curve, and sometimes that of a zigzag rectilinear line ; at other times it does not take any precise and determined form, and only produces a confused glimmer illuminating that portion of the sky in which it appears, but the last appearance is probably owing to the interposition of clouds which hide the actual flash from the observer. There is also ball lightning, which moves like a globe of fire through the atmosphere, with much less velocity than that of other kinds of lightning. It often happens that the electric flash of thunder-clouds is divided into 'several branches, forming what is called forked lightning. The colour of the light of lightning is usually white, sometimes purplish or violet, or greenish. Sir Charles Wheatstone has measured, by a very ingenious method, the mean duration of a flash of lightning. He used a wheel having a great number of flat silver spokes, which was turned with great rapidity on its axis ; the wheel being suddenly illuminated during its rotation by a light with an appreciable duration, for instance T Vth of a second : each spoke being displaced during that time will appear vii.j ATMOSPHERIC METEORS. 667 thickened on account of the persistence of the luminous impressions on the retina ; the matter of the wheel will appear more or less continuous. The same thing takes place with a carriage-wheel which rapidly passes before us. Now, Wheat-stone greatly increased the rapidity of the rotation, and always, when the lightning illuminated the wheel, it seemed immoveable, and the spokes remained distinct to the sight and at rest. He concluded from numerous experiments that lightning does not last so much as a thousandth part of a second. The violence of the discharge which is effected between two thunder-clouds gives rise to the noise which we know under the name of thunder. It must be remarked that the explosion is much sharper and more brilliant the nearer the lightning is to the observer, but in almost every case the detonation is accompanied by a pro- longed roll. The cause of this persistence of the noise of the discharge is due probably to two causes: first, it has been proved that a flash of lightning is often many miles in length, and one of the two extremities may be nearer the person who listens than the other ; and although the sound is produced at the same instant in the whole length of the flash, as it takes one second to travel 1,120 yards, many seconds will be required for a distance of 10 miles. Moreover the sound reflected from the clouds and the ground, gives rise to echoes more or less prolonged. The zigzag form of lightning also explains how it is that the roll of thunder does not die away gradually, and that during its duration it is heard louder at different times. The effects of thunderbolts present a perfect analogy with those produced by electrical discharges in machines and batteries ; only they are infinitely more intense, as we may well imagine from the prodigious grandeur of the scale on which Nature works. They have been seen to overturn and carry to a distance considerable masses, such as walls and masses of rock ; to melt and volatilize metals, to pierce holes through sand, which is then found vitrified and forms a kind of tube known as a fulgurite. This last singular phenomenon has been produced by the help of the great battery of the Conser- vatoire des Arts et Metiers, and tubes have been obtained similar to fulgurites by passing a discharge through a bed formed of sand mixed with salt. 668 PHYSICAL PHENOMENA. [BOOK We have said above that lightning sometimes reverses the poles of the magnetic needles in compasses, or completely demagnetizes them : at other times, it produces a contrary phenomenon and magnetizes pieces of steel which it strikes. Its physiological effects are not less curious ; unfortunately they are sometimes terrible. Men and animals struck with lightning are often killed on the spot. There are one or two examples in which the shock produced by it has cured persons afflicted with paralysis and rheumatism. Thunder-clouds, when they pass over objects situated on the ground, electrify them by induction. Such is the cause of the luminous tufts which are sometimes seen at the summits of pointed edifices, masts and ships' yards. These faint lights the ancients regarded as warnings, and sailors now call them Saint Elmo's fires ; they are explained by the considerable electric tension which con- ductors have when terminated in a point. In describing the lightning-conductor in the "Applications of Physics " which will follow this volume, we give details of the course followed by lightning and the means of preservation from its terrible influence. We have already mentioned the magnificent phenomenon known as the polar aurora, which is seen in all its beauty in the northern and southern regions of our globe. It is now no longer a matter of doubt that there exists a relationship between this luminous phenomenon and terrestrial magnetism ; that is, between the pro- duction of the aurora borealis and the variations of the electric currents which intersect the earth. Arago established, by exact observations, the coincidence of certain perturbations of the magnetic needle with the appearance of auroras. These agitations commence many hours before the appearance of the light, and they are more and more intense during its continuance. A magnificent experiment of M. de la Rive has placed beyond doubt the electrical or magnetic nature of the aurora. The auroras boreales are visible in our climate, but they are rare and of short duration. "In the north," says M. Charles Martins, " the phenomenon is seen with such a brilliancy and magnificence that nothing can be compared to it. Bright and varied like fire- vn.] ATMOSPHERIC METEORS. 