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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 \* ' ' Pa9e 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 force — 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 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 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. XXv
*•«»' 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 0° 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 ( TJffth „ „ ) 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 0° 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 0 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 - 16T\
„ 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>0l00;000th 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 toarest. 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 say> by adding to the whole weight an insignificant
FIG. 45. —Hydrostatic paradox. Pascal1:
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 I1 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 k»ss 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 forni3 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 river1 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 <