669 works, this spectacle changes every instant. The painter has not time to seize the forms and tints of these fugitive lights ; the poet must give up describing them. Never does one aurora borealis resemble another ; they vary infinitely." (Du Spitzberg au Sahara.) The aurora borealis reproduced in our frontispiece from the beautiful plates in the Voyage au Spitzberg et en Laponie, the obser- vation and description of which are due to M. Lottin, will give some idea of the magnificence of the phenomenon. The following is also a description which we have borrowed from M. Charles Martins, one of the savants who, with M. Bravais, Lottin, &c., composed the scientific commission of the expedition : " Sometimes the aurorse are simple diffused lights or lumi- nous sheets; sometimes agitated rays of a brilliant white, which pass over the whole firmament, starting from the horizon as if an invisible pencil passed over the celestial vault; sometimes it is at rest; the unfinished rays do not reach the zenith, but the aurora is continued at another point ; a cluster of rays starts out, spreading fan-like, then gets fainter and disappears. At other times long golden draperies float over the head of the spectator, folding over each other in a thousand ways, and undulate as if the wind agitated them, In appearance they are slightly raised in the atmosphere, and one was astonished not to hear the crackling of the sheets which glided one over the other. Generally, a lumi- nous arc is spread towards the north ; one blaok segment separates it from the horizon, and contrasts by its deep colour with the arc of brilliant white or red which darts out its rays, is extended, divided, and soon represents a luminous fan which fills the northern sky and rises gradually towards the aenith, where its rays, uniting, form a crown which, in its turn, darts luminous jets in every direction. Then the sky appears a cupola of fire ; blue, green, yellow, red, and white, join in the palpitating streamers of the aurora. But this brilliant spectacle only lasts a few seconds. The crown first ceases to send out its luminous jets, then by degrees fades away : a diffused light fills the sky ; here and there some lumi- nous patches, similar to light clouds, spread themselves and contract with wonderful activity, like a palpitating heart. Soon they fade in their turn : all is confused and effaced ; the aurora seems to be in its agony : the stars, which its light obscured,, shine with a fresh 670 PHYSICAL PHENOMENA. [BOOK vir. brightness, and the long polar night, dark and profound, again reigns alone among the snowy solitudes of earth and ocean." Bravais in discussing the forms of a great number of arcs, chosen from among the more regular ones, which had been observed simultaneously by two observers, and taking one seen at Bossekop and at Jupvig, distant from the first station about 10 miles showed that they could be considered as circular rings in perspective, having their centre on the radius of the earth directed towards the magnetic pole, and their plane perpendicular to this radius. He moreover con- cluded that the height of the rings above the surface of the earth is comprised between 60 and 120 miles, so that these phenomena occur in the regions near the extreme limits of the atmosphere. The brilliancy of the brightest aurora is considerable. Bravais was able to read by its light a page of small print almost as easily as by the light of the full moon. Auroras are then, to the sparse inhabitants of the icy regions near the poles, beneficent phenomena, and a distraction during the long nights lasting half a year; they contribute with the brightness of the moou and the twilight to lessen the sadness and monotony of Nature as she shows herself in those inhospitable regions. APPENDIX. . APPENDIX, DISCOVERY OF OXYGEN IN THE SUN BY PHOTOGRAPHY, AND A NEW THEORY OF THE SOLAR SPECTRUM.* I PROPOSE in this preliminary paper to indicate the means by which I have discovered oxygen, and probably nitrogen, in the sun, and also to present a new view of the constitution of the solar spectrum. Oxygen discloses itself ly bright lines or lands in the solar spectrum and does not give dark absorption lines like the metals. We must therefore change our theory of the solar spectrum, and no longer regard it merely as a continuous spectrum with certain rays absorbed by a layer of ignited metallic vapours, but as having also bright lines and bands superposed on the background of continuous spectrum. Such a conception not only opens the way to the discovery of others cf the non-metals, sulphur, phosphorus, selenium, chlorine, bromine, iodine, fluorine, carbon, &c., but also may account for some of the so-called dark lines, by regarding them as intervals between bright lines. It must be distinctly understood that in speaking of the solar spectrum here, I do not mean the spectrum of any limited area upon the disc or margin of the sun, but the spectrum of light from the whole disc. I have not used an image of the sun upon the slit of the spectroscope, but have employed the beam reflected from the flat mirror of the heliostat without any condenser. In support of the above assertions the accompanying photograph 1 Paper by Prof. Henry Draper, M.D. Read before the American Philoso- phical Society, July 20, 1877. We are indebted to Dr. Draper's kindness for the plate and illustrations which accompany this paper. 3 F G74 APPENDIX. of the solar spectrum with a comparison spectrum of air, and also with some of the lines of iron and aluminium, is introduced. The photograph itself is absolutely free from handwork or retouching. It is difficult to bring out in a single photograph the best points of these various substances, and I have therefore selected from the collection of original negatives that one which shows the oxygen coincidences most plainly. There are so many variables among the conditions which conspire for the production of a spectrum that many photographs must be taken to exhaust the best combinations. The pressure of the gas, the strength of the original current, the number of Leyden jars, the separation and nature of the terminals, the number of sparks per minute, and the duration of the interruption in each spark, are examples of these variables. In the photograph the upper spectrum is that of the sun, and above it are the wave-lengths of some of the lines to serve as reference numbers. The wave4engths used in this paper have been taken partly from Angstrom, and partly from my photograph of the diffraction- spectrum published in 1872. The lower spectrum is that of the open-air Leyden spark, the terminals being, one of iron and the other of aluminium. I have photographed oxygen, nitrogen, hydrogen, and carbonic acid, as well as other gases in Plltcker's tubes, and also in an apparatus in which the pressure could be varied, but for the present illustration the open-air spark was, all things considered, best. By other arrangements the nitrogen lines can readily be made as sharp as the oxygen are here, and the iron lines may be increased in number and distinctness. For the metals the electric arc gives the best photographic results, as Lockyer has so well shown ; but as my object was only to prove by the iron lines that the spectra had not shifted laterally past one another, those that are here shown at 4325, 4307, 4271, 4063, 4045, suffice. In the original collodion negative many more can be seen. Below the lower spectrum are the symbols for oxygen, nitrogen, iron, and aluminium. No close observation is needed to demonstrate to even the most casual observer that the oxygen lines are found in the sun as bright lines, while the iron lines have dark representatives. The bright iron line at G (4307), on account of the intentional overlapping of the two spectra, can be seen passing up into the dark absorption line in the sun. At the same time the quadruple oxygen line APPENDIX. 675 between 4345 and 4350 coincides exactly with the bright group in the solar spectrum above. This oxygen group alone is almost sufficient to prove the presence of oxygen in the sun, for not only does each of the four components have a representative in the solar spectrum, but the relative strength and the general aspect of the lines in each case is similar. I do not think that in com- parisons of the spectra of the elements and sun enough stress has been laid on the general appearance of lines apart from their mere position ; in photographic representations this point is very pro- minent. The fine double line at 4319, 4317, is plainly represented in the sun. Again, there is a remarkable coincidence in the double line at 4190, 4184. The line at 4133 is very distinctly marked. The strongest oxygen line is the triple one at 4076, 4072, 4069 ; and here again a fine coincidence is seen, though the air spectrum seems proportionately stronger than the solar. But it must be remembered that the solar spectrum has suffered from the trans- mission through our atmosphere, and this effect is plainest in the absorption at the ultra-violet and violet regions of the spectrum. From some experiments I made in the summer of 1873, it appeared that this local absorption is so great, when a maximum thickness of' air intervenes, that the exposure necessary to obtain 'the ultra-violet spectrum at sunset was two hundred times as long as at mid-day. I was at that time seeking for atmospheric lines above H like those at the red end of the spectrum, but it turned out that the absorptive action at the more refrangible end is a progressive enfeebling, as if a wedge of neutral-tinted glass were being drawn lengthwise along the spectrum towards the less refrangible end. I shall not attempt at this time to give a complete list of the oxygen lines with their wave-lengths accurately determined, and it will be noticed that some lines in the air spectrum which have bright analogues in the sun are not marked with the symbol of oxygen. This is because there has not yet been an opportunity to make the necessary detailed comparisons. In order to be certain that a line belongs to oxygen, I have compared, under various pressures, the spectra of air, oxygen, nitrogen, carbonic acid, carburetted hydrogen, and cyanogen. Where these gases were in Pliicker's tubes a double series of photographs has been needed, one set taken with and the other without Leyden jars. 3 F 2 676 APPENDIX. As to the spectrum of nitrogen, and the existence of this element in the sun, there is not yet certainty. Nevertheless, even by com- paring the diffused nitrogen lines of this particular photograph, in which nitrogen has been sacrificed to get the best effect for oxygen, the character of the evidence appears. The triple band between 4240, 4227, if traced upward into the sun, has approximate representatives. Again, at 4041 the same thing is seen, the solar bright line being especially marked. In another photograph the heavy line at 3995, which in this picture is opposite an insufficiently exposed part of the solar spectrum, shows a comparison band in the sun. The reason I did not use air in an exhausted Pliicker's tube for the production of a photograph to illustrate this paper, and thus get both oxygen and nitrogen lines well defined at the same time, was partly because a brighter light can be obtained with the open-air spark on account of the stronger current that can be used. This permits the slit to be more closed, and of course gives a sharper picture. Besides, the open-air spark enabled me to employ an iron terminal, and thus avoid any error arising from accidental displace- ment of the reference spectrum. In Pliicker's tubes with a Leyden spark the nitrogen lines are as plain as those of oxygen here. As far as I have seen, oxygen does not exhibit the change in the character of its lines that is so remarkable in hydrogen under the influence of pressure as shown by Frankland and Lockyer. The bright lines of oxygen in the spectrum of the solar disc have not been hitherto perceived, probably from the fact that in eye observation bright lines on a less bright background do not make the impression on the mind that dark lines do. When attention is called to their presence they are readily enough seen, even without the aid of a reference spectrum. The photograph, however, brings them into a greater prominence. From purely theoretical considera- tions derived from terrestrial chemistry and the nebular hypothesis, the presence of oxygen in the sun might have been strongly suspected, for this element is currently stated to form eight-ninths of the water of the globe, one-third of the crust of the earth, and one-fifth of the air, and should therefore probably be a large con- stituent of every member of the solar system. On the other hand, the discovery of oxygen, and probably other non-metals, in the sun, gives increased strength to the nebular hypothesis, because to many APPENDIX. 677 persons the absence of this important group has presented a con- siderable difficulty. At first sight it seems rather difficult to believe that an ignited gas in the solar envelope should not be indicated by dark lines in the solar spectrum, and should appear not to act under the law that " a gas when ignited absorbs rays of the same refrangibility as those it emits." But in fact the substances hitherto investigated in the sun are really metallic vapours, hydrogen probably coming under that rule. The non-metals obviously may behave differently. It is easy to speculate on the causes of such behaviour, and it may be suggested that the reason of the non-appearance of a dark line may be that the intensity of the light from a great thickness of ignited oxygen overpowers the effect of the photosphere, just as if a person were to look at a candle flame through a yard thickness of ignited sodium vapour, he would only see bright sodium lines, and no dark absorption lines. Of course, such an explanation would necessitate the hypothesis that ignited gases such as oxygen give forth a relatively large proportion of the solar light. In the outburst of T. Coronce Huggins showed that hydrogen could give bright lines on a background of spectrum analogous to that of the sun. However all that may be, I have no doubt of the existence of substances other than oxygen in the sun which are only indicated by bright lines. Attention may be called . to the bright bands near G, from wave-lengths 4307 to 4337, which are only partly accounted for by oxygen. Farther investigation in the direction I have thus far pursued will lead to the discovery of other elements in the sun, but it is not proper to conceal the principle on which such researches are to be conducted for the sake of personal advantage. It is also probable that this research may furnish the key to the enigma of the D 3 or Helium line, and the 1474 K or Corona line. The case of the D 3 line strengthens the argument in favour of the apparent exemption of certain substances from the common law of the relation of emission and absorption, for while there can be no doubt of the existence of an ignited gas in the chromosphere giving this line, there is no corresponding dark line in the spectrum of the solar disc. In thus extending the number of elements found in the sun we also increase the field of inquiry as to the phenomena of dissociation 678 APPENDIX. and recomposition. Oxygen, especially from its relation to the metals, may readily form compounds in the upper regions of the solar atmosphere which can give banded or channelled spectra. This subject requires careful investigation. The diffused and reflected light of the outer corona could be caused by such bodies cooled below the self-luminous point. This research has proved to be more tedious and difficult than would be supposed,, because so many conditions must conspire to produce a good photograph. There must be a uniform prime moving engine of two-horse power, a dynamo-electric machine thoroughly adjusted, a large Kuhmkorff coil with its Foucault break in the best order, a battery of Leyden jars carefully proportioned to the Pliicker's tube in use, a heliostat, which of course involves clear sunshine, an optical train of slit, prisms, lenses, and camera well focussed, and in addition to all this a photographic laboratory in such complete con- dition that wet sensitive-plates can be prepared which will bear an exposure of fifteen minutes and a prolonged development. It has been difficult to keep the Pliicker's tubes in order; often before the first exposure of a tube was over the tube was ruined by the strong Leyden sparks. Moreover, to procure tubes of known contents is troublesome. For example, my hydrogen tubes gave a spectrum photograph of fifteen lines of which only three belonged to hydrogen. In order to be sure that none of these were new hydrogen lines it was necessary to try tubes of various makers, to prepare pure hydrogen and employ that, to examine the spectrum of water, and finally to resort to comparison with the sun. The object in view in 1873, at the commencement of this research, was to secure the means of interpreting the photographs of the spectra of stars and other heavenly bodies obtained with my 28-inch reflector. It soon appeared that the spectra of nitrogen and other gases in Pliicker's tubes could be photographed, and at first some pictures of hydrogen, carbonic acid, and nitrogen were made, because these gases seemed to be of greatest astronomical importance on account of their relation to stars, nebulae, and comets. Before the subject of comparison spectra of the sun was carefully examined there was some confusion in the results, but by using hydrogen the source of these errors was found out. But in attempting to make a prolonged research in this direction, APPENDIX. G79 it soon appeared that it was essential to be able to control the electrical current with precision, both as to quantity and intensity, and moreover to have currents which, when once adjusted, would remain constant for hours together. These conditions are almost impossible to attain with any form of battery, but on the contrary are readily satisfied by dynamo-electric machines. Accordingly, I sought for a suitable dynamo-electric machine and motor to drive it, and after many delays procured a combination which is entirely satisfactory. I must here acknowledge my obligations for the suc- cessful issue of this search to Prof. George F. Barker, who was the first person in America to procure a Gramme machine. He was also the first to use a Brayton engine to drive a Gramme. FIG. 455. The Gramme machine. The dynamo-electric machine selected is one of Gramme s patent, made in Paris, and is a double-light machine, that is, it has two sets of brushes, and" is wound with wire of such a size as to give a current of sufficient intensity for my purposes. It is nominally a 350-candle-light machine, but the current varies in proportion to the rate of rotation, and I have also modified it by changing the interior connections. The machine can produce as a maximum a light equal to 500 standard candles, or by slowing the rotation of the bobbin, the current may be made as feeble as that of tho 680 APPENDIX. weakest battery. In practical use it is sometimes doing the work of more than fifty large Grove nitric acid cells, and sometimes the work of a single Smee. The Gramme machine could not be used to work an induction coil when it v first reached me, because when the whole current was sent through the Foucault interrupter of the Euhmkorff coil, making 1,000 breaks per minute, the electro-magnets of the Gramme did not become sufficiently magnetized to give an ap- preciable current. But by dividing the current so that one pair of the metallic brushes, which collect from the revolving bobbin, supplied the electro-magnets, the other pair could be used for exterior work, no manner whether interrupted or constant. The Fio. 40t5. Bray toil's petroleum motor. current obtained in this way from one pair of brushes when the Gramme bobbin is making 1,200 revolutions per minute is equal to 100 candles, and is greater in quantity and intensity than one would like to send through a valuable induction coil. I usually run the bobbin at 622 revolutions per minute, and this rate will readily give 1,000 10-inch sparks per minute with the 18-inch coil. Of course a Pliicker's tube lights up very vividly and generally ; in order to get the maximum effect I arrange the current so that the aluminium terminals are on the point of melting. The glass, particularly in the capillary part, often gets so hot as to char paper. The general appearance of the machine is shown in Fig. 455. APPENDIX. 681 As long as the Gramme bobbin is driven at a steady rate the current seems to be perfectly constant, but variations of speed make marked differences in the current, and this is especially to be avoided when one is so near the limit of endurance of Pliicker's tubes. A reliable and constant motor is therefore of prime importance for these purposes. A difference of one per cent, in the speed in the engine sometimes cannot be tolerated, and yet at another time one must have the power of increasing and diminishing the rate through wide limits. The only motor, among many I have examined and tried, that is perfectly satisfactory, is Brayton's Petroleum Ready Motor. This remarkable and admirable engine acts like an instrument of precision. It can be started with a match, and comes to its regular speed in less than a minute ; it preserves its rate entirely unchanged for hours together. Moreover, it is economical, cleanly, and not more noisy than a steam-engine. The one of two-horse power I have, ran for six months, day and night, supplying water and air to the aquaria in he Centennial Exhibition at Philadelphia. At any time on going into the laboratory it can be started in a lew seconds, even though it has not been running for days. 3 G INDEX. 3 G 2 INDEX. J^pinus, his method of magnetization, 524; his electrical condenser, 570. Aerolites, 15. Air, its weight and other qualities, 84. Air-condensing machines, 115. Air-pump, 85, 107, 129. Alcohol, vaporization of, 449. Alcohol thermometers, 427. Aldini's electrical experiments, 603 Amber, its electrical property known to the ancients, 531, 532, 535. Amianthus, its incombustibility, 482. Ampere, his researches in electro-magnet- ism, 605, 611, 613, 619. Analysis of light, 309 (see Spectrum Analysis). Aneroid barometers, 100. Angstrom, his map of lines in the solar spectrum, 325, 333, 355. Aqueous meteors (see Atmospheric Me- teors). Arabs, their early use of the compass, 519. Arago, his researches : velocity of sound, 133 ; photometry, 245 ; undulatory theory of light, 363 ; chromatic polari- zation of light, 392, 405 ; electro- magnetism, 615. Archimedes' principle of the loss of weight of immersed bodies, 74 ; its application to gases, 115. Arcturus, heat radiated by, 496 Areometer, or Hydrometer, 80. Armstrong's hydro-electrical machine, 559. Asbestos, its incombustibility, 482. Atmosphere, 84. Atmospheric currents, their effect on the barometer, 665. ATMOSPHERIC METEORS, Book VII., 643 670. Attraction, laws of, 13, 16. Attraction and repulsion : magnetic, 612 ; electrical, 531. Attwood's machine, 24, 25. Aurora borealis, 220 ; its electric or mag- netic nature, 521, 668 ; described, as seen at Spitzbergen, 669. Avalanches, 7. B. Babinet, M., on the interference of lumi- nous rays, 364, 365. Balance, 52. Barometer, 89-101. Barometric pressure, variations of, 664. Baroscope, 115. Bartholin, Dr. Erasmus, his discovery of double refraction of light, 376. Beams, pencils, and rays of light, 225. Becquerel, Edmond, his researches on phosphorescence, 344 ; his phosphoro- scope, 345. Bianchi's air-pump, 111-113. Biot, his researches; on phosphorescence, 343 ; properties of tourmaline, 391 ; polarization of light by simple refrac- tion, 392 : chromatic polarization, 399, 405. Bi-refractive substances (see Double Re- fraction of Light). Bismuth, its low power as a heat conductor, 479, 480 ; specific heat, 487. Bologna, Leaning Tower of, 50. Bologna phosphorus, 342. Borda's pendulum, 41. Bouguer's photometer, 244. Bourdon's aneroid barometer, 100. Boyle's improvements of the air-pump, 107. Brandt's discovery of phosphorescence, 341 : Breguet's metallic thermometer, 430. Brewster's investigations and discoveries ; the solar spectrum, 326 ; interference of luminous rays, 365 ; polarization of light by simple refraction, 392 ; chro- matic polarization, 399, 402. Bristol Cathedral, effects of heat and cold on leaden roof, 433. Brunner on expansion of ice by heat, 439. Buffon's experiments with burning mirrors, 462, 464. Bunsen's discoveries in spectrum analysis, 328-330; his electric battery, 597. Bunten's improvements in barometers, 96, 98. Burning glasses and burning mirrors, 462, 463. 686 INDEX. C. Caesium discovered by spectrum analysis, 329. Cagniard-Latour's Syren, 153. Calcium sulphides, their phosphorescence, 344. "Calorie," or unit of heat, 485. Calorimetry, measurement of the specific heat of 'bodies, 484-491. Camera obscura, 228, 230, 301. Canton's phosphorus, 342. Capacity, French and English units of, Introd. Cfiap., xxxv. Cathetometer, 95. Cat's-skin, electricity produced by, 536, 537, 561. Centrigrade thermometer, 424. Centre of gravity, 45. Centre of pressure on immersed bodies, 73. Charles' areometer, 80. Chemical balance, 52. Chemical harmonicon, 128. Chemical effects of electricity, 583. Chevalier, M. C., his modification of the camera obscura, 302. Chevreul, M, , his work ' ' Des Couleurs et de leurs Applications aux Arts Indus- triels," 321, 336. Chinese, their early use of the compass, 519. Chladni's illustrations of the vibrations of a plate, 176. Clang-tint of the voice and musical instru- ments, 151, 204, 214. Clarke's magneto-electric machine, 625. Clothing, bad conductors of heat used for, 481, 483. Clouds, 659. Cohesion of solids and liquids, 59, Colour, phenomena of, 218 (see Light). Coloured rings and colours of thin plates, Newton's discoveries, 368, 369. Combustion and flame, 519. Compass, magnetic, 497, 519. Compressibility of gases, 118 ; of liquids, 61. Compression a source of heat, 502. Concave mirrors, 259. Condensing machines, 115. Conduction, heat transmitted by, 477-483; table of conducting powers of solids, 479 ; conductivity of liquids and gases, 482, 483. Congelation of water and mercury, 445, 446 ; expansive force of frozen water, 446. Conical mirrors, 268. Contraction : by cold, 432 ; of iodide of silver, by heat, 432 ; of water between and 4, 441. Convex mirrors, 264. Cooke's aneroid barometer, 101. Coulomb's magnetic balance, 522 ; electric balance, 541. Cruikshank's electric trough pile, 593. Crystals, conductivity of heat in, 480. Ctesibius, invention of pumps ascribed to him, 102. Cuneus, his discovery of the Levden iar, 567, 568. Cupping, an illustration of atmospheric pressure, 91. Currents, 8 (and see Atmospheric Currents). Cylindrical mirrors, 267. D. Dalibard's electrical experiments : light- ning. 666. Dalton's formation of vapours in vacua, 452. Daniell's electric battery, 596. Davy, Sir H., his researches : reflection of radiant heat, 461 ; safety lamp, 481; melting ice by friction, 501 ; electrical experiments, 598-600 ; the voltaic arc, 638. De Dominis, Antonio, theory of the rain- bow, 650. Deleuil's air-pump, 112. Delisle's thermometer, 424. Density : of the earth, 44 ; of solid bodies, 57, 79, 80 ; of liquids, 70, 76. De Romas' electrical experiments : light- ning, 666. Desaguliers' experiment on falling bodies, 33. De Saussure's hair hygrometer, 655 ; his experiments, 665. Descartes' discovery of the laws of refrac- tion of light, 277 ; his laAv of double refraction of light, 379, 383 ; his theory of the rainbow, 650. Despretz, his experiments : expansion and contraction of water, 441 ; conductivity of liquids, 483 ; combustion, 499 ; electricity, 600. Dew, 659. Dew-drops, spherical form of, 60. Dial barometer, 99. Diffraction of light, 357-366. Dilatation by heat of solids, liquids, and gases, 416-420; thermometers, 421- 432. Double refraction of light, 376-384. Draper on the discovery of oxygen and nitrogen in the sun, Appendix. Drebbel, Cornelius, his air thermometer. 427. Drummond's light, 638. Duhamel's method of magnetization, 524. Dutch tears, or Rupert's drops, 435. E. Ear, the (see Hearing and the Voice). Ear of Dionysius, 159. Earth, the : its form and constitution, 5 ; oblateness, 40 ; density, 44 ; heat of its interior, 496 ; terrestrial magnetism, INDEX. 687 521, 525, 624 ; connection between aurora and terrestrial magnetism, 668. Earthquakes, 6, 124, 131, 161. Echoes, 139, 140. Eclipses of Jupiter's satellites, 233. ELECTRICITY, Book VI., 529642. Electricity a source of light, 220. Electric telegraph, 618. Electro-magnetism, 604-619. Equilibrium, phenomena and laws of, 1. 119; of heavy bodies, 45 ; of liquids, 70, 72 ; of bodies immersed in liquids, 73. Ether, 351. F. Fahrenheit's areometer, 82. Fahrenheit's thermometer, 424. Falling bodies, 12, 16, 33. Faraday's experiments : distribution of electricity on bodies, 540 ; Leyden jar with moveable coatings, 572 ; electrical experiments, 602 ; induction currents, 620. Fire (see Heat). Fire-syringe, 88. Fish, their movements in water, 77. Fizeau, M., his measurement of the velo- city of light, 235 ; experiments on the velocity of light, 356 ; contraction of iodide of silver by heat, 439 ; electro- magnetism, 629 ; the voltaic arc, 638. Florentine Academicians, their experi- ments on the compressibility of liquids, 61, 103 ; on the weight of air, 88. Fogs, 659. Force-pump, 105. Fortin, his improvements in barometers, 96, 97. Foucault, Leon, his measurement of the velocity of light, 235, 237, 353, 356 ; improvement on Bouguer's photometer, 245 ; discoveries affecting the solar spectrum, 331 ; researches in electro- magnetism, 628 ; the voltaic arc, 638. Fountains, 71, 93. Frank land and Lockyer, their researches in spectrum analysis, 329. Franklin's experiments : on absorption of heat, 472; causes of thunder and light- ning, 665. Fraunhofer's discovery of dark lines in the solar spectrum, 323-332, 337, 339 ; laws of diffraction, 358, 364. Freezing (see Congelation, Ice). Fresnel's proofs of the undulatory theory of light, 352, 403 ; diffraction phe- nomena, 358 ; experiment of the two mirrors, 360, 361 ; double refraction of light, 383. Friction a source of heat, 500. Friction, electricity produced by, 531, 532. Fusion of solid bodies, 444. G. Galileo's experiments : oh falling bodies, 16 ; inclined plane, 23 ; weight of air, 86 ; motion of the pendulum, 35 ; air thermometer, 427. Galvani's electrical experiments, 585, 602. Galvanometer, its invention by Nobili 609. Gases : weight, elasticity, compressibility, and density of, 86; pressure of, 118 ; their expansion by heat, 441. Gas microscope, 305. Gay-Lussac's improvements in barometers, 96, 98 ; expansion of gases, 442 ; in- strument for measuring heat-conduct- ing powers, 478; electrical experiments, 602. Geissler's tubes : stratification of the elec- tric light, 642. Geology affected by gravitation, 5. Ghost produced by reflected light, 271, 273. Gilbert, William, his discoveries in elec- tricity, 531. Glaciers, 7. Glass : fusion of, 444 ; electrical properties of, 532, 535, 536 ; perforated by elec- tricity, 578. Gold, its heat-conducting power, 479. Goniometer, 258. Graphic study of sound vibrations, 155, 197. Gravesande's improvements of the air- pump, 107. GRAVITY, Book I., 1119. Grimaldi's experiment : diffraction of light, 357, 361. Guericke, Otto de, the inventor of the air- pump, 86, 107 ; of the Magdeburg hemispheres, 91 ; of the baroscope, 115. H. Hail and sleet, 660. Haldat's instrument for measuring the pressure of liquids, 66. Hearing and the Voice, 208-214. HEAT, Book IV., 415508. Heat produced by electricity, 579, 582, 598, 600. Heat, French and English units of, Introd. Chap., xxxviii. Heliography, 338. Heliostat fo for constant reflection of solar rays, 258. Helmholtz, his resonance globe, 205 ; on colours of non-luminous bodies, 319. Herschel, Sir John, on measuring the intensity of light, 239 ; refraction of light, 283 ; colours of non-luminous bodies, 314 ; weight of molecules of light, 350 ; experiments on diffraction, 362 ; polarization of light, 392. INDEX. Hoar-frost, 659. Huyghens, his undulatory theory of light, 350, 361 ; double refraction of light, 376 ; polarization of light, 386, 392. Hydraulic press or ram, 62. Hydraulic tourniquet, 68. Hydrometers, 80. Hydrostatic balance, 81. Hydrostatic phenomena, 62. Hygrometers : De Saussure's hair hygro- meter, 655. I. Ice ; its expansion by heat, 439, 443, 444 ; ice-lenses, 464 ; a source of heat to colder bodies, 492 ; melted by friction, 501 ; electrical properties of, 535, 582 ; its crystalline texture, ice-flowers, 661. Icebergs, 7. Iceland spar, double refraction produced by, 376-383 ; polarization of light, 386 ; its contraction and expansion, 438 ; absorption of heat, 473 ; conduc- tivity of heat, 480. Indium discovered by spectrum analysis, 329. Induction, phenomena of (see Electricity). Interference of luminous waves, 358-366. Iodide of silver, its contraction by heat, 439. Iridescent colours in thin plates, 367. Iron : its expansion and contraction by heat and cold, 434, 438 ; fusing point, 444 ; heat-conducting power, 479 ; 480 ; specific heat, 487 ; as a magnetic substance, 509-528 ; fusion by electri- city, 598 ; by electro-magnetism, 630 ; magnetization of, 614, 626. J. Joule, Dr., experiments on the mechanical equivalent of heat, 505. Jupiter's satellites, their eclipses a proof of the velocity of light, 232. K. Kaleidoscope, 256. Kinnersley's thermometer, 566. Kirchhoff's discoveries : lines in the solar spectrum, 325, 331 ; new metals dis- covered by spectrum analysis, 328, 329. Koenig, M., his optical study of musical sounds by manometric flames, 199- 203. Laplace and Lavoisier : their measurement of linear expansion of solids, 436 ; ice calorimeter, 490 ; experiments on com- busion, 499. Leaning Tower of Pisa, 16, 50 ; of Bologna, 60. Leichtenberg's distribution of positive and negative electricities, 574. Length, French and English units of, Introd. Chap., xxxv. Lens of the solar microscope, 304 of the spectroscope, 327 ; diverging and con- verging lenses, their form and foci, images seen, 291, 300 ; lens-pri-m of the camera obscura, 301 ; megascope, 302 ; magic lantern phantascope, 303 ; solar microscope, 304 ; used in discover- ing the colours of thin plates, 369 ; burning glasses, Buffon's echelon lens, 463, 464 ; fire procured by lenses of ice, 464. Le Konx on the electric light and voltaic arc, 639. Leslie, his differential thermometer, 428 ; his experiments on the emissive powers of heat in bodies, 466. Leyden jar, 567 LFGHT, Book III., 215412. Light, electric, 631-642. Lightning, cause and phenomena of: ex- periments of Franklin, Dalibard, De Eomas, De Saussure, and Wheatstone, 220, 665-668. Liquids : weight of, 58 ; cohesion, 59 ; compressibility, 61 ; pressure, 62 ; density, 70 ; specific gravity, 82 ; expansion by heat, 432, 439. (See Ebullition, Evaporation, Heat, Vapori- zation ) Lissajous' method for the optical study of musical sounds, 193-199. Lockyer and Frankland, their researches in spectrum analysis, 329. M. Magdeburg hemispheres illustrating atmo- speric pressure, 92. Magic lantern, 303. Magic mirror, 257. MAGNETISM, Book V., 509528. Malus, his discovery of polarization of light by reflection and simple refrac- tion, 392. Manometer, 110. Mariotte's law of the compressibility of gases, 102-118. Mass distinguished from weight, 46. Mass, French and English units of, Introd. Chap., xxx vii. Matteucci's researches on phosphorescence, 343. Meyer, Dr., his theory of the mechanical equivalent of heat, 505. Mechanical equivalent of heat, 485, 505. Mechanical work, French and English units of, Introd. Chap., xxxviii. Megascope, 303. Melloni, his thermo-electric pile, reflecting powers of heat in bodies, 468 ; measure- ments of diathermanovis powers, 474. INDEX. 689 Mercury : cohesion of its particles, Torricelli's tube ; the barometer, 89 ; 94 ; purity of the liquid, 94 ; its expansion by heat, 421 ; co-efficients of cubic expansion by heat, 440 ; temperature of vaporization, 449 ; specific heat, 487. (See Barometer, Thermometers,) Metals, table of expansion by heat, 438. Meteorology : dew, clouds, hoar-frost, fogs, snow, sleet, hail, ice, variations of barometric pressure, wind, 659-665. (See Barometer, Thermometers.) Meteors, 124, 131, 161. Mirage, Monge's theory of the, 646, Mirrors, 252-270 : plane, 252 ; parallel or inclined, multiple reflections, 254 ; kaleidoscope, 256 ; concave mirrors, 259-264 ; convex, 264 ; cylindrical, 267 ; conical, 268 ; magic mirror, or polemoscope, 257. Molecular cohesion, 59. Monge, his theory of the mirage, 646. Moon, The, as a source of light, 220. Morin's machine for exhibiting the laws of falling bodies, 24, 29. Motion, phenomena of, 6 ; heat a source of motion, 504-508. Mother-of-pearl, iridescent colours of, 365 ; double refraction of, 384, Muschenbroeck, his improvements of the air-pump, 107 ; experiments with the Leyden jar, 567. Musical sounds : "pitch/' 151 ; the gamut, 185, 186 ; intervals, 188 ; modula- tions, 190 ; major scale, sharps and flats, 190 ; minor scale, 191 ; optical study of sounds, Lissajous' method, 193-199; Koenig's employment of manometric flames, 199-203 ; -quality of musical notes, clang-tint or timbre, 204; Helmholtz's resonance globe, 205; Koenig's apparatus, 206 ; harmonies in vowel sounds, 207. N. Nairne's electrical machine, 558. Necker, M. A., interference of luminous rays, 366. Newton's researches and experiments : on gravity, 34 ; colours in light sources, 306, 309, 310, 311, 313 ; emission theory of light, 349 ; diffraction, 358, 361 ; the soap-bubble and colours of thin plates, 367 ; coloured rings, 369 ; the rainbow, 60. Nicholson, invention of the areometer ascribed to him, 80. Nicol's prism, polarization of light shown by, 390. Nitrogen in the sun, Appendix. ISobili's galvanometer, 609. Nollet, Abbe, his electrical experiments, 557, 567. O. Oersted's discoveries and experiments in electro-magnetism, 604-619. Opacity and transparency, 222. Optical or luminous meteors, mirage, 646. Oxy-hydrogen blowpipe, 499. Oxygen in the sun, Appendix. P. Papin's improvements of the air-pump, 107 ; his digester, for raising the temperature of ebullition, 450. Pascal's law of equal pressures, 62 ; his experiment, the hydrostatic paradox, 69 ; experiments on the pressure of the atmosphere, 89, 90. Pencils, rays, and beams of light, 225. Pendulum researches of Galileo and Huyghens, 35 ; law of its motion, 35. Penumbra, 226. Percussion a source of heat, 502. Perier's experiments with the barometer, 90. Phantascope, 303. Phonautography, or graphic study of sono- rous vibrations, 155. Phosphorescence discovered by Brandt, 341 ; the glow-worm, flowers, animal- culse, &c,, 342 ; Becquerel's phosphoro- scope, 345. Phosphorescence produced by electric light, 642. Phosphorus, electrical properties of, 535. Photo- electrical microscope, 305. Photometers : Rumford's, 243 ; Bouguer's, 244. Pisa, Leaning Tower at, 16, 50. "Pitch" of sound, 151. Planets, as sources ot light, 219, 242. Plumb-line, 22, Pneumatic-syringe, 88. Poisson on the uudulatory theory of light, 363. Polarization of light, 385-405. Polemoscope, or magic mirror, 257. Pouillet, M., his pyrheliometer, 493, 496 ; researches in electro-magnetism, 618. Pressure : of the air upon the earth, 86, 91 ; of liquids, 62, 64 ; on bodies immersed in liquids, 73. Principle of Archimedes on the pressure of immersed bodies, 74 ; its application to gases, 115. Prism, the : its geometrical form, devia- tion of luminous rays, 288-291 ; lens- prism of the camera obscura, 301 ; decomposition of solar light, 307 ; its recomposition, 310. Prisms employed by Fraunhofer in his discoveries, 324. 690 INDEX. Prisms of Iceland spar, their effect in double refraction and polarization of light, 376, 386. Prisms, Nicol's prism, 390. Ptolemy's observation of atmospheric re- fraction, 277. Pumps, 102 119. Pyrheliometer of M. Pouillet, 493. Pyrometers, 430, 439. Q. Quartz, its unequal conductivity of heat, 480. R. Railway accidents caused by heat, 434. Rain, 8, 20. Rainbow, 308, 650. Ramsden's plate-glass electrical machine, 557. Rays, pencils, and beams of light, 225. Reaumur's thermometer, 424. Reflection of Light and Sound (see Light, Sound). Refraction of Light and Sound (see Light, Sound). Refrangibility of coloured rays, 307. Regnault's air-condensing pump, 117 ; compressibility of gases, 119; cubic expansion of mercury, 440 ; specific heats of bodies, 487, 491 ; mechanical equivalent of heat, 505. Resin, its electrical properties, 532, 535, 536, 552, 561. Robertson's phantascope, 303. Rochon, Abbe, experiments on solar rays, luminous and calorific, 337. Rock-crystal, double refraction of, 383. Rock-salt, a non-absorbent of heat, 473. Roemer's discovery of the velocity of light, 234. Rubidium discovered by spectrum analysis, 329. Ruhmkorff's induction coil and commuta- tor, b27, 629. Rumford's photometer, 243 ; his differen- tial thermometer, 428 ; experiments on combustion, 499 ; on heat produced by friction, 500. Rupert's drops, or Dutch tears, 435. Rutherford's photographs of the solar spec- trum, 338 ; maximum and minimum thermometers, 662. S. Safety -lamps, 481. St. Elmo's fires, electric lights so called, 604, 668. Savart's toothed wheel, 152 ; illustrations of the vibrations of a plate, 175. Scales (see Balance). Scattered light, 316. Schweigger's multiplier, 608 (see Elec- tricity). Scientific units, French and English, Jnlrod. Chap., xxxv. Seebeck's Syren, 154 ; researches on solar rays, 337 ; chromatic polarization of light, 399. Sextant, 258. Shadows, 226. Ships, equilibrium of, 76, 78. Silbermann's condensing pump, 116. Silhouettes, 227. Silver : its power of conducting heat, 479 ; specific heat, 487 ; fusion by electricity, 598. Siphon, 106. Sirius, velocity of its movement, 355. Sleet and hail, 660. Snell, Willebrod, his discovery of the laws of refraction of light, 277. Snow and snow crystals, 660. Soap-bubble, Newton's study of the, 367, 372. Sodium, its spectrum, 328, 329. Solar microscope, 302. Solar prominences in eclipses, 334. Solar spectrum, 307 ; discovery by Wol las- ton and Fraunhofer of dark lines, 323. Solar winds, their velocity, 356. Solenoid, or electrical magnet constructed by Ampere, 612. Sonometer, 164. SOUND, Book II., 121214. Sources of heat, 492-503. Specific gravity, 57 ; of bodies, methods of determining, 78 ; of liquids, 82 ; table of, 83. Spectra of stars, 326 ; of metallic vapours and gases, 327. Spectroscope, 327. Spectrum, Solar (see Solar Spectrum). Spectrum analysis, 326-335. Stars, as sources of light, 219 ; as heat radiators, 496. Stokes, Professor, his discovery of metallic vapours in the sun's atmosphere, 331 ; chemical solar rays, 339. Suction pump, 103, 105. Sun, The, as a source of light, 219, 242 ; its appearance and constitution, inten- sity of solar heat, 493 ; total heat radiated, 295. Surface, French and English units of, Introd. Chap., xxxvi. Swimming-bladder of fish, 77. Syrens for measuring vibrations of sound, 153. T. Temperature of space, 496. Temperature, its effect on magnets, 526 ; on electricity, 543. INDEX. 691 Terrestrial magnetism, 521, 525. Thalen's researches in spectrum analysis, 835. Thallium discovered by spectrum analysis, 329. Thermo-electric pile for study of pheno- mena of heat, 469 ; its use in measuring heat-radiation of stars, 496. Thermometers : expansion of gases by heat, 419 ; temperatures of melting ice and boiling water, 421 ; determination of zero and 100, 422, 423 ; thermo- metrical scales, Centigrade, Fahrenheit, Reaumur, and Delisle, 425; Walferdin's metastatic thermometer, 426 ; alcohol, ether, and gas as thermometers, Galileo and Cornelius Drebbel, 427; Leslie and Rumford's differential thermo- meters, 428 ; metallic dial thermo- meter, Breguet's metallic thermometer, pyrometers, 430 ; Kinnersley's electri- cal thermometer, 566 ; maximum and minimum thermometers, 662. Thermometric degrees, French and English, Introd. Chap., xxxviii. Thunder : effects of thunderbolts, 667. Tides, 15. Time, measures of (see Pendulum). Torricelli, his discovery of the principle of the barometer, 89. Tourmaline, double refraction of, 383 ; polarization of light by, 391 ; effects of tourmaline pincette, 400. Translucent and transparent substances. 222. Tyndall, Professor, on calorific solar rays, 340 ; expansive force of freezing water, 446 ; experiments on heat, 473, 475 ; influence of the ocean on climate, 488 ; amount of heat radiated by the sun, 495 ; crystalline texture of ice, ice- flowers, 661. U. Umbra and penumbra, 226. Undulatory theory of light, 372, 404. Unit of heat, or " calorie," 485. Units : French and English Scientific, Units, Introd. Chap., xxxv. Universal gravitation, 11. V. Vacuum, 85, 89, 90, 103, 107 (see Air Pump). Van Marum's electrical machine and ex- periments, 559, 580. Velocity, French and English units of, Introd: Chap., xxxviii. Velocity of light, 231-237, 353 ; of solar winds, 356 ; of falling bodies, 32 ; of sound, 132-137 ; of stars measured by the spectroscope, 333, 335. Vibrations of Sound (see Sound). Vidi's aneroid barometer, 101. Voice, human, 124. Volcanoes, 8. Volta, his experiment of electrical hail, 562 ; his electrical discoveries, 583, 585, 593, 597. Von Guericke, Otto, his electrical machine, 552. W. Walferdin's metastatic thermometer, 426 ; maximum and minimum thermometers, 663. "Water : salt and fresh, 70 ; expansion and contraction at different temperatures, 441 ; evaporation, ebullition, and vapo- rization, 444-452 ; electrical properties of, 534 ; its decomposition by the electric pile, 601 (see Force Pump, Pumps, Siphon, Suction Pump). Weight of bodies, 1, 45 ; of liquids, 58 ; of the air and gases, 84 ; of bodies in vacuo, 115. Weight, French and English units of, Introd. Chap., xxxvii. Wheatstone's experiments : meteors, 665. Wheel barometer, 99. Wind, its effect on the barometer, 665. Wollastou's experiments : in photometry, 245 ; discovery of dark lines in the solar spectrum, 323 ; researches in chro- matic polarization of light, 402 ; elec- tric pile, 594. Y. Young's principle of interference of lumi- nous waves, 358, 361. 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